diff --git a/docs/_toc.yml b/docs/_toc.yml index 2ab98058..1bff5c3c 100644 --- a/docs/_toc.yml +++ b/docs/_toc.yml @@ -8,9 +8,13 @@ parts: chapters: - file: md/installation - file: md/building_doc + - caption: Compartmental models + chapters: + - file: notebooks/definition + - file: notebooks/solution - caption: PyGOM workflow chapters: - - file: notebooks/model_spec + - file: notebooks/model_spec_2 - file: notebooks/insights sections: - file: notebooks/extract_info diff --git a/docs/md/intro.md b/docs/md/intro.md index ebbbb55c..16d8865a 100644 --- a/docs/md/intro.md +++ b/docs/md/intro.md @@ -6,16 +6,35 @@ PyGOM (Python Generic ODE Model) is a Python package which provides a simple int This is backed by a comprehensive and easy to use tool–box implementing functions to easily perform common operations such as parameter estimation and solving for deterministic or stochastic time evolution. The package source is freely available (hosted on [GitHub](https://github.com/ukhsa-collaboration/pygom)) and organized in a way that permits easy extension. With both the algebraic and numeric calculations performed automatically (but still accessible), the end user is freed to focus on model development. -## What is new in this release? - -The main objective of the current release (0.1.8) is to provide more comprehensive documentation on how to use PyGOM. - -The code underlying PyGOM's functionality is largely unchanged since the previous release, barring a few minor bug fixes. -The only significant changes which previous users should be aware of are: -- A move away from the {class}`DeterministicOde` class for deterministic simulations and instead employing {class}`SimulateOde` as our do-all class for deterministic or stochastic simulations as well as parameter fitting. -- Running simulations with random parameters does not require a special simulation function. Instead, PyGOM now recognises the parameter types handed to it (fixed or random) and acts accordingly. This means that stochastic simulations can now be performed with random parameters. - -Both these changes are outlined in more detail in the {doc}`Producing forecasts ` section. +## Release notes: + +### [0.1.9] - 2024-11-30 (Latest release) + +- Added + - Method {func}`solve_stochast` of {class}`SimulateOde` has 1 additional output (for a total of 3): the number of times each event occurs in between each time step. This is useful if you are interested in infection incidence rather than prevalence, for example. + - The adaptive tau leap can be bypassed and, instead, a constant step size for the tau leap algorithm can be specified with `SimulateOde._pre_tau`. + - When an output of a stochastic simulation needs to be mapped to the user defined time-points, this is performed via linear interpolation. +- Changed + - The {class}`Event` class has replaced the {class}`Transition` class as the fundamental building block. This allows for more flexibility when dealing with correlated transitions, for example. + - Internal methods {func}`add_func` and {func}`add_compiled_sympy_object` make the compilation of sympy objects more modular. +- Deprecated + - Models can still be defined via {class}`Transition` objects as before, but users are advised to switch to the {class}`Event` based approach. + - The birth rate state can still be defined as an `origin`, but can now also (and more accurately) be described as a `destination`. In the next version, this may remove the need to specify the transition type since between state transitions will uniquely have an origin and destination, births will uniquely have just a destination and deaths just an origin. +- Removed +- Fixed + - Minor bug fixes + +### [0.1.8] - 2024-08-06 + +- Added + - Comprehensive documentation of how to use PyGOM +- Changed + - Running simulations with random parameters does not require a special simulation function. Instead, PyGOM now recognises the parameter types handed to it (fixed or random) and acts accordingly. This means that stochastic simulations can now be performed with random parameters. +- Deprecated + - {class}`DeterministicOde` is deprecated with {class}`SimulateOde` now performing both deterministic and stochastic simulations. +- Removed +- Fixed + - Minor bug fixes ## Using this documentation This documentation is built using [JupyterBook](https://jupyterbook.org/en/stable/intro.html). diff --git a/docs/notebooks/Digraph.gv b/docs/notebooks/Digraph.gv new file mode 100644 index 00000000..dc974713 --- /dev/null +++ b/docs/notebooks/Digraph.gv @@ -0,0 +1,8 @@ +digraph { +rankdir=LR S + I + R + size="5,5" + S -> I [label="βSI/N"] + I -> R [label="γI"] +} diff --git a/docs/notebooks/Digraph.gv.pdf b/docs/notebooks/Digraph.gv.pdf new file mode 100644 index 00000000..7b29ade1 Binary files /dev/null and b/docs/notebooks/Digraph.gv.pdf differ diff --git a/docs/notebooks/common_models/Lotka_Volterra.ipynb b/docs/notebooks/common_models/Lotka_Volterra.ipynb index d38a2228..53d61545 100644 --- a/docs/notebooks/common_models/Lotka_Volterra.ipynb +++ b/docs/notebooks/common_models/Lotka_Volterra.ipynb @@ -30,22 +30,30 @@ "import matplotlib.pyplot as plt\n", "import math\n", "\n", - "# population density of predators and prey per square m\n", - "x0 = [1, 0.5]\n", + "# Initial populations\n", + "x0=[40, 20]\n", "\n", - "# total area we wish to consider\n", - "area=200\n", + "# Parameters from a snowshoe hare / Canadian lynx system\n", + "# https://mc-stan.org/users/documentation/case-studies/lotka-volterra-predator-prey.html\n", + "alpha=0.545\n", + "beta=0.028\n", + "gamma=0.803\n", + "delta=0.024\n", "\n", - "# total animal populations\n", - "x0 = [x * area for x in x0]\n", + "# scale up the population (this will need scaling in the predation parameters)\n", + "scale=10\n", "\n", - "ode = common_models.Lotka_Volterra({'alpha':0.1,\n", - " 'beta':0.2,\n", - " 'gamma':0.3,\n", - " 'delta':0.25,\n", - " 'A':area})\n", + "x0 = [x * scale for x in x0]\n", + "beta=beta/scale\n", + "delta=delta/scale\n", "\n", - "tmax=200 # maximum time over which to run solver\n", + "\n", + "ode = common_models.Lotka_Volterra({'alpha':alpha,\n", + " 'beta':beta,\n", + " 'gamma':gamma,\n", + " 'delta':delta})\n", + "\n", + "tmax=50 # maximum time over which to run solver\n", "dt=0.1 # timestep\n", "n_timestep=math.ceil(tmax/dt) # number of iterations\n", "t = np.linspace(0, tmax, n_timestep) # times at which solution will be evaluated\n", @@ -80,7 +88,7 @@ "ax.set_ylabel(\"Population number\")\n", "ax.plot(t, solution[:,0], label=\"prey\")\n", "ax.plot(t, solution[:,1], label=\"predator\")\n", - "ax.legend(loc=\"upper right\")\n", + "ax.legend()\n", "plt.show()" ] }, @@ -102,7 +110,7 @@ "np.random.seed(1)\n", "\n", "n_sim=1\n", - "solution, simT = ode.solve_stochast(t, n_sim, full_output=True)\n", + "solution, jump, simT = ode.solve_stochast(t, n_sim, full_output=True)\n", "\n", "f, ax = plt.subplots(figsize=(10, 2))\n", "\n", @@ -112,7 +120,7 @@ "ax.set_ylabel(\"Population number\")\n", "ax.plot(t, y[:,0], label=\"prey\")\n", "ax.plot(t, y[:,1], label=\"predator\")\n", - "ax.legend(loc=\"upper right\")\n", + "ax.legend()\n", "plt.show()" ] }, @@ -142,7 +150,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -156,12 +164,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/common_models/SEIR.ipynb b/docs/notebooks/common_models/SEIR.ipynb index f01627de..50ffa2af 100644 --- a/docs/notebooks/common_models/SEIR.ipynb +++ b/docs/notebooks/common_models/SEIR.ipynb @@ -21,7 +21,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "bd15619d", "metadata": {}, "outputs": [], @@ -70,7 +70,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "282ebfbd", "metadata": {}, "outputs": [], @@ -93,40 +93,53 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "0403f7c2", "metadata": { "tags": [ "hide-input" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Plot\n", "\n", - "f, axarr = plt.subplots(1,4, layout='constrained', figsize=(10, 4))\n", + "f, axarr = plt.subplots(1,4, layout='constrained', figsize=(10, 3))\n", "\n", "# Plot colours\n", "colours=[\"C1\", \"C3\", \"C0\", \"C2\"]\n", "stateList=[\"S\", \"E\", \"I\", \"R\"]\n", "\n", "for i in range(0, 4):\n", - " axarr[i].plot(t, solution[:,i], color=colours[i])\n", + " axarr[i].plot(t, solution[:,i], color=colours[i], label=\"SEIR\")\n", + " axarr[i].set_title(stateList[i])\n", " if i in [0,2,3]:\n", " if i in [2,3]:\n", " axarr[i].plot(t, solution2[:,i-1], color=colours[i], linestyle=\"dashed\")\n", " else:\n", - " axarr[i].plot(t, solution2[:,i], color=colours[i], linestyle=\"dashed\")\n", - " axarr[i].set_ylabel(stateList[i], rotation=0)\n", + " axarr[i].plot(t, solution2[:,i], color=colours[i], linestyle=\"dashed\", label=\"SIR\")\n", " axarr[i].set_xlabel('Time')\n", "\n", + "axarr[0].legend()\n", + "\n", "plt.show()" ] } ], "metadata": { "kernelspec": { - "display_name": "pygom_development", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -140,7 +153,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/common_models/SEIR_Birth_Death_Periodic_Waning_Intro.ipynb b/docs/notebooks/common_models/SEIR_Birth_Death_Periodic_Waning_Intro.ipynb index eaf90f5a..ceca12a0 100644 --- a/docs/notebooks/common_models/SEIR_Birth_Death_Periodic_Waning_Intro.ipynb +++ b/docs/notebooks/common_models/SEIR_Birth_Death_Periodic_Waning_Intro.ipynb @@ -20,15 +20,52 @@ "\\beta(t) &= \\beta_0 \\left(1+\\delta \\cos \\left(\\frac{2 \\pi t}{P} \\right) \\right)\n", "\\end{aligned}$$\n", "\n", - "We solve this set of equations deterministically:" + "We solve this set of equations stochastically:" ] }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 8, "id": "e7321259", - "metadata": {}, - "outputs": [], + "metadata": { + "tags": [ + "hide-output" + ] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Illegal jump, x: [1.000024e+06 2.000000e+00 0.000000e+00 0.000000e+00 1.000026e+06], new x: [ 1.000032e+06 -2.000000e+00 4.000000e+00 0.000000e+00 1.000034e+06]\n", + "Illegal jump, x: [1.000069e+06 0.000000e+00 3.000000e+00 5.000000e+00 1.000077e+06], new x: [ 1.000063e+06 5.000000e+00 -1.000000e+00 9.000000e+00 1.000076e+06]\n", + "Illegal jump, x: [1.000047e+06 4.000000e+00 3.000000e+00 1.000000e+01 1.000064e+06], new x: [ 1.000072e+06 -1.000000e+00 5.000000e+00 1.400000e+01 1.000090e+06]\n", + "Illegal jump, x: [9.999840e+05 6.000000e+00 6.000000e+00 5.300000e+01 1.000049e+06], new x: [ 9.999700e+05 -1.000000e+00 1.600000e+01 5.400000e+01 1.000039e+06]\n", + "Illegal jump, x: [7.458530e+05 2.000000e+01 3.100000e+01 2.546380e+05 1.000542e+06], new x: [ 7.491890e+05 -2.200000e+01 4.200000e+01 2.513270e+05 1.000536e+06]\n", + "Illegal jump, x: [7.551960e+05 2.200000e+01 5.300000e+01 2.452370e+05 1.000508e+06], new x: [ 7.593740e+05 3.500000e+01 -4.000000e+00 2.410880e+05 1.000493e+06]\n", + "Illegal jump, x: [7.551970e+05 2.200000e+01 5.300000e+01 2.452360e+05 1.000508e+06], new x: [ 7.592690e+05 8.300000e+01 -3.000000e+00 2.411400e+05 1.000489e+06]\n", + "Illegal jump, x: [7.640260e+05 1.400000e+01 4.400000e+01 2.364370e+05 1.000521e+06], new x: [ 7.65920e+05 5.80000e+01 -4.00000e+00 2.34556e+05 1.00053e+06]\n", + "Illegal jump, x: [7.67639e+05 2.80000e+01 4.20000e+01 2.32831e+05 1.00054e+06], new x: [ 7.701370e+05 -3.000000e+00 6.500000e+01 2.303990e+05 1.000598e+06]\n", + "Illegal jump, x: [7.81219e+05 3.10000e+01 5.20000e+01 2.19198e+05 1.00050e+06], new x: [ 7.842350e+05 -9.000000e+00 8.100000e+01 2.162050e+05 1.000512e+06]\n", + "Illegal jump, x: [8.068120e+05 2.400000e+01 5.000000e+01 1.937060e+05 1.000592e+06], new x: [ 8.118410e+05 -1.200000e+01 2.600000e+01 1.887500e+05 1.000605e+06]\n", + "Illegal jump, x: [8.172220e+05 1.300000e+01 2.300000e+01 1.832690e+05 1.000527e+06], new x: [ 8.208820e+05 -1.400000e+01 4.600000e+01 1.796150e+05 1.000529e+06]\n", + "Illegal jump, x: [8.281030e+05 6.000000e+00 1.700000e+01 1.724920e+05 1.000618e+06], new x: [ 8.323950e+05 3.200000e+01 -2.200000e+01 1.682580e+05 1.000663e+06]\n", + "Illegal jump, x: [8.47987e+05 2.70000e+01 2.50000e+01 1.52601e+05 1.00064e+06], new x: [ 8.484980e+05 -4.000000e+00 5.400000e+01 1.520860e+05 1.000634e+06]\n", + "Illegal jump, x: [8.876300e+05 5.300000e+01 1.050000e+02 1.129780e+05 1.000766e+06], new x: [ 8.884230e+05 -1.000000e+00 1.270000e+02 1.122270e+05 1.000776e+06]\n", + "Illegal jump, x: [8.090790e+05 3.100000e+01 5.000000e+01 1.915120e+05 1.000672e+06], new x: [ 8.110180e+05 -5.000000e+00 8.300000e+01 1.895800e+05 1.000676e+06]\n", + "Illegal jump, x: [8.090790e+05 3.000000e+01 5.100000e+01 1.915120e+05 1.000672e+06], new x: [ 8.11620e+05 -1.10000e+01 1.10000e+02 1.88891e+05 1.00061e+06]\n", + "Illegal jump, x: [8.583830e+05 3.800000e+01 6.200000e+01 1.415800e+05 1.000063e+06], new x: [ 8.596920e+05 -7.000000e+00 9.800000e+01 1.402600e+05 1.000043e+06]\n", + "Illegal jump, x: [1.000003e+06 2.000000e+00 0.000000e+00 0.000000e+00 1.000005e+06], new x: [ 1.000003e+06 -4.000000e+00 6.000000e+00 0.000000e+00 1.000005e+06]\n", + "Illegal jump, x: [1.000002e+06 2.000000e+00 0.000000e+00 0.000000e+00 1.000004e+06], new x: [ 1.000019e+06 -6.000000e+00 8.000000e+00 0.000000e+00 1.000021e+06]\n", + "Illegal jump, x: [1.000003e+06 2.000000e+00 0.000000e+00 0.000000e+00 1.000005e+06], new x: [ 1.000009e+06 -1.000000e+00 4.000000e+00 0.000000e+00 1.000012e+06]\n", + "Illegal jump, x: [9.99994e+05 0.00000e+00 2.00000e+00 0.00000e+00 9.99996e+05], new x: [ 1.000008e+06 3.000000e+00 -3.000000e+00 5.000000e+00 1.000013e+06]\n", + "Illegal jump, x: [9.99975e+05 2.00000e+00 3.00000e+00 2.00000e+00 9.99982e+05], new x: [ 9.99954e+05 -4.00000e+00 8.00000e+00 5.00000e+00 9.99963e+05]\n", + "Illegal jump, x: [9.99974e+05 2.00000e+00 3.00000e+00 2.00000e+00 9.99981e+05], new x: [ 9.99940e+05 7.00000e+00 -2.00000e+00 8.00000e+00 9.99953e+05]\n", + "Illegal jump, x: [8.43410e+05 4.80000e+01 7.80000e+01 1.56447e+05 9.99983e+05], new x: [ 8.44359e+05 -1.00000e+00 1.26000e+02 1.55526e+05 1.00001e+06]\n", + "Illegal jump, x: [8.52753e+05 7.30000e+01 1.22000e+02 1.46966e+05 9.99914e+05], new x: [ 8.53870e+05 -4.00000e+00 2.05000e+02 1.45836e+05 9.99907e+05]\n" + ] + } + ], "source": [ "from pygom import common_models\n", "import matplotlib.pyplot as plt\n", @@ -36,38 +73,50 @@ "import math\n", "\n", "# Set up PyGOM object\n", - "n_pop=1e5\n", - "mu=0.01/365\n", + "\n", + "# Parameters\n", + "\n", + "## population\n", + "n_pop=1e6\n", + "\n", + "## Seasonal driving\n", + "beta0=0.3 # R0 avg = beta0/gamma =1.2, R0 min = (beta0-delta)/gamma=0.8, R0 max = (beta0+delta)/gamma=1.6\n", + "delta=0.1\n", + "period=365\n", + "\n", + "## Virus\n", "alpha=1/2\n", "gamma=1/4\n", - "epsilon=100/(365*n_pop) # approximately 100*n_sus*365/(365*n_pop)=100*frac_sus~30 infections from external sources per year\n", + "mu=0.01/365\n", "w=1/(2*365) # waning rate, immunity lasts ~ 2 years.\n", - "beta0=1\n", - "delta=0.2\n", - "period=365\n", + "epsilon=50/(365*n_pop) # attack rate:approximately 100*n_sus*365/(365*n_pop)=100*frac_sus\n", + " # infections from external sources per year (approx 1 per week, just enough\n", + " # to spark an epidemic when winter arrives)\n", "\n", - "ode = common_models.SEIR_Birth_Death_Periodic_Waning_Intro({'mu':mu,\n", - " 'alpha':alpha,\n", - " 'gamma':gamma,\n", - " 'epsilon':epsilon,\n", - " 'w':w,\n", - " 'beta0':beta0,\n", - " 'delta':delta,\n", - " 'period':period,\n", - " 'N':n_pop})\n", + "model = common_models.SEIR_Birth_Death_Periodic_Waning_Intro({'beta0':beta0,\n", + " 'delta':delta,\n", + " 'period':period,\n", + " 'alpha':alpha,\n", + " 'gamma':gamma,\n", + " 'mu':mu,\n", + " 'w':w,\n", + " 'ar': epsilon})\n", "\n", "# Time range and increments\n", "tmax=365*20 # maximum time over which to run solver\n", - "dt=0.1 # timestep\n", + "dt=10 # output timestep\n", "n_timestep=math.ceil(tmax/dt) # number of iterations\n", "t = np.linspace(0, tmax, n_timestep) # times at which solution will be evaluated\n", "\n", "# Initial conditions\n", - "x0 = [n_pop, 0, 0, 0, t[0]]\n", + "x0 = [n_pop, 0, 0, 0, n_pop]\n", + "\n", + "model.initial_values = (x0, t[0])\n", "\n", - "ode.initial_values = (x0, t[0])\n", + "np.random.seed(1)\n", "\n", - "solution=ode.solve_determ(t[1::])" + "n_sim=2\n", + "solution, jump, simT = model.solve_stochast(t, n_sim, full_output=True)" ] }, { @@ -75,32 +124,46 @@ "id": "5eefb897", "metadata": {}, "source": [ - "Plotting the infection prevalence reveals that the system eventually reaches a state of annual epidemics." + "Plotting the infection prevalence over 2 simulations reveals that an initially large epidemic is eventually succeeded by a series of fairly regular annual epidemics of varying sizes." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "id": "30368b0d", "metadata": { "tags": [ "hide-input" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "f, ax = plt.subplots(figsize=(10, 2))\n", + "f, ax = plt.subplots(figsize=(10, 3))\n", "\n", "ax.set_xlabel(\"Time\")\n", - "ax.set_ylabel(\"Infection prevalence\")\n", - "ax.plot(t[30000:]/365, solution[30000:,2])\n", + "ax.set_title(\"Infection prevalence\")\n", + "ax.plot(t/365, solution[0][:,2], alpha=0.8, label=\"simulation 1\")\n", + "ax.plot(t/365, solution[1][:,2], alpha=0.8, label=\"simulation 2\")\n", + "plt.xticks(np.arange(0, 21, 1.0))\n", + "ax.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -114,12 +177,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/common_models/SIR.ipynb b/docs/notebooks/common_models/SIR.ipynb index 6d98dfd9..891c05dd 100644 --- a/docs/notebooks/common_models/SIR.ipynb +++ b/docs/notebooks/common_models/SIR.ipynb @@ -8,12 +8,28 @@ "\n", "{func}`.SIR`\n", "\n", - "The standard Susceptible-Infected-Recovered (SIR) model, which features heavily throughout this documentation, is defined by the following equations:\n", + "The standard Susceptible-Infected-Recovered (SIR) model features heavily throughout this documentation and so we outline its key features for anyone unfamiliar.\n", + "\n", + "```{warning}\n", + "There is some ambiguity in the naming of the Recovered class which is also commonly referred to as Removed.\n", + "In the latter sense, there is no distinction made between those who can no longer be infected due to infection acquired immunity and infection induced death.\n", + "However, for more complex models, the recovered class may become susceptible again due to the effects of immune waning and deaths versus recoveries are typically important to distinguish in real world applications.\n", + "Therefore, in this tutorial, the Recovered class will be reserved solely for those who survive infection.\n", + "```\n", + "\n", + "The assumptions of the SIR model can be stated as:\n", + "1) An average member of the population makes contact sufficient to transmit or receive infection with $c$ others per unit time. Each of these events carries a probability, $p$, of transmission such that each individual has an average of $cp = \\beta$ infectious contacts per unit time. This fixed contact rate reflects what is referred to as *standard* incidence, as opposed to *mass-action* incidence, where contacts per person are proportional to the total population size, $N$.\n", + "2) The population interacts heterogeneously as if a well mixed continuum.\n", + "For instance, a susceptible does not have contacts with other individuals, but with the entire population on average.\n", + "3) The infective class recovers at a rate, $\\gamma$.\n", + "4) No births, deaths (natural or from disease) or migration mean there is no entry into or departure from the population: $S(t)+I(t)+R(t)=N$.\n", + "\n", + "Under these assumptions, the rates of change of the population in each compartment (**S**usceptible, **I**nfected and **R**ecovered) are given by the following equations:\n", "\n", "$$\\begin{aligned}\n", - "\\frac{\\mathrm{d}S}{\\mathrm{d}t} &= - \\frac{\\beta SI}{N} \\\\\n", - "\\frac{\\mathrm{d}I}{\\mathrm{d}t} &= \\frac{\\beta SI}{N} - \\gamma I \\\\\n", - "\\frac{\\mathrm{d}R}{\\mathrm{d}t} &= \\gamma I\n", + "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta SI}{N} \\\\\n", + "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta SI}{N} - \\gamma I \\\\\n", + "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= \\gamma I.\n", "\\end{aligned}$$\n", "\n", "We solve deterministically for flu-like parameters:" diff --git a/docs/notebooks/common_models/SIR_Birth_Death.ipynb b/docs/notebooks/common_models/SIR_Birth_Death.ipynb index b0123894..0ab892e3 100644 --- a/docs/notebooks/common_models/SIR_Birth_Death.ipynb +++ b/docs/notebooks/common_models/SIR_Birth_Death.ipynb @@ -26,7 +26,11 @@ "cell_type": "code", "execution_count": null, "id": "1e5a8099", - "metadata": {}, + "metadata": { + "tags": [ + "hide-output" + ] + }, "outputs": [], "source": [ "from pygom import common_models\n", @@ -45,7 +49,7 @@ "R0=15\n", "beta=R0*gamma\n", "\n", - "ode = common_models.SIR_Birth_Death({'beta':beta, 'gamma':gamma, 'mu':mu, 'N':n_pop})\n", + "ode = common_models.SIR_Birth_Death({'beta':beta, 'gamma':gamma, 'mu':mu})\n", "\n", "# Time range and increments\n", "tmax=365*10 # maximum time over which to run solver\n", @@ -58,7 +62,7 @@ " s0=math.floor((gamma+mu)*n_pop/beta)\n", " i0=math.floor(mu*(n_pop-s0)*n_pop/(beta*s0))\n", " r0=n_pop-(s0+i0)\n", - " return [s0, i0, r0]\n", + " return [s0, i0, r0, n_pop]\n", "\n", "x0=sir_bd_endemic_eq(mu, beta, gamma, n_pop)\n", "ode.initial_values = (x0, t[0])\n", @@ -69,27 +73,27 @@ "n_sim=10\n", "np.random.seed(1)\n", "\n", - "solution, simT = ode.solve_stochast(t, n_sim, full_output=True)\n", + "solution, jumps, simT = ode.solve_stochast(t, n_sim, full_output=True)\n", "y=np.dstack(solution)\n", "\n", "############################\n", "# try larger population size\n", "############################\n", "n_pop=1e5\n", - "ode = common_models.SIR_Birth_Death({'beta':beta, 'gamma':gamma, 'mu':mu, 'N':n_pop}) # update parameter\n", + "ode = common_models.SIR_Birth_Death({'beta':beta, 'gamma':gamma, 'mu':mu}) # update parameter\n", "x0=sir_bd_endemic_eq(mu, beta, gamma, n_pop) # recalculate IC's\n", "ode.initial_values = (x0, t[0])\n", - "solution_2, simT_2 = ode.solve_stochast(t, n_sim, full_output=True) # simulate\n", + "solution_2, jumps_2, simT_2 = ode.solve_stochast(t, n_sim, full_output=True) # simulate\n", "y_2=np.dstack(solution_2)\n", "\n", "#################################\n", "# try even larger population size\n", "#################################\n", "n_pop=1e6\n", - "ode = common_models.SIR_Birth_Death({'beta':beta, 'gamma':gamma, 'mu':mu, 'N':n_pop}) # update parameter\n", + "ode = common_models.SIR_Birth_Death({'beta':beta, 'gamma':gamma, 'mu':mu}) # update parameter\n", "x0=sir_bd_endemic_eq(mu, beta, gamma, n_pop) # recalculate IC's\n", "ode.initial_values = (x0, t[0])\n", - "solution_3, simT_3 = ode.solve_stochast(t, n_sim, full_output=True) # simulate\n", + "solution_3, jumps_3, simT_3 = ode.solve_stochast(t, n_sim, full_output=True) # simulate\n", "y_3=np.dstack(solution_3)" ] }, @@ -143,7 +147,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pygom_development", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -157,7 +161,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/common_models/SIS_Periodic.ipynb b/docs/notebooks/common_models/SIS_Periodic.ipynb index 622cfc6b..1112c728 100644 --- a/docs/notebooks/common_models/SIS_Periodic.ipynb +++ b/docs/notebooks/common_models/SIS_Periodic.ipynb @@ -58,7 +58,8 @@ "\n", "# Initial conditions\n", "i0=0.1*n_pop\n", - "x0 = [i0, t[0]]\n", + "s0=n_pop-i0\n", + "x0 = [s0, i0]\n", "\n", "ode.initial_values = (x0, t[0])\n", "solution=ode.solve_determ(t[1::])" @@ -86,15 +87,15 @@ "f, ax = plt.subplots(figsize=(10, 4))\n", "\n", "ax.set_xlabel(\"Time\")\n", - "ax.set_ylabel(\"I\", rotation=0)\n", - "ax.plot(t, solution[:,0])\n", + "ax.set_title(\"Infected\")\n", + "ax.plot(t, solution[:,1])\n", "plt.show()" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -108,12 +109,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/compartmental_models.ipynb b/docs/notebooks/compartmental_models.ipynb new file mode 100644 index 00000000..83c0c014 --- /dev/null +++ b/docs/notebooks/compartmental_models.ipynb @@ -0,0 +1,823 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a3389d4e", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "source": [ + "# Compartmental models\n", + "\n", + "## Introduction\n", + "\n", + "Here we introduce the features of compartmental models which pygom can handle.\n", + "\n", + "A compartmental model represents transport of material between different states.\n", + "Common in epi do be humans between different disease states, but can be transport of molecules in chemistry or money in economics.\n", + "\n", + "We introduce increaseing complexity.\n", + "\n", + "How to solve them and define in pygom we leave until after htis intro.\n", + "\n", + "### Transitions between states\n", + "\n", + "In the simplest compartmental model, things go from one state to another.\n", + "\n", + "For example, SIR is defined by 2 events.\n", + "\n", + "- Infection takes an S to an I\n", + "- Recovery takes an I to an R\n", + "\n", + "We must supplement these reactions with the rate at which they occur to fully specify the dynamics of the system.\n", + "\n", + "Convention to graphically represent is boxes with arrows annotated with the rate.\n", + "Arrow is interpreted as 1 going to another." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4d5998e1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γI\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from graphviz import Digraph\n", + "\n", + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N')\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "295b35a9", + "metadata": {}, + "source": [ + "### Transitions into and out of the system\n", + "\n", + "It is not complicated to extend to transitions which are not between states, but take someone out.\n", + "\n", + "This could appear in the SIR model through births and deaths." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6092d317", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n", + "deadS\n", + "\n", + "\n", + "\n", + "S->deadS\n", + "\n", + "\n", + "μS\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γI\n", + "\n", + "\n", + "\n", + "deadI\n", + "\n", + "\n", + "\n", + "I->deadI\n", + "\n", + "\n", + "μI\n", + "\n", + "\n", + "\n", + "deadR\n", + "\n", + "\n", + "\n", + "R->deadR\n", + "\n", + "\n", + "μR\n", + "\n", + "\n", + "\n", + "bornS\n", + "\n", + "\n", + "\n", + "bornS->S\n", + "\n", + "\n", + "μN\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N')\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape='none', height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "e8f337ad", + "metadata": {}, + "source": [ + "### Correlated reaction\n", + "\n", + "Now we introduce case where we have correlated transitions.\n", + "For instance, if we wish to track the cumulative infecteds, every time an infection occurs as well as transporting S to I, the cumulative inf increments by 1.\n", + "We indicate this by colouring the arrows. Only 1 rate need be specified." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "0881968c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n", + "deadS\n", + "\n", + "\n", + "\n", + "S->deadS\n", + "\n", + "\n", + "μS\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γI\n", + "\n", + "\n", + "\n", + "deadI\n", + "\n", + "\n", + "\n", + "I->deadI\n", + "\n", + "\n", + "μI\n", + "\n", + "\n", + "\n", + "deadR\n", + "\n", + "\n", + "\n", + "R->deadR\n", + "\n", + "\n", + "μR\n", + "\n", + "\n", + "\n", + "bornS\n", + "\n", + "\n", + "\n", + "bornS->S\n", + "\n", + "\n", + "μN\n", + "\n", + "\n", + "\n", + "It\n", + "\n", + "\n", + "\n", + "Cumulative\n", + "Infections, Iₜₒₜ\n", + "\n", + "Cumulative\n", + "Infections, Iₜₒₜ\n", + "\n", + "\n", + "\n", + "It->Cumulative\n", + "Infections, Iₜₒₜ\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N', color=\"blue\")\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot.node(\"It\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('It', 'Cumulative\\nInfections, Iₜₒₜ', label='βSI/N', color=\"blue\")\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "27ebaa8f", + "metadata": {}, + "source": [ + "### Non unitary transitions\n", + "\n", + "Final feature we should account for is magnitude of transitions.\n", + "Whilst models tracking humans involve plus or minus one there are example where this isn't the case.\n", + "This is common in chemical systems, if we were tracking populations of H2 O2 and H2O in the synthesis of water, then one reaction results in population changes: H2: -2, O2: -1, H2O: +2.\n", + "In our case, let's say we want to track the net cost of the epidemic.\n", + "If each infection costs C pounds then we need this." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "eb304e22", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n", + "deadS\n", + "\n", + "\n", + "\n", + "S->deadS\n", + "\n", + "\n", + "μS\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γI\n", + "\n", + "\n", + "\n", + "deadI\n", + "\n", + "\n", + "\n", + "I->deadI\n", + "\n", + "\n", + "μI\n", + "\n", + "\n", + "\n", + "deadR\n", + "\n", + "\n", + "\n", + "R->deadR\n", + "\n", + "\n", + "μR\n", + "\n", + "\n", + "\n", + "bornS\n", + "\n", + "\n", + "\n", + "bornS->S\n", + "\n", + "\n", + "μN\n", + "\n", + "\n", + "\n", + "It\n", + "\n", + "\n", + "\n", + "Cumulative\n", + "Infections\n", + "\n", + "Cumulative\n", + "Infections\n", + "\n", + "\n", + "\n", + "It->Cumulative\n", + "Infections\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n", + "cost\n", + "\n", + "\n", + "\n", + "Money\n", + "Spent\n", + "\n", + "Money\n", + "Spent\n", + "\n", + "\n", + "\n", + "cost->Money\n", + "Spent\n", + "\n", + "\n", + "βSI/N\n", + "cost\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from graphviz import Digraph\n", + "import dot2tex\n", + "\n", + "\n", + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N', color=\"blue\")\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot.node(\"It\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('It', 'Cumulative\\nInfections', label='βSI/N', color=\"blue\")\n", + "\n", + "dot.node(\"cost\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('cost', 'Money\\nSpent', label='βSI/N', color=\"blue\", headlabel='cost')\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "8676a341", + "metadata": {}, + "source": [ + "## Definition\n", + "\n", + "gathering these features together, the fundamental unit is the Event, which consists of:\n", + "\n", + "1) A rate at which it occurs\n", + "2) Constituent Transitions which happen when the event occurs. Each Transition is then concerned by:\n", + " 1) Type (between states or birth/death)\n", + " 2) Magnitude of change\n", + "\n", + "For example, the infection event has:\n", + "\n", + "- Rate: $\\frac{\\beta S I}{N}$\n", + " - Transition 1: $I \\rightarrow S$, magnitude 1\n", + " - Transition 2: birth rate into $I_{tot}$, magnitude 1\n", + " - Transition 3: birth rate into $Money$, magnitude cost" + ] + }, + { + "cell_type": "markdown", + "id": "ea40824e", + "metadata": {}, + "source": [ + "## Solving these equations\n", + "\n", + "### ODE's\n", + "\n", + "Common to solve either as a deterministic set of Ordinary Differential Equations\n", + "\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta S I}{N} + \\mu N - \\mu S\\\\\n", + "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta S I}{N} - \\gamma I - \\mu I\\\\\n", + "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= \\gamma I - \\mu R\\\\\n", + "\\frac{\\mathrm{d} I_{\\mathrm{tot}}}{\\mathrm{d} t} &= \\frac{\\beta S I}{N}\\\\\n", + "\\frac{\\mathrm{d} M}{\\mathrm{d} t} &= \\frac{c \\beta S I}{N}\n", + "\\end{aligned}$$\n", + "\n", + "### Continuous time Markov chains\n", + "\n", + "Or we solve stochastic via..." + ] + }, + { + "cell_type": "markdown", + "id": "9ef5e992", + "metadata": {}, + "source": [ + "# Defining with pygom\n", + "\n", + "Depends on if you want to solve ODE's. Indeed PyGOM can be used for non-ode systems.\n", + "\n", + "## Simple SIR\n", + "\n", + "By the book we should do:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "558667d6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[ -I*S*beta/N],\n", + "[-I*gamma + I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from pygom import Event, Transition, SimulateOde\n", + "\n", + "#TODO: Birth/Death/Between is now obvious from origin/destination\n", + "\n", + "# 1) Infection\n", + "## Transition\n", + "transition_infection=Transition(origin='S', destination='I', transition_type='T', magnitude='1')\n", + "## Event\n", + "event_infection=Event(transition_list=[transition_infection],\n", + " rate='beta*S*I/N')\n", + "\n", + "# 2) Recovery\n", + "## Transition\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T', magnitude='1')\n", + "## Event\n", + "event_recovery=Event(transition_list=transition_recovery,\n", + " rate='gamma*I')\n", + "\n", + "# We specify states and parameters\n", + "params=['beta', 'gamma', 'N']\n", + "states=[('S', (0, None)), ('I', (0, None)), ('R', (0, None))]\n", + "\n", + "model=SimulateOde(state=states, param=params, event=[event_infection, event_recovery])\n", + "\n", + "model.get_ode_eqn()" + ] + }, + { + "cell_type": "markdown", + "id": "65f37f96", + "metadata": {}, + "source": [ + "Since it is fairly common to have change $\\pm 1$ and only one transition involved in an Event\n", + "\n", + "We can actually get away with:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "44d48f9e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[ -I*S*beta/N],\n", + "[-I*gamma + I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "transition_infection=Transition(origin='S', destination='I', transition_type='T', equation='beta*S*I/N')\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T', equation='gamma*I')\n", + "\n", + "# We specify states and parameters\n", + "params=['beta', 'gamma', 'N']\n", + "states=[('S', (0, None)), ('I', (0, None)), ('R', (0, None))]\n", + "\n", + "model=SimulateOde(state=states, param=params, event=[transition_infection, transition_recovery])\n", + "\n", + "model.get_ode_eqn()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pygom", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/notebooks/definition.ipynb b/docs/notebooks/definition.ipynb new file mode 100644 index 00000000..44e474cf --- /dev/null +++ b/docs/notebooks/definition.ipynb @@ -0,0 +1,359 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a3389d4e", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "source": [ + "# Introduction\n", + "\n", + "The main benefits of using PyGOM are probably most evident when it is applied to compartmental models.\n", + "This class of model is used to represent systems involving the transport of material (continuous or discrete) between different categories.\n", + "These are commonly employed in epidemiology, in which humans (or animals) may flow between different disease states, but are also found in chemistry, tracking the formation of molecules, or in economics, where money may move from one sector to another.\n", + "\n", + "To outline the key features of a compartmental model, we build on a simple Susceptible-Infected-Recovered (SIR) epidemic model with examples of increasing complexity.\n", + "\n", + "```{note}\n", + "For those unfamiliar with the SIR model, an outline can be found in the {doc}`common models ` section.\n", + "```\n", + "\n", + "## Transitions between states\n", + "\n", + "In the simplest SIR compartmental model, individuals move from one state to another through 2 types of transition:\n", + "\n", + "- Infection, which turns a Susceptible individual into an Infected one\n", + "- Recovery, which turns an Infected individual into a Recovered one\n", + "\n", + "To fully specify the dynamics of the system, we must supplement these events with the rate at which they occur.\n", + "In this case, infections occur at a rate $\\frac{\\beta S I}{N}$ and recoveries at a rate $\\gamma I$.\n", + "\n", + "We can graphically represent compartmental models using boxes (nodes) to indicate the states and arrows (directed edges) to show the transfer of individuals.\n", + "The arrows are then annotated with the rate at which the transitions occur and it is implied that a transition event leads to the transfer of one individual." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "4d5998e1", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "βSI/N\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γI\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from graphviz import Digraph\n", + "\n", + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.attr(size='5,5')\n", + "\n", + "dot.edge('S', 'I', label='βSI/N')\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "295b35a9", + "metadata": {}, + "source": [ + "## Transitions in to and out of the system\n", + "\n", + "It is not complicated to extend the compartmental model framework to transitions which are not between states.\n", + "This could appear in the SIR model through births and deaths, for example.\n", + "Here, we allow individuals to be born in a susceptible state at a rate, $\\mu$, proportional to the total population, $N$.\n", + "We also have deaths occurring from each compartment at the same rate, proportional to the population of the respective compartment.\n", + "\n", + "To indicate these graphically, birth and death processes lack an origin or a destination state respectively:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6092d317", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [], + "source": [ + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N')\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape='none', height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "e8f337ad", + "metadata": {}, + "source": [ + "```{note}\n", + "We may actually be interested in tracking the total number of deaths, in which case we would define a new compartment, say $D$, and have this as the destination state for the death processes. \n", + "```\n", + "\n", + "## Correlated transitions\n", + "\n", + "It is possible for an event to trigger multiple transitions to occur.\n", + "For instance, let's examine what happens if we wish to track the cumulative number of infections.\n", + "Every time an infection occurs, as well as an individual transferring from $S$ to $I$, the $I_{tot}$ compartment increments by 1 too.\n", + "We show this graphically as a birth process into $I_{tot}$ and indicate that it is correlated with the $S\\rightarrow I$ transition by a shared colour (the default colour, black, does not imply correlation so that recovery, births and deaths are independent processes).\n", + "Correlated transitions have the same underlying rate, so that, strictly speaking, only one rate needs be specified along the blue edges.\n", + "However, it can help for clarity to include the $\\frac{\\beta S I}{N}$ in both cases, as we have done here." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0881968c", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [], + "source": [ + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N', color=\"blue\")\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot.node(\"It\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('It', 'Iₜₒₜ', label='βSI/N', color=\"blue\")\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "27ebaa8f", + "metadata": {}, + "source": [ + "### Non singular transitions\n", + "\n", + "The final feature we should account for is the magnitude of transitions.\n", + "So far, we have only dealt with transitions which result in the state populations changing by $\\pm 1$.\n", + "This is typically the case for epidemic compartmental models, where we are dealing with the movement of individuals.\n", + "We could imagine scenarios, such as vaccinations being administered in batches of, say, 100, meaning that in one vaccination round 100 individuals will move from $S$ to $R$ in one go.\n", + "Or, perhaps, if we restrict our study a cohort of twins then each birth event increments the $S$ population by 2.\n", + "\n", + "It is more common, however, to find these kinds of situations in the study chemical systems.\n", + "For example, if we were tracking populations of $\\mathrm{H}_2$, $\\mathrm{O}_2$ and $\\mathrm{H}_2\\mathrm{O}$ in the synthesis of water, then one reaction results in population changes: $\\mathrm{H}_2$: -2, $\\mathrm{O}_2$: -1 and $\\mathrm{H}_2\\mathrm{O}$ +2.\n", + "\n", + "In our SIR model, let's say we wish to track the monetary cost of the epidemic, $M$.\n", + "With this example, we see that the magnitude of a transition need not be an integer quantity.\n", + "If each infection costs $c$ monetary units then we must add another correlated transition to our model.\n", + "This time, we must indicate that the transition has a different magnitude and we do so by adding a label of the amount to the arrowhead." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eb304e22", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [], + "source": [ + "from graphviz import Digraph\n", + "\n", + "\n", + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N', color=\"blue\")\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot.node(\"It\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('It', 'Iₜₒₜ', label='βSI/N', color=\"blue\")\n", + "\n", + "dot.node(\"cost\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('cost', 'M', label='βSI/N', color=\"blue\", headlabel='c')\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "8676a341", + "metadata": {}, + "source": [ + "# Definition\n", + "\n", + "Gathering these features together, we have the foundations of what a compartmental model is.\n", + "The fundamental unit we shall call the **Event** and this consists of:\n", + "\n", + "1) The rate at which it occurs\n", + "2) Constituent **Transitions** which are triggered when the event occurs. Each Transition is then defined by:\n", + " - i) Type (between states or birth/death)\n", + " - ii) Magnitude of the state change\n", + "\n", + "```{note}\n", + "This is why the classes {class}`.Event` and {class}`.Transition` are the building blocks of a PyGOM model, as outlined in the {doc}`Defining a system of differential equations ` section.\n", + "```\n", + "\n", + "For example, the compartmental model above consists of 6 events:\n", + "\n", + "1) The infection event which has a rate, $\\frac{\\beta S I}{N}$, and involves 3 transitions:\n", + " - Transition from $S \\rightarrow I$ with magnitude 1\n", + " - Birth rate into $I_{\\mathrm{tot}}$ with magnitude 1\n", + " - Birth rate into $M$, with magnitude $c$\n", + "2) The recovery event which has a rate, $\\gamma I$, and involves 1 transition:\n", + " - Transition from $I \\rightarrow R$ with magnitude 1\n", + "3) Events 3 to 6 are one birth and three death events" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pygom", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/notebooks/epijson.ipynb b/docs/notebooks/epijson.ipynb index 73ddd29e..7890e654 100644 --- a/docs/notebooks/epijson.ipynb +++ b/docs/notebooks/epijson.ipynb @@ -81,31 +81,25 @@ "The input Death indicates which column of the data is used and $R$ the corresponding state the data belongs to.\n", "```" ] - }, - { - "cell_type": "markdown", - "id": "caa1d2f1", - "metadata": {}, - "source": [ - "```{footbibliography}\n", - "```" - ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", "name": "python", - "version": "3.9.15" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/extract_info.ipynb b/docs/notebooks/extract_info.ipynb index 84875e30..ca3ace63 100644 --- a/docs/notebooks/extract_info.ipynb +++ b/docs/notebooks/extract_info.ipynb @@ -21,7 +21,7 @@ "outputs": [], "source": [ "from pygom import common_models\n", - "ode = common_models.SIR()" + "model = common_models.SIR()" ] }, { @@ -36,12 +36,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "5a2be3c1", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[ -I*S*beta/N],\n", + "[-I*gamma + I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.get_ode_eqn()" + "model.get_ode_eqn()" ] }, { @@ -56,13 +73,46 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "2089ef15", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "⎡ -Iâ‹…S⋅β ⎤\n", + "⎢dS/dt= ─────── ⎥\n", + "⎢ N ⎥\n", + "⎢ ⎥\n", + "⎢ Iâ‹…S⋅β⎥\n", + "⎢dI/dt= -I⋅γ + ─────⎥\n", + "⎢ N ⎥\n", + "⎢ ⎥\n", + "⎣dR/dt= I⋅γ ⎦\n" + ] + } + ], "source": [ - "ode.print_ode()\n", - "ode.print_ode(True)" + "model.print_ode()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "93a6e1f5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\begin{array}{cc}dS/dt= & - \\frac{I S \\beta}{N}\\\\dI/dt= & - I \\gamma + \\frac{I S \\beta}{N}\\\\dR/dt= & I \\gamma\\end{array}\n" + ] + } + ], + "source": [ + "model.print_ode(True)" ] }, { @@ -70,37 +120,144 @@ "id": "d9d71015", "metadata": {}, "source": [ - "We can check the model definition in terms of a transition matrix:" + "Also as seen before, we can check how each state changes due to each event occurring" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "id": "0ea90388", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}-1 & 0\\\\1 & -1\\\\0 & 1\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[-1, 0],\n", + "[ 1, -1],\n", + "[ 0, 1]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.get_transition_matrix()" + "model.get_StateChangeMatrix()" ] }, { "cell_type": "markdown", - "id": "9c7b5c60", + "id": "af7712ad", "metadata": {}, "source": [ - "where only the upper off diagonal triangle is necessary to fully define the system.\n", - "\n", - "We can even inspect the transitions graphically:" + "and the rate at which events occur:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "9b4f7f98", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.get_EventRateVector()" + ] + }, + { + "cell_type": "markdown", + "id": "18094a6a", + "metadata": {}, + "source": [ + "Again, graphical representation can help with verification:" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "e04194ea", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γ*I\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.get_transition_graph();" + "graph=model.get_transition_graph(show=False)\n", + "graph" ] }, { @@ -115,12 +272,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "1d55ef11", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.linear_ode()" + "model.linear_ode()" ] }, { @@ -137,32 +305,88 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "9c6ec971", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I \\beta}{N} & - \\frac{S \\beta}{N} & 0\\\\\\frac{I \\beta}{N} & - \\gamma + \\frac{S \\beta}{N} & 0\\\\0 & \\gamma & 0\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[-I*beta/N, -S*beta/N, 0],\n", + "[ I*beta/N, -gamma + S*beta/N, 0],\n", + "[ 0, gamma, 0]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.get_jacobian_eqn()" + "model.get_jacobian_eqn()" ] }, { "cell_type": "code", - "execution_count": null, - "id": "0a8b4ff6", + "execution_count": 10, + "id": "ed2b69f5", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[Matrix([\n", + " [ 0, 0, I*S/N**2],\n", + " [ 0, 0, 0],\n", + " [I*S/N**2, 0, -2*I*S*beta/N**3]]),\n", + " Matrix([\n", + " [ 0, 0, -I*S/N**2],\n", + " [ 0, 0, 0],\n", + " [-I*S/N**2, 0, 2*I*S*beta/N**3]]),\n", + " Matrix([\n", + " [0, 0, 0],\n", + " [0, 0, 0],\n", + " [0, 0, 0]])]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.get_hessian_eqn()" + "model.get_hessian_eqn()" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "id": "5e1c7dfb", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S}{N} & 0 & \\frac{I S \\beta}{N^{2}}\\\\\\frac{I S}{N} & - I & - \\frac{I S \\beta}{N^{2}}\\\\0 & I & 0\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[-I*S/N, 0, I*S*beta/N**2],\n", + "[ I*S/N, -I, -I*S*beta/N**2],\n", + "[ 0, I, 0]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "ode.get_grad_eqn()" + "model.get_grad_eqn()" ] }, { @@ -179,7 +403,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 12, "id": "d099d92b", "metadata": {}, "outputs": [ @@ -187,6 +411,7 @@ "name": "stdout", "output_type": "stream", "text": [ + "Update: In the latest version, between state transitions should be passed to SimulateODE via the Event objects.\n", "[S*beta/(N*gamma)]\n" ] } @@ -194,7 +419,7 @@ "source": [ "from pygom.model.epi_analysis import *\n", "\n", - "F, V = disease_progression_matrices(ode, 'I')\n", + "F, V = disease_progression_matrices(model, 'I')\n", "e = R0_from_matrix(F, V)\n", "print(e)" ] @@ -202,7 +427,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -216,12 +441,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/model_solver.ipynb b/docs/notebooks/model_solver.ipynb index 2c018cd2..d8bae317 100644 --- a/docs/notebooks/model_solver.ipynb +++ b/docs/notebooks/model_solver.ipynb @@ -361,7 +361,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "id": "118a869b", "metadata": {}, "outputs": [], @@ -372,7 +372,7 @@ "\n", "n_sim=1000 # number of simulations\n", "ode_S_F.parameters = fixed_param_set\n", - "solution_S_F, simT = ode_S_F.solve_stochast(t, n_sim, full_output=True)" + "solution_S_F, simJump, simT = ode_S_F.solve_stochast(t, n_sim, full_output=True)" ] }, { @@ -553,7 +553,7 @@ "\n", "# In this case n_sim and n_param_draw mean the same thing since we have new parameter set per simulation\n", "ode_S_R.parameters = random_param_set\n", - "solution_S_R, simT = ode_S_R.solve_stochast(t, n_sim, full_output=True)" + "solution_S_R, simJump, simT = ode_S_R.solve_stochast(t, n_sim, full_output=True)" ] }, { diff --git a/docs/notebooks/model_spec.ipynb b/docs/notebooks/model_spec.ipynb index 1d08ef2f..dc8023ed 100644 --- a/docs/notebooks/model_spec.ipynb +++ b/docs/notebooks/model_spec.ipynb @@ -5,86 +5,246 @@ "id": "5d9ccebd", "metadata": {}, "source": [ - "# Defining an ODE system\n", + "# Defining a system of differential equations\n", "\n", - "The starting point, when using PyGOM to study an ODE system, is to encapsulate the relevant information into a class {class}`.SimulateOde`.\n", - "Once defined as an instance of this class, the ODE system is ready for the application of PyGOM's various features such as simulation and parameter fitting.\n", + "The starting point, when using PyGOM to study a system of differential equations (DE's), is to encapsulate the relevant information into a class {class}`.SimulateOde`.\n", + "Once defined as an instance of this class, the system is ready for the application of PyGOM's various features such as simulation and parameter fitting.\n", "\n", - "## Equations vs Transitions\n", + "```{note}\n", + "Whilst the following section is quite long and involves some mathematics, we recommend not skipping it since there can be subtleties when it comes to correctly defining a model and these need to be precisely communicated to PyGOM.\n", + "```\n", + "\n", + "## Continuous time Markov chains\n", "\n", - "Firstly, we outline the two main ways we might think about defining our ODE system.\n", - "Typically, we may already know the set of equations which describes the rates of change of the dependent variables:\n", + "We first introduce a particular kind of system called a continuous time Markov chain (CTMC).\n", + "These commonly appear in the study of chemically reacting systems and epidemiology, where the quantities of interest typically refer to counts of something (be that molecules or people) in different compartments.\n", + "In general, and this will be the case we consider here, the variables may not only refer to discrete quantities but could take continuous values too.\n", "\n", - "$$\\frac{\\mathrm{d} \\mathbf{y}}{\\mathrm{d} t} = f(\\mathbf{y},\\boldsymbol{\\theta}, t)$$\n", + "In a CTMC, $n$ variables, $\\mathbf{y}(t) = \\left(y_{1}(t),\\ldots,y_{n}(t)\\right)$, describe the state of the system at time, $t$.\n", + "There are $T$ different types of event (which PyGOM refers to as **Transitions**) and the effect of an event occurring is to change the state by some amount.\n", + "Mathematically speaking, if event $j$ occurs then the variable $y_i$ changes by $\\mathcal{D}_{ij}$, which may depend on the current state, time and parameters, $\\boldsymbol{\\theta} = \\left(\\theta_{1},\\ldots, \\theta_{p}\\right)$:\n", "\n", - "where $\\mathbf{y} = \\left(y_{1},\\ldots,y_{n}\\right)$ is a vector of the dependent variables, $\\boldsymbol{\\theta} = \\left(\\theta_{1},\\ldots, \\theta_{p}\\right)$ is the set of parameters and $f$ is a vector function giving the rates of change of each dependent variable.\n", - "Typically, as we have used here, rates of change are with respect to time, $t$, though other variables such as position are also common.\n", + "$$\\begin{aligned}\n", + "\\Delta y_i \\text{ due to event of transition type, j } = \\mathcal{D}_{ij}(\\mathbf{y}, \\boldsymbol{\\theta}, t)\n", + "\\end{aligned}$$\n", "\n", - "Compartmental models, whereby the dependent variables represent categories or states, have another interpretation in which we may instead consider transitions between the different groups:\n", + "where $\\mathcal{D}$ is a $n \\times T$ matrix.\n", + "These events occur randomly in time and independently of each other at rates (also possibly dependent on the state of the system):\n", "\n", "$$\\begin{aligned}\n", - "y_i \\rightarrow y_j = f_{i,j}(\\mathbf{y},\\boldsymbol{\\theta}) \\\\\n", + "\\boldsymbol{\\lambda}(\\mathbf{y}, \\boldsymbol{\\theta}, t) = \\left(\\lambda_{1}(\\mathbf{y}, \\boldsymbol{\\theta}, t),\\ldots, \\lambda_{T}(\\mathbf{y}, \\boldsymbol{\\theta}, t)\\right)\n", "\\end{aligned}$$\n", "\n", - "where $i, j = \\{1,\\ldots, n\\}$ and $f_{i,j}$ are functions governing the rate at which members of group $i$ transition to group $j$.\n", - "Since flows are symmetric ($f_{i,j}=-f_{j,i}$) and a group cannot flow into itself ($f_{i,i}=0$), we need only specify rates for one half of the transition matrix ($i>j$ or $j>i$).\n", + "To demonstrate how this works with an example, consider a Susceptible-Infected-Recovered (SIR) epidemic model.\n", + "```{note}\n", + "For those unfamiliar with the SIR model, an outline can be found in the {doc}`common models ` section.\n", + "```\n", + "In this case, the state of the system is specified by 3 variables: $S$, $I$ and $R$.\n", + "There are 2 types of event, infection and recovery, which occur at rates $\\frac{\\beta S I}{N}$ and $\\gamma I$ respectively.\n", + "The result of an infection event happening is to reduce $S$ by 1, increment $I$ by 1 and leave $R$ unchanged. \n", + "Recovery reduces $I$ by 1 and increments $R$ by 1, leaving $S$ unchanged.\n", + "This information can be encapsulated in the framework above by the objects $\\mathbf{y}$, $\\boldsymbol{\\lambda}$ and $\\mathcal{D}$ as:\n", "\n", - "PyGOM allows the user flexibility in choosing which of these perspectives to use, or indeed combine, in order to build their models.\n", - "If given transitions, PyGOM will automatically convert these into equations and, {doc}`as we'll see later `, it can also attempt to reverse engineer transitions from equations.\n", + "$$\\begin{aligned}\n", + "\\mathbf{y}=\n", + "\\begin{pmatrix}\n", + "S\\\\\n", + "I\\\\\n", + "R\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\lambda} =\n", + "\\begin{pmatrix}\n", + "\\frac{\\beta S I}{N}\\\\\n", + "\\gamma I\n", + "\\end{pmatrix}\n", + "\\text{, } \\mathcal{D} =\n", + "\\begin{pmatrix}\n", + "-1 & 0\\\\\n", + "1 & -1\\\\\n", + "0 & 1\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\theta} =\n", + "\\Big( \\beta, \\gamma, N\\Big)\n", + "\\end{aligned}$$\n", "\n", - "## Example: SIR model\n", + "To fully specify the CTMC, this must be accompanied by a master equation which describes the probability that the system moves from the current state to the next.\n", + "We omit this information here and instead just note that the system evolves according to the two independent stochastic processes: infection and recovery.\n", + "Our SIR example is a special case in which the events involve transitions of individuals from one compartment to another, thus conserving the total number of individuals (note that the column sums of $\\mathcal{D}$ are all 0).\n", + "However, in general:\n", "\n", - "Here we use a Susceptible-Infected-Recovered epidemic model (an SIR model, for short) to demonstrate the two different ways PyGOM supports model specification.\n", - "Since we will frequently rely on the SIR model in examples throughout this tutorial, we take a moment here to outline its key features.\n", + "- Each event need not effect only 2 variables.\n", + "- Each event doesn't have to change variables by $\\pm 1$, or even by a constant amount.\n", + "- Variables don't have to be discrete and/or positive.\n", "\n", - "```{warning}\n", - "There is some ambiguity in the naming of the Recovered class which is also commonly referred to as Removed.\n", - "In the latter sense, there is no distinction made between those who can no longer be infected due to infection acquired immunity and infection induced death.\n", - "However, for more complex models, the recovered class may become susceptible again due to the effects of immune waning and deaths versus recoveries are typically important to distinguish in real world applications.\n", - "Therefore, in this tutorial, the Recovered class will be reserved solely for those who survive infection.\n", - "```\n", + "For example, let's introduce the variable, $E$, which tracks the net economic impact of the epidemic (negative for loss and positive for gain).\n", + "Let's assume that each infection costs a time dependent amount, $c_i=c_0 e^{-\\frac{t}{\\tau}}$, so that treatment becomes less expensive with time. In this case:\n", + "\n", + "- An infection event now causes a change in 3 variables ($S$, $I$ and $E$). These are correlated, despite not having direct flows between all of them.\n", + "- Upon an infection, $E$ decreases by a time varying, continuous amount.\n", + "- $E$ is not discrete and will take a negative value if any infections occur.\n", + "\n", + "The final kinds of processes we should account for are births and deaths.\n", + "If individuals are born in a susceptible state at a rate proportional to the total fixed population, $\\mu N$, this represents a flow of people with no explicit origin in the model.\n", + "Similarly, deaths occurring in each compartment ($S$, $I$, $R$) at rates ($\\mu S$, $\\mu I$, $\\mu R$) are flows with no explicit destination (unless we add an ``afterlife'' compartment).\n", + "Just to increase the scope of our example model, let's further assume (rather unrealistically) that each birth contributes an amount $c_b$ to the economy.\n", + "Including the economic modelling plus births and deaths in our model:\n", + "\n", + "$$\\begin{aligned}\n", + "\\mathbf{y}=\n", + "\\begin{pmatrix}\n", + "S\\\\\n", + "I\\\\\n", + "R\\\\\n", + "E\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\lambda} =\n", + "\\begin{pmatrix}\n", + "\\frac{\\beta S I}{N}\\\\\n", + "\\gamma I\\\\\n", + "\\mu N\\\\\n", + "\\mu S\\\\\n", + "\\mu I\\\\\n", + "\\mu R\n", + "\\end{pmatrix}\n", + "\\text{, } \\mathcal{D} =\n", + "\\begin{pmatrix}\n", + "-1 & 0 & 1 & -1 & 0 & 0\\\\\n", + "1 & -1 & 0 & 0 & -1 & 0\\\\\n", + "0 & 1 & 0 & 0 & 0 & -1\\\\\n", + "-c_i(t) & 0 & c_b & 0 & 0 & 0\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\theta} =\n", + "\\Big( \\beta, \\gamma, N, \\mu, c_0, \\tau, c_b, \\mu \\Big)\n", + "\\end{aligned}$$\n", + "\n", + "It is worth noting that in the infection process (first column of $\\mathcal{D}$), the pair of states, $S$ and $I$, do still have a special status in that they are involved in a ``true'' transition of individuals.\n", + "This is also true for the recovery process (second column of $\\mathcal{D}$), where people flow between $I$ and $R$. \n", + "We can further claim a similar status for births and deaths, which represent real flows in and out of the system.\n", + "The other changes which occur during an event might be viewed as correlated side-effects (which PyGOM will call **secondary effects**).\n", + "We can preserve this information by separating the matrix $\\mathcal{D}$ into the explicit origins, $\\mathbf{o}$, destinations, $\\mathbf{d}$ (where $o_k$ and $d_k$ are the respective origin and destination of transition $k$) and secondary effects, $\\mathcal{S}$: \n", + "\n", + "$$\\begin{aligned}\n", + "\\mathbf{y}=\n", + "\\begin{pmatrix}\n", + "S\\\\\n", + "I\\\\\n", + "R\\\\\n", + "E\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\lambda} =\n", + "\\begin{pmatrix}\n", + "\\frac{\\beta S I}{N}\\\\\n", + "\\gamma I\\\\\n", + "\\mu N\\\\\n", + "\\mu S\\\\\n", + "\\mu I\\\\\n", + "\\mu R\n", + "\\end{pmatrix}\n", + "\\text{, } \\mathbf{o}=\n", + "\\begin{pmatrix}\n", + "S\\\\\n", + "I\\\\\n", + "\\text{None}\\\\\n", + "S\\\\\n", + "I\\\\\n", + "R\n", + "\\end{pmatrix}\n", + "\\text{, } \\mathbf{d}=\n", + "\\begin{pmatrix}\n", + "I\\\\\n", + "R\\\\\n", + "S\\\\\n", + "\\text{None}\\\\\n", + "\\text{None}\\\\\n", + "\\text{None}\n", + "\\end{pmatrix}\n", + "\\text{, } \\mathcal{S} =\n", + "\\begin{pmatrix}\n", + "0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "-c_i(t) & 0 & c_b & 0 & 0 & 0\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\theta} =\n", + "\\Big( \\beta, \\gamma, N, \\mu, c_0, \\tau, c_b, \\mu \\Big)\n", + "\\end{aligned}$$\n", + "\n", + "Note that the \"None\" indicates that births have no origin and deaths no destination.\n", + "How PyGOM can solve for the time evolution of such a set of stochastic differential equations (SDE's) is a subject for later in this documentation [LINK].\n", + "The focus of the current section is how to successfully communicate all of the above details to PyGOM.\n", + "Before we get to this, we now consider the case where knowledge of the underlying transitions is either not necessary, or the system is not characterised by transitions in the first place.\n", + "\n", + "### Ordinary Differential Equations\n", + "\n", + "If we instead wish to study how the SIR (plus $E$) model evolves on average and are in a regime where non-integer population counts are not an issue, we can write a set of equations:\n", "\n", - "The assumptions of the SIR model can be stated as:\n", - "1) An average member of the population makes contact sufficient to transmit or receive infection with $c$ others per unit time. Each of these events carries a probability, $p$, of transmission such that each individual has an average of $cp = \\beta$ infectious contacts per unit time. This fixed contact rate reflects what is referred to as *standard* incidence, as opposed to *mass-action* incidence, where contacts per person are proportional to the total population size, $N$.\n", - "2) The population interacts heterogeneously as if a well mixed continuum.\n", - "For instance, a susceptible does not have contacts with other individuals, but with the entire population on average.\n", - "3) The infective class recovers at a rate, $\\gamma$.\n", - "4) No births, deaths (natural or from disease) or migration mean there is no entry into or departure from the population: $S(t)+I(t)+R(t)=N$.\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta SI}{N} + \\mu (N - S) \\\\\n", + "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta SI}{N} - (\\gamma+\\mu) I \\\\\n", + "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= (\\gamma-\\mu) I \\\\\n", + "\\frac{\\mathrm{d} E}{\\mathrm{d} t} &= c_b \\mu S - c_i(t) \\frac{\\beta SI}{N}\n", + "\\end{aligned}$$\n", "\n", - "Under these assumptions, the rates of change of the population in each compartment (**S**usceptible, **I**nfected and **R**ecovered) are given by the following equations:\n", + "These are examples of a type of equation known as Ordinary Differential Equations (ODE's):\n", + "a relationship between quantities and their rates of change with respect to one independent variable - in this case, time.\n", + "In general, a set of ODE's has the form:\n", "\n", "$$\\begin{aligned}\n", - "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta SI}{N} \\\\\n", - "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta SI}{N} - \\gamma I \\\\\n", - "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= \\gamma I.\n", + "\\frac{\\mathrm{d} \\mathbf{y}}{\\mathrm{d} t} = f(\\mathbf{y},\\boldsymbol{\\theta}, t)\n", "\\end{aligned}$$\n", "\n", - "However, it is equally valid to view this system as the result of two transitions; infection, which takes subjects from susceptible to infected and recovery, which takes them from infected to recovered:\n", + "where $\\mathbf{y}$ and $\\boldsymbol{\\theta}$ denote dependent variables and parameters respectively, as previously, and $f$ is a vector function giving the rates of change of each dependent variable.\n", + "In converting the CTMC model, these equations can be found via:\n", "\n", "$$\\begin{aligned}\n", - "S \\rightarrow I &= \\frac{\\beta SI}{N} \\\\\n", - "I \\rightarrow R &= \\gamma I\n", + "\\frac{\\mathrm{d} y_i}{\\mathrm{d} t}=f_i=\\sum_{\\text{transitions, }j} \\mathcal{D}_{ij}\\lambda_j\n", "\\end{aligned}$$\n", "\n", - "where the left hand side of each equation indicates the transition and the right hand side the rate at which it occurs.\n", + "Therefore, the familiar set of ODE's describing the SIR model are, in fact, an approximation of an underlying CTMC.\n", + "However, not all ODE's are necessarily the result of a CTMC.\n", + "In the table below we provide 2 examples of models which can be described through and ODE or a CTMC perspective and 2 models which only have an ODE interpretation:\n", + "\n", + "| Name | ODE | CTMC |\n", + "|----|---------|:------------------------:|\n", + "| Hooke's law | $\\begin{aligned} \\frac{\\mathrm{d}x}{\\mathrm{d}t}&=v\\\\ \\frac{\\mathrm{d}v}{\\mathrm{d}t}&= -\\frac{k}{m}x \\end{aligned}$ | NA|\n", + "| Newton's law of cooling | $\\begin{aligned} \\frac{\\mathrm{d}T}{\\mathrm{d}t}=-\\frac{1}{\\tau} \\left( T-T_{\\text{env}} \\right) \\end{aligned}$ | NA|\n", + "| Lotka-Volterra | $\\begin{aligned} \\frac{\\mathrm{d} n_1}{\\mathrm{d}t}&=\\alpha n_1 - \\beta n_1 n_2\\\\ \\frac{\\mathrm{d}n_2}{\\mathrm{d}t}&= -\\gamma n_2 + \\delta n_1 n_2 \\end{aligned}$ | $\\begin{aligned} \\boldsymbol{\\lambda} = \\begin{pmatrix} \\alpha n_1\\\\ \\beta n_1 n_2 \\\\ \\gamma n_2 \\\\ \\delta n_1 n_2 \\end{pmatrix} \\text{, } \\mathcal{D} = \\begin{pmatrix} 1 & -1 & 0 & 0\\\\ 0 & 0 & -1 & 1 \\end{pmatrix} \\end{aligned}$ |\n", + "| SIR | $\\begin{aligned} \\frac{\\mathrm{d} S}{\\mathrm{d}t}&=-\\frac{\\beta S I}{N}\\\\ \\frac{\\mathrm{d}I}{\\mathrm{d}t}&= \\frac{\\beta S I}{N} - \\gamma I\\\\ \\frac{\\mathrm{d}R}{\\mathrm{d}t}&= \\gamma I \\end{aligned}$ | $\\begin{aligned} \\boldsymbol{\\lambda} = \\begin{pmatrix} \\frac{\\beta S I}{N}\\\\ \\gamma I \\end{pmatrix} \\text{, } \\mathcal{D} = \\begin{pmatrix} -1 & 0\\\\ 1 & -1\\\\ 0 & 1 \\end{pmatrix} \\end{aligned}$ |\n", + "\n", + "The first, Hooke's law, describes the dynamics the position, $x$, and velocity, $v$, of a mass attached to a spring.\n", + "Whilst it is possible to introduce stochasticity to this system, perhaps due to random fluctuations in the spring properties, this will not take the form of a CTMC.\n", + "There is actually nothing to mathematically prevent one from modelling the system as a CTMC with $\\boldsymbol{\\lambda}= \\begin{pmatrix} 1\\\\ 1 \\end{pmatrix}$, $\\mathcal{D}=\\begin{pmatrix} v & 0 \\\\ 0 & -\\frac{k}{m} x \\end{pmatrix}$, the result just has no basis in reality.\n", + "The same story applies for Newton's law of cooling, where an object which is warmer than the environment approaches thermal equilibrium with its surroundings.\n", + "\n", + "As we have seen, an SIR is amenable to both a CTMC or an ODE approach.\n", + "Also included in the table is the Lotka-Volterra predator-prey model where we see that a CTMC implementation acts through 2 birth and 2 death processes.\n", + "\n", + "## ODE vs CTMC Definition in PyGOM\n", + "\n", + "PyGOM allows the user flexibility in choosing which of these perspectives to use, or indeed combine if possible, in order to build their models.\n", + "If stochastic solutions are required, however, then PyGOM *must* know the underlying transitions.\n", + "The easiest way is to supply this information directly, however, {doc}`in some cases `, it can also attempt to reverse engineer transitions if ODE's are instead supplied.\n", + "If stochastic solutions are not required (or, indeed, the system has no underlying CTMC), then the system can be specified either in terms of ODE's or transitions (if possible).\n", + "\n", "One advantage of specifying our system using the transition approach is that many will find transitions a more intuitive language when thinking about compartmental models.\n", "Perhaps more beneficial, though, is that when building models with transitions using PyGOM, it enables the computer to do our book-keeping when converting transitions to ODE equations.\n", "This reduces the error of, for example, including a flow out of one state, but forgetting to include it in the recipient state.\n", - "For example, in the case above, when indicating infections with $-\\frac{\\beta SI}{N}$ in the $S$ equation, we had to remember to include the opposite sign in the $I$ equation.\n", + "For example, in the case above, when indicating infections with $-\\frac{\\beta SI}{N}$ in the $\\frac{\\mathrm{d}S}{\\mathrm{d}t}$ equation, we had to remember to include the opposite sign in the $\\frac{\\mathrm{d}I}{\\mathrm{d}t}$ equation.\n", "\n", "## Defining the model with PyGOM\n", "\n", "Defining the system is handled by feeding {class}`.Transition` objects into the central class, {class}`.SimulateOde`.\n", "An instance of the {class}`.Transition` class takes one of four types, which are specified by the `transition_type` argument, letting {class}`.SimulateOde` know which type of information it is being given.\n", - "This type could be `Transition` or `ODE`, as we've just been discussing, or one of two other available options, namely `Birth` and `Death` processes.\n", + "This type could be `Transition` or `ODE`, as we've just been discussing, or one of two other available options, namely `Birth` and `Death` processes, which are essentially of the transition `Transition` type too, but without a destination state.\n", "The {class}`.Transition` class accepts 3 or 4 parameters depending on which type is being defined, as summarised in the below table:\n", "\n", "| | Transition | Equation | Birth | Death |\n", "|:---------------:|:-------------------------------:|:---------------------------------:|:--------------------------------------:|:--------------------------------------:|\n", "| transition_type | T | ODE | B | D |\n", - "| origin | State transition is from, $y_i$ | State equation pertains to, $y_i$ | State birth process populates, $y_i$ | State death process depletes, $y_i$ |\n", - "| destination | State transition is to, $y_j$ | n/a | n/a | n/a |\n", - "| equation | $f_{i,j}$ | $\\frac{dy_i}{dt}$ | $\\frac{dy_i}{dt}$ due to birth process | $\\frac{dy_i}{dt}$ due to death process |\n", + "| origin | $o_k$ | State equation pertains to, $y_i$ | State birth process populates, $y_i$ | State death process depletes, $y_i$ |\n", + "| destination | $d_k$ | n/a | n/a | n/a |\n", + "| equation | Rate of transition, $\\lambda_k$ | $\\frac{dy_i}{dt}$ | Birth rate, $\\lambda_k$ | Death rate, $\\lambda_k$ |\n", + "| secondary_effects | $\\mathcal{S}_k$ | n/a | $\\mathcal{S}_k$ | $\\mathcal{S}_k$ |\n", "\n", "```{note}\n", "Arguably, the state which the birth process populates could be defined as a destination rather than an origin, but this is not the convention adopted here.\n", @@ -93,10 +253,87 @@ "One of the four possible input types is also called \"transition\", which would incorrectly imply that it has a special place within the class, given that it shares its name.\n", "```\n", "\n", - "Let's see how this is implemented for our example SIR system.\n", + "Let's see how this is implemented for our example SIR(E) system without births and deaths.\n", "We import the relevant modules and then define our transitions:" ] }, + { + "cell_type": "markdown", + "id": "60510dec", + "metadata": {}, + "source": [ + "# Defining with pygom\n", + "\n", + "Depends on if you want to solve ODE's. Indeed PyGOM can be used for non-ode systems.\n", + "\n", + "## Simple SIR\n", + "\n", + "By the book we should do:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5a4393cc", + "metadata": {}, + "outputs": [], + "source": [ + "from pygom import Event, Transition, SimulateOde\n", + "\n", + "#TODO: Birth/Death/Between is now obvious from origin/destination\n", + "\n", + "# 1) Infection\n", + "## Transition\n", + "transition_infection=Transition(origin='S', destination='I', transition_type='T', magnitude='1')\n", + "## Event\n", + "event_infection=Event(transition_list=[transition_infection],\n", + " rate='beta*S*I/N')\n", + "\n", + "# 2) Recovery\n", + "## Transition\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T', magnitude='1')\n", + "## Event\n", + "event_recovery=Event(transition_list=transition_recovery,\n", + " rate='gamma*I')\n", + "\n", + "# We specify states and parameters\n", + "params=['beta', 'gamma', 'N']\n", + "states=[('S', (0, None)), ('I', (0, None)), ('R', (0, None))]\n", + "\n", + "model=SimulateOde(state=states, param=params, event=[event_infection, event_recovery])\n", + "\n", + "model.get_ode_eqn()" + ] + }, + { + "cell_type": "markdown", + "id": "2797d647", + "metadata": {}, + "source": [ + "Since it is fairly common to have change $\\pm 1$ and only one transition involved in an Event\n", + "\n", + "We can actually get away with:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a6854a9", + "metadata": {}, + "outputs": [], + "source": [ + "transition_infection=Transition(origin='S', destination='I', transition_type='T', equation='beta*S*I/N')\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T', equation='gamma*I')\n", + "\n", + "# We specify states and parameters\n", + "params=['beta', 'gamma', 'N']\n", + "states=[('S', (0, None)), ('I', (0, None)), ('R', (0, None))]\n", + "\n", + "model=SimulateOde(state=states, param=params, event=[transition_infection, transition_recovery])\n", + "\n", + "model.get_ode_eqn()" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -107,15 +344,22 @@ "from pygom import Transition, TransitionType\n", "\n", "# Define SIR model through a list of ODEs\n", + "# odeList = [\n", + "# Transition(transition_type=TransitionType.ODE, origin='S', equation='-beta*S*I/N + mu*N - mu*S'),\n", + "# Transition(transition_type=TransitionType.ODE, origin='I', equation='beta*S*I/N - gamma*I - mu*I'),\n", + "# Transition(transition_type=TransitionType.ODE, origin='R', equation='gamma*I- mu*I') \n", + "# ]\n", + "\n", "odeList = [\n", " Transition(transition_type=TransitionType.ODE, origin='S', equation='-beta*S*I/N'),\n", " Transition(transition_type=TransitionType.ODE, origin='I', equation='beta*S*I/N - gamma*I'),\n", - " Transition(transition_type=TransitionType.ODE, origin='R', equation='gamma*I') \n", + " Transition(transition_type=TransitionType.ODE, origin='R', equation='gamma*I'),\n", + " Transition(transition_type=TransitionType.ODE, origin='E', equation='-ci*beta*S*I/N') \n", "]\n", "\n", "# Define SIR model through a list of transitions\n", "transList = [\n", - " Transition(transition_type=TransitionType.T, origin='S', destination='I', equation='beta*S*I/N'),\n", + " Transition(transition_type=TransitionType.T, origin='S', destination='I', equation='beta*S*I/N', secondary_effects=[('E', '-ci')]),\n", " Transition(transition_type=TransitionType.T, origin='I', destination='R', equation='gamma*I')\n", "]" ] @@ -136,8 +380,8 @@ "metadata": {}, "outputs": [], "source": [ - "stateList = ['S', 'I', 'R']\n", - "paramList = ['beta', 'gamma', 'N']" + "stateList = ['S', 'I', 'R', 'E']\n", + "paramList = ['beta', 'gamma', 'N', 'ci']" ] }, { @@ -177,13 +421,14 @@ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\\\- \\frac{I S \\beta ci}{N}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ -I*S*beta/N],\n", "[-I*gamma + I*S*beta/N],\n", - "[ I*gamma]])" + "[ I*gamma],\n", + "[ -I*S*beta*ci/N]])" ] }, "execution_count": 4, @@ -204,13 +449,14 @@ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\\\- \\frac{I S \\beta ci}{N}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ -I*S*beta/N],\n", "[-I*gamma + I*S*beta/N],\n", - "[ I*gamma]])" + "[ I*gamma],\n", + "[ -I*S*beta*ci/N]])" ] }, "execution_count": 5, @@ -230,9 +476,7 @@ "## Modifying models\n", "\n", "Once an instance of {class}`.SimulateOde` has been defined it may be modified.\n", - "For example, let's say we wish to add birth and death processes to the the previously defined SIR model of `model_ode`.\n", - "Time dependent parameters can be complicated in PyGOM, so here we will assume that birth and death rates cancel out so that $N$ remains a constant parameter.\n", - "If we assume that the birth rate is proportional to the total population, $\\mu N$, then balance can be achieved with a death rate from each compartment also proportional to $\\mu$ giving a total death rate of $\\mu (S+I+R)=\\mu N$\n", + "For example, let's now add birth and death processes to the the previously defined SIR model of `model_ode`.\n", "We must update the parameters of the class to reflect any additions:" ] }, @@ -243,7 +487,7 @@ "metadata": {}, "outputs": [], "source": [ - "model_ode.param_list = model_ode.param_list + ['mu']" + "model_tra.param_list = model_tra.param_list + ['mu', 'cb']" ] }, { @@ -261,12 +505,12 @@ "metadata": {}, "outputs": [], "source": [ - "birthDeathList = [Transition(origin='S', equation='mu*N', transition_type=TransitionType.B), \n", + "birthDeathList = [Transition(origin='S', equation='mu*N', transition_type=TransitionType.B, secondary_effects=[('E', 'cb')]), \n", " Transition(origin='S', equation='mu*S', transition_type=TransitionType.D), \n", " Transition(origin='I', equation='mu*I', transition_type=TransitionType.D), \n", " Transition(origin='R', equation='mu*R', transition_type=TransitionType.D)]\n", "\n", - "model_ode.birth_death_list = birthDeathList" + "model_tra.birth_death_list = birthDeathList" ] }, { @@ -279,35 +523,73 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "id": "6cc2ba1a", "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N} + N \\mu - S \\mu\\\\- I \\gamma - I \\mu + \\frac{I S \\beta}{N}\\\\I \\gamma - R \\mu\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N} + N \\mu - S \\mu\\\\- I \\gamma - I \\mu + \\frac{I S \\beta}{N}\\\\I \\gamma - R \\mu\\\\- \\frac{I S \\beta ci}{N}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ -I*S*beta/N + N*mu - S*mu],\n", "[-I*gamma - I*mu + I*S*beta/N],\n", - "[ I*gamma - R*mu]])" + "[ I*gamma - R*mu],\n", + "[ -I*S*beta*ci/N]])" ] }, - "execution_count": 8, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "model_ode.get_ode_eqn()" + "model_tra.get_ode_eqn()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "357e133e", + "metadata": {}, + "outputs": [], + "source": [ + "class Transition:\n", + " rate='beta*S*I'\n", + " type='Transition'\n", + " origin='S'\n", + " destination='I'\n", + " secondary_effects=[('I_tot', '1'), ('B', 'i_cost')]\n", + "\n", + "\n", + "\n", + "\n", + "class Transition:\n", + " type='Transition'\n", + " origin='S'\n", + " destination='I'\n", + "\n", + "class Transition:\n", + " type='birth'\n", + " destination='I_tot'\n", + " change='1'\n", + "\n", + "class Transition:\n", + " type='death'\n", + " origin='B'\n", + " change='i_cost'\n", + "\n", + "class Event:\n", + " rate='beta*S*I'\n", + " transitions=[T1, T2, T3]" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -321,12 +603,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/model_spec_2.ipynb b/docs/notebooks/model_spec_2.ipynb new file mode 100644 index 00000000..aec35cea --- /dev/null +++ b/docs/notebooks/model_spec_2.ipynb @@ -0,0 +1,1369 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5d9ccebd", + "metadata": {}, + "source": [ + "# Defining a system of differential equations\n", + "\n", + "When using PyGOM to study a compartmental model or series of ODEs, the starting point is to encapsulate the relevant information into a class {class}`.SimulateOde`.\n", + "Once defined as an instance of this class, the system is ready for the application of PyGOM's various features such as simulation and parameter fitting.\n", + "\n", + "## Events and Transitions\n", + "\n", + "If we are dealing with a compartmental model, the easiest way to define this is by feeding {class}`.Transition` and {class}`.Event` objects into the central class, {class}`.SimulateOde`.\n", + "We demonstrate how this is done via the example of an SIR model with some added features.\n", + "\n", + "### Basic SIR model example\n", + "\n", + "We first import the relevant modules:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e9ec3eef", + "metadata": {}, + "outputs": [], + "source": [ + "from pygom import Event, Transition, SimulateOde" + ] + }, + { + "cell_type": "markdown", + "id": "a2ca0d71", + "metadata": {}, + "source": [ + "Next we specify the names of the states and parameters, which we can declare as lists.\n", + "Since we will most commonly be dealing with states which represent the counts of something, PyGOM will assume that the states are constrained to have a minimum value of zero and no upper bound.\n", + "If this is not the case, we can inform PyGOM about such limits by declaring the state as a tuple, with the first element being the state name and the second being another tuple containing the minimum and maximum allowed values.\n", + "We demonstrate below how this is done, even though in this case it's not necessary as we are specifying the default limits." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d73b3253", + "metadata": {}, + "outputs": [], + "source": [ + "params=['beta', 'gamma', 'N']\n", + "states=[('S', (0, None)), ('I', (0, None)), ('R', (0, None))]\n", + "# equivalent to:\n", + "# states=['S', 'I', 'R']" + ] + }, + { + "cell_type": "markdown", + "id": "3e6f1eb3", + "metadata": {}, + "source": [ + "Transitions are encapsulated in a {class}`.Transition` class.\n", + "We signify that a transition is between states by setting `transition_type`='T' and must also provide the origin and destination.\n", + "An {class}`.Event` object is then defined by the transition (or transitions) and the rate at which it occurs." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "0c2acdad", + "metadata": {}, + "outputs": [], + "source": [ + "# 1) Infection\n", + "## Transition\n", + "transition_infection=Transition(origin='S', destination='I', transition_type='T', magnitude='1')\n", + "## Event\n", + "event_infection=Event(transition_list=[transition_infection], rate='beta*S*I/N')\n", + "\n", + "# 2) Recovery\n", + "## Transition\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T', magnitude='1')\n", + "## Event\n", + "event_recovery=Event(transition_list=[transition_recovery], rate='gamma*I')" + ] + }, + { + "cell_type": "markdown", + "id": "f4bac138", + "metadata": {}, + "source": [ + "We are now ready to initialise the model object:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c30842fc", + "metadata": {}, + "outputs": [], + "source": [ + "model=SimulateOde(state=states, param=params, event=[event_infection, event_recovery])" + ] + }, + { + "cell_type": "markdown", + "id": "f3f82eff", + "metadata": {}, + "source": [ + "We can check that the state change matrix (introduced as $\\mathcal{D}$ {doc}`previously `), in which the columns correspond to events and the rows to the associated changes in the variables, is what we'd expect:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e25c3cbf", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}-1 & 0\\\\1 & -1\\\\0 & 1\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[-1, 0],\n", + "[ 1, -1],\n", + "[ 0, 1]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.get_StateChangeMatrix()" + ] + }, + { + "cell_type": "markdown", + "id": "fb8bad5a", + "metadata": {}, + "source": [ + "and we can also verify the event rate vector ($\\boldsymbol{\\lambda}$ from {doc}`before `) is correct:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "11230805", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.get_EventRateVector()" + ] + }, + { + "cell_type": "markdown", + "id": "3eedccbb", + "metadata": {}, + "source": [ + "We can actually get away with a more shorthand approach in the model definition.\n", + "PyGOM assumes that the magnitude of a transition is 1 unless told otherwise, so there is no need to specify the `magnitude` argument here.\n", + "Also, both events only involve one transition each, so it's a bit cumbersome to always have to wrap a {class}`.Transition` within an {class}`.Event`.\n", + "A shorthand is to add the rate information to the {class}`.Transition`, this time as a parameter called `equation` and to feed the transitions in directly where we previously input the event list." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "e71b6f08", + "metadata": {}, + "outputs": [], + "source": [ + "# 1) Infection\n", + "transition_infection=Transition(origin='S', destination='I', transition_type='T', equation='beta*S*I/N')\n", + "\n", + "# 2) Recovery\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T', equation='gamma*I')\n", + "\n", + "# (states and params already defined in previous code cell)\n", + "model2=SimulateOde(state=states, param=params, event=[transition_infection, transition_recovery])" + ] + }, + { + "cell_type": "markdown", + "id": "ed33bd64", + "metadata": {}, + "source": [ + "We briefly demonstrate that the end result is unchanged:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "11bfd223", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}-1 & 0\\\\1 & -1\\\\0 & 1\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[-1, 0],\n", + "[ 1, -1],\n", + "[ 0, 1]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model2.get_StateChangeMatrix()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5900f75d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model2.get_EventRateVector()" + ] + }, + { + "cell_type": "markdown", + "id": "3d7597f8", + "metadata": {}, + "source": [ + "When given a set of events and transitions, PyGOM can convert this into a set of ODEs:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "6842eeeb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\frac{I S \\beta}{N}\\\\- I \\gamma + \\frac{I S \\beta}{N}\\\\I \\gamma\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[ -I*S*beta/N],\n", + "[-I*gamma + I*S*beta/N],\n", + "[ I*gamma]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model2.get_ode_eqn()" + ] + }, + { + "cell_type": "markdown", + "id": "0d69c981", + "metadata": {}, + "source": [ + "and it can be helpful to verify visually that the model is defined as intended:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "fcabf41d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γ*I\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "graph=model2.get_transition_graph(show=False)\n", + "graph" + ] + }, + { + "cell_type": "markdown", + "id": "680ba09a", + "metadata": {}, + "source": [ + "### More complex example\n", + "\n", + "Let's now extend the above model so that it covers all of the aspects outlined in the {doc}`introduction to compartmental models `.\n", + "Firstly, let's introduce vital dynamics of birth and death.\n", + "The total population, $N$, will change if these rates are not balanced.\n", + "In fact, even if the rates are balanced, $N$ is subject to vary due to stochastic imbalances between births and deaths.\n", + "To track the potential evolution of this variable, we change $N$ from being a parameter to a state.\n", + "\n", + "```{note}\n", + "Another way to allow $N$ to vary is to define it as a derived parameter by passing:\n", + "\n", + " derived_parameters=[('N', 'S+I+R')]\n", + "\n", + "to {class}`.SimulateOde`\n", + "\n", + "```\n", + "\n", + "Birth and death {class}`.Transition` objects are indicated by `transition_type` B and D respectively and use `destination` and `origin` respectively to define the affected state.\n", + "\n", + "We now show this in practice.\n", + "Whilst it is possible in PyGOM to build on previously existing models, when changing variable definitions we would recommend starting from scratch as we do here:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "3cf274a7", + "metadata": {}, + "outputs": [], + "source": [ + "params=['beta', 'gamma', 'mu'] # now we have the birth rate parameter\n", + "states=['S', 'I', 'R', 'N'] # now we are treating the population count as a state\n", + "\n", + "# Transitions in and out of total population count\n", + "# These will be used in the following event definitions\n", + "birth_N=Transition(destination=\"N\", transition_type=\"B\")\n", + "death_N=Transition(origin=\"N\", transition_type=\"D\")\n", + "\n", + "# 1) Birth event into S\n", + "birth=Transition(destination=\"S\", transition_type=\"B\")\n", + "event_birth=Event(transition_list=[birth, birth_N], rate='mu*N')\n", + "\n", + "# 2) Death event of an S\n", + "death_S=Transition(origin=\"S\", transition_type=\"D\")\n", + "event_death_S=Event(transition_list=[death_S, death_N], rate='mu*S')\n", + "\n", + "# 3) Death event of an I\n", + "death_I=Transition(origin=\"I\", transition_type=\"D\")\n", + "event_death_I=Event(transition_list=[death_I, death_N], rate='mu*I')\n", + "\n", + "# 4) Death event of an R\n", + "death_R=Transition(origin=\"R\", transition_type=\"D\")\n", + "event_death_R=Event(transition_list=[death_R, death_N], rate='mu*R')\n", + "\n", + "model=SimulateOde(state=states, param=params, event=[event_infection,\n", + " event_recovery,\n", + " event_birth,\n", + " event_death_S,\n", + " event_death_I,\n", + " event_death_R])" + ] + }, + { + "cell_type": "markdown", + "id": "3181eac9", + "metadata": {}, + "source": [ + "As before, it's a good idea to check that the transition graph makes sense:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "0302c933", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "deathS3\n", + "\n", + "\n", + "\n", + "S->deathS3\n", + "\n", + "\n", + "μ*S\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γ*I\n", + "\n", + "\n", + "\n", + "deathI4\n", + "\n", + "\n", + "\n", + "I->deathI4\n", + "\n", + "\n", + "μ*I\n", + "\n", + "\n", + "\n", + "deathR5\n", + "\n", + "\n", + "\n", + "R->deathR5\n", + "\n", + "\n", + "μ*R\n", + "\n", + "\n", + "\n", + "N\n", + "\n", + "N\n", + "\n", + "\n", + "\n", + "deathN3\n", + "\n", + "\n", + "\n", + "N->deathN3\n", + "\n", + "\n", + "μ*S\n", + "\n", + "\n", + "\n", + "deathN4\n", + "\n", + "\n", + "\n", + "N->deathN4\n", + "\n", + "\n", + "μ*I\n", + "\n", + "\n", + "\n", + "deathN5\n", + "\n", + "\n", + "\n", + "N->deathN5\n", + "\n", + "\n", + "μ*R\n", + "\n", + "\n", + "\n", + "birthS2\n", + "\n", + "\n", + "\n", + "birthS2->S\n", + "\n", + "\n", + "μ*N\n", + "\n", + "\n", + "\n", + "birthN2\n", + "\n", + "\n", + "\n", + "birthN2->N\n", + "\n", + "\n", + "μ*N\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "graph=model.get_transition_graph(show=False)\n", + "graph" + ] + }, + { + "cell_type": "markdown", + "id": "f4256782", + "metadata": {}, + "source": [ + "Arrows in black represent transitions not correlated with any others.\n", + "Any non-black arrows which do share the same colour are correlated with each other and so are understood to change together when the underlying event occurs.\n", + "For example, the death of a recovered individual simultaneously decreases the $R$ and $N$ compartments by 1.\n", + "\n", + "```{note}\n", + "Whilst the colour pallette we have used is ostensibly friendly to those with colour-blindness, we appreciate that there is room for improvement.\n", + "If the user has installed the package in editable mode, they may wish to substitute in their preferred pallette by changing the `cols` variable of the `_transition_graph` module.\n", + "```\n", + "\n", + "Let's say we wish to replicate the {doc}`example ` where we track the money spent, $M$, during the epidemic due to each infection event costing $c$ units.\n", + "We also track the cumulative infections in $Itot$.\n", + "This is implemented by adding these as {class}`.Transition` instances to the infection {class}`.Event`.\n", + "Note that the cost transition requires us to specify the magnitude since it is not 1." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "50278709", + "metadata": {}, + "outputs": [], + "source": [ + "# Redo old stuff:\n", + "\n", + "params=['beta', 'gamma', 'mu', 'c']\n", + "states=['S', 'I', 'R', 'N', 'M', 'Itot']\n", + "\n", + "# Infection\n", + "transition_infection=Transition(origin='S', destination='I', transition_type='T')\n", + "transition_cost=Transition(destination='M', transition_type='B', magnitude='c') # we must declare the magnitude of the cost\n", + "transition_count=Transition(destination='Itot', transition_type='B')\n", + "event_infection=Event(transition_list=[transition_infection, transition_cost, transition_count], rate='beta*S*I/N')\n", + "\n", + "model=SimulateOde(state=states,\n", + " param=params,\n", + " event=[event_infection,\n", + " event_recovery,\n", + " event_birth,\n", + " event_death_S,\n", + " event_death_I,\n", + " event_death_R])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "905c0e9c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "deathS3\n", + "\n", + "\n", + "\n", + "S->deathS3\n", + "\n", + "\n", + "μ*S\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γ*I\n", + "\n", + "\n", + "\n", + "deathI4\n", + "\n", + "\n", + "\n", + "I->deathI4\n", + "\n", + "\n", + "μ*I\n", + "\n", + "\n", + "\n", + "deathR5\n", + "\n", + "\n", + "\n", + "R->deathR5\n", + "\n", + "\n", + "μ*R\n", + "\n", + "\n", + "\n", + "N\n", + "\n", + "N\n", + "\n", + "\n", + "\n", + "deathN3\n", + "\n", + "\n", + "\n", + "N->deathN3\n", + "\n", + "\n", + "μ*S\n", + "\n", + "\n", + "\n", + "deathN4\n", + "\n", + "\n", + "\n", + "N->deathN4\n", + "\n", + "\n", + "μ*I\n", + "\n", + "\n", + "\n", + "deathN5\n", + "\n", + "\n", + "\n", + "N->deathN5\n", + "\n", + "\n", + "μ*R\n", + "\n", + "\n", + "\n", + "M\n", + "\n", + "M\n", + "\n", + "\n", + "\n", + "Itot\n", + "\n", + "Itot\n", + "\n", + "\n", + "\n", + "birthM0\n", + "\n", + "\n", + "\n", + "birthM0->M\n", + "\n", + "\n", + "β*S*I/N\n", + "c\n", + "\n", + "\n", + "\n", + "birthItot0\n", + "\n", + "\n", + "\n", + "birthItot0->Itot\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "birthS2\n", + "\n", + "\n", + "\n", + "birthS2->S\n", + "\n", + "\n", + "μ*N\n", + "\n", + "\n", + "\n", + "birthN2\n", + "\n", + "\n", + "\n", + "birthN2->N\n", + "\n", + "\n", + "μ*N\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "graph=model.get_transition_graph(show=False)\n", + "graph" + ] + }, + { + "cell_type": "markdown", + "id": "0014f45e", + "metadata": {}, + "source": [ + "The $c$ beside the arrowhead indicates that this transition occurs in steps of $c$." + ] + }, + { + "cell_type": "markdown", + "id": "dfc6482b", + "metadata": {}, + "source": [ + "## Ordinary Differential Equations\n", + "\n", + "If we were not interested in stochastic dynamics, or our system cannot be visualised as a compartmental model, we might define our system via ODEs from the outset.\n", + "In general though, if a CTMC model does exist, it can be converted into a set of ODEs via:\n", + "\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d} y_i}{\\mathrm{d} t}=\\sum_{\\text{transitions, }j} \\mathcal{D}_{ij}\\lambda_j\n", + "\\end{aligned}$$\n", + "\n", + "For the current example, this results in:\n", + "\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta S I}{N} + \\mu N - \\mu S\\\\\n", + "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta S I}{N} - \\gamma I - \\mu I\\\\\n", + "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= \\gamma I - \\mu R\\\\\n", + "\\frac{\\mathrm{d} N}{\\mathrm{d} t} &= \\mu N - \\mu S - \\mu I - \\mu R = 0\\\\\n", + "\\frac{\\mathrm{d} I_{\\mathrm{tot}}}{\\mathrm{d} t} &= \\frac{\\beta S I}{N}\\\\\n", + "\\frac{\\mathrm{d} M}{\\mathrm{d} t} &= \\frac{c \\beta S I}{N}\n", + "\\end{aligned}$$\n", + "\n", + "To build a PyGOM object from this, we use {class}`.Transition` classes of the type, `ODE`, and pass a list of these in the `ode` argument." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "c2c1f766", + "metadata": {}, + "outputs": [], + "source": [ + "dSdt=Transition(transition_type='ODE', origin='S', equation='-beta*S*I/N + mu*N - mu*S')\n", + "dIdt=Transition(transition_type='ODE', origin='I', equation='beta*S*I - gamma*I - mu*I')\n", + "dRdt=Transition(transition_type='ODE', origin='R', equation='gamma*I - mu*R')\n", + "dNdt=Transition(transition_type='ODE', origin='N', equation='0')\n", + "dMdt=Transition(transition_type='ODE', origin='M', equation='beta*S*I/N')\n", + "dItotdt=Transition(transition_type='ODE', origin='Itot', equation='c*beta*S*I/N')\n", + "\n", + "model_ode=SimulateOde(state=states, param=params, ode=[dSdt, dIdt, dRdt, dNdt, dMdt, dItotdt])" + ] + }, + { + "cell_type": "markdown", + "id": "e7973af4", + "metadata": {}, + "source": [ + "In choosing this path, we have closed the door on the possibility of stochastic simulations.\n", + "For instance, PyGOM now cannot derive a state change matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "7ce0527e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\\\\\\\\\\\\\\\\\\\\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix(6, 0, [])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model_ode.get_StateChangeMatrix()" + ] + }, + { + "cell_type": "markdown", + "id": "d6f84d76", + "metadata": {}, + "source": [ + "The transition graph is also not very informative.\n", + "We are basically provided with our set of ODEs with some adorning arrows (which are also dashed, as we see below this is useful to differentiate between deterministic and stochastic processes)." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "6a623263", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "N\n", + "\n", + "N\n", + "\n", + "\n", + "\n", + "M\n", + "\n", + "M\n", + "\n", + "\n", + "\n", + "Itot\n", + "\n", + "Itot\n", + "\n", + "\n", + "\n", + "odeS\n", + "\n", + "\n", + "\n", + "odeS->S\n", + "\n", + "\n", + "-beta*S*I/N + mu*N - mu*S\n", + "\n", + "\n", + "\n", + "odeI\n", + "\n", + "\n", + "\n", + "odeI->I\n", + "\n", + "\n", + "beta*S*I - gamma*I - mu*I\n", + "\n", + "\n", + "\n", + "odeR\n", + "\n", + "\n", + "\n", + "odeR->R\n", + "\n", + "\n", + "gamma*I - mu*R\n", + "\n", + "\n", + "\n", + "odeN\n", + "\n", + "\n", + "\n", + "odeN->N\n", + "\n", + "\n", + "0\n", + "\n", + "\n", + "\n", + "odeM\n", + "\n", + "\n", + "\n", + "odeM->M\n", + "\n", + "\n", + "beta*S*I/N\n", + "\n", + "\n", + "\n", + "odeItot\n", + "\n", + "\n", + "\n", + "odeItot->Itot\n", + "\n", + "\n", + "c*beta*S*I/N\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "graph=model_ode.get_transition_graph(show=False)\n", + "graph" + ] + }, + { + "cell_type": "markdown", + "id": "a64d2b70", + "metadata": {}, + "source": [ + "## Combining ODEs and Transitions\n", + "\n", + "There could be cases where our system contains both stochastic and deterministic elements.\n", + "In our current example, each infection costs $c$ monetary units.\n", + "We could imagine this to be associated with one-off acute costs of the infection event such as a diagnostic test.\n", + "However, the symptoms which follow infection may introduce additional costs, say, $d$ units per person per day, perhaps due to treatment or money lost due to days not worked.\n", + "\n", + "These latter kind of effects we have just seen how to deal with, by using {class}`.Transition` objects of the type `ODE`.\n", + "It is then trivial to combine these, by using both the `event` and `ode` arguments of {class}`.SimulateOde`.\n", + "In doing so below, we will also learn how to build on a previously created model.\n", + "We add any new parameters to the model `param_list` and our ODEs to the `ode` attribute:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "3f28a83e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "deathS3\n", + "\n", + "\n", + "\n", + "S->deathS3\n", + "\n", + "\n", + "μ*S\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "γ*I\n", + "\n", + "\n", + "\n", + "deathI4\n", + "\n", + "\n", + "\n", + "I->deathI4\n", + "\n", + "\n", + "μ*I\n", + "\n", + "\n", + "\n", + "deathR5\n", + "\n", + "\n", + "\n", + "R->deathR5\n", + "\n", + "\n", + "μ*R\n", + "\n", + "\n", + "\n", + "N\n", + "\n", + "N\n", + "\n", + "\n", + "\n", + "deathN3\n", + "\n", + "\n", + "\n", + "N->deathN3\n", + "\n", + "\n", + "μ*S\n", + "\n", + "\n", + "\n", + "deathN4\n", + "\n", + "\n", + "\n", + "N->deathN4\n", + "\n", + "\n", + "μ*I\n", + "\n", + "\n", + "\n", + "deathN5\n", + "\n", + "\n", + "\n", + "N->deathN5\n", + "\n", + "\n", + "μ*R\n", + "\n", + "\n", + "\n", + "M\n", + "\n", + "M\n", + "\n", + "\n", + "\n", + "Itot\n", + "\n", + "Itot\n", + "\n", + "\n", + "\n", + "birthM0\n", + "\n", + "\n", + "\n", + "birthM0->M\n", + "\n", + "\n", + "β*S*I/N\n", + "c\n", + "\n", + "\n", + "\n", + "birthItot0\n", + "\n", + "\n", + "\n", + "birthItot0->Itot\n", + "\n", + "\n", + "β*S*I/N\n", + "\n", + "\n", + "\n", + "birthS2\n", + "\n", + "\n", + "\n", + "birthS2->S\n", + "\n", + "\n", + "μ*N\n", + "\n", + "\n", + "\n", + "birthN2\n", + "\n", + "\n", + "\n", + "birthN2->N\n", + "\n", + "\n", + "μ*N\n", + "\n", + "\n", + "\n", + "odeM\n", + "\n", + "\n", + "\n", + "odeM->M\n", + "\n", + "\n", + "I*d\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "disease_cost=Transition(origin=\"M\", equation=\"I*d\", transition_type=\"ODE\")\n", + "\n", + "model.param_list=model.param_list+['d']\n", + "model.ode_list=[disease_cost]\n", + "\n", + "graph=model.get_transition_graph(show=False)\n", + "graph" + ] + }, + { + "cell_type": "markdown", + "id": "dd978ec3", + "metadata": {}, + "source": [ + "where the deterministic transition is indicated by a dashed line type.\n", + "The $c$ magnitude indicator next to the blue arrowhead looks like it could instead be associated with the dashed arrowhead, so care needs to be taken when interpreting these graphs until this feature has been optimised." + ] + }, + { + "cell_type": "markdown", + "id": "d2992932", + "metadata": {}, + "source": [ + "## ODE vs Event definition in PyGOM\n", + "\n", + "PyGOM allows the user flexibility in choosing which of these perspectives to use, or indeed combine if possible, in order to build their models.\n", + "If stochastic solutions are required, however, then PyGOM *must* know the underlying transitions.\n", + "The easiest way is to supply this information directly, however, {doc}`in some cases `, it can also attempt to reverse engineer transitions if ODE's are instead supplied.\n", + "If stochastic solutions are not required (or, indeed, the system is not based on a compartmental model), then the system can be specified either in terms of ODEs or transitions (if applicable).\n", + "\n", + "One advantage of specifying our system using the transition approach is that many will find transitions a more intuitive language when thinking about compartmental models.\n", + "Perhaps more beneficial, though, is that when building models with transitions using PyGOM, it enables the computer to do our book-keeping when converting transitions to ODE equations.\n", + "This reduces the error of, for example, including a flow out of one state, but forgetting to include it in the recipient state.\n", + "For example, in the case above, when indicating infections with $-\\frac{\\beta SI}{N}$ in the $\\frac{\\mathrm{d}S}{\\mathrm{d}t}$ equation, we had to remember to include the opposite sign in the $\\frac{\\mathrm{d}I}{\\mathrm{d}t}$ equation." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pygom", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/notebooks/paramfit/params_via_abc.ipynb b/docs/notebooks/paramfit/params_via_abc.ipynb index 0e54b10d..797adaa3 100644 --- a/docs/notebooks/paramfit/params_via_abc.ipynb +++ b/docs/notebooks/paramfit/params_via_abc.ipynb @@ -111,7 +111,7 @@ "n_pop=1e4\n", "paramEval=[('beta', 0.5), ('alpha', 1), ('gamma', 0.5), ('N', n_pop)]\n", "\n", - "ode_SEIR = common_models.SEIR_N(param=paramEval)" + "ode_SEIR = common_models.SEIR(param=paramEval)" ] }, { diff --git a/docs/notebooks/paramfit/params_via_optimization.ipynb b/docs/notebooks/paramfit/params_via_optimization.ipynb index 3d24e6e6..275b9eb3 100644 --- a/docs/notebooks/paramfit/params_via_optimization.ipynb +++ b/docs/notebooks/paramfit/params_via_optimization.ipynb @@ -49,7 +49,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "id": "857371e4", "metadata": {}, "outputs": [], @@ -60,7 +60,7 @@ "theta = [0.4, 0.3, 0.3] # initial guess for [beta, alpha, gamma]\n", "\n", "paramEval=[('beta', theta[0]), ('alpha', theta[1]), ('gamma', theta[2]), ('N', n_pop)]\n", - "ode_SEIR = common_models.SEIR_N(param=paramEval)" + "ode_SEIR = common_models.SEIR(param=paramEval)" ] }, { @@ -276,7 +276,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "id": "c826a9db", "metadata": { "tags": [ @@ -298,7 +298,7 @@ "source": [ "pars=res.x\n", "\n", - "ode_est = common_models.SEIR_N([('beta', pars[0]), ('alpha', pars[1]), ('gamma', pars[2]), ('N', n_pop)])\n", + "ode_est = common_models.SEIR([('beta', pars[0]), ('alpha', pars[1]), ('gamma', pars[2]), ('N', n_pop)])\n", "ode_est.initial_values = (x0, t[0])\n", "solution = ode_est.integrate(t[1::])\n", "\n", diff --git a/docs/notebooks/solution.ipynb b/docs/notebooks/solution.ipynb new file mode 100644 index 00000000..02d46ce4 --- /dev/null +++ b/docs/notebooks/solution.ipynb @@ -0,0 +1,179 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ea40824e", + "metadata": {}, + "source": [ + "# Mathematical description\n", + "\n", + "In order to solve the time evolution of the compartmental model, we require some translation into mathematics.\n", + "The different solving methods of PyGOM is a subject for a {doc}`later chapter `, for now we introduce the two ways such systems may be viewed. Recall the model of the previous section:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "895795ea", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [], + "source": [ + "from graphviz import Digraph\n", + "\n", + "\n", + "dot = Digraph()\n", + "\n", + "dot.body.extend(['rankdir=LR'])\n", + "\n", + "states=['S', 'I', 'R']\n", + "\n", + "for s in states:\n", + " dot.node(s)\n", + "\n", + "dot.edge('S', 'I', label='βSI/N', color=\"blue\")\n", + "dot.edge('I', 'R', label='γI')\n", + "\n", + "dot.node(\"bornS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('bornS', 'S', label=\"μN\")\n", + "\n", + "dot.node(\"deadS\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('S', 'deadS', label=\"μS\")\n", + "\n", + "dot.node(\"deadI\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('I', 'deadI', label=\"μI\")\n", + "\n", + "dot.node(\"deadR\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('R', 'deadR', label=\"μR\")\n", + "\n", + "dot.node(\"It\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('It', 'Iₜₒₜ', label='βSI/N', color=\"blue\")\n", + "\n", + "dot.node(\"cost\", label=\"\", shape=\"none\", height=\"0\", width=\"0\")\n", + "dot.edge('cost', 'M', label='βSI/N', color=\"blue\", headlabel='c')\n", + "\n", + "dot" + ] + }, + { + "cell_type": "markdown", + "id": "1ca0b101", + "metadata": {}, + "source": [ + "## Ordinary Differential Equations\n", + "\n", + "One way to frame these mathematically is via Ordinary Differential Equations (ODEs): a relationship between quantities and their rates of change with respect to one independent variable - in this case, time.\n", + "In general, $n$ variables, $\\mathbf{y}(t) = \\left(y_{1}(t),\\ldots,y_{n}(t)\\right)$, describe the state of the system at time, $t$.\n", + "The rates of change of these variables are governed by the current state of the system, time and parameters, $\\boldsymbol{\\theta} = \\left(\\theta_{1},\\ldots, \\theta_{p}\\right)$:\n", + "\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d} \\mathbf{y}}{\\mathrm{d} t} = f(\\mathbf{y},\\boldsymbol{\\theta}, t)\n", + "\\end{aligned}$$\n", + "\n", + "where $f$ is a vector function giving the rates of change of each dependent variable.\n", + "For the example in question, the ODEs are:\n", + "\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta S I}{N} + \\mu N - \\mu S\\\\\n", + "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta S I}{N} - \\gamma I - \\mu I\\\\\n", + "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= \\gamma I - \\mu R\\\\\n", + "\\frac{\\mathrm{d} I_{\\mathrm{tot}}}{\\mathrm{d} t} &= \\frac{\\beta S I}{N}\\\\\n", + "\\frac{\\mathrm{d} M}{\\mathrm{d} t} &= \\frac{c \\beta S I}{N}\n", + "\\end{aligned}$$\n", + "\n", + "In framing the problem in this way we are making two approximations.\n", + "Firstly, we are allowing the population numbers to be treated as continuous variables.\n", + "Having non integer numbers of people is clearly not realistic, but can be acceptable when considering large populations.\n", + "Secondly, in taking the net effect of the underlying processes, we confine ourselves to study only the deterministic evolution of the system.\n", + "\n", + "## Continuous Time Markov Chains\n", + "\n", + "In a Continuous Time Markov Chain (CTMC), we again have the vector of variables, $\\mathbf{y}(t)$, describing the state of the system.\n", + "There are $N_E$ different types of event and the effect of an event occurring is to change the state by some amount.\n", + "Mathematically speaking, if event $j$ occurs then the variable $y_i$ changes by $\\mathcal{D}_{ij}$, which, as with ODEs, may depend on the current state, time and parameters:\n", + "\n", + "$$\\begin{aligned}\n", + "\\Delta y_i \\text{ due to event of transition type, j } = \\mathcal{D}_{ij}(\\mathbf{y}, \\boldsymbol{\\theta}, t)\n", + "\\end{aligned}$$\n", + "\n", + "where $\\mathcal{D}$ is a $n \\times N_E$ matrix.\n", + "These events occur randomly in time and independently of each other at rates (also possibly dependent on the state of the system):\n", + "\n", + "$$\\begin{aligned}\n", + "\\boldsymbol{\\lambda}(\\mathbf{y}, \\boldsymbol{\\theta}, t) = \\left(\\lambda_{1}(\\mathbf{y}, \\boldsymbol{\\theta}, t),\\ldots, \\lambda_{N_E}(\\mathbf{y}, \\boldsymbol{\\theta}, t)\\right)\n", + "\\end{aligned}$$\n", + "\n", + "For our case:\n", + "\n", + "$$\\begin{aligned}\n", + "\\mathbf{y}=\n", + "\\begin{pmatrix}\n", + "S\\\\\n", + "I\\\\\n", + "R\\\\\n", + "I_{\\mathrm{tot}}\\\\\n", + "M\n", + "\\end{pmatrix}\n", + "\\text{, } \\boldsymbol{\\lambda} =\n", + "\\begin{pmatrix}\n", + "\\frac{\\beta S I}{N}, \\gamma I, \\mu N, \\mu S, \\mu I, \\mu R\n", + "\\end{pmatrix}\n", + "\\text{, } \\mathcal{D} =\n", + "\\begin{pmatrix}\n", + "-1 & 0 & 1 & -1 & 0 & 0\\\\\n", + "1 & -1 & 0 & 0 & -1 & 0\\\\\n", + "0 & 1 & 0 & 0 & 0 & -1\\\\\n", + "1 & 0 & 0 & 0 & 0 & 0\\\\\n", + "c & 0 & 0 & 0 & 0 & 0\n", + "\\end{pmatrix}\n", + "\\end{aligned}$$\n", + "\n", + "where the column and row vector formatting of $\\mathbf{y}$ and $\\boldsymbol{\\lambda}$ respectively is to better illustrate their context with the matrix, $\\mathcal{D}$.\n", + "How we solve a mathematical problem framed in this way will be covered later on, for now we note that it is possible to derive exact, stochastic solutions, unlike in the ODE case.\n", + "\n", + "```{warning}\n", + "**Not all ODEs are CTMCs**\n", + "\n", + "It is worth including a warning at this point.\n", + "We've seen that our SIR example model is amenable to both an ODE and a CTMC approach, however, this is not the case for all systems.\n", + "Borrowing an example from physics, Hooke's Law describes how the position, $x$, and velocity, $v$, of a mass, $m$, attached to a spring (with spring constant, $k$) evolves with time.\n", + "The set of ODEs are as follows:\n", + "\n", + "$$\\begin{aligned}\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t}&=v\\\\\n", + "\\frac{\\mathrm{d}v}{\\mathrm{d}t}&= -\\frac{k}{m}x\n", + "\\end{aligned}$$\n", + "\n", + "Whilst it is possible to introduce stochasticity to this system, perhaps due to random fluctuations in the spring properties, this will not take the form of a CTMC.\n", + "There is actually nothing to mathematically forbid one from modelling the system as a CTMC with $\\boldsymbol{\\lambda}= \\begin{pmatrix} 1\\\\ 1 \\end{pmatrix}$, $\\mathcal{D}=\\begin{pmatrix} v & 0 \\\\ 0 & -\\frac{k}{m} x \\end{pmatrix}$, but the resulting dynamics will not have a basis in reality since the underlying system is not a compartmental model.\n", + "\n", + "It is therefore useful to remember that whilst PyGOM can be, in principle, used for any system of ODEs, it should only be used to provide stochastic results for true compartmental models.\n", + "```" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pygom", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/notebooks/time_dependent_params.ipynb b/docs/notebooks/time_dependent_params.ipynb index c0cf2bad..31665434 100644 --- a/docs/notebooks/time_dependent_params.ipynb +++ b/docs/notebooks/time_dependent_params.ipynb @@ -12,26 +12,15 @@ "As an example, let's consider an SIR model with periodic infectivity ($\\beta(t)$) and add in immune waning too (so we can witness multiple seasons):\n", "\n", "$$\\begin{aligned}\n", - "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta(t) SI}{N} + w R \\\\\n", + "\\frac{\\mathrm{d} S}{\\mathrm{d} t} &= -\\frac{\\beta(t) SI}{N} + w R + a S\\\\\n", "\\frac{\\mathrm{d} I}{\\mathrm{d} t} &= \\frac{\\beta(t) SI}{N}- \\gamma I \\\\\n", "\\frac{\\mathrm{d} R}{\\mathrm{d} t} &= \\gamma I - w R \\\\\n", - "\\beta(t) &= \\beta_0 \\left(1+\\delta \\cos \\left(\\frac{2 \\pi t}{P} \\right) \\right)\n", + "\\beta(t) &= \\beta_0 \\left(1-\\delta \\cos \\left(\\frac{2 \\pi t}{P} \\right) \\right)\n", "\\end{aligned}$$\n", "\n", "where $\\beta_0$ is some baseline infection rate, $\\delta$ is the magnitude of oscillations from the baseline ($-1<\\delta<1$ so that $\\beta>0$), $P$ is the oscillation period and $w$ is the waning rate.\n", - "PyGOM cannot handle the time dependence explicitly, instead we must define a dummy variable, $\\tau$, to play the same role.\n", - "We append our set of equations with an extra one:\n", - "\n", - "$$\\begin{aligned}\n", - "\\frac{\\mathrm{d} \\tau}{\\mathrm{d} t} &= 1\n", - "\\end{aligned}$$\n", - "\n", - "This takes the place of an extra ``state'' in our system, so we need to treat it as such by:\n", - "\n", - "- Declaring it in our state list\n", - "- Including the equation above in our ode list\n", - "- Providing an initial condition (best set $\\tau_0=0$ if $t_0=0$ so that that $\\tau=t$)\n", "\n", + "The variable, $t$, has a special status in PyGOM, so that if it is found within a function it will be interpreted as referring to time.\n", "We must also provide the functional form of $\\beta$ which we do by including it as a `derived parameter`.\n", "In the following we put all of these requirements into code:" ] @@ -43,19 +32,30 @@ "metadata": {}, "outputs": [], "source": [ - "from pygom import SimulateOde, Transition, TransitionType\n", + "from pygom import SimulateOde, Transition, TransitionType, Event\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# Define SIR model\n", - "stateList = ['S', 'I', 'R', 'tau'] # now we have added tau to the states\n", - "paramList = ['gamma', 'N', 'beta0', 'delta', 'period', 'w']\n", - "derived_param = [('beta', 'beta0*(1+delta*cos(2*3.14*tau/period))')] # beta (with tau instead of t)\n", - "\n", - "odeList=[Transition(origin='S', equation='-beta*S*I/N + w*R', transition_type=TransitionType.ODE),\n", - " Transition(origin='I', equation='beta*S*I/N - gamma*I', transition_type=TransitionType.ODE),\n", - " Transition(origin='R', equation='gamma*I - w*R', transition_type=TransitionType.ODE),\n", - " Transition(origin='tau', equation='1', transition_type=TransitionType.ODE)] # d(tau)/dt = 1\n", + "stateList = ['S', 'I', 'R'] # now we have added tau to the states\n", + "paramList = ['gamma', 'N', 'beta0', 'delta', 'period', 'w', 'a']\n", + "derived_param = [('betaT', 'beta0*(1-delta*cos(2*3.14159*t/period))')]\n", + "\n", + "# Infection\n", + "## Internal\n", + "transition_infection_int=Transition(origin='S', destination='I', transition_type='T')\n", + "event_infection_int=Event(transition_list=[transition_infection_int], rate='betaT*S*I/N')\n", + "## External importation\n", + "transition_infection_ext=Transition(origin='S', destination='I', transition_type='T')\n", + "event_infection_ext=Event(transition_list=[transition_infection_ext], rate='a*S')\n", + "\n", + "# Recovery\n", + "transition_recovery=Transition(origin='I', destination='R', transition_type='T')\n", + "event_recovery=Event(transition_list=[transition_recovery], rate='gamma*I')\n", + "\n", + "# Waning\n", + "transition_waning=Transition(origin='R', destination='S', transition_type='T')\n", + "event_waning=Event(transition_list=[transition_waning], rate='w*R')\n", "\n", "# Set parameter values\n", "gamma=0.25 # Recovery rate\n", @@ -64,32 +64,34 @@ "period=365 # Period 1 year\n", "delta=0.2 # beta varies between 0.8 and 1.2 times beta0\n", "w=2/(365) # timescale of immune waning of order 0.5 year\n", + "a=50/(365*n_pop) # roughly 50 introductions per year\n", "\n", "params=[('gamma', gamma),\n", " ('N', n_pop),\n", " ('beta0', beta0),\n", " ('delta', delta),\n", " ('period', period),\n", - " ('w', w)]\n", + " ('w', w),\n", + " ('a', a)]\n", "\n", "# Initial conditions\n", - "i0=1\n", - "x0 = [n_pop-i0, i0, 0, 0] # We specify tau0=0 in [s0, i0, r0, tau0]\n", + "i0=0\n", + "x0 = [n_pop-i0, i0, 0]\n", "\n", "# Time range and increments\n", - "tmax=10*365 # run for 10 years\n", - "dt=0.1 # timestep\n", + "tmax=5*365 # run for 10 years\n", + "dt=10 # time intervals for output\n", "n_timestep=int(tmax/dt) # number of iterations\n", "t = np.linspace(0, tmax, n_timestep) # times at which solution will be evaluated\n", "\n", "# Set up pygom object\n", - "ode = SimulateOde(stateList,\n", - " paramList,\n", - " ode=odeList,\n", - " derived_param=derived_param)\n", + "model = SimulateOde(stateList,\n", + " paramList,\n", + " event=[event_infection_int, event_infection_ext, event_recovery, event_waning],\n", + " derived_param=derived_param)\n", "\n", - "ode.initial_values = (x0, t[0]) # (initial state conditions, initial timepoint)\n", - "ode.parameters=params" + "model.initial_values = (x0, t[0]) # (initial state conditions, initial timepoint)\n", + "model.parameters=params" ] }, { @@ -97,53 +99,54 @@ "id": "1dcdfcc4", "metadata": {}, "source": [ - "We may then solve this deterministically and plot the result:" + "We may then solve this, for now let's do so stochastically, and plot the result:" ] }, { "cell_type": "code", "execution_count": null, "id": "a8057a58", - "metadata": {}, + "metadata": { + "tags": [ + "hide-output" + ] + }, "outputs": [], "source": [ - "solution = ode.solve_determ(t[1::])\n", - "\n", - "f, axarr = plt.subplots(2,2, layout='constrained', figsize=(10, 4))\n", - "\n", - "axarr[0][0].plot(t/365, solution[:,0], color='C1')\n", - "axarr[0][1].plot(t/365, solution[:,1], color='C0')\n", - "axarr[1][0].plot(t/365, solution[:,2], color='C2')\n", - "axarr[1][1].plot(t/365, solution[:,3]/365, color='C3')\n", - "axarr[0][0].set_title(\"S\")\n", - "axarr[0][0].set_xlabel(\"Time (years)\")\n", - "axarr[0][1].set_title(\"I\")\n", - "axarr[0][1].set_xlabel(\"Time (years)\")\n", - "axarr[1][0].set_title(\"R\")\n", - "axarr[1][0].set_xlabel(\"Time (years)\")\n", - "axarr[1][1].set_title(\"tau (years)\")\n", - "axarr[1][1].set_xlabel(\"Time (years)\")\n", - "\n", - "plt.show()" + "np.random.seed(1)\n", + "solution, simJump, simT = model.solve_stochast(t, 1, full_output=True)" ] }, { - "cell_type": "markdown", - "id": "dc691a8f", - "metadata": {}, + "cell_type": "code", + "execution_count": null, + "id": "bd03e27a", + "metadata": { + "tags": [ + "hide-input" + ] + }, + "outputs": [], "source": [ - "```{warning}\n", - "PyGOM cannot be used to solve time dependent systems stochastically.\n", - "This is because our dummy variable, $\\tau$, representing time will be treated the same as the other state variables and thus also evolves stochastically.\n", - "Mathematically, the equation $\\frac{\\mathrm{d} \\tau}{\\mathrm{d} t} = 1$ implies stochastic evolution according to $\\mathrm{d} \\tau \\sim \\mathrm{Poisson}(\\mathrm{d} t)$.\n", - "Whilst $\\tau$ might vaguely follow a similar trajectory to time, we will likely lose too much precision for most applications.\n", - "```" + "f, axarr = plt.subplots(1,3, layout='constrained', figsize=(10, 4))\n", + "\n", + "axarr[0].plot(t/365, solution[0][:,0], color='C1')\n", + "axarr[1].plot(t/365, solution[0][:,1], color='C0')\n", + "axarr[2].plot(t/365, solution[0][:,2], color='C2')\n", + "axarr[0].set_title(\"S\")\n", + "axarr[0].set_xlabel(\"Time (years)\")\n", + "axarr[1].set_title(\"I\")\n", + "axarr[1].set_xlabel(\"Time (years)\")\n", + "axarr[2].set_title(\"R\")\n", + "axarr[2].set_xlabel(\"Time (years)\")\n", + "\n", + "plt.show()" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -157,12 +160,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/docs/notebooks/unroll/unrollSimple.ipynb b/docs/notebooks/unroll/unrollSimple.ipynb index 7d5894d4..0ced1567 100644 --- a/docs/notebooks/unroll/unrollSimple.ipynb +++ b/docs/notebooks/unroll/unrollSimple.ipynb @@ -36,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "52daed16", "metadata": {}, "outputs": [], @@ -65,12 +65,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "16280343", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\\\\\\\\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix(3, 0, [])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "model.get_transition_matrix()" + "model.get_StateChangeMatrix()" ] }, { @@ -85,10 +99,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "id": "768a4cd0", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Update: In the latest version, you should define births as having a destination state instead of an origin.\n", + "Update: In the latest version, you should define births as having a destination state instead of an origin.\n", + "Update: In the latest version, you should define births as having a destination state instead of an origin.\n", + "Update: In the latest version, between state transitions should be passed to SimulateODE via the Event objects.\n", + "Update: In the latest version, birth/death transitions should be passed to SimulateODE via the Event objects.\n" + ] + } + ], "source": [ "model = model.get_unrolled_obj()" ] @@ -103,12 +129,61 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "id": "5750fc80", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}-1 & 0 & 1 & -1 & 1 & 1 & 0 & 0\\\\1 & -1 & 0 & 0 & 0 & 0 & -1 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & 0 & -1\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[-1, 0, 1, -1, 1, 1, 0, 0],\n", + "[ 1, -1, 0, 0, 0, 0, -1, 0],\n", + "[ 0, 1, 0, 0, 0, 0, 0, -1]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "model.get_transition_matrix()" + "model.get_StateChangeMatrix()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "af92a531", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{I S \\beta}{I + R + S}\\\\I \\gamma\\\\B S\\\\S \\mu\\\\B R\\\\B I\\\\I \\mu\\\\R \\mu\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[I*S*beta/(I + R + S)],\n", + "[ I*gamma],\n", + "[ B*S],\n", + "[ S*mu],\n", + "[ B*R],\n", + "[ B*I],\n", + "[ I*mu],\n", + "[ R*mu]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.get_EventRateVector()" ] }, { @@ -123,12 +198,136 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "id": "8251b87f", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "S->I\n", + "\n", + "\n", + "I*S*β/(I + R + S)\n", + "\n", + "\n", + "\n", + "deathS3\n", + "\n", + "\n", + "\n", + "S->deathS3\n", + "\n", + "\n", + "S*μ\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "I*γ\n", + "\n", + "\n", + "\n", + "deathI6\n", + "\n", + "\n", + "\n", + "I->deathI6\n", + "\n", + "\n", + "I*μ\n", + "\n", + "\n", + "\n", + "deathR7\n", + "\n", + "\n", + "\n", + "R->deathR7\n", + "\n", + "\n", + "R*μ\n", + "\n", + "\n", + "\n", + "birthS2\n", + "\n", + "\n", + "\n", + "birthS2->S\n", + "\n", + "\n", + "B*S\n", + "\n", + "\n", + "\n", + "birthS4\n", + "\n", + "\n", + "\n", + "birthS4->S\n", + "\n", + "\n", + "B*R\n", + "\n", + "\n", + "\n", + "birthS5\n", + "\n", + "\n", + "\n", + "birthS5->S\n", + "\n", + "\n", + "B*I\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "model.get_transition_graph();" + "graph=model.get_transition_graph(show=False)\n", + "graph" ] }, { @@ -163,7 +362,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "id": "280c4be4", "metadata": {}, "outputs": [], @@ -190,13 +389,128 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "id": "1b6cb187", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Update: In the latest version, you should define births as having a destination state instead of an origin.\n", + "Update: In the latest version, between state transitions should be passed to SimulateODE via the Event objects.\n", + "Update: In the latest version, birth/death transitions should be passed to SimulateODE via the Event objects.\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "L\n", + "\n", + "L\n", + "\n", + "\n", + "\n", + "S->L\n", + "\n", + "\n", + "A*S*&bη;*δ + I*S*&bη;\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "L->I\n", + "\n", + "\n", + "L*κ*p\n", + "\n", + "\n", + "\n", + "A\n", + "\n", + "A\n", + "\n", + "\n", + "\n", + "L->A\n", + "\n", + "\n", + "-L*κ*p + L*κ\n", + "\n", + "\n", + "\n", + "deathI4\n", + "\n", + "\n", + "\n", + "I->deathI4\n", + "\n", + "\n", + "I*α\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "A->R\n", + "\n", + "\n", + "A*η\n", + "\n", + "\n", + "\n", + "birthR5\n", + "\n", + "\n", + "\n", + "birthR5->R\n", + "\n", + "\n", + "I*α*f\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "model = model.get_unrolled_obj()\n", - "model.get_transition_graph();" + "graph=model.get_transition_graph(show=False)\n", + "graph" ] }, { @@ -211,10 +525,120 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "id": "59ce2a8a", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Update: In the latest version, between state transitions should be passed to SimulateODE via the Event objects.\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "S\n", + "\n", + "S\n", + "\n", + "\n", + "\n", + "L\n", + "\n", + "L\n", + "\n", + "\n", + "\n", + "S->L\n", + "\n", + "\n", + "A*S*&bη;*δ + I*S*&bη;\n", + "\n", + "\n", + "\n", + "I\n", + "\n", + "I\n", + "\n", + "\n", + "\n", + "L->I\n", + "\n", + "\n", + "L*κ*p\n", + "\n", + "\n", + "\n", + "A\n", + "\n", + "A\n", + "\n", + "\n", + "\n", + "L->A\n", + "\n", + "\n", + "-L*κ*p + L*κ\n", + "\n", + "\n", + "\n", + "R\n", + "\n", + "R\n", + "\n", + "\n", + "\n", + "I->R\n", + "\n", + "\n", + "I*α*f\n", + "\n", + "\n", + "\n", + "D\n", + "\n", + "D\n", + "\n", + "\n", + "\n", + "I->D\n", + "\n", + "\n", + "-I*α*f + I*α\n", + "\n", + "\n", + "\n", + "A->R\n", + "\n", + "\n", + "A*η\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "stateList = ['S', 'L', 'I', 'A', 'R', 'D']\n", "paramList = ['beta', 'p', 'kappa', 'alpha', 'f', 'delta', 'eta']\n", @@ -226,13 +650,14 @@ " Transition(origin='D', equation='(1-f)*alpha*I', transition_type=TransitionType.ODE)]\n", "model = SimulateOde(stateList, paramList, ode=odeList)\n", "model = model.get_unrolled_obj()\n", - "model.get_transition_graph();" + "graph=model.get_transition_graph(show=False)\n", + "graph" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('sphinx-doc')", + "display_name": "pygom", "language": "python", "name": "python3" }, @@ -246,12 +671,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.19" - }, - "vscode": { - "interpreter": { - "hash": "4dc1e323c80fe09539c74ad5c5a7c7d8d9ff99e04f7b3dbd3680daf878629d6e" - } + "version": "3.11.10" } }, "nbformat": 4, diff --git a/notebooks/sympy_bug_hunt.ipynb b/notebooks/sympy_bug_hunt.ipynb new file mode 100644 index 00000000..de0eb6f5 --- /dev/null +++ b/notebooks/sympy_bug_hunt.ipynb @@ -0,0 +1,311 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Debug adaptive tau leap\n", + "\n", + "First, we set up SIR model with time dependent infectivity" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from pygom import SimulateOde, Transition, TransitionType\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import random\n", + "import math\n", + "import sympy\n", + "\n", + "###################\n", + "# ODE specification\n", + "###################\n", + "\n", + "# Define SIR model\n", + "stateList = ['S', 'I', 'R']\n", + "paramList = ['beta', 'gamma', 'N']\n", + "transitionList = [Transition(origin='S', destination='I', equation='beta*(1+0.99*cos(2*3.14*t/(10)))*S*I/N', transition_type=TransitionType.T),\n", + " Transition(origin='I', destination='R', equation='gamma*I', transition_type=TransitionType.T)]\n", + "\n", + "n_pop=1e4 # Total population is fixed\n", + "\n", + "beta=0.4\n", + "gamma=1/4\n", + "\n", + "params=[('beta', beta), ('gamma', gamma), ('N', n_pop)]\n", + "\n", + "# Initial conditions\n", + "i0=10\n", + "x0 = [n_pop-i0, i0, 0]\n", + "\n", + "\n", + "# Set up pygom object (D_F suffix implies Deterministic_Fixed)\n", + "model = SimulateOde(stateList, paramList, transition=transitionList)\n", + "model.initial_values = (x0, np.float64(0)) # (initial state conditions, initial timepoint)\n", + "model.parameters=params" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As part of the class initialisation, the string equations get turned into sympy expressions. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "I*S*beta*(0.99*cos(0.628*t) + 1)/N\n", + "\n" + ] + } + ], + "source": [ + "eqn=model._transitionVector[0]\n", + "print(eqn)\n", + "print(type(eqn))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see which variables/states are present in this equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{S, t, I, beta, N}\n" + ] + } + ], + "source": [ + "print(eqn.free_symbols)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This promisingly includes time, t.\n", + "If we want to perform operations with the variables, such as derivatives, we can't define the variable externally" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta\n", + "False\n", + "0\n" + ] + } + ], + "source": [ + "state=sympy.symbols(\"beta\")\n", + "print(state)\n", + "print(state in eqn.free_symbols)\n", + "print(sympy.diff(eqn, state))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Instead, we have to take them from where they were defined in the class:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta\n", + "True\n", + "I*S*(0.99*cos(0.628*t) + 1)/N\n" + ] + } + ], + "source": [ + "state=model._paramDict['beta']\n", + "print(state)\n", + "print(state in eqn.free_symbols)\n", + "print(sympy.diff(eqn, state))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Trouble is, when we pull time from the same dictionary, it is not recognised like the other variables" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t\n", + "False\n", + "0\n" + ] + } + ], + "source": [ + "state=model._paramDict['t']\n", + "print(state)\n", + "print(state in eqn.free_symbols)\n", + "print(sympy.diff(eqn, state))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True\n" + ] + } + ], + "source": [ + "# So I think this is because the t used in eqn is new (created in the check equantion function)\n", + "# but the t we want is model._t which gets into _pramDict in line 97 of base_ode_model.py\n", + "print(model._paramDict['t'] == model._t)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "False\n" + ] + } + ], + "source": [ + "# which as before is _not_ in the equation\n", + "print(model._t in eqn.free_symbols)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle t$" + ], + "text/plain": [ + "t" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# So lets get the t in the equation and replace it with model_t\n", + "\n", + "# can't index sets\n", + "eqn_t = [symb for symb in eqn.free_symbols if str(symb)=='t'][0]\n", + "eqn_t" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# A little bit of light substitution\n", + "new_eqn = eqn.subs(eqn_t, model._t)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t\n", + "True\n", + "-0.62172*I*S*beta*sin(0.628*t)/N\n" + ] + } + ], + "source": [ + "# Lets try that again\n", + "state=model._paramDict['t']\n", + "print(state)\n", + "print(state in new_eqn.free_symbols)\n", + "print(sympy.diff(new_eqn, state))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.14" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/src/pygom/model/_model_verification.py b/src/pygom/model/_model_verification.py index 32a6a411..7043c9da 100644 --- a/src/pygom/model/_model_verification.py +++ b/src/pygom/model/_model_verification.py @@ -1,10 +1,15 @@ import numpy as np +from sympy import parse_expr + # Although reimporting * is not generally recommended # we have to do it here so that it has all the mathematical # functions ready to use when evaluating the equations. # An alternative is to check for all the maths functions, such # as exp, log, trigonometric etc.. and convert them to sympy + +# TODO: is the above comment still relevant? Can't see any * import. + from sympy.functions.elementary.exponential import (exp_polar, exp, log, LambertW) ln = log @@ -72,7 +77,7 @@ def checkEquation(input_str, input_var, derived_var, subs_derived=True): An symbol starting with an underscore is not allowed, and should be checked prior to using this function """ - + if isinstance(input_str, str): input_str = [input_str] assert hasattr(input_str, '__iter__'), "Expecting an iterable" @@ -82,7 +87,9 @@ def checkEquation(input_str, input_var, derived_var, subs_derived=True): assert isinstance(_inputStr, str), "Equation should be in string format" # create the symbols in the local environment for _d in input_var: + #print(_d) for _s in _d.keys(): + #print(_s) if isinstance(_d[_s], tuple): # only the first element, as we made this as a vector _isReal = True if _d[_s][0].is_real else False @@ -92,13 +99,15 @@ def checkEquation(input_str, input_var, derived_var, subs_derived=True): else: _isReal = True if _d[_s].is_real else False exec("""%s = symbols('%s', real=%s)""" % (_s, _s, _isReal)) + #print("\n") for _key, _value in derived_var.items(): _isReal = True if _value.is_real else False exec("""%s = symbols('%s', real=%s)""" % (_key, _key, _isReal)) # if the evaluation fails then there is a problem with the # variables (either state or parameters), success means that # it returns a symbolic expression - _eqn = eval(_inputStr) + # _eqn = eval(_inputStr) + _eqn = parse_expr(_inputStr, locals()) # print _inputStr, type(_eqn), isinstance(_eqn, Expr) if subs_derived: # because these are the derived parameters, we need to substitute @@ -107,6 +116,8 @@ def checkEquation(input_str, input_var, derived_var, subs_derived=True): for _key, _value in derived_var.items(): _eqn = eval("_eqn.subs(%s, %s)" % (_key, _value)) list_out.append(_eqn) + # print(_eqn) + # print(_eqn.free_symbols) if len(list_out) == 1: return list_out[0] diff --git a/src/pygom/model/_tau_leap.c b/src/pygom/model/_tau_leap.c new file mode 100644 index 00000000..ee9ec96b --- /dev/null +++ b/src/pygom/model/_tau_leap.c @@ -0,0 +1,30889 @@ +/* Generated by Cython 3.0.11 */ + +/* BEGIN: Cython Metadata +{ + "distutils": { + "depends": [ + "C:\\Users\\Joseph.Gibson\\AppData\\Local\\Temp\\pip-build-env-0gbdjllr\\overlay\\Lib\\site-packages\\numpy\\_core\\include\\numpy\\arrayobject.h", + "C:\\Users\\Joseph.Gibson\\AppData\\Local\\Temp\\pip-build-env-0gbdjllr\\overlay\\Lib\\site-packages\\numpy\\_core\\include\\numpy\\arrayscalars.h", + "C:\\Users\\Joseph.Gibson\\AppData\\Local\\Temp\\pip-build-env-0gbdjllr\\overlay\\Lib\\site-packages\\numpy\\_core\\include\\numpy\\ndarrayobject.h", + "C:\\Users\\Joseph.Gibson\\AppData\\Local\\Temp\\pip-build-env-0gbdjllr\\overlay\\Lib\\site-packages\\numpy\\_core\\include\\numpy\\ndarraytypes.h", + "C:\\Users\\Joseph.Gibson\\AppData\\Local\\Temp\\pip-build-env-0gbdjllr\\overlay\\Lib\\site-packages\\numpy\\_core\\include\\numpy\\ufuncobject.h" + ], + "extra_compile_args": [ + "-std=c99" + ], + "include_dirs": [ + "C:\\Users\\Joseph.Gibson\\AppData\\Local\\Temp\\pip-build-env-0gbdjllr\\overlay\\Lib\\site-packages\\numpy\\_core\\include" + ], + "name": "pygom.model._tau_leap", + "sources": [ + "src/pygom/model/_tau_leap.pyx" + ] + }, + "module_name": "pygom.model._tau_leap" +} +END: Cython Metadata */ + +#ifndef PY_SSIZE_T_CLEAN +#define PY_SSIZE_T_CLEAN +#endif /* PY_SSIZE_T_CLEAN */ +#if defined(CYTHON_LIMITED_API) && 0 + #ifndef Py_LIMITED_API + #if CYTHON_LIMITED_API+0 > 0x03030000 + #define Py_LIMITED_API CYTHON_LIMITED_API + #else + #define Py_LIMITED_API 0x03030000 + #endif + #endif +#endif + +#include "Python.h" +#ifndef Py_PYTHON_H + #error Python headers needed to compile C extensions, please install development version of Python. +#elif PY_VERSION_HEX < 0x02070000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000) + #error Cython requires Python 2.7+ or Python 3.3+. +#else +#if defined(CYTHON_LIMITED_API) && CYTHON_LIMITED_API +#define __PYX_EXTRA_ABI_MODULE_NAME "limited" +#else +#define __PYX_EXTRA_ABI_MODULE_NAME "" +#endif +#define CYTHON_ABI "3_0_11" __PYX_EXTRA_ABI_MODULE_NAME +#define __PYX_ABI_MODULE_NAME "_cython_" CYTHON_ABI +#define __PYX_TYPE_MODULE_PREFIX __PYX_ABI_MODULE_NAME "." +#define CYTHON_HEX_VERSION 0x03000BF0 +#define CYTHON_FUTURE_DIVISION 1 +#include +#ifndef offsetof + #define offsetof(type, member) ( (size_t) & ((type*)0) -> member ) +#endif +#if !defined(_WIN32) && !defined(WIN32) && !defined(MS_WINDOWS) + #ifndef __stdcall + #define __stdcall + #endif + #ifndef __cdecl + #define __cdecl + #endif + #ifndef __fastcall + #define __fastcall + #endif +#endif +#ifndef DL_IMPORT + #define DL_IMPORT(t) t +#endif +#ifndef DL_EXPORT + #define DL_EXPORT(t) t +#endif +#define __PYX_COMMA , +#ifndef HAVE_LONG_LONG + #define HAVE_LONG_LONG +#endif +#ifndef PY_LONG_LONG + #define PY_LONG_LONG LONG_LONG +#endif +#ifndef Py_HUGE_VAL + #define Py_HUGE_VAL HUGE_VAL +#endif +#define __PYX_LIMITED_VERSION_HEX PY_VERSION_HEX +#if defined(GRAALVM_PYTHON) + /* For very preliminary testing purposes. Most variables are set the same as PyPy. + The existence of this section does not imply that anything works or is even tested */ + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #define CYTHON_COMPILING_IN_LIMITED_API 0 + #define CYTHON_COMPILING_IN_GRAAL 1 + #define CYTHON_COMPILING_IN_NOGIL 0 + #undef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 0 + #undef CYTHON_USE_TYPE_SPECS + #define CYTHON_USE_TYPE_SPECS 0 + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #if PY_VERSION_HEX < 0x03050000 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #undef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 0 + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #undef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 1 + #undef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 0 + #undef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 0 + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_GIL + #define CYTHON_FAST_GIL 0 + #undef CYTHON_METH_FASTCALL + #define CYTHON_METH_FASTCALL 0 + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #ifndef CYTHON_PEP487_INIT_SUBCLASS + #define CYTHON_PEP487_INIT_SUBCLASS (PY_MAJOR_VERSION >= 3) + #endif + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 1 + #undef CYTHON_USE_MODULE_STATE + #define CYTHON_USE_MODULE_STATE 0 + #undef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 0 + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 + #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC + #define CYTHON_UPDATE_DESCRIPTOR_DOC 0 + #endif + #undef CYTHON_USE_FREELISTS + #define CYTHON_USE_FREELISTS 0 +#elif defined(PYPY_VERSION) + #define CYTHON_COMPILING_IN_PYPY 1 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #define CYTHON_COMPILING_IN_LIMITED_API 0 + #define CYTHON_COMPILING_IN_GRAAL 0 + #define CYTHON_COMPILING_IN_NOGIL 0 + #undef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 0 + #ifndef CYTHON_USE_TYPE_SPECS + #define CYTHON_USE_TYPE_SPECS 0 + #endif + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #if PY_VERSION_HEX < 0x03050000 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #undef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 0 + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #undef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 1 + #undef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 0 + #undef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 0 + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_GIL + #define CYTHON_FAST_GIL 0 + #undef CYTHON_METH_FASTCALL + #define CYTHON_METH_FASTCALL 0 + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #ifndef CYTHON_PEP487_INIT_SUBCLASS + #define CYTHON_PEP487_INIT_SUBCLASS (PY_MAJOR_VERSION >= 3) + #endif + #if PY_VERSION_HEX < 0x03090000 + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 0 + #elif !defined(CYTHON_PEP489_MULTI_PHASE_INIT) + #define CYTHON_PEP489_MULTI_PHASE_INIT 1 + #endif + #undef CYTHON_USE_MODULE_STATE + #define CYTHON_USE_MODULE_STATE 0 + #undef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1 && PYPY_VERSION_NUM >= 0x07030C00) + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 + #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC + #define CYTHON_UPDATE_DESCRIPTOR_DOC 0 + #endif + #undef CYTHON_USE_FREELISTS + #define CYTHON_USE_FREELISTS 0 +#elif defined(CYTHON_LIMITED_API) + #ifdef Py_LIMITED_API + #undef __PYX_LIMITED_VERSION_HEX + #define __PYX_LIMITED_VERSION_HEX Py_LIMITED_API + #endif + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #define CYTHON_COMPILING_IN_LIMITED_API 1 + #define CYTHON_COMPILING_IN_GRAAL 0 + #define CYTHON_COMPILING_IN_NOGIL 0 + #undef CYTHON_CLINE_IN_TRACEBACK + #define CYTHON_CLINE_IN_TRACEBACK 0 + #undef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 0 + #undef CYTHON_USE_TYPE_SPECS + #define CYTHON_USE_TYPE_SPECS 1 + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #undef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 0 + #ifndef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #endif + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #undef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 0 + #undef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 0 + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_GIL + #define CYTHON_FAST_GIL 0 + #undef CYTHON_METH_FASTCALL + #define CYTHON_METH_FASTCALL 0 + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #ifndef CYTHON_PEP487_INIT_SUBCLASS + #define CYTHON_PEP487_INIT_SUBCLASS 1 + #endif + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 0 + #undef CYTHON_USE_MODULE_STATE + #define CYTHON_USE_MODULE_STATE 1 + #ifndef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 0 + #endif + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 + #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC + #define CYTHON_UPDATE_DESCRIPTOR_DOC 0 + #endif + #undef CYTHON_USE_FREELISTS + #define CYTHON_USE_FREELISTS 0 +#elif defined(Py_GIL_DISABLED) || defined(Py_NOGIL) + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #define CYTHON_COMPILING_IN_LIMITED_API 0 + #define CYTHON_COMPILING_IN_GRAAL 0 + #define CYTHON_COMPILING_IN_NOGIL 1 + #ifndef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 1 + #endif + #ifndef CYTHON_USE_TYPE_SPECS + #define CYTHON_USE_TYPE_SPECS 0 + #endif + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #ifndef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #ifndef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #endif + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #ifndef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 1 + #endif + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #ifndef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 1 + #endif + #ifndef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 1 + #endif + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_GIL + #define CYTHON_FAST_GIL 0 + #ifndef CYTHON_METH_FASTCALL + #define CYTHON_METH_FASTCALL 1 + #endif + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #ifndef CYTHON_PEP487_INIT_SUBCLASS + #define CYTHON_PEP487_INIT_SUBCLASS 1 + #endif + #ifndef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 1 + #endif + #ifndef CYTHON_USE_MODULE_STATE + #define CYTHON_USE_MODULE_STATE 0 + #endif + #ifndef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 1 + #endif + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 + #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC + #define CYTHON_UPDATE_DESCRIPTOR_DOC 1 + #endif + #ifndef CYTHON_USE_FREELISTS + #define CYTHON_USE_FREELISTS 0 + #endif +#else + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_CPYTHON 1 + #define CYTHON_COMPILING_IN_LIMITED_API 0 + #define CYTHON_COMPILING_IN_GRAAL 0 + #define CYTHON_COMPILING_IN_NOGIL 0 + #ifndef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 1 + #endif + #ifndef CYTHON_USE_TYPE_SPECS + #define CYTHON_USE_TYPE_SPECS 0 + #endif + #ifndef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 1 + #endif + #if PY_MAJOR_VERSION < 3 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #ifndef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 1 + #endif + #ifndef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 1 + #endif + #ifndef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 1 + #endif + #if PY_VERSION_HEX < 0x030300F0 || PY_VERSION_HEX >= 0x030B00A2 + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #elif !defined(CYTHON_USE_UNICODE_WRITER) + #define CYTHON_USE_UNICODE_WRITER 1 + #endif + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #ifndef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 1 + #endif + #ifndef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 1 + #endif + #ifndef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 1 + #endif + #ifndef CYTHON_FAST_GIL + #define CYTHON_FAST_GIL (PY_MAJOR_VERSION < 3 || PY_VERSION_HEX >= 0x03060000 && PY_VERSION_HEX < 0x030C00A6) + #endif + #ifndef CYTHON_METH_FASTCALL + #define CYTHON_METH_FASTCALL (PY_VERSION_HEX >= 0x030700A1) + #endif + #ifndef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 1 + #endif + #ifndef CYTHON_PEP487_INIT_SUBCLASS + #define CYTHON_PEP487_INIT_SUBCLASS 1 + #endif + #if PY_VERSION_HEX < 0x03050000 + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 0 + #elif !defined(CYTHON_PEP489_MULTI_PHASE_INIT) + #define CYTHON_PEP489_MULTI_PHASE_INIT 1 + #endif + #ifndef CYTHON_USE_MODULE_STATE + #define CYTHON_USE_MODULE_STATE 0 + #endif + #if PY_VERSION_HEX < 0x030400a1 + #undef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 0 + #elif !defined(CYTHON_USE_TP_FINALIZE) + #define CYTHON_USE_TP_FINALIZE 1 + #endif + #if PY_VERSION_HEX < 0x030600B1 + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #elif !defined(CYTHON_USE_DICT_VERSIONS) + #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX < 0x030C00A5) + #endif + #if PY_VERSION_HEX < 0x030700A3 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 + #elif !defined(CYTHON_USE_EXC_INFO_STACK) + #define CYTHON_USE_EXC_INFO_STACK 1 + #endif + #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC + #define CYTHON_UPDATE_DESCRIPTOR_DOC 1 + #endif + #ifndef CYTHON_USE_FREELISTS + #define CYTHON_USE_FREELISTS 1 + #endif +#endif +#if !defined(CYTHON_FAST_PYCCALL) +#define CYTHON_FAST_PYCCALL (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1) +#endif +#if !defined(CYTHON_VECTORCALL) +#define CYTHON_VECTORCALL (CYTHON_FAST_PYCCALL && PY_VERSION_HEX >= 0x030800B1) +#endif +#define CYTHON_BACKPORT_VECTORCALL (CYTHON_METH_FASTCALL && PY_VERSION_HEX < 0x030800B1) +#if CYTHON_USE_PYLONG_INTERNALS + #if PY_MAJOR_VERSION < 3 + #include "longintrepr.h" + #endif + #undef SHIFT + #undef BASE + #undef MASK + #ifdef SIZEOF_VOID_P + enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) }; + #endif +#endif +#ifndef __has_attribute + #define __has_attribute(x) 0 +#endif +#ifndef __has_cpp_attribute + #define __has_cpp_attribute(x) 0 +#endif +#ifndef CYTHON_RESTRICT + #if defined(__GNUC__) + #define CYTHON_RESTRICT __restrict__ + #elif defined(_MSC_VER) && _MSC_VER >= 1400 + #define CYTHON_RESTRICT __restrict + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_RESTRICT restrict + #else + #define CYTHON_RESTRICT + #endif +#endif +#ifndef CYTHON_UNUSED + #if defined(__cplusplus) + /* for clang __has_cpp_attribute(maybe_unused) is true even before C++17 + * but leads to warnings with -pedantic, since it is a C++17 feature */ + #if ((defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) || __cplusplus >= 201703L) + #if __has_cpp_attribute(maybe_unused) + #define CYTHON_UNUSED [[maybe_unused]] + #endif + #endif + #endif +#endif +#ifndef CYTHON_UNUSED +# if defined(__GNUC__) +# if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +#endif +#ifndef CYTHON_UNUSED_VAR +# if defined(__cplusplus) + template void CYTHON_UNUSED_VAR( const T& ) { } +# else +# define CYTHON_UNUSED_VAR(x) (void)(x) +# endif +#endif +#ifndef CYTHON_MAYBE_UNUSED_VAR + #define CYTHON_MAYBE_UNUSED_VAR(x) CYTHON_UNUSED_VAR(x) +#endif +#ifndef CYTHON_NCP_UNUSED +# if CYTHON_COMPILING_IN_CPYTHON +# define CYTHON_NCP_UNUSED +# else +# define CYTHON_NCP_UNUSED CYTHON_UNUSED +# endif +#endif +#ifndef CYTHON_USE_CPP_STD_MOVE + #if defined(__cplusplus) && (\ + __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1600)) + #define CYTHON_USE_CPP_STD_MOVE 1 + #else + #define CYTHON_USE_CPP_STD_MOVE 0 + #endif +#endif +#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None) +#ifdef _MSC_VER + #ifndef _MSC_STDINT_H_ + #if _MSC_VER < 1300 + typedef unsigned char uint8_t; + typedef unsigned short uint16_t; + typedef unsigned int uint32_t; + #else + typedef unsigned __int8 uint8_t; + typedef unsigned __int16 uint16_t; + typedef unsigned __int32 uint32_t; + #endif + #endif + #if _MSC_VER < 1300 + #ifdef _WIN64 + typedef unsigned long long __pyx_uintptr_t; + #else + typedef unsigned int __pyx_uintptr_t; + #endif + #else + #ifdef _WIN64 + typedef unsigned __int64 __pyx_uintptr_t; + #else + typedef unsigned __int32 __pyx_uintptr_t; + #endif + #endif +#else + #include + typedef uintptr_t __pyx_uintptr_t; +#endif +#ifndef CYTHON_FALLTHROUGH + #if defined(__cplusplus) + /* for clang __has_cpp_attribute(fallthrough) is true even before C++17 + * but leads to warnings with -pedantic, since it is a C++17 feature */ + #if ((defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) || __cplusplus >= 201703L) + #if __has_cpp_attribute(fallthrough) + #define CYTHON_FALLTHROUGH [[fallthrough]] + #endif + #endif + #ifndef CYTHON_FALLTHROUGH + #if __has_cpp_attribute(clang::fallthrough) + #define CYTHON_FALLTHROUGH [[clang::fallthrough]] + #elif __has_cpp_attribute(gnu::fallthrough) + #define CYTHON_FALLTHROUGH [[gnu::fallthrough]] + #endif + #endif + #endif + #ifndef CYTHON_FALLTHROUGH + #if __has_attribute(fallthrough) + #define CYTHON_FALLTHROUGH __attribute__((fallthrough)) + #else + #define CYTHON_FALLTHROUGH + #endif + #endif + #if defined(__clang__) && defined(__apple_build_version__) + #if __apple_build_version__ < 7000000 + #undef CYTHON_FALLTHROUGH + #define CYTHON_FALLTHROUGH + #endif + #endif +#endif +#ifdef __cplusplus + template + struct __PYX_IS_UNSIGNED_IMPL {static const bool value = T(0) < T(-1);}; + #define __PYX_IS_UNSIGNED(type) (__PYX_IS_UNSIGNED_IMPL::value) +#else + #define __PYX_IS_UNSIGNED(type) (((type)-1) > 0) +#endif +#if CYTHON_COMPILING_IN_PYPY == 1 + #define __PYX_NEED_TP_PRINT_SLOT (PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x030A0000) +#else + #define __PYX_NEED_TP_PRINT_SLOT (PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000) +#endif +#define __PYX_REINTERPRET_FUNCION(func_pointer, other_pointer) ((func_pointer)(void(*)(void))(other_pointer)) + +#ifndef CYTHON_INLINE + #if defined(__clang__) + #define CYTHON_INLINE __inline__ __attribute__ ((__unused__)) + #elif defined(__GNUC__) + #define CYTHON_INLINE __inline__ + #elif defined(_MSC_VER) + #define CYTHON_INLINE __inline + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_INLINE inline + #else + #define CYTHON_INLINE + #endif +#endif + +#define __PYX_BUILD_PY_SSIZE_T "n" +#define CYTHON_FORMAT_SSIZE_T "z" +#if PY_MAJOR_VERSION < 3 + #define __Pyx_BUILTIN_MODULE_NAME "__builtin__" + #define __Pyx_DefaultClassType PyClass_Type + #define __Pyx_PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) +#else + #define __Pyx_BUILTIN_MODULE_NAME "builtins" + #define __Pyx_DefaultClassType PyType_Type +#if CYTHON_COMPILING_IN_LIMITED_API + static CYTHON_INLINE PyObject* __Pyx_PyCode_New(int a, int p, int k, int l, int s, int f, + PyObject *code, PyObject *c, PyObject* n, PyObject *v, + PyObject *fv, PyObject *cell, PyObject* fn, + PyObject *name, int fline, PyObject *lnos) { + PyObject *exception_table = NULL; + PyObject *types_module=NULL, *code_type=NULL, *result=NULL; + #if __PYX_LIMITED_VERSION_HEX < 0x030B0000 + PyObject *version_info; + PyObject *py_minor_version = NULL; + #endif + long minor_version = 0; + PyObject *type, *value, *traceback; + PyErr_Fetch(&type, &value, &traceback); + #if __PYX_LIMITED_VERSION_HEX >= 0x030B0000 + minor_version = 11; + #else + if (!(version_info = PySys_GetObject("version_info"))) goto end; + if (!(py_minor_version = PySequence_GetItem(version_info, 1))) goto end; + minor_version = PyLong_AsLong(py_minor_version); + Py_DECREF(py_minor_version); + if (minor_version == -1 && PyErr_Occurred()) goto end; + #endif + if (!(types_module = PyImport_ImportModule("types"))) goto end; + if (!(code_type = PyObject_GetAttrString(types_module, "CodeType"))) goto end; + if (minor_version <= 7) { + (void)p; + result = PyObject_CallFunction(code_type, "iiiiiOOOOOOiOO", a, k, l, s, f, code, + c, n, v, fn, name, fline, lnos, fv, cell); + } else if (minor_version <= 10) { + result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOiOO", a,p, k, l, s, f, code, + c, n, v, fn, name, fline, lnos, fv, cell); + } else { + if (!(exception_table = PyBytes_FromStringAndSize(NULL, 0))) goto end; + result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOOiOO", a,p, k, l, s, f, code, + c, n, v, fn, name, name, fline, lnos, exception_table, fv, cell); + } + end: + Py_XDECREF(code_type); + Py_XDECREF(exception_table); + Py_XDECREF(types_module); + if (type) { + PyErr_Restore(type, value, traceback); + } + return result; + } + #ifndef CO_OPTIMIZED + #define CO_OPTIMIZED 0x0001 + #endif + #ifndef CO_NEWLOCALS + #define CO_NEWLOCALS 0x0002 + #endif + #ifndef CO_VARARGS + #define CO_VARARGS 0x0004 + #endif + #ifndef CO_VARKEYWORDS + #define CO_VARKEYWORDS 0x0008 + #endif + #ifndef CO_ASYNC_GENERATOR + #define CO_ASYNC_GENERATOR 0x0200 + #endif + #ifndef CO_GENERATOR + #define CO_GENERATOR 0x0020 + #endif + #ifndef CO_COROUTINE + #define CO_COROUTINE 0x0080 + #endif +#elif PY_VERSION_HEX >= 0x030B0000 + static CYTHON_INLINE PyCodeObject* __Pyx_PyCode_New(int a, int p, int k, int l, int s, int f, + PyObject *code, PyObject *c, PyObject* n, PyObject *v, + PyObject *fv, PyObject *cell, PyObject* fn, + PyObject *name, int fline, PyObject *lnos) { + PyCodeObject *result; + PyObject *empty_bytes = PyBytes_FromStringAndSize("", 0); + if (!empty_bytes) return NULL; + result = + #if PY_VERSION_HEX >= 0x030C0000 + PyUnstable_Code_NewWithPosOnlyArgs + #else + PyCode_NewWithPosOnlyArgs + #endif + (a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, name, fline, lnos, empty_bytes); + Py_DECREF(empty_bytes); + return result; + } +#elif PY_VERSION_HEX >= 0x030800B2 && !CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_NewWithPosOnlyArgs(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) +#else + #define __Pyx_PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) +#endif +#endif +#if PY_VERSION_HEX >= 0x030900A4 || defined(Py_IS_TYPE) + #define __Pyx_IS_TYPE(ob, type) Py_IS_TYPE(ob, type) +#else + #define __Pyx_IS_TYPE(ob, type) (((const PyObject*)ob)->ob_type == (type)) +#endif +#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_Is) + #define __Pyx_Py_Is(x, y) Py_Is(x, y) +#else + #define __Pyx_Py_Is(x, y) ((x) == (y)) +#endif +#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsNone) + #define __Pyx_Py_IsNone(ob) Py_IsNone(ob) +#else + #define __Pyx_Py_IsNone(ob) __Pyx_Py_Is((ob), Py_None) +#endif +#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsTrue) + #define __Pyx_Py_IsTrue(ob) Py_IsTrue(ob) +#else + #define __Pyx_Py_IsTrue(ob) __Pyx_Py_Is((ob), Py_True) +#endif +#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsFalse) + #define __Pyx_Py_IsFalse(ob) Py_IsFalse(ob) +#else + #define __Pyx_Py_IsFalse(ob) __Pyx_Py_Is((ob), Py_False) +#endif +#define __Pyx_NoneAsNull(obj) (__Pyx_Py_IsNone(obj) ? NULL : (obj)) +#if PY_VERSION_HEX >= 0x030900F0 && !CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyObject_GC_IsFinalized(o) PyObject_GC_IsFinalized(o) +#else + #define __Pyx_PyObject_GC_IsFinalized(o) _PyGC_FINALIZED(o) +#endif +#ifndef CO_COROUTINE + #define CO_COROUTINE 0x80 +#endif +#ifndef CO_ASYNC_GENERATOR + #define CO_ASYNC_GENERATOR 0x200 +#endif +#ifndef Py_TPFLAGS_CHECKTYPES + #define Py_TPFLAGS_CHECKTYPES 0 +#endif +#ifndef Py_TPFLAGS_HAVE_INDEX + #define Py_TPFLAGS_HAVE_INDEX 0 +#endif +#ifndef Py_TPFLAGS_HAVE_NEWBUFFER + #define Py_TPFLAGS_HAVE_NEWBUFFER 0 +#endif +#ifndef Py_TPFLAGS_HAVE_FINALIZE + #define Py_TPFLAGS_HAVE_FINALIZE 0 +#endif +#ifndef Py_TPFLAGS_SEQUENCE + #define Py_TPFLAGS_SEQUENCE 0 +#endif +#ifndef Py_TPFLAGS_MAPPING + #define Py_TPFLAGS_MAPPING 0 +#endif +#ifndef METH_STACKLESS + #define METH_STACKLESS 0 +#endif +#if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL) + #ifndef METH_FASTCALL + #define METH_FASTCALL 0x80 + #endif + typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs); + typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args, + Py_ssize_t nargs, PyObject *kwnames); +#else + #if PY_VERSION_HEX >= 0x030d00A4 + # define __Pyx_PyCFunctionFast PyCFunctionFast + # define __Pyx_PyCFunctionFastWithKeywords PyCFunctionFastWithKeywords + #else + # define __Pyx_PyCFunctionFast _PyCFunctionFast + # define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords + #endif +#endif +#if CYTHON_METH_FASTCALL + #define __Pyx_METH_FASTCALL METH_FASTCALL + #define __Pyx_PyCFunction_FastCall __Pyx_PyCFunctionFast + #define __Pyx_PyCFunction_FastCallWithKeywords __Pyx_PyCFunctionFastWithKeywords +#else + #define __Pyx_METH_FASTCALL METH_VARARGS + #define __Pyx_PyCFunction_FastCall PyCFunction + #define __Pyx_PyCFunction_FastCallWithKeywords PyCFunctionWithKeywords +#endif +#if CYTHON_VECTORCALL + #define __pyx_vectorcallfunc vectorcallfunc + #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET PY_VECTORCALL_ARGUMENTS_OFFSET + #define __Pyx_PyVectorcall_NARGS(n) PyVectorcall_NARGS((size_t)(n)) +#elif CYTHON_BACKPORT_VECTORCALL + typedef PyObject *(*__pyx_vectorcallfunc)(PyObject *callable, PyObject *const *args, + size_t nargsf, PyObject *kwnames); + #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET ((size_t)1 << (8 * sizeof(size_t) - 1)) + #define __Pyx_PyVectorcall_NARGS(n) ((Py_ssize_t)(((size_t)(n)) & ~__Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET)) +#else + #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET 0 + #define __Pyx_PyVectorcall_NARGS(n) ((Py_ssize_t)(n)) +#endif +#if PY_MAJOR_VERSION >= 0x030900B1 +#define __Pyx_PyCFunction_CheckExact(func) PyCFunction_CheckExact(func) +#else +#define __Pyx_PyCFunction_CheckExact(func) PyCFunction_Check(func) +#endif +#define __Pyx_CyOrPyCFunction_Check(func) PyCFunction_Check(func) +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func) (((PyCFunctionObject*)(func))->m_ml->ml_meth) +#elif !CYTHON_COMPILING_IN_LIMITED_API +#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func) PyCFunction_GET_FUNCTION(func) +#endif +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_CyOrPyCFunction_GET_FLAGS(func) (((PyCFunctionObject*)(func))->m_ml->ml_flags) +static CYTHON_INLINE PyObject* __Pyx_CyOrPyCFunction_GET_SELF(PyObject *func) { + return (__Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_STATIC) ? NULL : ((PyCFunctionObject*)func)->m_self; +} +#endif +static CYTHON_INLINE int __Pyx__IsSameCFunction(PyObject *func, void *cfunc) { +#if CYTHON_COMPILING_IN_LIMITED_API + return PyCFunction_Check(func) && PyCFunction_GetFunction(func) == (PyCFunction) cfunc; +#else + return PyCFunction_Check(func) && PyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc; +#endif +} +#define __Pyx_IsSameCFunction(func, cfunc) __Pyx__IsSameCFunction(func, cfunc) +#if __PYX_LIMITED_VERSION_HEX < 0x030900B1 + #define __Pyx_PyType_FromModuleAndSpec(m, s, b) ((void)m, PyType_FromSpecWithBases(s, b)) + typedef PyObject *(*__Pyx_PyCMethod)(PyObject *, PyTypeObject *, PyObject *const *, size_t, PyObject *); +#else + #define __Pyx_PyType_FromModuleAndSpec(m, s, b) PyType_FromModuleAndSpec(m, s, b) + #define __Pyx_PyCMethod PyCMethod +#endif +#ifndef METH_METHOD + #define METH_METHOD 0x200 +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc) + #define PyObject_Malloc(s) PyMem_Malloc(s) + #define PyObject_Free(p) PyMem_Free(p) + #define PyObject_Realloc(p) PyMem_Realloc(p) +#endif +#if CYTHON_COMPILING_IN_LIMITED_API + #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0) + #define __Pyx_PyFrame_SetLineNumber(frame, lineno) +#else + #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0) + #define __Pyx_PyFrame_SetLineNumber(frame, lineno) (frame)->f_lineno = (lineno) +#endif +#if CYTHON_COMPILING_IN_LIMITED_API + #define __Pyx_PyThreadState_Current PyThreadState_Get() +#elif !CYTHON_FAST_THREAD_STATE + #define __Pyx_PyThreadState_Current PyThreadState_GET() +#elif PY_VERSION_HEX >= 0x030d00A1 + #define __Pyx_PyThreadState_Current PyThreadState_GetUnchecked() +#elif PY_VERSION_HEX >= 0x03060000 + #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet() +#elif PY_VERSION_HEX >= 0x03000000 + #define __Pyx_PyThreadState_Current PyThreadState_GET() +#else + #define __Pyx_PyThreadState_Current _PyThreadState_Current +#endif +#if CYTHON_COMPILING_IN_LIMITED_API +static CYTHON_INLINE void *__Pyx_PyModule_GetState(PyObject *op) +{ + void *result; + result = PyModule_GetState(op); + if (!result) + Py_FatalError("Couldn't find the module state"); + return result; +} +#endif +#define __Pyx_PyObject_GetSlot(obj, name, func_ctype) __Pyx_PyType_GetSlot(Py_TYPE(obj), name, func_ctype) +#if CYTHON_COMPILING_IN_LIMITED_API + #define __Pyx_PyType_GetSlot(type, name, func_ctype) ((func_ctype) PyType_GetSlot((type), Py_##name)) +#else + #define __Pyx_PyType_GetSlot(type, name, func_ctype) ((type)->name) +#endif +#if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT) +#include "pythread.h" +#define Py_tss_NEEDS_INIT 0 +typedef int Py_tss_t; +static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) { + *key = PyThread_create_key(); + return 0; +} +static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) { + Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t)); + *key = Py_tss_NEEDS_INIT; + return key; +} +static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) { + PyObject_Free(key); +} +static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) { + return *key != Py_tss_NEEDS_INIT; +} +static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) { + PyThread_delete_key(*key); + *key = Py_tss_NEEDS_INIT; +} +static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) { + return PyThread_set_key_value(*key, value); +} +static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) { + return PyThread_get_key_value(*key); +} +#endif +#if PY_MAJOR_VERSION < 3 + #if CYTHON_COMPILING_IN_PYPY + #if PYPY_VERSION_NUM < 0x07030600 + #if defined(__cplusplus) && __cplusplus >= 201402L + [[deprecated("`with nogil:` inside a nogil function will not release the GIL in PyPy2 < 7.3.6")]] + #elif defined(__GNUC__) || defined(__clang__) + __attribute__ ((__deprecated__("`with nogil:` inside a nogil function will not release the GIL in PyPy2 < 7.3.6"))) + #elif defined(_MSC_VER) + __declspec(deprecated("`with nogil:` inside a nogil function will not release the GIL in PyPy2 < 7.3.6")) + #endif + static CYTHON_INLINE int PyGILState_Check(void) { + return 0; + } + #else // PYPY_VERSION_NUM < 0x07030600 + #endif // PYPY_VERSION_NUM < 0x07030600 + #else + static CYTHON_INLINE int PyGILState_Check(void) { + PyThreadState * tstate = _PyThreadState_Current; + return tstate && (tstate == PyGILState_GetThisThreadState()); + } + #endif +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030d0000 || defined(_PyDict_NewPresized) +#define __Pyx_PyDict_NewPresized(n) ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n)) +#else +#define __Pyx_PyDict_NewPresized(n) PyDict_New() +#endif +#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION + #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y) +#else + #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y) +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX > 0x030600B4 && PY_VERSION_HEX < 0x030d0000 && CYTHON_USE_UNICODE_INTERNALS +#define __Pyx_PyDict_GetItemStrWithError(dict, name) _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash) +static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStr(PyObject *dict, PyObject *name) { + PyObject *res = __Pyx_PyDict_GetItemStrWithError(dict, name); + if (res == NULL) PyErr_Clear(); + return res; +} +#elif PY_MAJOR_VERSION >= 3 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07020000) +#define __Pyx_PyDict_GetItemStrWithError PyDict_GetItemWithError +#define __Pyx_PyDict_GetItemStr PyDict_GetItem +#else +static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStrWithError(PyObject *dict, PyObject *name) { +#if CYTHON_COMPILING_IN_PYPY + return PyDict_GetItem(dict, name); +#else + PyDictEntry *ep; + PyDictObject *mp = (PyDictObject*) dict; + long hash = ((PyStringObject *) name)->ob_shash; + assert(hash != -1); + ep = (mp->ma_lookup)(mp, name, hash); + if (ep == NULL) { + return NULL; + } + return ep->me_value; +#endif +} +#define __Pyx_PyDict_GetItemStr PyDict_GetItem +#endif +#if CYTHON_USE_TYPE_SLOTS + #define __Pyx_PyType_GetFlags(tp) (((PyTypeObject *)tp)->tp_flags) + #define __Pyx_PyType_HasFeature(type, feature) ((__Pyx_PyType_GetFlags(type) & (feature)) != 0) + #define __Pyx_PyObject_GetIterNextFunc(obj) (Py_TYPE(obj)->tp_iternext) +#else + #define __Pyx_PyType_GetFlags(tp) (PyType_GetFlags((PyTypeObject *)tp)) + #define __Pyx_PyType_HasFeature(type, feature) PyType_HasFeature(type, feature) + #define __Pyx_PyObject_GetIterNextFunc(obj) PyIter_Next +#endif +#if CYTHON_COMPILING_IN_LIMITED_API + #define __Pyx_SetItemOnTypeDict(tp, k, v) PyObject_GenericSetAttr((PyObject*)tp, k, v) +#else + #define __Pyx_SetItemOnTypeDict(tp, k, v) PyDict_SetItem(tp->tp_dict, k, v) +#endif +#if CYTHON_USE_TYPE_SPECS && PY_VERSION_HEX >= 0x03080000 +#define __Pyx_PyHeapTypeObject_GC_Del(obj) {\ + PyTypeObject *type = Py_TYPE((PyObject*)obj);\ + assert(__Pyx_PyType_HasFeature(type, Py_TPFLAGS_HEAPTYPE));\ + PyObject_GC_Del(obj);\ + Py_DECREF(type);\ +} +#else +#define __Pyx_PyHeapTypeObject_GC_Del(obj) PyObject_GC_Del(obj) +#endif +#if CYTHON_COMPILING_IN_LIMITED_API + #define CYTHON_PEP393_ENABLED 1 + #define __Pyx_PyUnicode_READY(op) (0) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GetLength(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_ReadChar(u, i) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((void)u, 1114111U) + #define __Pyx_PyUnicode_KIND(u) ((void)u, (0)) + #define __Pyx_PyUnicode_DATA(u) ((void*)u) + #define __Pyx_PyUnicode_READ(k, d, i) ((void)k, PyUnicode_ReadChar((PyObject*)(d), i)) + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GetLength(u)) +#elif PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND) + #define CYTHON_PEP393_ENABLED 1 + #if PY_VERSION_HEX >= 0x030C0000 + #define __Pyx_PyUnicode_READY(op) (0) + #else + #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\ + 0 : _PyUnicode_Ready((PyObject *)(op))) + #endif + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) PyUnicode_MAX_CHAR_VALUE(u) + #define __Pyx_PyUnicode_KIND(u) ((int)PyUnicode_KIND(u)) + #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u) + #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i) + #define __Pyx_PyUnicode_WRITE(k, d, i, ch) PyUnicode_WRITE(k, d, i, (Py_UCS4) ch) + #if PY_VERSION_HEX >= 0x030C0000 + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_LENGTH(u)) + #else + #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000 + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length)) + #else + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u))) + #endif + #endif +#else + #define CYTHON_PEP393_ENABLED 0 + #define PyUnicode_1BYTE_KIND 1 + #define PyUnicode_2BYTE_KIND 2 + #define PyUnicode_4BYTE_KIND 4 + #define __Pyx_PyUnicode_READY(op) (0) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i])) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((sizeof(Py_UNICODE) == 2) ? 65535U : 1114111U) + #define __Pyx_PyUnicode_KIND(u) ((int)sizeof(Py_UNICODE)) + #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u)) + #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i])) + #define __Pyx_PyUnicode_WRITE(k, d, i, ch) (((void)(k)), ((Py_UNICODE*)d)[i] = (Py_UNICODE) ch) + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_SIZE(u)) +#endif +#if CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b) +#else + #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\ + PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b)) +#endif +#if CYTHON_COMPILING_IN_PYPY + #if !defined(PyUnicode_DecodeUnicodeEscape) + #define PyUnicode_DecodeUnicodeEscape(s, size, errors) PyUnicode_Decode(s, size, "unicode_escape", errors) + #endif + #if !defined(PyUnicode_Contains) || (PY_MAJOR_VERSION == 2 && PYPY_VERSION_NUM < 0x07030500) + #undef PyUnicode_Contains + #define PyUnicode_Contains(u, s) PySequence_Contains(u, s) + #endif + #if !defined(PyByteArray_Check) + #define PyByteArray_Check(obj) PyObject_TypeCheck(obj, &PyByteArray_Type) + #endif + #if !defined(PyObject_Format) + #define PyObject_Format(obj, fmt) PyObject_CallMethod(obj, "__format__", "O", fmt) + #endif +#endif +#define __Pyx_PyString_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b)) +#define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b)) +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b) +#else + #define __Pyx_PyString_Format(a, b) PyString_Format(a, b) +#endif +#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII) + #define PyObject_ASCII(o) PyObject_Repr(o) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBaseString_Type PyUnicode_Type + #define PyStringObject PyUnicodeObject + #define PyString_Type PyUnicode_Type + #define PyString_Check PyUnicode_Check + #define PyString_CheckExact PyUnicode_CheckExact +#ifndef PyObject_Unicode + #define PyObject_Unicode PyObject_Str +#endif +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj) + #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj) +#else + #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj)) + #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj)) +#endif +#if CYTHON_COMPILING_IN_CPYTHON + #define __Pyx_PySequence_ListKeepNew(obj)\ + (likely(PyList_CheckExact(obj) && Py_REFCNT(obj) == 1) ? __Pyx_NewRef(obj) : PySequence_List(obj)) +#else + #define __Pyx_PySequence_ListKeepNew(obj) PySequence_List(obj) +#endif +#ifndef PySet_CheckExact + #define PySet_CheckExact(obj) __Pyx_IS_TYPE(obj, &PySet_Type) +#endif +#if PY_VERSION_HEX >= 0x030900A4 + #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt) + #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size) +#else + #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt) + #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size) +#endif +#if CYTHON_ASSUME_SAFE_MACROS + #define __Pyx_PySequence_ITEM(o, i) PySequence_ITEM(o, i) + #define __Pyx_PySequence_SIZE(seq) Py_SIZE(seq) + #define __Pyx_PyTuple_SET_ITEM(o, i, v) (PyTuple_SET_ITEM(o, i, v), (0)) + #define __Pyx_PyList_SET_ITEM(o, i, v) (PyList_SET_ITEM(o, i, v), (0)) + #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_GET_SIZE(o) + #define __Pyx_PyList_GET_SIZE(o) PyList_GET_SIZE(o) + #define __Pyx_PySet_GET_SIZE(o) PySet_GET_SIZE(o) + #define __Pyx_PyBytes_GET_SIZE(o) PyBytes_GET_SIZE(o) + #define __Pyx_PyByteArray_GET_SIZE(o) PyByteArray_GET_SIZE(o) +#else + #define __Pyx_PySequence_ITEM(o, i) PySequence_GetItem(o, i) + #define __Pyx_PySequence_SIZE(seq) PySequence_Size(seq) + #define __Pyx_PyTuple_SET_ITEM(o, i, v) PyTuple_SetItem(o, i, v) + #define __Pyx_PyList_SET_ITEM(o, i, v) PyList_SetItem(o, i, v) + #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_Size(o) + #define __Pyx_PyList_GET_SIZE(o) PyList_Size(o) + #define __Pyx_PySet_GET_SIZE(o) PySet_Size(o) + #define __Pyx_PyBytes_GET_SIZE(o) PyBytes_Size(o) + #define __Pyx_PyByteArray_GET_SIZE(o) PyByteArray_Size(o) +#endif +#if __PYX_LIMITED_VERSION_HEX >= 0x030d00A1 + #define __Pyx_PyImport_AddModuleRef(name) PyImport_AddModuleRef(name) +#else + static CYTHON_INLINE PyObject *__Pyx_PyImport_AddModuleRef(const char *name) { + PyObject *module = PyImport_AddModule(name); + Py_XINCREF(module); + return module; + } +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyIntObject PyLongObject + #define PyInt_Type PyLong_Type + #define PyInt_Check(op) PyLong_Check(op) + #define PyInt_CheckExact(op) PyLong_CheckExact(op) + #define __Pyx_Py3Int_Check(op) PyLong_Check(op) + #define __Pyx_Py3Int_CheckExact(op) PyLong_CheckExact(op) + #define PyInt_FromString PyLong_FromString + #define PyInt_FromUnicode PyLong_FromUnicode + #define PyInt_FromLong PyLong_FromLong + #define PyInt_FromSize_t PyLong_FromSize_t + #define PyInt_FromSsize_t PyLong_FromSsize_t + #define PyInt_AsLong PyLong_AsLong + #define PyInt_AS_LONG PyLong_AS_LONG + #define PyInt_AsSsize_t PyLong_AsSsize_t + #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask + #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask + #define PyNumber_Int PyNumber_Long +#else + #define __Pyx_Py3Int_Check(op) (PyLong_Check(op) || PyInt_Check(op)) + #define __Pyx_Py3Int_CheckExact(op) (PyLong_CheckExact(op) || PyInt_CheckExact(op)) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBoolObject PyLongObject +#endif +#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY + #ifndef PyUnicode_InternFromString + #define PyUnicode_InternFromString(s) PyUnicode_FromString(s) + #endif +#endif +#if PY_VERSION_HEX < 0x030200A4 + typedef long Py_hash_t; + #define __Pyx_PyInt_FromHash_t PyInt_FromLong + #define __Pyx_PyInt_AsHash_t __Pyx_PyIndex_AsHash_t +#else + #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t + #define __Pyx_PyInt_AsHash_t __Pyx_PyIndex_AsSsize_t +#endif +#if CYTHON_USE_ASYNC_SLOTS + #if PY_VERSION_HEX >= 0x030500B1 + #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods + #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async) + #else + #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved)) + #endif +#else + #define __Pyx_PyType_AsAsync(obj) NULL +#endif +#ifndef __Pyx_PyAsyncMethodsStruct + typedef struct { + unaryfunc am_await; + unaryfunc am_aiter; + unaryfunc am_anext; + } __Pyx_PyAsyncMethodsStruct; +#endif + +#if defined(_WIN32) || defined(WIN32) || defined(MS_WINDOWS) + #if !defined(_USE_MATH_DEFINES) + #define _USE_MATH_DEFINES + #endif +#endif +#include +#ifdef NAN +#define __PYX_NAN() ((float) NAN) +#else +static CYTHON_INLINE float __PYX_NAN() { + float value; + memset(&value, 0xFF, sizeof(value)); + return value; +} +#endif +#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL) +#define __Pyx_truncl trunc +#else +#define __Pyx_truncl truncl +#endif + +#define __PYX_MARK_ERR_POS(f_index, lineno) \ + { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__; (void)__pyx_clineno; } +#define __PYX_ERR(f_index, lineno, Ln_error) \ + { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; } + +#ifdef CYTHON_EXTERN_C + #undef __PYX_EXTERN_C + #define __PYX_EXTERN_C CYTHON_EXTERN_C +#elif defined(__PYX_EXTERN_C) + #ifdef _MSC_VER + #pragma message ("Please do not define the '__PYX_EXTERN_C' macro externally. Use 'CYTHON_EXTERN_C' instead.") + #else + #warning Please do not define the '__PYX_EXTERN_C' macro externally. Use 'CYTHON_EXTERN_C' instead. + #endif +#else + #ifdef __cplusplus + #define __PYX_EXTERN_C extern "C" + #else + #define __PYX_EXTERN_C extern + #endif +#endif + +#define __PYX_HAVE__pygom__model___tau_leap +#define __PYX_HAVE_API__pygom__model___tau_leap +/* Early includes */ +#include +#include + + /* Using NumPy API declarations from "numpy/__init__.cython-30.pxd" */ + +#include "numpy/arrayobject.h" +#include "numpy/ndarrayobject.h" +#include "numpy/ndarraytypes.h" +#include "numpy/arrayscalars.h" +#include "numpy/ufuncobject.h" +#include +#include "pythread.h" +#include +#ifdef _OPENMP +#include +#endif /* _OPENMP */ + +#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS) +#define CYTHON_WITHOUT_ASSERTIONS +#endif + +typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding; + const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry; + +#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0 +#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0 +#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8) +#define __PYX_DEFAULT_STRING_ENCODING "" +#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString +#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#define __Pyx_uchar_cast(c) ((unsigned char)c) +#define __Pyx_long_cast(x) ((long)x) +#define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\ + (sizeof(type) < sizeof(Py_ssize_t)) ||\ + (sizeof(type) > sizeof(Py_ssize_t) &&\ + likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX) &&\ + (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\ + v == (type)PY_SSIZE_T_MIN))) ||\ + (sizeof(type) == sizeof(Py_ssize_t) &&\ + (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX))) ) +static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) { + return (size_t) i < (size_t) limit; +} +#if defined (__cplusplus) && __cplusplus >= 201103L + #include + #define __Pyx_sst_abs(value) std::abs(value) +#elif SIZEOF_INT >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) abs(value) +#elif SIZEOF_LONG >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) labs(value) +#elif defined (_MSC_VER) + #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value)) +#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define __Pyx_sst_abs(value) llabs(value) +#elif defined (__GNUC__) + #define __Pyx_sst_abs(value) __builtin_llabs(value) +#else + #define __Pyx_sst_abs(value) ((value<0) ? -value : value) +#endif +static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s); +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*); +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length); +static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char*); +#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l) +#define __Pyx_PyBytes_FromString PyBytes_FromString +#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*); +#if PY_MAJOR_VERSION < 3 + #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#else + #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize +#endif +#define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyObject_AsWritableString(s) ((char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableSString(s) ((signed char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s) +#define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s) +#define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s) +#define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s) +#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s) +#define __Pyx_PyUnicode_FromOrdinal(o) PyUnicode_FromOrdinal((int)o) +#define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode +#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj) +#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None) +static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b); +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*); +static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*); +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x); +#define __Pyx_PySequence_Tuple(obj)\ + (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj)) +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*); +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t); +static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject*); +#if CYTHON_ASSUME_SAFE_MACROS +#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x)) +#else +#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x) +#endif +#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x)) +#if PY_MAJOR_VERSION >= 3 +#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x)) +#else +#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x)) +#endif +#if CYTHON_USE_PYLONG_INTERNALS + #if PY_VERSION_HEX >= 0x030C00A7 + #ifndef _PyLong_SIGN_MASK + #define _PyLong_SIGN_MASK 3 + #endif + #ifndef _PyLong_NON_SIZE_BITS + #define _PyLong_NON_SIZE_BITS 3 + #endif + #define __Pyx_PyLong_Sign(x) (((PyLongObject*)x)->long_value.lv_tag & _PyLong_SIGN_MASK) + #define __Pyx_PyLong_IsNeg(x) ((__Pyx_PyLong_Sign(x) & 2) != 0) + #define __Pyx_PyLong_IsNonNeg(x) (!__Pyx_PyLong_IsNeg(x)) + #define __Pyx_PyLong_IsZero(x) (__Pyx_PyLong_Sign(x) & 1) + #define __Pyx_PyLong_IsPos(x) (__Pyx_PyLong_Sign(x) == 0) + #define __Pyx_PyLong_CompactValueUnsigned(x) (__Pyx_PyLong_Digits(x)[0]) + #define __Pyx_PyLong_DigitCount(x) ((Py_ssize_t) (((PyLongObject*)x)->long_value.lv_tag >> _PyLong_NON_SIZE_BITS)) + #define __Pyx_PyLong_SignedDigitCount(x)\ + ((1 - (Py_ssize_t) __Pyx_PyLong_Sign(x)) * __Pyx_PyLong_DigitCount(x)) + #if defined(PyUnstable_Long_IsCompact) && defined(PyUnstable_Long_CompactValue) + #define __Pyx_PyLong_IsCompact(x) PyUnstable_Long_IsCompact((PyLongObject*) x) + #define __Pyx_PyLong_CompactValue(x) PyUnstable_Long_CompactValue((PyLongObject*) x) + #else + #define __Pyx_PyLong_IsCompact(x) (((PyLongObject*)x)->long_value.lv_tag < (2 << _PyLong_NON_SIZE_BITS)) + #define __Pyx_PyLong_CompactValue(x) ((1 - (Py_ssize_t) __Pyx_PyLong_Sign(x)) * (Py_ssize_t) __Pyx_PyLong_Digits(x)[0]) + #endif + typedef Py_ssize_t __Pyx_compact_pylong; + typedef size_t __Pyx_compact_upylong; + #else + #define __Pyx_PyLong_IsNeg(x) (Py_SIZE(x) < 0) + #define __Pyx_PyLong_IsNonNeg(x) (Py_SIZE(x) >= 0) + #define __Pyx_PyLong_IsZero(x) (Py_SIZE(x) == 0) + #define __Pyx_PyLong_IsPos(x) (Py_SIZE(x) > 0) + #define __Pyx_PyLong_CompactValueUnsigned(x) ((Py_SIZE(x) == 0) ? 0 : __Pyx_PyLong_Digits(x)[0]) + #define __Pyx_PyLong_DigitCount(x) __Pyx_sst_abs(Py_SIZE(x)) + #define __Pyx_PyLong_SignedDigitCount(x) Py_SIZE(x) + #define __Pyx_PyLong_IsCompact(x) (Py_SIZE(x) == 0 || Py_SIZE(x) == 1 || Py_SIZE(x) == -1) + #define __Pyx_PyLong_CompactValue(x)\ + ((Py_SIZE(x) == 0) ? (sdigit) 0 : ((Py_SIZE(x) < 0) ? -(sdigit)__Pyx_PyLong_Digits(x)[0] : (sdigit)__Pyx_PyLong_Digits(x)[0])) + typedef sdigit __Pyx_compact_pylong; + typedef digit __Pyx_compact_upylong; + #endif + #if PY_VERSION_HEX >= 0x030C00A5 + #define __Pyx_PyLong_Digits(x) (((PyLongObject*)x)->long_value.ob_digit) + #else + #define __Pyx_PyLong_Digits(x) (((PyLongObject*)x)->ob_digit) + #endif +#endif +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII +#include +static int __Pyx_sys_getdefaultencoding_not_ascii; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + PyObject* ascii_chars_u = NULL; + PyObject* ascii_chars_b = NULL; + const char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + if (strcmp(default_encoding_c, "ascii") == 0) { + __Pyx_sys_getdefaultencoding_not_ascii = 0; + } else { + char ascii_chars[128]; + int c; + for (c = 0; c < 128; c++) { + ascii_chars[c] = (char) c; + } + __Pyx_sys_getdefaultencoding_not_ascii = 1; + ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL); + if (!ascii_chars_u) goto bad; + ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL); + if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) { + PyErr_Format( + PyExc_ValueError, + "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.", + default_encoding_c); + goto bad; + } + Py_DECREF(ascii_chars_u); + Py_DECREF(ascii_chars_b); + } + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + Py_XDECREF(ascii_chars_u); + Py_XDECREF(ascii_chars_b); + return -1; +} +#endif +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3 +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL) +#else +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL) +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +#include +static char* __PYX_DEFAULT_STRING_ENCODING; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1); + if (!__PYX_DEFAULT_STRING_ENCODING) goto bad; + strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c); + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + return -1; +} +#endif +#endif + + +/* Test for GCC > 2.95 */ +#if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95))) + #define likely(x) __builtin_expect(!!(x), 1) + #define unlikely(x) __builtin_expect(!!(x), 0) +#else /* !__GNUC__ or GCC < 2.95 */ + #define likely(x) (x) + #define unlikely(x) (x) +#endif /* __GNUC__ */ +static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; } + +#if !CYTHON_USE_MODULE_STATE +static PyObject *__pyx_m = NULL; +#endif +static int __pyx_lineno; +static int __pyx_clineno = 0; +static const char * __pyx_cfilenm = __FILE__; +static const char *__pyx_filename; + +/* Header.proto */ +#if !defined(CYTHON_CCOMPLEX) + #if defined(__cplusplus) + #define CYTHON_CCOMPLEX 1 + #elif (defined(_Complex_I) && !defined(_MSC_VER)) || ((defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L) && !defined(__STDC_NO_COMPLEX__) && !defined(_MSC_VER)) + #define CYTHON_CCOMPLEX 1 + #else + #define CYTHON_CCOMPLEX 0 + #endif +#endif +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #include + #else + #include + #endif +#endif +#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__) + #undef _Complex_I + #define _Complex_I 1.0fj +#endif + +/* #### Code section: filename_table ### */ + +static const char *__pyx_f[] = { + "src\\\\pygom\\\\model\\\\_tau_leap.pyx", + "", + "__init__.cython-30.pxd", + "type.pxd", +}; +/* #### Code section: utility_code_proto_before_types ### */ +/* ForceInitThreads.proto */ +#ifndef __PYX_FORCE_INIT_THREADS + #define __PYX_FORCE_INIT_THREADS 0 +#endif + +/* NoFastGil.proto */ +#define __Pyx_PyGILState_Ensure PyGILState_Ensure +#define __Pyx_PyGILState_Release PyGILState_Release +#define __Pyx_FastGIL_Remember() +#define __Pyx_FastGIL_Forget() +#define __Pyx_FastGilFuncInit() + +/* BufferFormatStructs.proto */ +struct __Pyx_StructField_; +#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0) +typedef struct { + const char* name; + struct __Pyx_StructField_* fields; + size_t size; + size_t arraysize[8]; + int ndim; + char typegroup; + char is_unsigned; + int flags; +} __Pyx_TypeInfo; +typedef struct __Pyx_StructField_ { + __Pyx_TypeInfo* type; + const char* name; + size_t offset; +} __Pyx_StructField; +typedef struct { + __Pyx_StructField* field; + size_t parent_offset; +} __Pyx_BufFmt_StackElem; +typedef struct { + __Pyx_StructField root; + __Pyx_BufFmt_StackElem* head; + size_t fmt_offset; + size_t new_count, enc_count; + size_t struct_alignment; + int is_complex; + char enc_type; + char new_packmode; + char enc_packmode; + char is_valid_array; +} __Pyx_BufFmt_Context; + +/* Atomics.proto */ +#include +#ifndef CYTHON_ATOMICS + #define CYTHON_ATOMICS 1 +#endif +#define __PYX_CYTHON_ATOMICS_ENABLED() CYTHON_ATOMICS +#define __pyx_atomic_int_type int +#define __pyx_nonatomic_int_type int +#if CYTHON_ATOMICS && (defined(__STDC_VERSION__) &&\ + (__STDC_VERSION__ >= 201112L) &&\ + !defined(__STDC_NO_ATOMICS__)) + #include +#elif CYTHON_ATOMICS && (defined(__cplusplus) && (\ + (__cplusplus >= 201103L) ||\ + (defined(_MSC_VER) && _MSC_VER >= 1700))) + #include +#endif +#if CYTHON_ATOMICS && (defined(__STDC_VERSION__) &&\ + (__STDC_VERSION__ >= 201112L) &&\ + !defined(__STDC_NO_ATOMICS__) &&\ + ATOMIC_INT_LOCK_FREE == 2) + #undef __pyx_atomic_int_type + #define __pyx_atomic_int_type atomic_int + #define __pyx_atomic_incr_aligned(value) atomic_fetch_add_explicit(value, 1, memory_order_relaxed) + #define __pyx_atomic_decr_aligned(value) atomic_fetch_sub_explicit(value, 1, memory_order_acq_rel) + #if defined(__PYX_DEBUG_ATOMICS) && defined(_MSC_VER) + #pragma message ("Using standard C atomics") + #elif defined(__PYX_DEBUG_ATOMICS) + #warning "Using standard C atomics" + #endif +#elif CYTHON_ATOMICS && (defined(__cplusplus) && (\ + (__cplusplus >= 201103L) ||\ +\ + (defined(_MSC_VER) && _MSC_VER >= 1700)) &&\ + ATOMIC_INT_LOCK_FREE == 2) + #undef __pyx_atomic_int_type + #define __pyx_atomic_int_type std::atomic_int + #define __pyx_atomic_incr_aligned(value) std::atomic_fetch_add_explicit(value, 1, std::memory_order_relaxed) + #define __pyx_atomic_decr_aligned(value) std::atomic_fetch_sub_explicit(value, 1, std::memory_order_acq_rel) + #if defined(__PYX_DEBUG_ATOMICS) && defined(_MSC_VER) + #pragma message ("Using standard C++ atomics") + #elif defined(__PYX_DEBUG_ATOMICS) + #warning "Using standard C++ atomics" + #endif +#elif CYTHON_ATOMICS && (__GNUC__ >= 5 || (__GNUC__ == 4 &&\ + (__GNUC_MINOR__ > 1 ||\ + (__GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL__ >= 2)))) + #define __pyx_atomic_incr_aligned(value) __sync_fetch_and_add(value, 1) + #define __pyx_atomic_decr_aligned(value) __sync_fetch_and_sub(value, 1) + #ifdef __PYX_DEBUG_ATOMICS + #warning "Using GNU atomics" + #endif +#elif CYTHON_ATOMICS && defined(_MSC_VER) + #include + #undef __pyx_atomic_int_type + #define __pyx_atomic_int_type long + #undef __pyx_nonatomic_int_type + #define __pyx_nonatomic_int_type long + #pragma intrinsic (_InterlockedExchangeAdd) + #define __pyx_atomic_incr_aligned(value) _InterlockedExchangeAdd(value, 1) + #define __pyx_atomic_decr_aligned(value) _InterlockedExchangeAdd(value, -1) + #ifdef __PYX_DEBUG_ATOMICS + #pragma message ("Using MSVC atomics") + #endif +#else + #undef CYTHON_ATOMICS + #define CYTHON_ATOMICS 0 + #ifdef __PYX_DEBUG_ATOMICS + #warning "Not using atomics" + #endif +#endif +#if CYTHON_ATOMICS + #define __pyx_add_acquisition_count(memview)\ + __pyx_atomic_incr_aligned(__pyx_get_slice_count_pointer(memview)) + #define __pyx_sub_acquisition_count(memview)\ + __pyx_atomic_decr_aligned(__pyx_get_slice_count_pointer(memview)) +#else + #define __pyx_add_acquisition_count(memview)\ + __pyx_add_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock) + #define __pyx_sub_acquisition_count(memview)\ + __pyx_sub_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock) +#endif + +/* MemviewSliceStruct.proto */ +struct __pyx_memoryview_obj; +typedef struct { + struct __pyx_memoryview_obj *memview; + char *data; + Py_ssize_t shape[8]; + Py_ssize_t strides[8]; + Py_ssize_t suboffsets[8]; +} __Pyx_memviewslice; +#define __Pyx_MemoryView_Len(m) (m.shape[0]) + +/* #### Code section: numeric_typedefs ### */ + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":769 + * # in Cython to enable them only on the right systems. + * + * ctypedef npy_int8 int8_t # <<<<<<<<<<<<<< + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + */ +typedef npy_int8 __pyx_t_5numpy_int8_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":770 + * + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t # <<<<<<<<<<<<<< + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t + */ +typedef npy_int16 __pyx_t_5numpy_int16_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":771 + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t # <<<<<<<<<<<<<< + * ctypedef npy_int64 int64_t + * #ctypedef npy_int96 int96_t + */ +typedef npy_int32 __pyx_t_5numpy_int32_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":772 + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t # <<<<<<<<<<<<<< + * #ctypedef npy_int96 int96_t + * #ctypedef npy_int128 int128_t + */ +typedef npy_int64 __pyx_t_5numpy_int64_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":776 + * #ctypedef npy_int128 int128_t + * + * ctypedef npy_uint8 uint8_t # <<<<<<<<<<<<<< + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + */ +typedef npy_uint8 __pyx_t_5numpy_uint8_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":777 + * + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t # <<<<<<<<<<<<<< + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t + */ +typedef npy_uint16 __pyx_t_5numpy_uint16_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":778 + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t # <<<<<<<<<<<<<< + * ctypedef npy_uint64 uint64_t + * #ctypedef npy_uint96 uint96_t + */ +typedef npy_uint32 __pyx_t_5numpy_uint32_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":779 + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t # <<<<<<<<<<<<<< + * #ctypedef npy_uint96 uint96_t + * #ctypedef npy_uint128 uint128_t + */ +typedef npy_uint64 __pyx_t_5numpy_uint64_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":783 + * #ctypedef npy_uint128 uint128_t + * + * ctypedef npy_float32 float32_t # <<<<<<<<<<<<<< + * ctypedef npy_float64 float64_t + * #ctypedef npy_float80 float80_t + */ +typedef npy_float32 __pyx_t_5numpy_float32_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":784 + * + * ctypedef npy_float32 float32_t + * ctypedef npy_float64 float64_t # <<<<<<<<<<<<<< + * #ctypedef npy_float80 float80_t + * #ctypedef npy_float128 float128_t + */ +typedef npy_float64 __pyx_t_5numpy_float64_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":791 + * ctypedef double complex complex128_t + * + * ctypedef npy_longlong longlong_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulonglong_t + * + */ +typedef npy_longlong __pyx_t_5numpy_longlong_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":792 + * + * ctypedef npy_longlong longlong_t + * ctypedef npy_ulonglong ulonglong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_intp intp_t + */ +typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":794 + * ctypedef npy_ulonglong ulonglong_t + * + * ctypedef npy_intp intp_t # <<<<<<<<<<<<<< + * ctypedef npy_uintp uintp_t + * + */ +typedef npy_intp __pyx_t_5numpy_intp_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":795 + * + * ctypedef npy_intp intp_t + * ctypedef npy_uintp uintp_t # <<<<<<<<<<<<<< + * + * ctypedef npy_double float_t + */ +typedef npy_uintp __pyx_t_5numpy_uintp_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":797 + * ctypedef npy_uintp uintp_t + * + * ctypedef npy_double float_t # <<<<<<<<<<<<<< + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t + */ +typedef npy_double __pyx_t_5numpy_float_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":798 + * + * ctypedef npy_double float_t + * ctypedef npy_double double_t # <<<<<<<<<<<<<< + * ctypedef npy_longdouble longdouble_t + * + */ +typedef npy_double __pyx_t_5numpy_double_t; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":799 + * ctypedef npy_double float_t + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t # <<<<<<<<<<<<<< + * + * ctypedef float complex cfloat_t + */ +typedef npy_longdouble __pyx_t_5numpy_longdouble_t; +/* #### Code section: complex_type_declarations ### */ +/* Declarations.proto */ +#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #ifdef __cplusplus + typedef ::std::complex< float > __pyx_t_float_complex; + #else + typedef float _Complex __pyx_t_float_complex; + #endif +#else + typedef struct { float real, imag; } __pyx_t_float_complex; +#endif +static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float); + +/* Declarations.proto */ +#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #ifdef __cplusplus + typedef ::std::complex< double > __pyx_t_double_complex; + #else + typedef double _Complex __pyx_t_double_complex; + #endif +#else + typedef struct { double real, imag; } __pyx_t_double_complex; +#endif +static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double); + +/* Declarations.proto */ +#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #ifdef __cplusplus + typedef ::std::complex< long double > __pyx_t_long_double_complex; + #else + typedef long double _Complex __pyx_t_long_double_complex; + #endif +#else + typedef struct { long double real, imag; } __pyx_t_long_double_complex; +#endif +static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double, long double); + +/* #### Code section: type_declarations ### */ + +/*--- Type declarations ---*/ +struct __pyx_array_obj; +struct __pyx_MemviewEnum_obj; +struct __pyx_memoryview_obj; +struct __pyx_memoryviewslice_obj; + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":1095 + * + * # Iterator API added in v1.6 + * ctypedef int (*NpyIter_IterNextFunc)(NpyIter* it) noexcept nogil # <<<<<<<<<<<<<< + * ctypedef void (*NpyIter_GetMultiIndexFunc)(NpyIter* it, npy_intp* outcoords) noexcept nogil + * + */ +typedef int (*__pyx_t_5numpy_NpyIter_IterNextFunc)(NpyIter *); + +/* "../../AppData/Local/Temp/pip-build-env-0gbdjllr/overlay/Lib/site-packages/numpy/__init__.cython-30.pxd":1096 + * # Iterator API added in v1.6 + * ctypedef int (*NpyIter_IterNextFunc)(NpyIter* it) noexcept nogil + * ctypedef void (*NpyIter_GetMultiIndexFunc)(NpyIter* it, npy_intp* outcoords) noexcept nogil # <<<<<<<<<<<<<< + * + * cdef extern from "numpy/arrayobject.h": + */ +typedef void (*__pyx_t_5numpy_NpyIter_GetMultiIndexFunc)(NpyIter *, npy_intp *); +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_jn; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_jn; +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_yn; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_yn; +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_in; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_in; +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_kn; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_kn; + +/* "scipy/special/cython_special.pxd":6 + * double + * + * cpdef number_t spherical_jn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil # <<<<<<<<<<<<<< + * cpdef number_t spherical_yn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_in(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + */ +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_jn { + int __pyx_n; + int derivative; +}; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_jn { + int __pyx_n; + int derivative; +}; + +/* "scipy/special/cython_special.pxd":7 + * + * cpdef number_t spherical_jn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_yn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil # <<<<<<<<<<<<<< + * cpdef number_t spherical_in(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_kn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + */ +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_yn { + int __pyx_n; + int derivative; +}; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_yn { + int __pyx_n; + int derivative; +}; + +/* "scipy/special/cython_special.pxd":8 + * cpdef number_t spherical_jn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_yn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_in(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil # <<<<<<<<<<<<<< + * cpdef number_t spherical_kn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * + */ +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_in { + int __pyx_n; + int derivative; +}; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_in { + int __pyx_n; + int derivative; +}; + +/* "scipy/special/cython_special.pxd":9 + * cpdef number_t spherical_yn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_in(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil + * cpdef number_t spherical_kn(Py_ssize_t n, number_t z, bint derivative=*) noexcept nogil # <<<<<<<<<<<<<< + * + * ctypedef fused Dd_number_t: + */ +struct __pyx_fuse_0__pyx_opt_args_5scipy_7special_14cython_special_spherical_kn { + int __pyx_n; + int derivative; +}; +struct __pyx_fuse_1__pyx_opt_args_5scipy_7special_14cython_special_spherical_kn { + int __pyx_n; + int derivative; +}; + +/* "View.MemoryView":114 + * @cython.collection_type("sequence") + * @cname("__pyx_array") + * cdef class array: # <<<<<<<<<<<<<< + * + * cdef: + */ +struct __pyx_array_obj { + PyObject_HEAD + struct __pyx_vtabstruct_array *__pyx_vtab; + char *data; + Py_ssize_t len; + char *format; + int ndim; + Py_ssize_t *_shape; + Py_ssize_t *_strides; + Py_ssize_t itemsize; + PyObject *mode; + PyObject *_format; + void (*callback_free_data)(void *); + int free_data; + int dtype_is_object; +}; + + +/* "View.MemoryView":302 + * + * @cname('__pyx_MemviewEnum') + * cdef class Enum(object): # <<<<<<<<<<<<<< + * cdef object name + * def __init__(self, name): + */ +struct __pyx_MemviewEnum_obj { + PyObject_HEAD + PyObject *name; +}; + + +/* "View.MemoryView":337 + * + * @cname('__pyx_memoryview') + * cdef class memoryview: # <<<<<<<<<<<<<< + * + * cdef object obj + */ +struct __pyx_memoryview_obj { + PyObject_HEAD + struct __pyx_vtabstruct_memoryview *__pyx_vtab; + PyObject *obj; + PyObject *_size; + PyObject *_array_interface; + PyThread_type_lock lock; + __pyx_atomic_int_type acquisition_count; + Py_buffer view; + int flags; + int dtype_is_object; + __Pyx_TypeInfo *typeinfo; +}; + + +/* "View.MemoryView":952 + * @cython.collection_type("sequence") + * @cname('__pyx_memoryviewslice') + * cdef class _memoryviewslice(memoryview): # <<<<<<<<<<<<<< + * "Internal class for passing memoryview slices to Python" + * + */ +struct __pyx_memoryviewslice_obj { + struct __pyx_memoryview_obj __pyx_base; + __Pyx_memviewslice from_slice; + PyObject *from_object; + PyObject *(*to_object_func)(char *); + int (*to_dtype_func)(char *, PyObject *); +}; + + + +/* "View.MemoryView":114 + * @cython.collection_type("sequence") + * @cname("__pyx_array") + * cdef class array: # <<<<<<<<<<<<<< + * + * cdef: + */ + +struct __pyx_vtabstruct_array { + PyObject *(*get_memview)(struct __pyx_array_obj *); +}; +static struct __pyx_vtabstruct_array *__pyx_vtabptr_array; + + +/* "View.MemoryView":337 + * + * @cname('__pyx_memoryview') + * cdef class memoryview: # <<<<<<<<<<<<<< + * + * cdef object obj + */ + +struct __pyx_vtabstruct_memoryview { + char *(*get_item_pointer)(struct __pyx_memoryview_obj *, PyObject *); + PyObject *(*is_slice)(struct __pyx_memoryview_obj *, PyObject *); + PyObject *(*setitem_slice_assignment)(struct __pyx_memoryview_obj *, PyObject *, PyObject *); + PyObject *(*setitem_slice_assign_scalar)(struct __pyx_memoryview_obj *, struct __pyx_memoryview_obj *, PyObject *); + PyObject *(*setitem_indexed)(struct __pyx_memoryview_obj *, PyObject *, PyObject *); + PyObject *(*convert_item_to_object)(struct __pyx_memoryview_obj *, char *); + PyObject *(*assign_item_from_object)(struct __pyx_memoryview_obj *, char *, PyObject *); + PyObject *(*_get_base)(struct __pyx_memoryview_obj *); +}; +static struct __pyx_vtabstruct_memoryview *__pyx_vtabptr_memoryview; + + +/* "View.MemoryView":952 + * @cython.collection_type("sequence") + * @cname('__pyx_memoryviewslice') + * cdef class _memoryviewslice(memoryview): # <<<<<<<<<<<<<< + * "Internal class for passing memoryview slices to Python" + * + */ + +struct __pyx_vtabstruct__memoryviewslice { + struct __pyx_vtabstruct_memoryview __pyx_base; +}; +static struct __pyx_vtabstruct__memoryviewslice *__pyx_vtabptr__memoryviewslice; +/* #### Code section: utility_code_proto ### */ + +/* --- Runtime support code (head) --- */ +/* Refnanny.proto */ +#ifndef CYTHON_REFNANNY + #define CYTHON_REFNANNY 0 +#endif +#if CYTHON_REFNANNY + typedef struct { + void (*INCREF)(void*, PyObject*, Py_ssize_t); + void (*DECREF)(void*, PyObject*, Py_ssize_t); + void (*GOTREF)(void*, PyObject*, Py_ssize_t); + void (*GIVEREF)(void*, PyObject*, Py_ssize_t); + void* (*SetupContext)(const char*, Py_ssize_t, const char*); + void (*FinishContext)(void**); + } __Pyx_RefNannyAPIStruct; + static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL; + static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname); + #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL; +#ifdef WITH_THREAD + #define __Pyx_RefNannySetupContext(name, acquire_gil)\ + if (acquire_gil) {\ + PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\ + __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), (__LINE__), (__FILE__));\ + PyGILState_Release(__pyx_gilstate_save);\ + } else {\ + __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), (__LINE__), (__FILE__));\ + } + #define __Pyx_RefNannyFinishContextNogil() {\ + PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\ + __Pyx_RefNannyFinishContext();\ + PyGILState_Release(__pyx_gilstate_save);\ + } +#else + #define __Pyx_RefNannySetupContext(name, acquire_gil)\ + __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), (__LINE__), (__FILE__)) + #define __Pyx_RefNannyFinishContextNogil() __Pyx_RefNannyFinishContext() +#endif + #define __Pyx_RefNannyFinishContextNogil() {\ + PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\ + __Pyx_RefNannyFinishContext();\ + PyGILState_Release(__pyx_gilstate_save);\ + } + #define __Pyx_RefNannyFinishContext()\ + __Pyx_RefNanny->FinishContext(&__pyx_refnanny) + #define __Pyx_INCREF(r) __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), (__LINE__)) + #define __Pyx_DECREF(r) __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), (__LINE__)) + #define __Pyx_GOTREF(r) __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), (__LINE__)) + #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), (__LINE__)) + #define __Pyx_XINCREF(r) do { if((r) == NULL); else {__Pyx_INCREF(r); }} while(0) + #define __Pyx_XDECREF(r) do { if((r) == NULL); else {__Pyx_DECREF(r); }} while(0) + #define __Pyx_XGOTREF(r) do { if((r) == NULL); else {__Pyx_GOTREF(r); }} while(0) + #define __Pyx_XGIVEREF(r) do { if((r) == NULL); else {__Pyx_GIVEREF(r);}} while(0) +#else + #define __Pyx_RefNannyDeclarations + #define __Pyx_RefNannySetupContext(name, acquire_gil) + #define __Pyx_RefNannyFinishContextNogil() + #define __Pyx_RefNannyFinishContext() + #define __Pyx_INCREF(r) Py_INCREF(r) + #define __Pyx_DECREF(r) Py_DECREF(r) + #define __Pyx_GOTREF(r) + #define __Pyx_GIVEREF(r) + #define __Pyx_XINCREF(r) Py_XINCREF(r) + #define __Pyx_XDECREF(r) Py_XDECREF(r) + #define __Pyx_XGOTREF(r) + #define __Pyx_XGIVEREF(r) +#endif +#define __Pyx_Py_XDECREF_SET(r, v) do {\ + PyObject *tmp = (PyObject *) r;\ + r = v; Py_XDECREF(tmp);\ + } while (0) +#define __Pyx_XDECREF_SET(r, v) do {\ + PyObject *tmp = (PyObject *) r;\ + r = v; __Pyx_XDECREF(tmp);\ + } while (0) +#define __Pyx_DECREF_SET(r, v) do {\ + PyObject *tmp = (PyObject *) r;\ + r = v; __Pyx_DECREF(tmp);\ + } while (0) +#define __Pyx_CLEAR(r) do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0) +#define __Pyx_XCLEAR(r) do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0) + +/* PyErrExceptionMatches.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err) +static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err); +#else +#define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err) +#endif + +/* PyThreadStateGet.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyThreadState_declare PyThreadState *__pyx_tstate; +#define __Pyx_PyThreadState_assign __pyx_tstate = __Pyx_PyThreadState_Current; +#if PY_VERSION_HEX >= 0x030C00A6 +#define __Pyx_PyErr_Occurred() (__pyx_tstate->current_exception != NULL) +#define __Pyx_PyErr_CurrentExceptionType() (__pyx_tstate->current_exception ? (PyObject*) Py_TYPE(__pyx_tstate->current_exception) : (PyObject*) NULL) +#else +#define __Pyx_PyErr_Occurred() (__pyx_tstate->curexc_type != NULL) +#define __Pyx_PyErr_CurrentExceptionType() (__pyx_tstate->curexc_type) +#endif +#else +#define __Pyx_PyThreadState_declare +#define __Pyx_PyThreadState_assign +#define __Pyx_PyErr_Occurred() (PyErr_Occurred() != NULL) +#define __Pyx_PyErr_CurrentExceptionType() PyErr_Occurred() +#endif + +/* PyErrFetchRestore.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL) +#define __Pyx_ErrRestoreWithState(type, value, tb) __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A6 +#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL)) +#else +#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc) +#endif +#else +#define __Pyx_PyErr_Clear() PyErr_Clear() +#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc) +#define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestoreInState(tstate, type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchInState(tstate, type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb) +#endif + +/* PyObjectGetAttrStr.proto */ +#if CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name); +#else +#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n) +#endif + +/* PyObjectGetAttrStrNoError.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name); + +/* GetBuiltinName.proto */ +static PyObject *__Pyx_GetBuiltinName(PyObject *name); + +/* TupleAndListFromArray.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n); +static CYTHON_INLINE PyObject* __Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n); +#endif + +/* IncludeStringH.proto */ +#include + +/* BytesEquals.proto */ +static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals); + +/* UnicodeEquals.proto */ +static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals); + +/* fastcall.proto */ +#if CYTHON_AVOID_BORROWED_REFS + #define __Pyx_Arg_VARARGS(args, i) PySequence_GetItem(args, i) +#elif CYTHON_ASSUME_SAFE_MACROS + #define __Pyx_Arg_VARARGS(args, i) PyTuple_GET_ITEM(args, i) +#else + #define __Pyx_Arg_VARARGS(args, i) PyTuple_GetItem(args, i) +#endif +#if CYTHON_AVOID_BORROWED_REFS + #define __Pyx_Arg_NewRef_VARARGS(arg) __Pyx_NewRef(arg) + #define __Pyx_Arg_XDECREF_VARARGS(arg) Py_XDECREF(arg) +#else + #define __Pyx_Arg_NewRef_VARARGS(arg) arg + #define __Pyx_Arg_XDECREF_VARARGS(arg) +#endif +#define __Pyx_NumKwargs_VARARGS(kwds) PyDict_Size(kwds) +#define __Pyx_KwValues_VARARGS(args, nargs) NULL +#define __Pyx_GetKwValue_VARARGS(kw, kwvalues, s) __Pyx_PyDict_GetItemStrWithError(kw, s) +#define __Pyx_KwargsAsDict_VARARGS(kw, kwvalues) PyDict_Copy(kw) +#if CYTHON_METH_FASTCALL + #define __Pyx_Arg_FASTCALL(args, i) args[i] + #define __Pyx_NumKwargs_FASTCALL(kwds) PyTuple_GET_SIZE(kwds) + #define __Pyx_KwValues_FASTCALL(args, nargs) ((args) + (nargs)) + static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s); +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000 + CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues); + #else + #define __Pyx_KwargsAsDict_FASTCALL(kw, kwvalues) _PyStack_AsDict(kwvalues, kw) + #endif + #define __Pyx_Arg_NewRef_FASTCALL(arg) arg /* no-op, __Pyx_Arg_FASTCALL is direct and this needs + to have the same reference counting */ + #define __Pyx_Arg_XDECREF_FASTCALL(arg) +#else + #define __Pyx_Arg_FASTCALL __Pyx_Arg_VARARGS + #define __Pyx_NumKwargs_FASTCALL __Pyx_NumKwargs_VARARGS + #define __Pyx_KwValues_FASTCALL __Pyx_KwValues_VARARGS + #define __Pyx_GetKwValue_FASTCALL __Pyx_GetKwValue_VARARGS + #define __Pyx_KwargsAsDict_FASTCALL __Pyx_KwargsAsDict_VARARGS + #define __Pyx_Arg_NewRef_FASTCALL(arg) __Pyx_Arg_NewRef_VARARGS(arg) + #define __Pyx_Arg_XDECREF_FASTCALL(arg) __Pyx_Arg_XDECREF_VARARGS(arg) +#endif +#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS +#define __Pyx_ArgsSlice_VARARGS(args, start, stop) __Pyx_PyTuple_FromArray(&__Pyx_Arg_VARARGS(args, start), stop - start) +#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) __Pyx_PyTuple_FromArray(&__Pyx_Arg_FASTCALL(args, start), stop - start) +#else +#define __Pyx_ArgsSlice_VARARGS(args, start, stop) PyTuple_GetSlice(args, start, stop) +#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) PyTuple_GetSlice(args, start, stop) +#endif + +/* RaiseArgTupleInvalid.proto */ +static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact, + Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found); + +/* RaiseDoubleKeywords.proto */ +static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name); + +/* ParseKeywords.proto */ +static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject *const *kwvalues, + PyObject **argnames[], + PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args, + const char* function_name); + +/* ArgTypeTest.proto */ +#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\ + ((likely(__Pyx_IS_TYPE(obj, type) | (none_allowed && (obj == Py_None)))) ? 1 :\ + __Pyx__ArgTypeTest(obj, type, name, exact)) +static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact); + +/* RaiseException.proto */ +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause); + +/* PyFunctionFastCall.proto */ +#if CYTHON_FAST_PYCALL +#if !CYTHON_VECTORCALL +#define __Pyx_PyFunction_FastCall(func, args, nargs)\ + __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL) +static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs); +#endif +#define __Pyx_BUILD_ASSERT_EXPR(cond)\ + (sizeof(char [1 - 2*!(cond)]) - 1) +#ifndef Py_MEMBER_SIZE +#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member) +#endif +#if !CYTHON_VECTORCALL +#if PY_VERSION_HEX >= 0x03080000 + #include "frameobject.h" +#if PY_VERSION_HEX >= 0x030b00a6 && !CYTHON_COMPILING_IN_LIMITED_API + #ifndef Py_BUILD_CORE + #define Py_BUILD_CORE 1 + #endif + #include "internal/pycore_frame.h" +#endif + #define __Pxy_PyFrame_Initialize_Offsets() + #define __Pyx_PyFrame_GetLocalsplus(frame) ((frame)->f_localsplus) +#else + static size_t __pyx_pyframe_localsplus_offset = 0; + #include "frameobject.h" + #define __Pxy_PyFrame_Initialize_Offsets()\ + ((void)__Pyx_BUILD_ASSERT_EXPR(sizeof(PyFrameObject) == offsetof(PyFrameObject, f_localsplus) + Py_MEMBER_SIZE(PyFrameObject, f_localsplus)),\ + (void)(__pyx_pyframe_localsplus_offset = ((size_t)PyFrame_Type.tp_basicsize) - Py_MEMBER_SIZE(PyFrameObject, f_localsplus))) + #define __Pyx_PyFrame_GetLocalsplus(frame)\ + (assert(__pyx_pyframe_localsplus_offset), (PyObject **)(((char *)(frame)) + __pyx_pyframe_localsplus_offset)) +#endif +#endif +#endif + +/* PyObjectCall.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw); +#else +#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw) +#endif + +/* PyObjectCallMethO.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg); +#endif + +/* PyObjectFastCall.proto */ +#define __Pyx_PyObject_FastCall(func, args, nargs) __Pyx_PyObject_FastCallDict(func, args, (size_t)(nargs), NULL) +static CYTHON_INLINE PyObject* __Pyx_PyObject_FastCallDict(PyObject *func, PyObject **args, size_t nargs, PyObject *kwargs); + +/* RaiseUnexpectedTypeError.proto */ +static int __Pyx_RaiseUnexpectedTypeError(const char *expected, PyObject *obj); + +/* GCCDiagnostics.proto */ +#if !defined(__INTEL_COMPILER) && defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) +#define __Pyx_HAS_GCC_DIAGNOSTIC +#endif + +/* BuildPyUnicode.proto */ +static PyObject* __Pyx_PyUnicode_BuildFromAscii(Py_ssize_t ulength, char* chars, int clength, + int prepend_sign, char padding_char); + +/* CIntToPyUnicode.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_int(int value, Py_ssize_t width, char padding_char, char format_char); + +/* CIntToPyUnicode.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_Py_ssize_t(Py_ssize_t value, Py_ssize_t width, char padding_char, char format_char); + +/* JoinPyUnicode.proto */ +static PyObject* __Pyx_PyUnicode_Join(PyObject* value_tuple, Py_ssize_t value_count, Py_ssize_t result_ulength, + Py_UCS4 max_char); + +/* StrEquals.proto */ +#if PY_MAJOR_VERSION >= 3 +#define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals +#else +#define __Pyx_PyString_Equals __Pyx_PyBytes_Equals +#endif + +/* PyObjectFormatSimple.proto */ +#if CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyObject_FormatSimple(s, f) (\ + likely(PyUnicode_CheckExact(s)) ? (Py_INCREF(s), s) :\ + PyObject_Format(s, f)) +#elif PY_MAJOR_VERSION < 3 + #define __Pyx_PyObject_FormatSimple(s, f) (\ + likely(PyUnicode_CheckExact(s)) ? (Py_INCREF(s), s) :\ + likely(PyString_CheckExact(s)) ? PyUnicode_FromEncodedObject(s, NULL, "strict") :\ + PyObject_Format(s, f)) +#elif CYTHON_USE_TYPE_SLOTS + #define __Pyx_PyObject_FormatSimple(s, f) (\ + likely(PyUnicode_CheckExact(s)) ? (Py_INCREF(s), s) :\ + likely(PyLong_CheckExact(s)) ? PyLong_Type.tp_repr(s) :\ + likely(PyFloat_CheckExact(s)) ? PyFloat_Type.tp_repr(s) :\ + PyObject_Format(s, f)) +#else + #define __Pyx_PyObject_FormatSimple(s, f) (\ + likely(PyUnicode_CheckExact(s)) ? (Py_INCREF(s), s) :\ + PyObject_Format(s, f)) +#endif + +CYTHON_UNUSED static int __pyx_array_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/ +static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *); /*proto*/ +/* GetAttr.proto */ +static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *); + +/* GetItemInt.proto */ +#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\ + (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\ + __Pyx_GetItemInt_Generic(o, to_py_func(i)))) +#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\ + (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL)) +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i, + int wraparound, int boundscheck); +#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\ + (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL)) +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i, + int wraparound, int boundscheck); +static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j); +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, + int is_list, int wraparound, int boundscheck); + +/* PyObjectCallOneArg.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg); + +/* ObjectGetItem.proto */ +#if CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject *key); +#else +#define __Pyx_PyObject_GetItem(obj, key) PyObject_GetItem(obj, key) +#endif + +/* KeywordStringCheck.proto */ +static int __Pyx_CheckKeywordStrings(PyObject *kw, const char* function_name, int kw_allowed); + +/* DivInt[Py_ssize_t].proto */ +static CYTHON_INLINE Py_ssize_t __Pyx_div_Py_ssize_t(Py_ssize_t, Py_ssize_t); + +/* UnaryNegOverflows.proto */ +#define __Pyx_UNARY_NEG_WOULD_OVERFLOW(x)\ + (((x) < 0) & ((unsigned long)(x) == 0-(unsigned long)(x))) + +/* GetAttr3.proto */ +static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *, PyObject *, PyObject *); + +/* PyDictVersioning.proto */ +#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS +#define __PYX_DICT_VERSION_INIT ((PY_UINT64_T) -1) +#define __PYX_GET_DICT_VERSION(dict) (((PyDictObject*)(dict))->ma_version_tag) +#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\ + (version_var) = __PYX_GET_DICT_VERSION(dict);\ + (cache_var) = (value); +#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\ + static PY_UINT64_T __pyx_dict_version = 0;\ + static PyObject *__pyx_dict_cached_value = NULL;\ + if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\ + (VAR) = __pyx_dict_cached_value;\ + } else {\ + (VAR) = __pyx_dict_cached_value = (LOOKUP);\ + __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\ + }\ +} +static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj); +static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj); +static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version); +#else +#define __PYX_GET_DICT_VERSION(dict) (0) +#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var) +#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) (VAR) = (LOOKUP); +#endif + +/* GetModuleGlobalName.proto */ +#if CYTHON_USE_DICT_VERSIONS +#define __Pyx_GetModuleGlobalName(var, name) do {\ + static PY_UINT64_T __pyx_dict_version = 0;\ + static PyObject *__pyx_dict_cached_value = NULL;\ + (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\ + (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\ + __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\ +} while(0) +#define __Pyx_GetModuleGlobalNameUncached(var, name) do {\ + PY_UINT64_T __pyx_dict_version;\ + PyObject *__pyx_dict_cached_value;\ + (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\ +} while(0) +static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value); +#else +#define __Pyx_GetModuleGlobalName(var, name) (var) = __Pyx__GetModuleGlobalName(name) +#define __Pyx_GetModuleGlobalNameUncached(var, name) (var) = __Pyx__GetModuleGlobalName(name) +static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name); +#endif + +/* AssertionsEnabled.proto */ +#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag) + #define __Pyx_init_assertions_enabled() (0) + #define __pyx_assertions_enabled() (1) +#elif CYTHON_COMPILING_IN_LIMITED_API || (CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030C0000) + static int __pyx_assertions_enabled_flag; + #define __pyx_assertions_enabled() (__pyx_assertions_enabled_flag) + static int __Pyx_init_assertions_enabled(void) { + PyObject *builtins, *debug, *debug_str; + int flag; + builtins = PyEval_GetBuiltins(); + if (!builtins) goto bad; + debug_str = PyUnicode_FromStringAndSize("__debug__", 9); + if (!debug_str) goto bad; + debug = PyObject_GetItem(builtins, debug_str); + Py_DECREF(debug_str); + if (!debug) goto bad; + flag = PyObject_IsTrue(debug); + Py_DECREF(debug); + if (flag == -1) goto bad; + __pyx_assertions_enabled_flag = flag; + return 0; + bad: + __pyx_assertions_enabled_flag = 1; + return -1; + } +#else + #define __Pyx_init_assertions_enabled() (0) + #define __pyx_assertions_enabled() (!Py_OptimizeFlag) +#endif + +/* RaiseTooManyValuesToUnpack.proto */ +static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected); + +/* RaiseNeedMoreValuesToUnpack.proto */ +static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index); + +/* RaiseNoneIterError.proto */ +static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void); + +/* ExtTypeTest.proto */ +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type); + +/* GetTopmostException.proto */ +#if CYTHON_USE_EXC_INFO_STACK && CYTHON_FAST_THREAD_STATE +static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate); +#endif + +/* SaveResetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +#else +#define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb) +#define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb) +#endif + +/* GetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb) +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb); +#endif + +/* SwapException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ExceptionSwap(type, value, tb) __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb); +#endif + +/* Import.proto */ +static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level); + +/* ImportDottedModule.proto */ +static PyObject *__Pyx_ImportDottedModule(PyObject *name, PyObject *parts_tuple); +#if PY_MAJOR_VERSION >= 3 +static PyObject *__Pyx_ImportDottedModule_WalkParts(PyObject *module, PyObject *name, PyObject *parts_tuple); +#endif + +/* FastTypeChecks.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type) +#define __Pyx_TypeCheck2(obj, type1, type2) __Pyx_IsAnySubtype2(Py_TYPE(obj), (PyTypeObject *)type1, (PyTypeObject *)type2) +static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b); +static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b); +static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type); +static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2); +#else +#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type) +#define __Pyx_TypeCheck2(obj, type1, type2) (PyObject_TypeCheck(obj, (PyTypeObject *)type1) || PyObject_TypeCheck(obj, (PyTypeObject *)type2)) +#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type) +#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2)) +#endif +#define __Pyx_PyErr_ExceptionMatches2(err1, err2) __Pyx_PyErr_GivenExceptionMatches2(__Pyx_PyErr_CurrentExceptionType(), err1, err2) +#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception) + +CYTHON_UNUSED static int __pyx_memoryview_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/ +/* ListCompAppend.proto */ +#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS +static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) { + PyListObject* L = (PyListObject*) list; + Py_ssize_t len = Py_SIZE(list); + if (likely(L->allocated > len)) { + Py_INCREF(x); + #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000 + L->ob_item[len] = x; + #else + PyList_SET_ITEM(list, len, x); + #endif + __Pyx_SET_SIZE(list, len + 1); + return 0; + } + return PyList_Append(list, x); +} +#else +#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x) +#endif + +/* PySequenceMultiply.proto */ +#define __Pyx_PySequence_Multiply_Left(mul, seq) __Pyx_PySequence_Multiply(seq, mul) +static CYTHON_INLINE PyObject* __Pyx_PySequence_Multiply(PyObject *seq, Py_ssize_t mul); + +/* SetItemInt.proto */ +#define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\ + (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\ + __Pyx_SetItemInt_Generic(o, to_py_func(i), v))) +static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v); +static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, + int is_list, int wraparound, int boundscheck); + +/* RaiseUnboundLocalError.proto */ +static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname); + +/* DivInt[long].proto */ +static CYTHON_INLINE long __Pyx_div_long(long, long); + +/* PySequenceContains.proto */ +static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) { + int result = PySequence_Contains(seq, item); + return unlikely(result < 0) ? result : (result == (eq == Py_EQ)); +} + +/* ImportFrom.proto */ +static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name); + +/* HasAttr.proto */ +static CYTHON_INLINE int __Pyx_HasAttr(PyObject *, PyObject *); + +/* IsLittleEndian.proto */ +static CYTHON_INLINE int __Pyx_Is_Little_Endian(void); + +/* BufferFormatCheck.proto */ +static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts); +static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx, + __Pyx_BufFmt_StackElem* stack, + __Pyx_TypeInfo* type); + +/* BufferGetAndValidate.proto */ +#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\ + ((obj == Py_None || obj == NULL) ?\ + (__Pyx_ZeroBuffer(buf), 0) :\ + __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)) +static int __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj, + __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack); +static void __Pyx_ZeroBuffer(Py_buffer* buf); +static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info); +static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 }; +static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 }; + +/* PyObject_GenericGetAttrNoDict.proto */ +#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000 +static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name); +#else +#define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr +#endif + +/* PyObject_GenericGetAttr.proto */ +#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000 +static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name); +#else +#define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr +#endif + +/* IncludeStructmemberH.proto */ +#include + +/* FixUpExtensionType.proto */ +#if CYTHON_USE_TYPE_SPECS +static int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type); +#endif + +/* PyObjectCallNoArg.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func); + +/* PyObjectGetMethod.proto */ +static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method); + +/* PyObjectCallMethod0.proto */ +static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name); + +/* ValidateBasesTuple.proto */ +#if CYTHON_COMPILING_IN_CPYTHON || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_USE_TYPE_SPECS +static int __Pyx_validate_bases_tuple(const char *type_name, Py_ssize_t dictoffset, PyObject *bases); +#endif + +/* PyType_Ready.proto */ +CYTHON_UNUSED static int __Pyx_PyType_Ready(PyTypeObject *t); + +/* SetVTable.proto */ +static int __Pyx_SetVtable(PyTypeObject* typeptr , void* vtable); + +/* GetVTable.proto */ +static void* __Pyx_GetVtable(PyTypeObject *type); + +/* MergeVTables.proto */ +#if !CYTHON_COMPILING_IN_LIMITED_API +static int __Pyx_MergeVtables(PyTypeObject *type); +#endif + +/* SetupReduce.proto */ +#if !CYTHON_COMPILING_IN_LIMITED_API +static int __Pyx_setup_reduce(PyObject* type_obj); +#endif + +/* TypeImport.proto */ +#ifndef __PYX_HAVE_RT_ImportType_proto_3_0_11 +#define __PYX_HAVE_RT_ImportType_proto_3_0_11 +#if defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L +#include +#endif +#if (defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L) || __cplusplus >= 201103L +#define __PYX_GET_STRUCT_ALIGNMENT_3_0_11(s) alignof(s) +#else +#define __PYX_GET_STRUCT_ALIGNMENT_3_0_11(s) sizeof(void*) +#endif +enum __Pyx_ImportType_CheckSize_3_0_11 { + __Pyx_ImportType_CheckSize_Error_3_0_11 = 0, + __Pyx_ImportType_CheckSize_Warn_3_0_11 = 1, + __Pyx_ImportType_CheckSize_Ignore_3_0_11 = 2 +}; +static PyTypeObject *__Pyx_ImportType_3_0_11(PyObject* module, const char *module_name, const char *class_name, size_t size, size_t alignment, enum __Pyx_ImportType_CheckSize_3_0_11 check_size); +#endif + +/* FetchSharedCythonModule.proto */ +static PyObject *__Pyx_FetchSharedCythonABIModule(void); + +/* FetchCommonType.proto */ +#if !CYTHON_USE_TYPE_SPECS +static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type); +#else +static PyTypeObject* __Pyx_FetchCommonTypeFromSpec(PyObject *module, PyType_Spec *spec, PyObject *bases); +#endif + +/* PyMethodNew.proto */ +#if CYTHON_COMPILING_IN_LIMITED_API +static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) { + PyObject *typesModule=NULL, *methodType=NULL, *result=NULL; + CYTHON_UNUSED_VAR(typ); + if (!self) + return __Pyx_NewRef(func); + typesModule = PyImport_ImportModule("types"); + if (!typesModule) return NULL; + methodType = PyObject_GetAttrString(typesModule, "MethodType"); + Py_DECREF(typesModule); + if (!methodType) return NULL; + result = PyObject_CallFunctionObjArgs(methodType, func, self, NULL); + Py_DECREF(methodType); + return result; +} +#elif PY_MAJOR_VERSION >= 3 +static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) { + CYTHON_UNUSED_VAR(typ); + if (!self) + return __Pyx_NewRef(func); + return PyMethod_New(func, self); +} +#else + #define __Pyx_PyMethod_New PyMethod_New +#endif + +/* PyVectorcallFastCallDict.proto */ +#if CYTHON_METH_FASTCALL +static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw); +#endif + +/* CythonFunctionShared.proto */ +#define __Pyx_CyFunction_USED +#define __Pyx_CYFUNCTION_STATICMETHOD 0x01 +#define __Pyx_CYFUNCTION_CLASSMETHOD 0x02 +#define __Pyx_CYFUNCTION_CCLASS 0x04 +#define __Pyx_CYFUNCTION_COROUTINE 0x08 +#define __Pyx_CyFunction_GetClosure(f)\ + (((__pyx_CyFunctionObject *) (f))->func_closure) +#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API + #define __Pyx_CyFunction_GetClassObj(f)\ + (((__pyx_CyFunctionObject *) (f))->func_classobj) +#else + #define __Pyx_CyFunction_GetClassObj(f)\ + ((PyObject*) ((PyCMethodObject *) (f))->mm_class) +#endif +#define __Pyx_CyFunction_SetClassObj(f, classobj)\ + __Pyx__CyFunction_SetClassObj((__pyx_CyFunctionObject *) (f), (classobj)) +#define __Pyx_CyFunction_Defaults(type, f)\ + ((type *)(((__pyx_CyFunctionObject *) (f))->defaults)) +#define __Pyx_CyFunction_SetDefaultsGetter(f, g)\ + ((__pyx_CyFunctionObject *) (f))->defaults_getter = (g) +typedef struct { +#if CYTHON_COMPILING_IN_LIMITED_API + PyObject_HEAD + PyObject *func; +#elif PY_VERSION_HEX < 0x030900B1 + PyCFunctionObject func; +#else + PyCMethodObject func; +#endif +#if CYTHON_BACKPORT_VECTORCALL + __pyx_vectorcallfunc func_vectorcall; +#endif +#if PY_VERSION_HEX < 0x030500A0 || CYTHON_COMPILING_IN_LIMITED_API + PyObject *func_weakreflist; +#endif + PyObject *func_dict; + PyObject *func_name; + PyObject *func_qualname; + PyObject *func_doc; + PyObject *func_globals; + PyObject *func_code; + PyObject *func_closure; +#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API + PyObject *func_classobj; +#endif + void *defaults; + int defaults_pyobjects; + size_t defaults_size; + int flags; + PyObject *defaults_tuple; + PyObject *defaults_kwdict; + PyObject *(*defaults_getter)(PyObject *); + PyObject *func_annotations; + PyObject *func_is_coroutine; +} __pyx_CyFunctionObject; +#undef __Pyx_CyOrPyCFunction_Check +#define __Pyx_CyFunction_Check(obj) __Pyx_TypeCheck(obj, __pyx_CyFunctionType) +#define __Pyx_CyOrPyCFunction_Check(obj) __Pyx_TypeCheck2(obj, __pyx_CyFunctionType, &PyCFunction_Type) +#define __Pyx_CyFunction_CheckExact(obj) __Pyx_IS_TYPE(obj, __pyx_CyFunctionType) +static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void *cfunc); +#undef __Pyx_IsSameCFunction +#define __Pyx_IsSameCFunction(func, cfunc) __Pyx__IsSameCyOrCFunction(func, cfunc) +static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject* op, PyMethodDef *ml, + int flags, PyObject* qualname, + PyObject *closure, + PyObject *module, PyObject *globals, + PyObject* code); +static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj); +static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *m, + size_t size, + int pyobjects); +static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *m, + PyObject *tuple); +static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *m, + PyObject *dict); +static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *m, + PyObject *dict); +static int __pyx_CyFunction_init(PyObject *module); +#if CYTHON_METH_FASTCALL +static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames); +static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames); +static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames); +static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames); +#if CYTHON_BACKPORT_VECTORCALL +#define __Pyx_CyFunction_func_vectorcall(f) (((__pyx_CyFunctionObject*)f)->func_vectorcall) +#else +#define __Pyx_CyFunction_func_vectorcall(f) (((PyCFunctionObject*)f)->vectorcall) +#endif +#endif + +/* CythonFunction.proto */ +static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml, + int flags, PyObject* qualname, + PyObject *closure, + PyObject *module, PyObject *globals, + PyObject* code); + +/* CLineInTraceback.proto */ +#ifdef CYTHON_CLINE_IN_TRACEBACK +#define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0) +#else +static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line); +#endif + +/* CodeObjectCache.proto */ +#if !CYTHON_COMPILING_IN_LIMITED_API +typedef struct { + PyCodeObject* code_object; + int code_line; +} __Pyx_CodeObjectCacheEntry; +struct __Pyx_CodeObjectCache { + int count; + int max_count; + __Pyx_CodeObjectCacheEntry* entries; +}; +static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL}; +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line); +static PyCodeObject *__pyx_find_code_object(int code_line); +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object); +#endif + +/* AddTraceback.proto */ +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename); + +#if PY_MAJOR_VERSION < 3 + static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags); + static void __Pyx_ReleaseBuffer(Py_buffer *view); +#else + #define __Pyx_GetBuffer PyObject_GetBuffer + #define __Pyx_ReleaseBuffer PyBuffer_Release +#endif + + +/* BufferStructDeclare.proto */ +typedef struct { + Py_ssize_t shape, strides, suboffsets; +} __Pyx_Buf_DimInfo; +typedef struct { + size_t refcount; + Py_buffer pybuffer; +} __Pyx_Buffer; +typedef struct { + __Pyx_Buffer *rcbuffer; + char *data; + __Pyx_Buf_DimInfo diminfo[8]; +} __Pyx_LocalBuf_ND; + +/* MemviewSliceIsContig.proto */ +static int __pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, char order, int ndim); + +/* OverlappingSlices.proto */ +static int __pyx_slices_overlap(__Pyx_memviewslice *slice1, + __Pyx_memviewslice *slice2, + int ndim, size_t itemsize); + +/* TypeInfoCompare.proto */ +static int __pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b); + +/* MemviewSliceValidateAndInit.proto */ +static int __Pyx_ValidateAndInit_memviewslice( + int *axes_specs, + int c_or_f_flag, + int buf_flags, + int ndim, + __Pyx_TypeInfo *dtype, + __Pyx_BufFmt_StackElem stack[], + __Pyx_memviewslice *memviewslice, + PyObject *original_obj); + +/* ObjectToMemviewSlice.proto */ +static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_double(PyObject *, int writable_flag); + +/* ObjectToMemviewSlice.proto */ +static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_nn___pyx_t_5numpy_int64_t(PyObject *, int writable_flag); + +/* RealImag.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #define __Pyx_CREAL(z) ((z).real()) + #define __Pyx_CIMAG(z) ((z).imag()) + #else + #define __Pyx_CREAL(z) (__real__(z)) + #define __Pyx_CIMAG(z) (__imag__(z)) + #endif +#else + #define __Pyx_CREAL(z) ((z).real) + #define __Pyx_CIMAG(z) ((z).imag) +#endif +#if defined(__cplusplus) && CYTHON_CCOMPLEX\ + && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103) + #define __Pyx_SET_CREAL(z,x) ((z).real(x)) + #define __Pyx_SET_CIMAG(z,y) ((z).imag(y)) +#else + #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x) + #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y) +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #define __Pyx_c_eq_float(a, b) ((a)==(b)) + #define __Pyx_c_sum_float(a, b) ((a)+(b)) + #define __Pyx_c_diff_float(a, b) ((a)-(b)) + #define __Pyx_c_prod_float(a, b) ((a)*(b)) + #define __Pyx_c_quot_float(a, b) ((a)/(b)) + #define __Pyx_c_neg_float(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_float(z) ((z)==(float)0) + #define __Pyx_c_conj_float(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_float(z) (::std::abs(z)) + #define __Pyx_c_pow_float(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_float(z) ((z)==0) + #define __Pyx_c_conj_float(z) (conjf(z)) + #if 1 + #define __Pyx_c_abs_float(z) (cabsf(z)) + #define __Pyx_c_pow_float(a, b) (cpowf(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex); + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex); + #endif +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #define __Pyx_c_eq_double(a, b) ((a)==(b)) + #define __Pyx_c_sum_double(a, b) ((a)+(b)) + #define __Pyx_c_diff_double(a, b) ((a)-(b)) + #define __Pyx_c_prod_double(a, b) ((a)*(b)) + #define __Pyx_c_quot_double(a, b) ((a)/(b)) + #define __Pyx_c_neg_double(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_double(z) ((z)==(double)0) + #define __Pyx_c_conj_double(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (::std::abs(z)) + #define __Pyx_c_pow_double(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_double(z) ((z)==0) + #define __Pyx_c_conj_double(z) (conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (cabs(z)) + #define __Pyx_c_pow_double(a, b) (cpow(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex); + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex); + #endif +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #define __Pyx_c_eq_long__double(a, b) ((a)==(b)) + #define __Pyx_c_sum_long__double(a, b) ((a)+(b)) + #define __Pyx_c_diff_long__double(a, b) ((a)-(b)) + #define __Pyx_c_prod_long__double(a, b) ((a)*(b)) + #define __Pyx_c_quot_long__double(a, b) ((a)/(b)) + #define __Pyx_c_neg_long__double(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_long__double(z) ((z)==(long double)0) + #define __Pyx_c_conj_long__double(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_long__double(z) (::std::abs(z)) + #define __Pyx_c_pow_long__double(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_long__double(z) ((z)==0) + #define __Pyx_c_conj_long__double(z) (conjl(z)) + #if 1 + #define __Pyx_c_abs_long__double(z) (cabsl(z)) + #define __Pyx_c_pow_long__double(a, b) (cpowl(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_sum_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_diff_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_prod_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_neg_long__double(__pyx_t_long_double_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_long__double(__pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_conj_long__double(__pyx_t_long_double_complex); + #if 1 + static CYTHON_INLINE long double __Pyx_c_abs_long__double(__pyx_t_long_double_complex); + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_pow_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex); + #endif +#endif + +/* MemviewSliceCopyTemplate.proto */ +static __Pyx_memviewslice +__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs, + const char *mode, int ndim, + size_t sizeof_dtype, int contig_flag, + int dtype_is_object); + +/* MemviewSliceInit.proto */ +#define __Pyx_BUF_MAX_NDIMS %(BUF_MAX_NDIMS)d +#define __Pyx_MEMVIEW_DIRECT 1 +#define __Pyx_MEMVIEW_PTR 2 +#define __Pyx_MEMVIEW_FULL 4 +#define __Pyx_MEMVIEW_CONTIG 8 +#define __Pyx_MEMVIEW_STRIDED 16 +#define __Pyx_MEMVIEW_FOLLOW 32 +#define __Pyx_IS_C_CONTIG 1 +#define __Pyx_IS_F_CONTIG 2 +static int __Pyx_init_memviewslice( + struct __pyx_memoryview_obj *memview, + int ndim, + __Pyx_memviewslice *memviewslice, + int memview_is_new_reference); +static CYTHON_INLINE int __pyx_add_acquisition_count_locked( + __pyx_atomic_int_type *acquisition_count, PyThread_type_lock lock); +static CYTHON_INLINE int __pyx_sub_acquisition_count_locked( + __pyx_atomic_int_type *acquisition_count, PyThread_type_lock lock); +#define __pyx_get_slice_count_pointer(memview) (&memview->acquisition_count) +#define __PYX_INC_MEMVIEW(slice, have_gil) __Pyx_INC_MEMVIEW(slice, have_gil, __LINE__) +#define __PYX_XCLEAR_MEMVIEW(slice, have_gil) __Pyx_XCLEAR_MEMVIEW(slice, have_gil, __LINE__) +static CYTHON_INLINE void __Pyx_INC_MEMVIEW(__Pyx_memviewslice *, int, int); +static CYTHON_INLINE void __Pyx_XCLEAR_MEMVIEW(__Pyx_memviewslice *, int, int); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_npy_int64(npy_int64 value); + +/* CIntFromPy.proto */ +static CYTHON_INLINE npy_int64 __Pyx_PyInt_As_npy_int64(PyObject *); + +/* CIntFromPy.proto */ +static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *); + +/* CIntFromPy.proto */ +static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value); + +/* CIntFromPy.proto */ +static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *); + +/* FormatTypeName.proto */ +#if CYTHON_COMPILING_IN_LIMITED_API +typedef PyObject *__Pyx_TypeName; +#define __Pyx_FMT_TYPENAME "%U" +static __Pyx_TypeName __Pyx_PyType_GetName(PyTypeObject* tp); +#define __Pyx_DECREF_TypeName(obj) Py_XDECREF(obj) +#else +typedef const char *__Pyx_TypeName; +#define __Pyx_FMT_TYPENAME "%.200s" +#define __Pyx_PyType_GetName(tp) ((tp)->tp_name) +#define __Pyx_DECREF_TypeName(obj) +#endif + +/* CheckBinaryVersion.proto */ +static unsigned long __Pyx_get_runtime_version(void); +static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer); + +/* FunctionImport.proto */ +static int __Pyx_ImportFunction_3_0_11(PyObject *module, const char *funcname, void (**f)(void), const char *sig); + +/* InitStrings.proto */ +static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); + +/* #### Code section: module_declarations ### */ +static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *__pyx_v_self); /* proto*/ +static char *__pyx_memoryview_get_item_pointer(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto*/ +static PyObject *__pyx_memoryview_is_slice(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj); /* proto*/ +static PyObject *__pyx_memoryview_setitem_slice_assignment(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_dst, PyObject *__pyx_v_src); /* proto*/ +static PyObject *__pyx_memoryview_setitem_slice_assign_scalar(struct __pyx_memoryview_obj *__pyx_v_self, struct __pyx_memoryview_obj *__pyx_v_dst, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryview_setitem_indexed(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryview_convert_item_to_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/ +static PyObject *__pyx_memoryview_assign_item_from_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryview__get_base(struct __pyx_memoryview_obj *__pyx_v_self); /* proto*/ +static PyObject *__pyx_memoryviewslice_convert_item_to_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/ +static PyObject *__pyx_memoryviewslice_assign_item_from_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryviewslice__get_base(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_8itemsize_itemsize(PyArray_Descr *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_9alignment_alignment(PyArray_Descr *__pyx_v_self); /* proto*/ +static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_6fields_fields(PyArray_Descr *__pyx_v_self); /* proto*/ +static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_5names_names(PyArray_Descr *__pyx_v_self); /* proto*/ +static CYTHON_INLINE PyArray_ArrayDescr *__pyx_f_5numpy_5dtype_8subarray_subarray(PyArray_Descr *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_uint64 __pyx_f_5numpy_5dtype_5flags_flags(PyArray_Descr *__pyx_v_self); /* proto*/ +static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_7numiter_numiter(PyArrayMultiIterObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_4size_size(PyArrayMultiIterObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_5index_index(PyArrayMultiIterObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_2nd_nd(PyArrayMultiIterObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp *__pyx_f_5numpy_9broadcast_10dimensions_dimensions(PyArrayMultiIterObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE void **__pyx_f_5numpy_9broadcast_5iters_iters(PyArrayMultiIterObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE PyObject *__pyx_f_5numpy_7ndarray_4base_base(PyArrayObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE PyArray_Descr *__pyx_f_5numpy_7ndarray_5descr_descr(PyArrayObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE int __pyx_f_5numpy_7ndarray_4ndim_ndim(PyArrayObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_5shape_shape(PyArrayObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_7strides_strides(PyArrayObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE npy_intp __pyx_f_5numpy_7ndarray_4size_size(PyArrayObject *__pyx_v_self); /* proto*/ +static CYTHON_INLINE char *__pyx_f_5numpy_7ndarray_4data_data(PyArrayObject *__pyx_v_self); /* proto*/ + +/* Module declarations from "libc.string" */ + +/* Module declarations from "libc.stdio" */ + +/* Module declarations from "__builtin__" */ + +/* Module declarations from "cpython.type" */ + +/* Module declarations from "cpython" */ + +/* Module declarations from "cpython.object" */ + +/* Module declarations from "cpython.ref" */ + +/* Module declarations from "numpy" */ + +/* Module declarations from "numpy" */ + +/* Module declarations from "scipy.special.cython_special" */ +static double (*__pyx_f_5scipy_7special_14cython_special_pdtr)(double, double, int __pyx_skip_dispatch); /*proto*/ + +/* Module declarations from "libc.math" */ + +/* Module declarations from "cython.view" */ + +/* Module declarations from "cython.dataclasses" */ + +/* Module declarations from "cython" */ + +/* Module declarations from "pygom.model._tau_leap" */ +static PyObject *__pyx_collections_abc_Sequence = 0; +static PyObject *generic = 0; +static PyObject *strided = 0; +static PyObject *indirect = 0; +static PyObject *contiguous = 0; +static PyObject *indirect_contiguous = 0; +static int __pyx_memoryview_thread_locks_used; +static PyThread_type_lock __pyx_memoryview_thread_locks[8]; +static int __pyx_array_allocate_buffer(struct __pyx_array_obj *); /*proto*/ +static struct __pyx_array_obj *__pyx_array_new(PyObject *, Py_ssize_t, char *, char *, char *); /*proto*/ +static PyObject *__pyx_memoryview_new(PyObject *, int, int, __Pyx_TypeInfo *); /*proto*/ +static CYTHON_INLINE int __pyx_memoryview_check(PyObject *); /*proto*/ +static PyObject *_unellipsify(PyObject *, int); /*proto*/ +static int assert_direct_dimensions(Py_ssize_t *, int); /*proto*/ +static struct __pyx_memoryview_obj *__pyx_memview_slice(struct __pyx_memoryview_obj *, PyObject *); /*proto*/ +static int __pyx_memoryview_slice_memviewslice(__Pyx_memviewslice *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int, int); /*proto*/ +static char *__pyx_pybuffer_index(Py_buffer *, char *, Py_ssize_t, Py_ssize_t); /*proto*/ +static int __pyx_memslice_transpose(__Pyx_memviewslice *); /*proto*/ +static PyObject *__pyx_memoryview_fromslice(__Pyx_memviewslice, int, PyObject *(*)(char *), int (*)(char *, PyObject *), int); /*proto*/ +static __Pyx_memviewslice *__pyx_memoryview_get_slice_from_memoryview(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/ +static void __pyx_memoryview_slice_copy(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/ +static PyObject *__pyx_memoryview_copy_object(struct __pyx_memoryview_obj *); /*proto*/ +static PyObject *__pyx_memoryview_copy_object_from_slice(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/ +static Py_ssize_t abs_py_ssize_t(Py_ssize_t); /*proto*/ +static char __pyx_get_best_slice_order(__Pyx_memviewslice *, int); /*proto*/ +static void _copy_strided_to_strided(char *, Py_ssize_t *, char *, Py_ssize_t *, Py_ssize_t *, Py_ssize_t *, int, size_t); /*proto*/ +static void copy_strided_to_strided(__Pyx_memviewslice *, __Pyx_memviewslice *, int, size_t); /*proto*/ +static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *, int); /*proto*/ +static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *, Py_ssize_t *, Py_ssize_t, int, char); /*proto*/ +static void *__pyx_memoryview_copy_data_to_temp(__Pyx_memviewslice *, __Pyx_memviewslice *, char, int); /*proto*/ +static int __pyx_memoryview_err_extents(int, Py_ssize_t, Py_ssize_t); /*proto*/ +static int __pyx_memoryview_err_dim(PyObject *, PyObject *, int); /*proto*/ +static int __pyx_memoryview_err(PyObject *, PyObject *); /*proto*/ +static int __pyx_memoryview_err_no_memory(void); /*proto*/ +static int __pyx_memoryview_copy_contents(__Pyx_memviewslice, __Pyx_memviewslice, int, int, int); /*proto*/ +static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *, int, int); /*proto*/ +static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *, int, int, int); /*proto*/ +static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/ +static void __pyx_memoryview_refcount_objects_in_slice(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/ +static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *, int, size_t, void *, int); /*proto*/ +static void __pyx_memoryview__slice_assign_scalar(char *, Py_ssize_t *, Py_ssize_t *, int, size_t, void *); /*proto*/ +static PyObject *__pyx_unpickle_Enum__set_state(struct __pyx_MemviewEnum_obj *, PyObject *); /*proto*/ +/* #### Code section: typeinfo ### */ +static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float64_t = { "float64_t", NULL, sizeof(__pyx_t_5numpy_float64_t), { 0 }, 0, 'R', 0, 0 }; +static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_int64_t = { "int64_t", NULL, sizeof(__pyx_t_5numpy_int64_t), { 0 }, 0, __PYX_IS_UNSIGNED(__pyx_t_5numpy_int64_t) ? 'U' : 'I', __PYX_IS_UNSIGNED(__pyx_t_5numpy_int64_t), 0 }; +static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 }; +/* #### Code section: before_global_var ### */ +#define __Pyx_MODULE_NAME "pygom.model._tau_leap" +extern int __pyx_module_is_main_pygom__model___tau_leap; +int __pyx_module_is_main_pygom__model___tau_leap = 0; + +/* Implementation of "pygom.model._tau_leap" */ +/* #### Code section: global_var ### */ +static PyObject *__pyx_builtin_range; +static PyObject *__pyx_builtin_print; +static PyObject *__pyx_builtin___import__; +static PyObject *__pyx_builtin_ValueError; +static PyObject *__pyx_builtin_MemoryError; +static PyObject *__pyx_builtin_enumerate; +static PyObject *__pyx_builtin_TypeError; +static PyObject *__pyx_builtin_AssertionError; +static PyObject *__pyx_builtin_Ellipsis; +static PyObject *__pyx_builtin_id; +static PyObject *__pyx_builtin_IndexError; +static PyObject *__pyx_builtin_ImportError; +/* #### Code section: string_decls ### */ +static const char __pyx_k_[] = ": "; +static const char __pyx_k_O[] = "O"; +static const char __pyx_k_c[] = "c"; +static const char __pyx_k_i[] = "i"; +static const char __pyx_k_j[] = "j"; +static const char __pyx_k_x[] = "x"; +static const char __pyx_k__2[] = "."; +static const char __pyx_k__3[] = "*"; +static const char __pyx_k__6[] = "'"; +static const char __pyx_k__7[] = ")"; +static const char __pyx_k_gc[] = "gc"; +static const char __pyx_k_id[] = "id"; +static const char __pyx_k_mu[] = "mu"; +static const char __pyx_k_np[] = "np"; +static const char __pyx_k__25[] = "?"; +static const char __pyx_k_abc[] = "abc"; +static const char __pyx_k_and[] = " and "; +static const char __pyx_k_got[] = " (got "; +static const char __pyx_k_new[] = "__new__"; +static const char __pyx_k_obj[] = "obj"; +static const char __pyx_k_sum[] = "sum"; +static const char __pyx_k_sys[] = "sys"; +static const char __pyx_k_base[] = "base"; +static const char __pyx_k_dict[] = "__dict__"; +static const char __pyx_k_main[] = "__main__"; +static const char __pyx_k_mode[] = "mode"; +static const char __pyx_k_name[] = "name"; +static const char __pyx_k_ndim[] = "ndim"; +static const char __pyx_k_pack[] = "pack"; +static const char __pyx_k_safe[] = "safe"; +static const char __pyx_k_size[] = "size"; +static const char __pyx_k_spec[] = "__spec__"; +static const char __pyx_k_step[] = "step"; +static const char __pyx_k_stop[] = "stop"; +static const char __pyx_k_test[] = "__test__"; +static const char __pyx_k_ASCII[] = "ASCII"; +static const char __pyx_k_class[] = "__class__"; +static const char __pyx_k_count[] = "count"; +static const char __pyx_k_error[] = "error"; +static const char __pyx_k_flags[] = "flags"; +static const char __pyx_k_index[] = "index"; +static const char __pyx_k_numpy[] = "numpy"; +static const char __pyx_k_print[] = "print"; +static const char __pyx_k_range[] = "range"; +static const char __pyx_k_rates[] = "rates"; +static const char __pyx_k_shape[] = "shape"; +static const char __pyx_k_start[] = "start"; +static const char __pyx_k_enable[] = "enable"; +static const char __pyx_k_encode[] = "encode"; +static const char __pyx_k_format[] = "format"; +static const char __pyx_k_import[] = "__import__"; +static const char __pyx_k_name_2[] = "__name__"; +static const char __pyx_k_pickle[] = "pickle"; +static const char __pyx_k_reduce[] = "__reduce__"; +static const char __pyx_k_struct[] = "struct"; +static const char __pyx_k_unpack[] = "unpack"; +static const char __pyx_k_update[] = "update"; +static const char __pyx_k_x_view[] = "x_view"; +static const char __pyx_k_cdf_val[] = "cdf_val"; +static const char __pyx_k_disable[] = "disable"; +static const char __pyx_k_epsilon[] = "epsilon"; +static const char __pyx_k_fortran[] = "fortran"; +static const char __pyx_k_max_cdf[] = "max_cdf"; +static const char __pyx_k_memview[] = "memview"; +static const char __pyx_k_n_rates[] = "n_rates"; +static const char __pyx_k_new_cdf[] = "new_cdf"; +static const char __pyx_k_Ellipsis[] = "Ellipsis"; +static const char __pyx_k_Sequence[] = "Sequence"; +static const char __pyx_k_getstate[] = "__getstate__"; +static const char __pyx_k_itemsize[] = "itemsize"; +static const char __pyx_k_pyx_type[] = "__pyx_type"; +static const char __pyx_k_register[] = "register"; +static const char __pyx_k_setstate[] = "__setstate__"; +static const char __pyx_k_TypeError[] = "TypeError"; +static const char __pyx_k_enumerate[] = "enumerate"; +static const char __pyx_k_isenabled[] = "isenabled"; +static const char __pyx_k_pyx_state[] = "__pyx_state"; +static const char __pyx_k_reduce_ex[] = "__reduce_ex__"; +static const char __pyx_k_tau_scale[] = "tau_scale"; +static const char __pyx_k_IndexError[] = "IndexError"; +static const char __pyx_k_ValueError[] = "ValueError"; +static const char __pyx_k_pyx_result[] = "__pyx_result"; +static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__"; +static const char __pyx_k_rates_view[] = "rates_view"; +static const char __pyx_k_total_rate[] = "total_rate"; +static const char __pyx_k_ImportError[] = "ImportError"; +static const char __pyx_k_MemoryError[] = "MemoryError"; +static const char __pyx_k_PickleError[] = "PickleError"; +static const char __pyx_k_collections[] = "collections"; +static const char __pyx_k_count_error[] = "count error"; +static const char __pyx_k_n_reactants[] = "n_reactants"; +static const char __pyx_k_initializing[] = "_initializing"; +static const char __pyx_k_is_coroutine[] = "_is_coroutine"; +static const char __pyx_k_pyx_checksum[] = "__pyx_checksum"; +static const char __pyx_k_reactant_mat[] = "reactant_mat"; +static const char __pyx_k_stringsource[] = ""; +static const char __pyx_k_version_info[] = "version_info"; +static const char __pyx_k_class_getitem[] = "__class_getitem__"; +static const char __pyx_k_reduce_cython[] = "__reduce_cython__"; +static const char __pyx_k_AssertionError[] = "AssertionError"; +static const char __pyx_k_View_MemoryView[] = "View.MemoryView"; +static const char __pyx_k_allocate_buffer[] = "allocate_buffer"; +static const char __pyx_k_collections_abc[] = "collections.abc"; +static const char __pyx_k_dtype_is_object[] = "dtype_is_object"; +static const char __pyx_k_pyx_PickleError[] = "__pyx_PickleError"; +static const char __pyx_k_setstate_cython[] = "__setstate_cython__"; +static const char __pyx_k_pyx_unpickle_Enum[] = "__pyx_unpickle_Enum"; +static const char __pyx_k_reactant_mat_view[] = "reactant_mat_view"; +static const char __pyx_k_asyncio_coroutines[] = "asyncio.coroutines"; +static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback"; +static const char __pyx_k_strided_and_direct[] = ""; +static const char __pyx_k_strided_and_indirect[] = ""; +static const char __pyx_k_Invalid_shape_in_axis[] = "Invalid shape in axis "; +static const char __pyx_k_contiguous_and_direct[] = ""; +static const char __pyx_k_pygom_model__tau_leap[] = "pygom.model._tau_leap"; +static const char __pyx_k_Cannot_index_with_type[] = "Cannot index with type '"; +static const char __pyx_k_MemoryView_of_r_object[] = ""; +static const char __pyx_k_MemoryView_of_r_at_0x_x[] = ""; +static const char __pyx_k_contiguous_and_indirect[] = ""; +static const char __pyx_k_cy_test_tau_leap_safety[] = "_cy_test_tau_leap_safety"; +static const char __pyx_k_Dimension_d_is_not_direct[] = "Dimension %d is not direct"; +static const char __pyx_k_Index_out_of_bounds_axis_d[] = "Index out of bounds (axis %d)"; +static const char __pyx_k_Step_may_not_be_zero_axis_d[] = "Step may not be zero (axis %d)"; +static const char __pyx_k_itemsize_0_for_cython_array[] = "itemsize <= 0 for cython.array"; +static const char __pyx_k_src_pygom_model__tau_leap_pyx[] = "src\\pygom\\model\\_tau_leap.pyx"; +static const char __pyx_k_unable_to_allocate_array_data[] = "unable to allocate array data."; +static const char __pyx_k_strided_and_direct_or_indirect[] = ""; +static const char __pyx_k_All_dimensions_preceding_dimensi[] = "All dimensions preceding dimension %d must be indexed and not sliced"; +static const char __pyx_k_Buffer_view_does_not_expose_stri[] = "Buffer view does not expose strides"; +static const char __pyx_k_Can_only_create_a_buffer_that_is[] = "Can only create a buffer that is contiguous in memory."; +static const char __pyx_k_Cannot_assign_to_read_only_memor[] = "Cannot assign to read-only memoryview"; +static const char __pyx_k_Cannot_create_writable_memory_vi[] = "Cannot create writable memory view from read-only memoryview"; +static const char __pyx_k_Cannot_transpose_memoryview_with[] = "Cannot transpose memoryview with indirect dimensions"; +static const char __pyx_k_Empty_shape_tuple_for_cython_arr[] = "Empty shape tuple for cython.array"; +static const char __pyx_k_Incompatible_checksums_0x_x_vs_0[] = "Incompatible checksums (0x%x vs (0x82a3537, 0x6ae9995, 0xb068931) = (name))"; +static const char __pyx_k_Indirect_dimensions_not_supporte[] = "Indirect dimensions not supported"; +static const char __pyx_k_Invalid_mode_expected_c_or_fortr[] = "Invalid mode, expected 'c' or 'fortran', got "; +static const char __pyx_k_Out_of_bounds_on_buffer_access_a[] = "Out of bounds on buffer access (axis "; +static const char __pyx_k_Unable_to_convert_item_to_object[] = "Unable to convert item to object"; +static const char __pyx_k_got_differing_extents_in_dimensi[] = "got differing extents in dimension "; +static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__"; +static const char __pyx_k_numpy__core_multiarray_failed_to[] = "numpy._core.multiarray failed to import"; +static const char __pyx_k_numpy__core_umath_failed_to_impo[] = "numpy._core.umath failed to import"; +static const char __pyx_k_unable_to_allocate_shape_and_str[] = "unable to allocate shape and strides."; +/* #### Code section: decls ### */ +static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array___cinit__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_shape, Py_ssize_t __pyx_v_itemsize, PyObject *__pyx_v_format, PyObject *__pyx_v_mode, int __pyx_v_allocate_buffer); /* proto */ +static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_2__getbuffer__(struct __pyx_array_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */ +static void __pyx_array___pyx_pf_15View_dot_MemoryView_5array_4__dealloc__(struct __pyx_array_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_5array_7memview___get__(struct __pyx_array_obj *__pyx_v_self); /* proto */ +static Py_ssize_t __pyx_array___pyx_pf_15View_dot_MemoryView_5array_6__len__(struct __pyx_array_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_8__getattr__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_attr); /* proto */ +static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_10__getitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item); /* proto */ +static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_12__setitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item, PyObject *__pyx_v_value); /* proto */ +static PyObject *__pyx_pf___pyx_array___reduce_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_array_2__setstate_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */ +static int __pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum___init__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v_name); /* proto */ +static PyObject *__pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum_2__repr__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_MemviewEnum___reduce_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_MemviewEnum_2__setstate_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* proto */ +static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview___cinit__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj, int __pyx_v_flags, int __pyx_v_dtype_is_object); /* proto */ +static void __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_2__dealloc__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_4__getitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto */ +static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_6__setitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto */ +static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_8__getbuffer__(struct __pyx_memoryview_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_1T___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4base___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_5shape___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_7strides___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_10suboffsets___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4ndim___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_8itemsize___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_6nbytes___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4size___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static Py_ssize_t __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_10__len__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_12__repr__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_14__str__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_16is_c_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_18is_f_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_20copy(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_22copy_fortran(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryview___reduce_cython__(CYTHON_UNUSED struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryview_2__setstate_cython__(CYTHON_UNUSED struct __pyx_memoryview_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */ +static void __pyx_memoryviewslice___pyx_pf_15View_dot_MemoryView_16_memoryviewslice___dealloc__(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryviewslice___reduce_cython__(CYTHON_UNUSED struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryviewslice_2__setstate_cython__(CYTHON_UNUSED struct __pyx_memoryviewslice_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView___pyx_unpickle_Enum(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */ +static PyObject *__pyx_pf_5pygom_5model_9_tau_leap__cy_test_tau_leap_safety(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_reactant_mat, PyArrayObject *__pyx_v_rates, double __pyx_v_tau_scale, double __pyx_v_epsilon); /* proto */ +static PyObject *__pyx_tp_new_array(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +/* #### Code section: late_includes ### */ +/* #### Code section: module_state ### */ +typedef struct { + PyObject *__pyx_d; + PyObject *__pyx_b; + PyObject *__pyx_cython_runtime; + PyObject *__pyx_empty_tuple; + PyObject *__pyx_empty_bytes; + PyObject *__pyx_empty_unicode; + #ifdef __Pyx_CyFunction_USED + PyTypeObject *__pyx_CyFunctionType; + #endif + #ifdef __Pyx_FusedFunction_USED + PyTypeObject *__pyx_FusedFunctionType; + #endif + #ifdef __Pyx_Generator_USED + PyTypeObject *__pyx_GeneratorType; + #endif + #ifdef __Pyx_IterableCoroutine_USED + PyTypeObject *__pyx_IterableCoroutineType; + #endif + #ifdef __Pyx_Coroutine_USED + PyTypeObject *__pyx_CoroutineAwaitType; + #endif + #ifdef __Pyx_Coroutine_USED + PyTypeObject *__pyx_CoroutineType; + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + PyTypeObject *__pyx_ptype_7cpython_4type_type; + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + PyTypeObject *__pyx_ptype_5numpy_dtype; + PyTypeObject *__pyx_ptype_5numpy_flatiter; + PyTypeObject *__pyx_ptype_5numpy_broadcast; + PyTypeObject *__pyx_ptype_5numpy_ndarray; + PyTypeObject *__pyx_ptype_5numpy_generic; + PyTypeObject *__pyx_ptype_5numpy_number; + PyTypeObject *__pyx_ptype_5numpy_integer; + PyTypeObject *__pyx_ptype_5numpy_signedinteger; + PyTypeObject *__pyx_ptype_5numpy_unsignedinteger; + PyTypeObject *__pyx_ptype_5numpy_inexact; + PyTypeObject *__pyx_ptype_5numpy_floating; + PyTypeObject *__pyx_ptype_5numpy_complexfloating; + PyTypeObject *__pyx_ptype_5numpy_flexible; + PyTypeObject *__pyx_ptype_5numpy_character; + PyTypeObject *__pyx_ptype_5numpy_ufunc; + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + #endif + #if CYTHON_USE_MODULE_STATE + PyObject *__pyx_type___pyx_array; + PyObject *__pyx_type___pyx_MemviewEnum; + PyObject *__pyx_type___pyx_memoryview; + PyObject *__pyx_type___pyx_memoryviewslice; + #endif + PyTypeObject *__pyx_array_type; + PyTypeObject *__pyx_MemviewEnum_type; + PyTypeObject *__pyx_memoryview_type; + PyTypeObject *__pyx_memoryviewslice_type; + PyObject *__pyx_kp_u_; + PyObject *__pyx_n_s_ASCII; + PyObject *__pyx_kp_s_All_dimensions_preceding_dimensi; + PyObject *__pyx_n_s_AssertionError; + PyObject *__pyx_kp_s_Buffer_view_does_not_expose_stri; + PyObject *__pyx_kp_s_Can_only_create_a_buffer_that_is; + PyObject *__pyx_kp_s_Cannot_assign_to_read_only_memor; + PyObject *__pyx_kp_s_Cannot_create_writable_memory_vi; + PyObject *__pyx_kp_u_Cannot_index_with_type; + PyObject *__pyx_kp_s_Cannot_transpose_memoryview_with; + PyObject *__pyx_kp_s_Dimension_d_is_not_direct; + PyObject *__pyx_n_s_Ellipsis; + PyObject *__pyx_kp_s_Empty_shape_tuple_for_cython_arr; + PyObject *__pyx_n_s_ImportError; + PyObject *__pyx_kp_s_Incompatible_checksums_0x_x_vs_0; + PyObject *__pyx_n_s_IndexError; + PyObject *__pyx_kp_s_Index_out_of_bounds_axis_d; + PyObject *__pyx_kp_s_Indirect_dimensions_not_supporte; + PyObject *__pyx_kp_u_Invalid_mode_expected_c_or_fortr; + PyObject *__pyx_kp_u_Invalid_shape_in_axis; + PyObject *__pyx_n_s_MemoryError; + PyObject *__pyx_kp_s_MemoryView_of_r_at_0x_x; + PyObject *__pyx_kp_s_MemoryView_of_r_object; + PyObject *__pyx_n_b_O; + PyObject *__pyx_kp_u_Out_of_bounds_on_buffer_access_a; + PyObject *__pyx_n_s_PickleError; + PyObject *__pyx_n_s_Sequence; + PyObject *__pyx_kp_s_Step_may_not_be_zero_axis_d; + PyObject *__pyx_n_s_TypeError; + PyObject *__pyx_kp_s_Unable_to_convert_item_to_object; + PyObject *__pyx_n_s_ValueError; + PyObject *__pyx_n_s_View_MemoryView; + PyObject *__pyx_kp_u__2; + PyObject *__pyx_n_s__25; + PyObject *__pyx_n_s__3; + PyObject *__pyx_kp_u__6; + PyObject *__pyx_kp_u__7; + PyObject *__pyx_n_s_abc; + PyObject *__pyx_n_s_allocate_buffer; + PyObject *__pyx_kp_u_and; + PyObject *__pyx_n_s_asyncio_coroutines; + PyObject *__pyx_n_s_base; + PyObject *__pyx_n_s_c; + PyObject *__pyx_n_u_c; + PyObject *__pyx_n_s_cdf_val; + PyObject *__pyx_n_s_class; + PyObject *__pyx_n_s_class_getitem; + PyObject *__pyx_n_s_cline_in_traceback; + PyObject *__pyx_n_s_collections; + PyObject *__pyx_kp_s_collections_abc; + PyObject *__pyx_kp_s_contiguous_and_direct; + PyObject *__pyx_kp_s_contiguous_and_indirect; + PyObject *__pyx_n_s_count; + PyObject *__pyx_kp_u_count_error; + PyObject *__pyx_n_s_cy_test_tau_leap_safety; + PyObject *__pyx_n_s_dict; + PyObject *__pyx_kp_u_disable; + PyObject *__pyx_n_s_dtype_is_object; + PyObject *__pyx_kp_u_enable; + PyObject *__pyx_n_s_encode; + PyObject *__pyx_n_s_enumerate; + PyObject *__pyx_n_s_epsilon; + PyObject *__pyx_n_s_error; + PyObject *__pyx_n_s_flags; + PyObject *__pyx_n_s_format; + PyObject *__pyx_n_s_fortran; + PyObject *__pyx_n_u_fortran; + PyObject *__pyx_kp_u_gc; + PyObject *__pyx_n_s_getstate; + PyObject *__pyx_kp_u_got; + PyObject *__pyx_kp_u_got_differing_extents_in_dimensi; + PyObject *__pyx_n_s_i; + PyObject *__pyx_n_s_id; + PyObject *__pyx_n_s_import; + PyObject *__pyx_n_s_index; + PyObject *__pyx_n_s_initializing; + PyObject *__pyx_n_s_is_coroutine; + PyObject *__pyx_kp_u_isenabled; + PyObject *__pyx_n_s_itemsize; + PyObject *__pyx_kp_s_itemsize_0_for_cython_array; + PyObject *__pyx_n_s_j; + PyObject *__pyx_n_s_main; + PyObject *__pyx_n_s_max_cdf; + PyObject *__pyx_n_s_memview; + PyObject *__pyx_n_s_mode; + PyObject *__pyx_n_s_mu; + PyObject *__pyx_n_s_n_rates; + PyObject *__pyx_n_s_n_reactants; + PyObject *__pyx_n_s_name; + PyObject *__pyx_n_s_name_2; + PyObject *__pyx_n_s_ndim; + PyObject *__pyx_n_s_new; + PyObject *__pyx_n_s_new_cdf; + PyObject *__pyx_kp_s_no_default___reduce___due_to_non; + PyObject *__pyx_n_s_np; + PyObject *__pyx_n_s_numpy; + PyObject *__pyx_kp_u_numpy__core_multiarray_failed_to; + PyObject *__pyx_kp_u_numpy__core_umath_failed_to_impo; + PyObject *__pyx_n_s_obj; + PyObject *__pyx_n_s_pack; + PyObject *__pyx_n_s_pickle; + PyObject *__pyx_n_s_print; + PyObject *__pyx_n_s_pygom_model__tau_leap; + PyObject *__pyx_n_s_pyx_PickleError; + PyObject *__pyx_n_s_pyx_checksum; + PyObject *__pyx_n_s_pyx_result; + PyObject *__pyx_n_s_pyx_state; + PyObject *__pyx_n_s_pyx_type; + PyObject *__pyx_n_s_pyx_unpickle_Enum; + PyObject *__pyx_n_s_pyx_vtable; + PyObject *__pyx_n_s_range; + PyObject *__pyx_n_s_rates; + PyObject *__pyx_n_s_rates_view; + PyObject *__pyx_n_s_reactant_mat; + PyObject *__pyx_n_s_reactant_mat_view; + PyObject *__pyx_n_s_reduce; + PyObject *__pyx_n_s_reduce_cython; + PyObject *__pyx_n_s_reduce_ex; + PyObject *__pyx_n_s_register; + PyObject *__pyx_n_s_safe; + PyObject *__pyx_n_s_setstate; + PyObject *__pyx_n_s_setstate_cython; + PyObject *__pyx_n_s_shape; + PyObject *__pyx_n_s_size; + PyObject *__pyx_n_s_spec; + PyObject *__pyx_kp_s_src_pygom_model__tau_leap_pyx; + PyObject *__pyx_n_s_start; + PyObject *__pyx_n_s_step; + PyObject *__pyx_n_s_stop; + PyObject *__pyx_kp_s_strided_and_direct; + PyObject *__pyx_kp_s_strided_and_direct_or_indirect; + PyObject *__pyx_kp_s_strided_and_indirect; + PyObject *__pyx_kp_s_stringsource; + PyObject *__pyx_n_s_struct; + PyObject *__pyx_n_s_sum; + PyObject *__pyx_n_s_sys; + PyObject *__pyx_n_s_tau_scale; + PyObject *__pyx_n_s_test; + PyObject *__pyx_n_s_total_rate; + PyObject *__pyx_kp_s_unable_to_allocate_array_data; + PyObject *__pyx_kp_s_unable_to_allocate_shape_and_str; + PyObject *__pyx_n_s_unpack; + PyObject *__pyx_n_s_update; + PyObject *__pyx_n_s_version_info; + PyObject *__pyx_n_s_x; + PyObject *__pyx_n_s_x_view; + PyObject *__pyx_int_0; + PyObject *__pyx_int_1; + PyObject *__pyx_int_3; + PyObject *__pyx_int_112105877; + PyObject *__pyx_int_136983863; + PyObject *__pyx_int_184977713; + PyObject *__pyx_int_neg_1; + PyObject *__pyx_slice__5; + PyObject *__pyx_tuple__4; + PyObject *__pyx_tuple__8; + PyObject *__pyx_tuple__9; + PyObject *__pyx_tuple__10; + PyObject *__pyx_tuple__11; + PyObject *__pyx_tuple__12; + PyObject *__pyx_tuple__13; + PyObject *__pyx_tuple__14; + PyObject *__pyx_tuple__15; + PyObject *__pyx_tuple__16; + PyObject *__pyx_tuple__17; + PyObject *__pyx_tuple__18; + PyObject *__pyx_tuple__19; + PyObject *__pyx_tuple__20; + PyObject *__pyx_tuple__21; + PyObject *__pyx_tuple__23; + PyObject *__pyx_codeobj__22; + PyObject *__pyx_codeobj__24; +} __pyx_mstate; + +#if CYTHON_USE_MODULE_STATE +#ifdef __cplusplus +namespace { + extern struct PyModuleDef __pyx_moduledef; +} /* anonymous namespace */ +#else +static struct PyModuleDef __pyx_moduledef; +#endif + +#define __pyx_mstate(o) ((__pyx_mstate *)__Pyx_PyModule_GetState(o)) + +#define __pyx_mstate_global (__pyx_mstate(PyState_FindModule(&__pyx_moduledef))) + +#define __pyx_m (PyState_FindModule(&__pyx_moduledef)) +#else +static __pyx_mstate __pyx_mstate_global_static = +#ifdef __cplusplus + {}; +#else + {0}; +#endif +static __pyx_mstate *__pyx_mstate_global = &__pyx_mstate_global_static; +#endif +/* #### Code section: module_state_clear ### */ +#if CYTHON_USE_MODULE_STATE +static int __pyx_m_clear(PyObject *m) { + __pyx_mstate *clear_module_state = __pyx_mstate(m); + if (!clear_module_state) return 0; + Py_CLEAR(clear_module_state->__pyx_d); + Py_CLEAR(clear_module_state->__pyx_b); + Py_CLEAR(clear_module_state->__pyx_cython_runtime); + Py_CLEAR(clear_module_state->__pyx_empty_tuple); + Py_CLEAR(clear_module_state->__pyx_empty_bytes); + Py_CLEAR(clear_module_state->__pyx_empty_unicode); + #ifdef __Pyx_CyFunction_USED + Py_CLEAR(clear_module_state->__pyx_CyFunctionType); + #endif + #ifdef __Pyx_FusedFunction_USED + Py_CLEAR(clear_module_state->__pyx_FusedFunctionType); + #endif + Py_CLEAR(clear_module_state->__pyx_ptype_7cpython_4type_type); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_dtype); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_flatiter); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_broadcast); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_ndarray); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_generic); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_number); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_integer); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_signedinteger); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_unsignedinteger); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_inexact); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_floating); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_complexfloating); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_flexible); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_character); + Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_ufunc); + Py_CLEAR(clear_module_state->__pyx_array_type); + Py_CLEAR(clear_module_state->__pyx_type___pyx_array); + Py_CLEAR(clear_module_state->__pyx_MemviewEnum_type); + Py_CLEAR(clear_module_state->__pyx_type___pyx_MemviewEnum); + Py_CLEAR(clear_module_state->__pyx_memoryview_type); + Py_CLEAR(clear_module_state->__pyx_type___pyx_memoryview); + Py_CLEAR(clear_module_state->__pyx_memoryviewslice_type); + Py_CLEAR(clear_module_state->__pyx_type___pyx_memoryviewslice); + Py_CLEAR(clear_module_state->__pyx_kp_u_); + Py_CLEAR(clear_module_state->__pyx_n_s_ASCII); + Py_CLEAR(clear_module_state->__pyx_kp_s_All_dimensions_preceding_dimensi); + Py_CLEAR(clear_module_state->__pyx_n_s_AssertionError); + Py_CLEAR(clear_module_state->__pyx_kp_s_Buffer_view_does_not_expose_stri); + Py_CLEAR(clear_module_state->__pyx_kp_s_Can_only_create_a_buffer_that_is); + Py_CLEAR(clear_module_state->__pyx_kp_s_Cannot_assign_to_read_only_memor); + Py_CLEAR(clear_module_state->__pyx_kp_s_Cannot_create_writable_memory_vi); + Py_CLEAR(clear_module_state->__pyx_kp_u_Cannot_index_with_type); + Py_CLEAR(clear_module_state->__pyx_kp_s_Cannot_transpose_memoryview_with); + Py_CLEAR(clear_module_state->__pyx_kp_s_Dimension_d_is_not_direct); + Py_CLEAR(clear_module_state->__pyx_n_s_Ellipsis); + Py_CLEAR(clear_module_state->__pyx_kp_s_Empty_shape_tuple_for_cython_arr); + Py_CLEAR(clear_module_state->__pyx_n_s_ImportError); + Py_CLEAR(clear_module_state->__pyx_kp_s_Incompatible_checksums_0x_x_vs_0); + Py_CLEAR(clear_module_state->__pyx_n_s_IndexError); + Py_CLEAR(clear_module_state->__pyx_kp_s_Index_out_of_bounds_axis_d); + Py_CLEAR(clear_module_state->__pyx_kp_s_Indirect_dimensions_not_supporte); + Py_CLEAR(clear_module_state->__pyx_kp_u_Invalid_mode_expected_c_or_fortr); + Py_CLEAR(clear_module_state->__pyx_kp_u_Invalid_shape_in_axis); + Py_CLEAR(clear_module_state->__pyx_n_s_MemoryError); + Py_CLEAR(clear_module_state->__pyx_kp_s_MemoryView_of_r_at_0x_x); + Py_CLEAR(clear_module_state->__pyx_kp_s_MemoryView_of_r_object); + Py_CLEAR(clear_module_state->__pyx_n_b_O); + Py_CLEAR(clear_module_state->__pyx_kp_u_Out_of_bounds_on_buffer_access_a); + Py_CLEAR(clear_module_state->__pyx_n_s_PickleError); + Py_CLEAR(clear_module_state->__pyx_n_s_Sequence); + Py_CLEAR(clear_module_state->__pyx_kp_s_Step_may_not_be_zero_axis_d); + Py_CLEAR(clear_module_state->__pyx_n_s_TypeError); + Py_CLEAR(clear_module_state->__pyx_kp_s_Unable_to_convert_item_to_object); + Py_CLEAR(clear_module_state->__pyx_n_s_ValueError); + Py_CLEAR(clear_module_state->__pyx_n_s_View_MemoryView); + Py_CLEAR(clear_module_state->__pyx_kp_u__2); + Py_CLEAR(clear_module_state->__pyx_n_s__25); + Py_CLEAR(clear_module_state->__pyx_n_s__3); + Py_CLEAR(clear_module_state->__pyx_kp_u__6); + Py_CLEAR(clear_module_state->__pyx_kp_u__7); + Py_CLEAR(clear_module_state->__pyx_n_s_abc); + Py_CLEAR(clear_module_state->__pyx_n_s_allocate_buffer); + Py_CLEAR(clear_module_state->__pyx_kp_u_and); + Py_CLEAR(clear_module_state->__pyx_n_s_asyncio_coroutines); + Py_CLEAR(clear_module_state->__pyx_n_s_base); + Py_CLEAR(clear_module_state->__pyx_n_s_c); + Py_CLEAR(clear_module_state->__pyx_n_u_c); + Py_CLEAR(clear_module_state->__pyx_n_s_cdf_val); + Py_CLEAR(clear_module_state->__pyx_n_s_class); + Py_CLEAR(clear_module_state->__pyx_n_s_class_getitem); + Py_CLEAR(clear_module_state->__pyx_n_s_cline_in_traceback); + Py_CLEAR(clear_module_state->__pyx_n_s_collections); + Py_CLEAR(clear_module_state->__pyx_kp_s_collections_abc); + Py_CLEAR(clear_module_state->__pyx_kp_s_contiguous_and_direct); + Py_CLEAR(clear_module_state->__pyx_kp_s_contiguous_and_indirect); + Py_CLEAR(clear_module_state->__pyx_n_s_count); + Py_CLEAR(clear_module_state->__pyx_kp_u_count_error); + Py_CLEAR(clear_module_state->__pyx_n_s_cy_test_tau_leap_safety); + Py_CLEAR(clear_module_state->__pyx_n_s_dict); + Py_CLEAR(clear_module_state->__pyx_kp_u_disable); + Py_CLEAR(clear_module_state->__pyx_n_s_dtype_is_object); + Py_CLEAR(clear_module_state->__pyx_kp_u_enable); + Py_CLEAR(clear_module_state->__pyx_n_s_encode); + Py_CLEAR(clear_module_state->__pyx_n_s_enumerate); + Py_CLEAR(clear_module_state->__pyx_n_s_epsilon); + Py_CLEAR(clear_module_state->__pyx_n_s_error); + Py_CLEAR(clear_module_state->__pyx_n_s_flags); + Py_CLEAR(clear_module_state->__pyx_n_s_format); + Py_CLEAR(clear_module_state->__pyx_n_s_fortran); + Py_CLEAR(clear_module_state->__pyx_n_u_fortran); + Py_CLEAR(clear_module_state->__pyx_kp_u_gc); + Py_CLEAR(clear_module_state->__pyx_n_s_getstate); + Py_CLEAR(clear_module_state->__pyx_kp_u_got); + Py_CLEAR(clear_module_state->__pyx_kp_u_got_differing_extents_in_dimensi); + Py_CLEAR(clear_module_state->__pyx_n_s_i); + Py_CLEAR(clear_module_state->__pyx_n_s_id); + Py_CLEAR(clear_module_state->__pyx_n_s_import); + Py_CLEAR(clear_module_state->__pyx_n_s_index); + Py_CLEAR(clear_module_state->__pyx_n_s_initializing); + Py_CLEAR(clear_module_state->__pyx_n_s_is_coroutine); + Py_CLEAR(clear_module_state->__pyx_kp_u_isenabled); + Py_CLEAR(clear_module_state->__pyx_n_s_itemsize); + Py_CLEAR(clear_module_state->__pyx_kp_s_itemsize_0_for_cython_array); + Py_CLEAR(clear_module_state->__pyx_n_s_j); + Py_CLEAR(clear_module_state->__pyx_n_s_main); + Py_CLEAR(clear_module_state->__pyx_n_s_max_cdf); + Py_CLEAR(clear_module_state->__pyx_n_s_memview); + Py_CLEAR(clear_module_state->__pyx_n_s_mode); + Py_CLEAR(clear_module_state->__pyx_n_s_mu); + Py_CLEAR(clear_module_state->__pyx_n_s_n_rates); + Py_CLEAR(clear_module_state->__pyx_n_s_n_reactants); + Py_CLEAR(clear_module_state->__pyx_n_s_name); + Py_CLEAR(clear_module_state->__pyx_n_s_name_2); + Py_CLEAR(clear_module_state->__pyx_n_s_ndim); + Py_CLEAR(clear_module_state->__pyx_n_s_new); + Py_CLEAR(clear_module_state->__pyx_n_s_new_cdf); + Py_CLEAR(clear_module_state->__pyx_kp_s_no_default___reduce___due_to_non); + Py_CLEAR(clear_module_state->__pyx_n_s_np); + Py_CLEAR(clear_module_state->__pyx_n_s_numpy); + Py_CLEAR(clear_module_state->__pyx_kp_u_numpy__core_multiarray_failed_to); + Py_CLEAR(clear_module_state->__pyx_kp_u_numpy__core_umath_failed_to_impo); + Py_CLEAR(clear_module_state->__pyx_n_s_obj); + Py_CLEAR(clear_module_state->__pyx_n_s_pack); + Py_CLEAR(clear_module_state->__pyx_n_s_pickle); + Py_CLEAR(clear_module_state->__pyx_n_s_print); + Py_CLEAR(clear_module_state->__pyx_n_s_pygom_model__tau_leap); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_PickleError); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_checksum); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_result); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_state); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_type); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_unpickle_Enum); + Py_CLEAR(clear_module_state->__pyx_n_s_pyx_vtable); + Py_CLEAR(clear_module_state->__pyx_n_s_range); + Py_CLEAR(clear_module_state->__pyx_n_s_rates); + Py_CLEAR(clear_module_state->__pyx_n_s_rates_view); + Py_CLEAR(clear_module_state->__pyx_n_s_reactant_mat); + Py_CLEAR(clear_module_state->__pyx_n_s_reactant_mat_view); + Py_CLEAR(clear_module_state->__pyx_n_s_reduce); + Py_CLEAR(clear_module_state->__pyx_n_s_reduce_cython); + Py_CLEAR(clear_module_state->__pyx_n_s_reduce_ex); + Py_CLEAR(clear_module_state->__pyx_n_s_register); + Py_CLEAR(clear_module_state->__pyx_n_s_safe); + Py_CLEAR(clear_module_state->__pyx_n_s_setstate); + Py_CLEAR(clear_module_state->__pyx_n_s_setstate_cython); + Py_CLEAR(clear_module_state->__pyx_n_s_shape); + Py_CLEAR(clear_module_state->__pyx_n_s_size); + Py_CLEAR(clear_module_state->__pyx_n_s_spec); + Py_CLEAR(clear_module_state->__pyx_kp_s_src_pygom_model__tau_leap_pyx); + Py_CLEAR(clear_module_state->__pyx_n_s_start); + Py_CLEAR(clear_module_state->__pyx_n_s_step); + Py_CLEAR(clear_module_state->__pyx_n_s_stop); + Py_CLEAR(clear_module_state->__pyx_kp_s_strided_and_direct); + Py_CLEAR(clear_module_state->__pyx_kp_s_strided_and_direct_or_indirect); + Py_CLEAR(clear_module_state->__pyx_kp_s_strided_and_indirect); + Py_CLEAR(clear_module_state->__pyx_kp_s_stringsource); + Py_CLEAR(clear_module_state->__pyx_n_s_struct); + Py_CLEAR(clear_module_state->__pyx_n_s_sum); + Py_CLEAR(clear_module_state->__pyx_n_s_sys); + Py_CLEAR(clear_module_state->__pyx_n_s_tau_scale); + Py_CLEAR(clear_module_state->__pyx_n_s_test); + Py_CLEAR(clear_module_state->__pyx_n_s_total_rate); + Py_CLEAR(clear_module_state->__pyx_kp_s_unable_to_allocate_array_data); + Py_CLEAR(clear_module_state->__pyx_kp_s_unable_to_allocate_shape_and_str); + Py_CLEAR(clear_module_state->__pyx_n_s_unpack); + Py_CLEAR(clear_module_state->__pyx_n_s_update); + Py_CLEAR(clear_module_state->__pyx_n_s_version_info); + Py_CLEAR(clear_module_state->__pyx_n_s_x); + Py_CLEAR(clear_module_state->__pyx_n_s_x_view); + Py_CLEAR(clear_module_state->__pyx_int_0); + Py_CLEAR(clear_module_state->__pyx_int_1); + Py_CLEAR(clear_module_state->__pyx_int_3); + Py_CLEAR(clear_module_state->__pyx_int_112105877); + Py_CLEAR(clear_module_state->__pyx_int_136983863); + Py_CLEAR(clear_module_state->__pyx_int_184977713); + Py_CLEAR(clear_module_state->__pyx_int_neg_1); + Py_CLEAR(clear_module_state->__pyx_slice__5); + Py_CLEAR(clear_module_state->__pyx_tuple__4); + Py_CLEAR(clear_module_state->__pyx_tuple__8); + Py_CLEAR(clear_module_state->__pyx_tuple__9); + Py_CLEAR(clear_module_state->__pyx_tuple__10); + Py_CLEAR(clear_module_state->__pyx_tuple__11); + Py_CLEAR(clear_module_state->__pyx_tuple__12); + Py_CLEAR(clear_module_state->__pyx_tuple__13); + Py_CLEAR(clear_module_state->__pyx_tuple__14); + Py_CLEAR(clear_module_state->__pyx_tuple__15); + Py_CLEAR(clear_module_state->__pyx_tuple__16); + Py_CLEAR(clear_module_state->__pyx_tuple__17); + Py_CLEAR(clear_module_state->__pyx_tuple__18); + Py_CLEAR(clear_module_state->__pyx_tuple__19); + Py_CLEAR(clear_module_state->__pyx_tuple__20); + Py_CLEAR(clear_module_state->__pyx_tuple__21); + Py_CLEAR(clear_module_state->__pyx_tuple__23); + Py_CLEAR(clear_module_state->__pyx_codeobj__22); + Py_CLEAR(clear_module_state->__pyx_codeobj__24); + return 0; +} +#endif +/* #### Code section: module_state_traverse ### */ +#if CYTHON_USE_MODULE_STATE +static int __pyx_m_traverse(PyObject *m, visitproc visit, void *arg) { + __pyx_mstate *traverse_module_state = __pyx_mstate(m); + if (!traverse_module_state) return 0; + Py_VISIT(traverse_module_state->__pyx_d); + Py_VISIT(traverse_module_state->__pyx_b); + Py_VISIT(traverse_module_state->__pyx_cython_runtime); + Py_VISIT(traverse_module_state->__pyx_empty_tuple); + Py_VISIT(traverse_module_state->__pyx_empty_bytes); + Py_VISIT(traverse_module_state->__pyx_empty_unicode); + #ifdef __Pyx_CyFunction_USED + Py_VISIT(traverse_module_state->__pyx_CyFunctionType); + #endif + #ifdef __Pyx_FusedFunction_USED + Py_VISIT(traverse_module_state->__pyx_FusedFunctionType); + #endif + Py_VISIT(traverse_module_state->__pyx_ptype_7cpython_4type_type); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_dtype); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_flatiter); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_broadcast); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_ndarray); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_generic); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_number); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_integer); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_signedinteger); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_unsignedinteger); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_inexact); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_floating); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_complexfloating); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_flexible); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_character); + Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_ufunc); + Py_VISIT(traverse_module_state->__pyx_array_type); + Py_VISIT(traverse_module_state->__pyx_type___pyx_array); + Py_VISIT(traverse_module_state->__pyx_MemviewEnum_type); + Py_VISIT(traverse_module_state->__pyx_type___pyx_MemviewEnum); + Py_VISIT(traverse_module_state->__pyx_memoryview_type); + Py_VISIT(traverse_module_state->__pyx_type___pyx_memoryview); + Py_VISIT(traverse_module_state->__pyx_memoryviewslice_type); + Py_VISIT(traverse_module_state->__pyx_type___pyx_memoryviewslice); + Py_VISIT(traverse_module_state->__pyx_kp_u_); + Py_VISIT(traverse_module_state->__pyx_n_s_ASCII); + Py_VISIT(traverse_module_state->__pyx_kp_s_All_dimensions_preceding_dimensi); + Py_VISIT(traverse_module_state->__pyx_n_s_AssertionError); + Py_VISIT(traverse_module_state->__pyx_kp_s_Buffer_view_does_not_expose_stri); + Py_VISIT(traverse_module_state->__pyx_kp_s_Can_only_create_a_buffer_that_is); + Py_VISIT(traverse_module_state->__pyx_kp_s_Cannot_assign_to_read_only_memor); + Py_VISIT(traverse_module_state->__pyx_kp_s_Cannot_create_writable_memory_vi); + Py_VISIT(traverse_module_state->__pyx_kp_u_Cannot_index_with_type); + Py_VISIT(traverse_module_state->__pyx_kp_s_Cannot_transpose_memoryview_with); + Py_VISIT(traverse_module_state->__pyx_kp_s_Dimension_d_is_not_direct); + Py_VISIT(traverse_module_state->__pyx_n_s_Ellipsis); + Py_VISIT(traverse_module_state->__pyx_kp_s_Empty_shape_tuple_for_cython_arr); + Py_VISIT(traverse_module_state->__pyx_n_s_ImportError); + Py_VISIT(traverse_module_state->__pyx_kp_s_Incompatible_checksums_0x_x_vs_0); + Py_VISIT(traverse_module_state->__pyx_n_s_IndexError); + Py_VISIT(traverse_module_state->__pyx_kp_s_Index_out_of_bounds_axis_d); + Py_VISIT(traverse_module_state->__pyx_kp_s_Indirect_dimensions_not_supporte); + Py_VISIT(traverse_module_state->__pyx_kp_u_Invalid_mode_expected_c_or_fortr); + Py_VISIT(traverse_module_state->__pyx_kp_u_Invalid_shape_in_axis); + Py_VISIT(traverse_module_state->__pyx_n_s_MemoryError); + Py_VISIT(traverse_module_state->__pyx_kp_s_MemoryView_of_r_at_0x_x); + Py_VISIT(traverse_module_state->__pyx_kp_s_MemoryView_of_r_object); + Py_VISIT(traverse_module_state->__pyx_n_b_O); + Py_VISIT(traverse_module_state->__pyx_kp_u_Out_of_bounds_on_buffer_access_a); + Py_VISIT(traverse_module_state->__pyx_n_s_PickleError); + Py_VISIT(traverse_module_state->__pyx_n_s_Sequence); + Py_VISIT(traverse_module_state->__pyx_kp_s_Step_may_not_be_zero_axis_d); + Py_VISIT(traverse_module_state->__pyx_n_s_TypeError); + Py_VISIT(traverse_module_state->__pyx_kp_s_Unable_to_convert_item_to_object); + Py_VISIT(traverse_module_state->__pyx_n_s_ValueError); + Py_VISIT(traverse_module_state->__pyx_n_s_View_MemoryView); + Py_VISIT(traverse_module_state->__pyx_kp_u__2); + Py_VISIT(traverse_module_state->__pyx_n_s__25); + Py_VISIT(traverse_module_state->__pyx_n_s__3); + Py_VISIT(traverse_module_state->__pyx_kp_u__6); + Py_VISIT(traverse_module_state->__pyx_kp_u__7); + Py_VISIT(traverse_module_state->__pyx_n_s_abc); + Py_VISIT(traverse_module_state->__pyx_n_s_allocate_buffer); + Py_VISIT(traverse_module_state->__pyx_kp_u_and); + Py_VISIT(traverse_module_state->__pyx_n_s_asyncio_coroutines); + Py_VISIT(traverse_module_state->__pyx_n_s_base); + Py_VISIT(traverse_module_state->__pyx_n_s_c); + Py_VISIT(traverse_module_state->__pyx_n_u_c); + Py_VISIT(traverse_module_state->__pyx_n_s_cdf_val); + Py_VISIT(traverse_module_state->__pyx_n_s_class); + Py_VISIT(traverse_module_state->__pyx_n_s_class_getitem); + Py_VISIT(traverse_module_state->__pyx_n_s_cline_in_traceback); + Py_VISIT(traverse_module_state->__pyx_n_s_collections); + Py_VISIT(traverse_module_state->__pyx_kp_s_collections_abc); + Py_VISIT(traverse_module_state->__pyx_kp_s_contiguous_and_direct); + Py_VISIT(traverse_module_state->__pyx_kp_s_contiguous_and_indirect); + Py_VISIT(traverse_module_state->__pyx_n_s_count); + Py_VISIT(traverse_module_state->__pyx_kp_u_count_error); + Py_VISIT(traverse_module_state->__pyx_n_s_cy_test_tau_leap_safety); + Py_VISIT(traverse_module_state->__pyx_n_s_dict); + Py_VISIT(traverse_module_state->__pyx_kp_u_disable); + Py_VISIT(traverse_module_state->__pyx_n_s_dtype_is_object); + Py_VISIT(traverse_module_state->__pyx_kp_u_enable); + Py_VISIT(traverse_module_state->__pyx_n_s_encode); + Py_VISIT(traverse_module_state->__pyx_n_s_enumerate); + Py_VISIT(traverse_module_state->__pyx_n_s_epsilon); + Py_VISIT(traverse_module_state->__pyx_n_s_error); + Py_VISIT(traverse_module_state->__pyx_n_s_flags); + Py_VISIT(traverse_module_state->__pyx_n_s_format); + Py_VISIT(traverse_module_state->__pyx_n_s_fortran); + Py_VISIT(traverse_module_state->__pyx_n_u_fortran); + Py_VISIT(traverse_module_state->__pyx_kp_u_gc); + Py_VISIT(traverse_module_state->__pyx_n_s_getstate); + Py_VISIT(traverse_module_state->__pyx_kp_u_got); + Py_VISIT(traverse_module_state->__pyx_kp_u_got_differing_extents_in_dimensi); + Py_VISIT(traverse_module_state->__pyx_n_s_i); + Py_VISIT(traverse_module_state->__pyx_n_s_id); + Py_VISIT(traverse_module_state->__pyx_n_s_import); + Py_VISIT(traverse_module_state->__pyx_n_s_index); + Py_VISIT(traverse_module_state->__pyx_n_s_initializing); + Py_VISIT(traverse_module_state->__pyx_n_s_is_coroutine); + Py_VISIT(traverse_module_state->__pyx_kp_u_isenabled); + Py_VISIT(traverse_module_state->__pyx_n_s_itemsize); + Py_VISIT(traverse_module_state->__pyx_kp_s_itemsize_0_for_cython_array); + Py_VISIT(traverse_module_state->__pyx_n_s_j); + Py_VISIT(traverse_module_state->__pyx_n_s_main); + Py_VISIT(traverse_module_state->__pyx_n_s_max_cdf); + Py_VISIT(traverse_module_state->__pyx_n_s_memview); + Py_VISIT(traverse_module_state->__pyx_n_s_mode); + Py_VISIT(traverse_module_state->__pyx_n_s_mu); + Py_VISIT(traverse_module_state->__pyx_n_s_n_rates); + Py_VISIT(traverse_module_state->__pyx_n_s_n_reactants); + Py_VISIT(traverse_module_state->__pyx_n_s_name); + Py_VISIT(traverse_module_state->__pyx_n_s_name_2); + Py_VISIT(traverse_module_state->__pyx_n_s_ndim); + Py_VISIT(traverse_module_state->__pyx_n_s_new); + Py_VISIT(traverse_module_state->__pyx_n_s_new_cdf); + Py_VISIT(traverse_module_state->__pyx_kp_s_no_default___reduce___due_to_non); + Py_VISIT(traverse_module_state->__pyx_n_s_np); + Py_VISIT(traverse_module_state->__pyx_n_s_numpy); + Py_VISIT(traverse_module_state->__pyx_kp_u_numpy__core_multiarray_failed_to); + Py_VISIT(traverse_module_state->__pyx_kp_u_numpy__core_umath_failed_to_impo); + Py_VISIT(traverse_module_state->__pyx_n_s_obj); + Py_VISIT(traverse_module_state->__pyx_n_s_pack); + Py_VISIT(traverse_module_state->__pyx_n_s_pickle); + Py_VISIT(traverse_module_state->__pyx_n_s_print); + Py_VISIT(traverse_module_state->__pyx_n_s_pygom_model__tau_leap); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_PickleError); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_checksum); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_result); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_state); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_type); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_unpickle_Enum); + Py_VISIT(traverse_module_state->__pyx_n_s_pyx_vtable); + Py_VISIT(traverse_module_state->__pyx_n_s_range); + Py_VISIT(traverse_module_state->__pyx_n_s_rates); + Py_VISIT(traverse_module_state->__pyx_n_s_rates_view); + Py_VISIT(traverse_module_state->__pyx_n_s_reactant_mat); + Py_VISIT(traverse_module_state->__pyx_n_s_reactant_mat_view); + Py_VISIT(traverse_module_state->__pyx_n_s_reduce); + Py_VISIT(traverse_module_state->__pyx_n_s_reduce_cython); + Py_VISIT(traverse_module_state->__pyx_n_s_reduce_ex); + Py_VISIT(traverse_module_state->__pyx_n_s_register); + Py_VISIT(traverse_module_state->__pyx_n_s_safe); + Py_VISIT(traverse_module_state->__pyx_n_s_setstate); + Py_VISIT(traverse_module_state->__pyx_n_s_setstate_cython); + Py_VISIT(traverse_module_state->__pyx_n_s_shape); + Py_VISIT(traverse_module_state->__pyx_n_s_size); + Py_VISIT(traverse_module_state->__pyx_n_s_spec); + Py_VISIT(traverse_module_state->__pyx_kp_s_src_pygom_model__tau_leap_pyx); + Py_VISIT(traverse_module_state->__pyx_n_s_start); + Py_VISIT(traverse_module_state->__pyx_n_s_step); + Py_VISIT(traverse_module_state->__pyx_n_s_stop); + Py_VISIT(traverse_module_state->__pyx_kp_s_strided_and_direct); + Py_VISIT(traverse_module_state->__pyx_kp_s_strided_and_direct_or_indirect); + Py_VISIT(traverse_module_state->__pyx_kp_s_strided_and_indirect); + Py_VISIT(traverse_module_state->__pyx_kp_s_stringsource); + Py_VISIT(traverse_module_state->__pyx_n_s_struct); + Py_VISIT(traverse_module_state->__pyx_n_s_sum); + Py_VISIT(traverse_module_state->__pyx_n_s_sys); + Py_VISIT(traverse_module_state->__pyx_n_s_tau_scale); + Py_VISIT(traverse_module_state->__pyx_n_s_test); + Py_VISIT(traverse_module_state->__pyx_n_s_total_rate); + Py_VISIT(traverse_module_state->__pyx_kp_s_unable_to_allocate_array_data); + Py_VISIT(traverse_module_state->__pyx_kp_s_unable_to_allocate_shape_and_str); + Py_VISIT(traverse_module_state->__pyx_n_s_unpack); + Py_VISIT(traverse_module_state->__pyx_n_s_update); + Py_VISIT(traverse_module_state->__pyx_n_s_version_info); + Py_VISIT(traverse_module_state->__pyx_n_s_x); + Py_VISIT(traverse_module_state->__pyx_n_s_x_view); + Py_VISIT(traverse_module_state->__pyx_int_0); + Py_VISIT(traverse_module_state->__pyx_int_1); + Py_VISIT(traverse_module_state->__pyx_int_3); + Py_VISIT(traverse_module_state->__pyx_int_112105877); + Py_VISIT(traverse_module_state->__pyx_int_136983863); + Py_VISIT(traverse_module_state->__pyx_int_184977713); + Py_VISIT(traverse_module_state->__pyx_int_neg_1); + Py_VISIT(traverse_module_state->__pyx_slice__5); + Py_VISIT(traverse_module_state->__pyx_tuple__4); + Py_VISIT(traverse_module_state->__pyx_tuple__8); + Py_VISIT(traverse_module_state->__pyx_tuple__9); + Py_VISIT(traverse_module_state->__pyx_tuple__10); + Py_VISIT(traverse_module_state->__pyx_tuple__11); + Py_VISIT(traverse_module_state->__pyx_tuple__12); + Py_VISIT(traverse_module_state->__pyx_tuple__13); + Py_VISIT(traverse_module_state->__pyx_tuple__14); + Py_VISIT(traverse_module_state->__pyx_tuple__15); + Py_VISIT(traverse_module_state->__pyx_tuple__16); + Py_VISIT(traverse_module_state->__pyx_tuple__17); + Py_VISIT(traverse_module_state->__pyx_tuple__18); + Py_VISIT(traverse_module_state->__pyx_tuple__19); + Py_VISIT(traverse_module_state->__pyx_tuple__20); + Py_VISIT(traverse_module_state->__pyx_tuple__21); + Py_VISIT(traverse_module_state->__pyx_tuple__23); + Py_VISIT(traverse_module_state->__pyx_codeobj__22); + Py_VISIT(traverse_module_state->__pyx_codeobj__24); + return 0; +} +#endif +/* #### Code section: module_state_defines ### */ +#define __pyx_d __pyx_mstate_global->__pyx_d +#define __pyx_b __pyx_mstate_global->__pyx_b +#define __pyx_cython_runtime __pyx_mstate_global->__pyx_cython_runtime +#define __pyx_empty_tuple __pyx_mstate_global->__pyx_empty_tuple +#define __pyx_empty_bytes __pyx_mstate_global->__pyx_empty_bytes +#define __pyx_empty_unicode __pyx_mstate_global->__pyx_empty_unicode +#ifdef __Pyx_CyFunction_USED +#define __pyx_CyFunctionType __pyx_mstate_global->__pyx_CyFunctionType +#endif +#ifdef __Pyx_FusedFunction_USED +#define __pyx_FusedFunctionType __pyx_mstate_global->__pyx_FusedFunctionType +#endif +#ifdef __Pyx_Generator_USED +#define __pyx_GeneratorType __pyx_mstate_global->__pyx_GeneratorType +#endif +#ifdef __Pyx_IterableCoroutine_USED +#define __pyx_IterableCoroutineType __pyx_mstate_global->__pyx_IterableCoroutineType +#endif +#ifdef __Pyx_Coroutine_USED +#define __pyx_CoroutineAwaitType __pyx_mstate_global->__pyx_CoroutineAwaitType +#endif +#ifdef __Pyx_Coroutine_USED +#define __pyx_CoroutineType __pyx_mstate_global->__pyx_CoroutineType +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#define __pyx_ptype_7cpython_4type_type __pyx_mstate_global->__pyx_ptype_7cpython_4type_type +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#define __pyx_ptype_5numpy_dtype __pyx_mstate_global->__pyx_ptype_5numpy_dtype +#define __pyx_ptype_5numpy_flatiter __pyx_mstate_global->__pyx_ptype_5numpy_flatiter +#define __pyx_ptype_5numpy_broadcast __pyx_mstate_global->__pyx_ptype_5numpy_broadcast +#define __pyx_ptype_5numpy_ndarray __pyx_mstate_global->__pyx_ptype_5numpy_ndarray +#define __pyx_ptype_5numpy_generic __pyx_mstate_global->__pyx_ptype_5numpy_generic +#define __pyx_ptype_5numpy_number __pyx_mstate_global->__pyx_ptype_5numpy_number +#define __pyx_ptype_5numpy_integer __pyx_mstate_global->__pyx_ptype_5numpy_integer +#define __pyx_ptype_5numpy_signedinteger __pyx_mstate_global->__pyx_ptype_5numpy_signedinteger +#define __pyx_ptype_5numpy_unsignedinteger __pyx_mstate_global->__pyx_ptype_5numpy_unsignedinteger +#define __pyx_ptype_5numpy_inexact __pyx_mstate_global->__pyx_ptype_5numpy_inexact +#define __pyx_ptype_5numpy_floating __pyx_mstate_global->__pyx_ptype_5numpy_floating +#define __pyx_ptype_5numpy_complexfloating __pyx_mstate_global->__pyx_ptype_5numpy_complexfloating +#define __pyx_ptype_5numpy_flexible __pyx_mstate_global->__pyx_ptype_5numpy_flexible +#define __pyx_ptype_5numpy_character __pyx_mstate_global->__pyx_ptype_5numpy_character +#define __pyx_ptype_5numpy_ufunc __pyx_mstate_global->__pyx_ptype_5numpy_ufunc +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#endif +#if CYTHON_USE_MODULE_STATE +#define __pyx_type___pyx_array __pyx_mstate_global->__pyx_type___pyx_array +#define __pyx_type___pyx_MemviewEnum __pyx_mstate_global->__pyx_type___pyx_MemviewEnum +#define __pyx_type___pyx_memoryview __pyx_mstate_global->__pyx_type___pyx_memoryview +#define __pyx_type___pyx_memoryviewslice __pyx_mstate_global->__pyx_type___pyx_memoryviewslice +#endif +#define __pyx_array_type __pyx_mstate_global->__pyx_array_type +#define __pyx_MemviewEnum_type __pyx_mstate_global->__pyx_MemviewEnum_type +#define __pyx_memoryview_type __pyx_mstate_global->__pyx_memoryview_type +#define __pyx_memoryviewslice_type __pyx_mstate_global->__pyx_memoryviewslice_type +#define __pyx_kp_u_ __pyx_mstate_global->__pyx_kp_u_ +#define __pyx_n_s_ASCII __pyx_mstate_global->__pyx_n_s_ASCII +#define __pyx_kp_s_All_dimensions_preceding_dimensi __pyx_mstate_global->__pyx_kp_s_All_dimensions_preceding_dimensi +#define __pyx_n_s_AssertionError __pyx_mstate_global->__pyx_n_s_AssertionError +#define __pyx_kp_s_Buffer_view_does_not_expose_stri __pyx_mstate_global->__pyx_kp_s_Buffer_view_does_not_expose_stri +#define __pyx_kp_s_Can_only_create_a_buffer_that_is __pyx_mstate_global->__pyx_kp_s_Can_only_create_a_buffer_that_is +#define __pyx_kp_s_Cannot_assign_to_read_only_memor __pyx_mstate_global->__pyx_kp_s_Cannot_assign_to_read_only_memor +#define __pyx_kp_s_Cannot_create_writable_memory_vi __pyx_mstate_global->__pyx_kp_s_Cannot_create_writable_memory_vi +#define __pyx_kp_u_Cannot_index_with_type __pyx_mstate_global->__pyx_kp_u_Cannot_index_with_type +#define __pyx_kp_s_Cannot_transpose_memoryview_with __pyx_mstate_global->__pyx_kp_s_Cannot_transpose_memoryview_with +#define __pyx_kp_s_Dimension_d_is_not_direct __pyx_mstate_global->__pyx_kp_s_Dimension_d_is_not_direct +#define __pyx_n_s_Ellipsis __pyx_mstate_global->__pyx_n_s_Ellipsis +#define __pyx_kp_s_Empty_shape_tuple_for_cython_arr __pyx_mstate_global->__pyx_kp_s_Empty_shape_tuple_for_cython_arr +#define __pyx_n_s_ImportError __pyx_mstate_global->__pyx_n_s_ImportError +#define __pyx_kp_s_Incompatible_checksums_0x_x_vs_0 __pyx_mstate_global->__pyx_kp_s_Incompatible_checksums_0x_x_vs_0 +#define __pyx_n_s_IndexError __pyx_mstate_global->__pyx_n_s_IndexError +#define __pyx_kp_s_Index_out_of_bounds_axis_d __pyx_mstate_global->__pyx_kp_s_Index_out_of_bounds_axis_d +#define __pyx_kp_s_Indirect_dimensions_not_supporte __pyx_mstate_global->__pyx_kp_s_Indirect_dimensions_not_supporte +#define __pyx_kp_u_Invalid_mode_expected_c_or_fortr __pyx_mstate_global->__pyx_kp_u_Invalid_mode_expected_c_or_fortr +#define __pyx_kp_u_Invalid_shape_in_axis __pyx_mstate_global->__pyx_kp_u_Invalid_shape_in_axis +#define __pyx_n_s_MemoryError __pyx_mstate_global->__pyx_n_s_MemoryError +#define __pyx_kp_s_MemoryView_of_r_at_0x_x __pyx_mstate_global->__pyx_kp_s_MemoryView_of_r_at_0x_x +#define __pyx_kp_s_MemoryView_of_r_object __pyx_mstate_global->__pyx_kp_s_MemoryView_of_r_object +#define __pyx_n_b_O __pyx_mstate_global->__pyx_n_b_O +#define __pyx_kp_u_Out_of_bounds_on_buffer_access_a __pyx_mstate_global->__pyx_kp_u_Out_of_bounds_on_buffer_access_a +#define __pyx_n_s_PickleError __pyx_mstate_global->__pyx_n_s_PickleError +#define __pyx_n_s_Sequence __pyx_mstate_global->__pyx_n_s_Sequence +#define __pyx_kp_s_Step_may_not_be_zero_axis_d __pyx_mstate_global->__pyx_kp_s_Step_may_not_be_zero_axis_d +#define __pyx_n_s_TypeError __pyx_mstate_global->__pyx_n_s_TypeError +#define __pyx_kp_s_Unable_to_convert_item_to_object __pyx_mstate_global->__pyx_kp_s_Unable_to_convert_item_to_object +#define __pyx_n_s_ValueError __pyx_mstate_global->__pyx_n_s_ValueError +#define __pyx_n_s_View_MemoryView __pyx_mstate_global->__pyx_n_s_View_MemoryView +#define __pyx_kp_u__2 __pyx_mstate_global->__pyx_kp_u__2 +#define __pyx_n_s__25 __pyx_mstate_global->__pyx_n_s__25 +#define __pyx_n_s__3 __pyx_mstate_global->__pyx_n_s__3 +#define __pyx_kp_u__6 __pyx_mstate_global->__pyx_kp_u__6 +#define __pyx_kp_u__7 __pyx_mstate_global->__pyx_kp_u__7 +#define __pyx_n_s_abc __pyx_mstate_global->__pyx_n_s_abc +#define __pyx_n_s_allocate_buffer __pyx_mstate_global->__pyx_n_s_allocate_buffer +#define __pyx_kp_u_and __pyx_mstate_global->__pyx_kp_u_and +#define __pyx_n_s_asyncio_coroutines __pyx_mstate_global->__pyx_n_s_asyncio_coroutines +#define __pyx_n_s_base __pyx_mstate_global->__pyx_n_s_base +#define __pyx_n_s_c __pyx_mstate_global->__pyx_n_s_c +#define __pyx_n_u_c __pyx_mstate_global->__pyx_n_u_c +#define __pyx_n_s_cdf_val __pyx_mstate_global->__pyx_n_s_cdf_val +#define __pyx_n_s_class __pyx_mstate_global->__pyx_n_s_class +#define __pyx_n_s_class_getitem __pyx_mstate_global->__pyx_n_s_class_getitem +#define __pyx_n_s_cline_in_traceback __pyx_mstate_global->__pyx_n_s_cline_in_traceback +#define __pyx_n_s_collections __pyx_mstate_global->__pyx_n_s_collections +#define __pyx_kp_s_collections_abc __pyx_mstate_global->__pyx_kp_s_collections_abc +#define __pyx_kp_s_contiguous_and_direct __pyx_mstate_global->__pyx_kp_s_contiguous_and_direct +#define __pyx_kp_s_contiguous_and_indirect __pyx_mstate_global->__pyx_kp_s_contiguous_and_indirect +#define __pyx_n_s_count __pyx_mstate_global->__pyx_n_s_count +#define __pyx_kp_u_count_error __pyx_mstate_global->__pyx_kp_u_count_error +#define __pyx_n_s_cy_test_tau_leap_safety __pyx_mstate_global->__pyx_n_s_cy_test_tau_leap_safety +#define __pyx_n_s_dict __pyx_mstate_global->__pyx_n_s_dict +#define __pyx_kp_u_disable __pyx_mstate_global->__pyx_kp_u_disable +#define __pyx_n_s_dtype_is_object __pyx_mstate_global->__pyx_n_s_dtype_is_object +#define __pyx_kp_u_enable __pyx_mstate_global->__pyx_kp_u_enable +#define __pyx_n_s_encode __pyx_mstate_global->__pyx_n_s_encode +#define __pyx_n_s_enumerate __pyx_mstate_global->__pyx_n_s_enumerate +#define __pyx_n_s_epsilon __pyx_mstate_global->__pyx_n_s_epsilon +#define __pyx_n_s_error __pyx_mstate_global->__pyx_n_s_error +#define __pyx_n_s_flags __pyx_mstate_global->__pyx_n_s_flags +#define __pyx_n_s_format __pyx_mstate_global->__pyx_n_s_format +#define __pyx_n_s_fortran __pyx_mstate_global->__pyx_n_s_fortran +#define __pyx_n_u_fortran __pyx_mstate_global->__pyx_n_u_fortran +#define __pyx_kp_u_gc __pyx_mstate_global->__pyx_kp_u_gc +#define __pyx_n_s_getstate __pyx_mstate_global->__pyx_n_s_getstate +#define __pyx_kp_u_got __pyx_mstate_global->__pyx_kp_u_got +#define __pyx_kp_u_got_differing_extents_in_dimensi __pyx_mstate_global->__pyx_kp_u_got_differing_extents_in_dimensi +#define __pyx_n_s_i __pyx_mstate_global->__pyx_n_s_i +#define __pyx_n_s_id __pyx_mstate_global->__pyx_n_s_id +#define __pyx_n_s_import __pyx_mstate_global->__pyx_n_s_import +#define __pyx_n_s_index __pyx_mstate_global->__pyx_n_s_index +#define __pyx_n_s_initializing __pyx_mstate_global->__pyx_n_s_initializing +#define __pyx_n_s_is_coroutine __pyx_mstate_global->__pyx_n_s_is_coroutine +#define __pyx_kp_u_isenabled __pyx_mstate_global->__pyx_kp_u_isenabled +#define __pyx_n_s_itemsize __pyx_mstate_global->__pyx_n_s_itemsize +#define __pyx_kp_s_itemsize_0_for_cython_array __pyx_mstate_global->__pyx_kp_s_itemsize_0_for_cython_array +#define __pyx_n_s_j __pyx_mstate_global->__pyx_n_s_j +#define __pyx_n_s_main __pyx_mstate_global->__pyx_n_s_main +#define __pyx_n_s_max_cdf __pyx_mstate_global->__pyx_n_s_max_cdf +#define __pyx_n_s_memview __pyx_mstate_global->__pyx_n_s_memview +#define __pyx_n_s_mode __pyx_mstate_global->__pyx_n_s_mode +#define __pyx_n_s_mu __pyx_mstate_global->__pyx_n_s_mu +#define __pyx_n_s_n_rates __pyx_mstate_global->__pyx_n_s_n_rates +#define __pyx_n_s_n_reactants __pyx_mstate_global->__pyx_n_s_n_reactants +#define __pyx_n_s_name __pyx_mstate_global->__pyx_n_s_name +#define __pyx_n_s_name_2 __pyx_mstate_global->__pyx_n_s_name_2 +#define __pyx_n_s_ndim __pyx_mstate_global->__pyx_n_s_ndim +#define __pyx_n_s_new __pyx_mstate_global->__pyx_n_s_new +#define __pyx_n_s_new_cdf __pyx_mstate_global->__pyx_n_s_new_cdf +#define __pyx_kp_s_no_default___reduce___due_to_non __pyx_mstate_global->__pyx_kp_s_no_default___reduce___due_to_non +#define __pyx_n_s_np __pyx_mstate_global->__pyx_n_s_np +#define __pyx_n_s_numpy __pyx_mstate_global->__pyx_n_s_numpy +#define __pyx_kp_u_numpy__core_multiarray_failed_to __pyx_mstate_global->__pyx_kp_u_numpy__core_multiarray_failed_to +#define __pyx_kp_u_numpy__core_umath_failed_to_impo __pyx_mstate_global->__pyx_kp_u_numpy__core_umath_failed_to_impo +#define __pyx_n_s_obj __pyx_mstate_global->__pyx_n_s_obj +#define __pyx_n_s_pack __pyx_mstate_global->__pyx_n_s_pack +#define __pyx_n_s_pickle __pyx_mstate_global->__pyx_n_s_pickle +#define __pyx_n_s_print __pyx_mstate_global->__pyx_n_s_print +#define __pyx_n_s_pygom_model__tau_leap __pyx_mstate_global->__pyx_n_s_pygom_model__tau_leap +#define __pyx_n_s_pyx_PickleError __pyx_mstate_global->__pyx_n_s_pyx_PickleError +#define __pyx_n_s_pyx_checksum __pyx_mstate_global->__pyx_n_s_pyx_checksum +#define __pyx_n_s_pyx_result __pyx_mstate_global->__pyx_n_s_pyx_result +#define __pyx_n_s_pyx_state __pyx_mstate_global->__pyx_n_s_pyx_state +#define __pyx_n_s_pyx_type __pyx_mstate_global->__pyx_n_s_pyx_type +#define __pyx_n_s_pyx_unpickle_Enum __pyx_mstate_global->__pyx_n_s_pyx_unpickle_Enum +#define __pyx_n_s_pyx_vtable __pyx_mstate_global->__pyx_n_s_pyx_vtable +#define __pyx_n_s_range __pyx_mstate_global->__pyx_n_s_range +#define __pyx_n_s_rates __pyx_mstate_global->__pyx_n_s_rates +#define __pyx_n_s_rates_view __pyx_mstate_global->__pyx_n_s_rates_view +#define __pyx_n_s_reactant_mat __pyx_mstate_global->__pyx_n_s_reactant_mat +#define __pyx_n_s_reactant_mat_view __pyx_mstate_global->__pyx_n_s_reactant_mat_view +#define __pyx_n_s_reduce __pyx_mstate_global->__pyx_n_s_reduce +#define __pyx_n_s_reduce_cython __pyx_mstate_global->__pyx_n_s_reduce_cython +#define __pyx_n_s_reduce_ex __pyx_mstate_global->__pyx_n_s_reduce_ex +#define __pyx_n_s_register __pyx_mstate_global->__pyx_n_s_register +#define __pyx_n_s_safe __pyx_mstate_global->__pyx_n_s_safe +#define __pyx_n_s_setstate __pyx_mstate_global->__pyx_n_s_setstate +#define __pyx_n_s_setstate_cython __pyx_mstate_global->__pyx_n_s_setstate_cython +#define __pyx_n_s_shape __pyx_mstate_global->__pyx_n_s_shape +#define __pyx_n_s_size __pyx_mstate_global->__pyx_n_s_size +#define __pyx_n_s_spec __pyx_mstate_global->__pyx_n_s_spec +#define __pyx_kp_s_src_pygom_model__tau_leap_pyx __pyx_mstate_global->__pyx_kp_s_src_pygom_model__tau_leap_pyx +#define __pyx_n_s_start __pyx_mstate_global->__pyx_n_s_start +#define __pyx_n_s_step __pyx_mstate_global->__pyx_n_s_step +#define __pyx_n_s_stop __pyx_mstate_global->__pyx_n_s_stop +#define __pyx_kp_s_strided_and_direct __pyx_mstate_global->__pyx_kp_s_strided_and_direct +#define __pyx_kp_s_strided_and_direct_or_indirect __pyx_mstate_global->__pyx_kp_s_strided_and_direct_or_indirect +#define __pyx_kp_s_strided_and_indirect __pyx_mstate_global->__pyx_kp_s_strided_and_indirect +#define __pyx_kp_s_stringsource __pyx_mstate_global->__pyx_kp_s_stringsource +#define __pyx_n_s_struct __pyx_mstate_global->__pyx_n_s_struct +#define __pyx_n_s_sum __pyx_mstate_global->__pyx_n_s_sum +#define __pyx_n_s_sys __pyx_mstate_global->__pyx_n_s_sys +#define __pyx_n_s_tau_scale __pyx_mstate_global->__pyx_n_s_tau_scale +#define __pyx_n_s_test __pyx_mstate_global->__pyx_n_s_test +#define __pyx_n_s_total_rate __pyx_mstate_global->__pyx_n_s_total_rate +#define __pyx_kp_s_unable_to_allocate_array_data __pyx_mstate_global->__pyx_kp_s_unable_to_allocate_array_data +#define __pyx_kp_s_unable_to_allocate_shape_and_str __pyx_mstate_global->__pyx_kp_s_unable_to_allocate_shape_and_str +#define __pyx_n_s_unpack __pyx_mstate_global->__pyx_n_s_unpack +#define __pyx_n_s_update __pyx_mstate_global->__pyx_n_s_update +#define __pyx_n_s_version_info __pyx_mstate_global->__pyx_n_s_version_info +#define __pyx_n_s_x __pyx_mstate_global->__pyx_n_s_x +#define __pyx_n_s_x_view __pyx_mstate_global->__pyx_n_s_x_view +#define __pyx_int_0 __pyx_mstate_global->__pyx_int_0 +#define __pyx_int_1 __pyx_mstate_global->__pyx_int_1 +#define __pyx_int_3 __pyx_mstate_global->__pyx_int_3 +#define __pyx_int_112105877 __pyx_mstate_global->__pyx_int_112105877 +#define __pyx_int_136983863 __pyx_mstate_global->__pyx_int_136983863 +#define __pyx_int_184977713 __pyx_mstate_global->__pyx_int_184977713 +#define __pyx_int_neg_1 __pyx_mstate_global->__pyx_int_neg_1 +#define __pyx_slice__5 __pyx_mstate_global->__pyx_slice__5 +#define __pyx_tuple__4 __pyx_mstate_global->__pyx_tuple__4 +#define __pyx_tuple__8 __pyx_mstate_global->__pyx_tuple__8 +#define __pyx_tuple__9 __pyx_mstate_global->__pyx_tuple__9 +#define __pyx_tuple__10 __pyx_mstate_global->__pyx_tuple__10 +#define __pyx_tuple__11 __pyx_mstate_global->__pyx_tuple__11 +#define __pyx_tuple__12 __pyx_mstate_global->__pyx_tuple__12 +#define __pyx_tuple__13 __pyx_mstate_global->__pyx_tuple__13 +#define __pyx_tuple__14 __pyx_mstate_global->__pyx_tuple__14 +#define __pyx_tuple__15 __pyx_mstate_global->__pyx_tuple__15 +#define __pyx_tuple__16 __pyx_mstate_global->__pyx_tuple__16 +#define __pyx_tuple__17 __pyx_mstate_global->__pyx_tuple__17 +#define __pyx_tuple__18 __pyx_mstate_global->__pyx_tuple__18 +#define __pyx_tuple__19 __pyx_mstate_global->__pyx_tuple__19 +#define __pyx_tuple__20 __pyx_mstate_global->__pyx_tuple__20 +#define __pyx_tuple__21 __pyx_mstate_global->__pyx_tuple__21 +#define __pyx_tuple__23 __pyx_mstate_global->__pyx_tuple__23 +#define __pyx_codeobj__22 __pyx_mstate_global->__pyx_codeobj__22 +#define __pyx_codeobj__24 __pyx_mstate_global->__pyx_codeobj__24 +/* #### Code section: module_code ### */ + +/* "View.MemoryView":131 + * cdef bint dtype_is_object + * + * def __cinit__(array self, tuple shape, Py_ssize_t itemsize, format not None, # <<<<<<<<<<<<<< + * mode="c", bint allocate_buffer=True): + * + */ + +/* Python wrapper */ +static int __pyx_array___cinit__(PyObject *__pyx_v_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/ +static int __pyx_array___cinit__(PyObject *__pyx_v_self, PyObject *__pyx_args, PyObject *__pyx_kwds) { + PyObject *__pyx_v_shape = 0; + Py_ssize_t __pyx_v_itemsize; + PyObject 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(__pyx_v_start >= __pyx_v_shape); + if (__pyx_t_2) { + + /* "View.MemoryView":836 + * start = 0 + * elif start >= shape: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + if (__pyx_v_negative_step) { + + /* "View.MemoryView":837 + * elif start >= shape: + * if negative_step: + * start = shape - 1 # <<<<<<<<<<<<<< + * else: + * start = shape + */ + __pyx_v_start = (__pyx_v_shape - 1); + + /* "View.MemoryView":836 + * start = 0 + * elif start >= shape: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + goto __pyx_L11; + } + + /* "View.MemoryView":839 + * start = shape - 1 + * else: + * start = shape # <<<<<<<<<<<<<< + * else: + * if negative_step: + */ + /*else*/ { + __pyx_v_start = __pyx_v_shape; + } + __pyx_L11:; + + /* "View.MemoryView":835 + * if start < 0: + * start = 0 + * elif start >= shape: # <<<<<<<<<<<<<< + * if negative_step: + * start = shape - 1 + */ + } + __pyx_L9:; + + /* "View.MemoryView":830 + * + * + * if have_start: # <<<<<<<<<<<<<< + * if start < 0: + * start += shape + */ + goto __pyx_L8; + } + + /* "View.MemoryView":841 + * start = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + /*else*/ { + if (__pyx_v_negative_step) { + + /* "View.MemoryView":842 + * else: + * if negative_step: + * start = shape - 1 # <<<<<<<<<<<<<< + * else: + * start = 0 + */ + __pyx_v_start = (__pyx_v_shape - 1); + + /* "View.MemoryView":841 + * start = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + goto __pyx_L12; + } + + /* "View.MemoryView":844 + * start = shape - 1 + * else: + * start = 0 # <<<<<<<<<<<<<< + * + * if have_stop: + */ + /*else*/ { + __pyx_v_start = 0; + } + __pyx_L12:; + } + __pyx_L8:; + + /* "View.MemoryView":846 + * start = 0 + * + * if have_stop: # <<<<<<<<<<<<<< + * if stop < 0: + * stop += shape + */ + __pyx_t_2 = (__pyx_v_have_stop != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":847 + * + * if have_stop: + * if stop < 0: # <<<<<<<<<<<<<< + * stop += shape + * if stop < 0: + */ + __pyx_t_2 = (__pyx_v_stop < 0); + if (__pyx_t_2) { + + /* "View.MemoryView":848 + * if have_stop: + * if stop < 0: + * stop += shape # <<<<<<<<<<<<<< + * if stop < 0: + * stop = 0 + */ + __pyx_v_stop = (__pyx_v_stop + __pyx_v_shape); + + /* "View.MemoryView":849 + * if stop < 0: + * stop += shape + * if stop < 0: # <<<<<<<<<<<<<< + * stop = 0 + * elif stop > shape: + */ + __pyx_t_2 = (__pyx_v_stop < 0); + if (__pyx_t_2) { + + /* "View.MemoryView":850 + * stop += shape + * if stop < 0: + * stop = 0 # <<<<<<<<<<<<<< + * elif stop > shape: + * stop = shape + */ + __pyx_v_stop = 0; + + /* "View.MemoryView":849 + * if stop < 0: + * stop += shape + * if stop < 0: # <<<<<<<<<<<<<< + * stop = 0 + * elif stop > shape: + */ + } + + /* "View.MemoryView":847 + * + * if have_stop: + * if stop < 0: # <<<<<<<<<<<<<< + * stop += shape + * if stop < 0: + */ + goto __pyx_L14; + } + + /* "View.MemoryView":851 + * if stop < 0: + * stop = 0 + * elif stop > shape: # <<<<<<<<<<<<<< + * stop = shape + * else: + */ + __pyx_t_2 = (__pyx_v_stop > __pyx_v_shape); + if (__pyx_t_2) { + + /* "View.MemoryView":852 + * stop = 0 + * elif stop > shape: + * stop = shape # <<<<<<<<<<<<<< + * else: + * if negative_step: + */ + __pyx_v_stop = __pyx_v_shape; + + /* "View.MemoryView":851 + * if stop < 0: + * stop = 0 + * elif stop > shape: # <<<<<<<<<<<<<< + * stop = shape + * else: + */ + } + __pyx_L14:; + + /* "View.MemoryView":846 + * start = 0 + * + * if have_stop: # <<<<<<<<<<<<<< + * if stop < 0: + * stop += shape + */ + goto __pyx_L13; + } + + /* "View.MemoryView":854 + * stop = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * stop = -1 + * else: + */ + /*else*/ { + if (__pyx_v_negative_step) { + + /* "View.MemoryView":855 + * else: + * if negative_step: + * stop = -1 # <<<<<<<<<<<<<< + * else: + * stop = shape + */ + __pyx_v_stop = -1L; + + /* "View.MemoryView":854 + * stop = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * stop = -1 + * else: + */ + goto __pyx_L16; + } + + /* "View.MemoryView":857 + * stop = -1 + * else: + * stop = shape # <<<<<<<<<<<<<< + * + * + */ + /*else*/ { + __pyx_v_stop = __pyx_v_shape; + } + __pyx_L16:; + } + __pyx_L13:; + + /* "View.MemoryView":861 + * + * with cython.cdivision(True): + * new_shape = (stop - start) // step # <<<<<<<<<<<<<< + * + * if (stop - start) - step * new_shape: + */ + __pyx_v_new_shape = ((__pyx_v_stop - __pyx_v_start) / __pyx_v_step); + + /* "View.MemoryView":863 + * new_shape = (stop - start) // step + * + * if (stop - start) - step * new_shape: # <<<<<<<<<<<<<< + * new_shape += 1 + * + */ + __pyx_t_2 = (((__pyx_v_stop - __pyx_v_start) - (__pyx_v_step * __pyx_v_new_shape)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":864 + * + * if (stop - start) - step * new_shape: + * new_shape += 1 # <<<<<<<<<<<<<< + * + * if new_shape < 0: + */ + __pyx_v_new_shape = (__pyx_v_new_shape + 1); + + /* "View.MemoryView":863 + * 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__pyx_memoryview_fromslice((__pyx_v_memviewslice[0]), __pyx_v_memview->view.ndim, __pyx_v_to_object_func, __pyx_v_to_dtype_func, __pyx_v_memview->dtype_is_object); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 1101, __pyx_L1_error) + __Pyx_GOTREF(__pyx_t_4); + __pyx_r = __pyx_t_4; + __pyx_t_4 = 0; + goto __pyx_L0; + + /* "View.MemoryView":1087 + * + * @cname('__pyx_memoryview_copy_object_from_slice') + * cdef memoryview_copy_from_slice(memoryview memview, __Pyx_memviewslice *memviewslice): # <<<<<<<<<<<<<< + * """ + * Create a new memoryview object from a given memoryview object and slice. + */ + + /* function exit code */ + __pyx_L1_error:; + __Pyx_XDECREF(__pyx_t_4); + __Pyx_AddTraceback("View.MemoryView.memoryview_copy_from_slice", __pyx_clineno, __pyx_lineno, __pyx_filename); + __pyx_r = 0; + __pyx_L0:; + __Pyx_XGIVEREF(__pyx_r); + __Pyx_RefNannyFinishContext(); + return __pyx_r; +} + +/* "View.MemoryView":1109 + * + * + * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) noexcept nogil: # <<<<<<<<<<<<<< + * return -arg if arg < 0 else arg + * + */ + +static Py_ssize_t abs_py_ssize_t(Py_ssize_t __pyx_v_arg) { + Py_ssize_t __pyx_r; + Py_ssize_t __pyx_t_1; + int __pyx_t_2; + + /* "View.MemoryView":1110 + * + * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) noexcept nogil: + * return -arg if arg < 0 else arg # <<<<<<<<<<<<<< + * + * @cname('__pyx_get_best_slice_order') + */ + __pyx_t_2 = (__pyx_v_arg < 0); + if (__pyx_t_2) { + __pyx_t_1 = (-__pyx_v_arg); + } else { + __pyx_t_1 = __pyx_v_arg; + } + __pyx_r = __pyx_t_1; + goto __pyx_L0; + + /* "View.MemoryView":1109 + * + * + * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) noexcept nogil: # <<<<<<<<<<<<<< + * return -arg if arg < 0 else arg + * + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1113 + * + * @cname('__pyx_get_best_slice_order') + * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) noexcept nogil: # <<<<<<<<<<<<<< + * """ + * Figure out the best memory access order for a given slice. + */ + +static char __pyx_get_best_slice_order(__Pyx_memviewslice *__pyx_v_mslice, int __pyx_v_ndim) { + int __pyx_v_i; + Py_ssize_t __pyx_v_c_stride; + Py_ssize_t __pyx_v_f_stride; + char __pyx_r; + int __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + int __pyx_t_4; + + /* "View.MemoryView":1118 + * """ + * cdef int i + * cdef Py_ssize_t c_stride = 0 # <<<<<<<<<<<<<< + * cdef Py_ssize_t f_stride = 0 + * + */ + __pyx_v_c_stride = 0; + + /* "View.MemoryView":1119 + * cdef int i + * cdef Py_ssize_t c_stride = 0 + * cdef Py_ssize_t f_stride = 0 # <<<<<<<<<<<<<< + * + * for i in range(ndim - 1, -1, -1): + */ + __pyx_v_f_stride = 0; + + /* "View.MemoryView":1121 + * cdef Py_ssize_t f_stride = 0 + * + * for i in range(ndim - 1, -1, -1): # <<<<<<<<<<<<<< + * if mslice.shape[i] > 1: + * c_stride = mslice.strides[i] + */ + for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) { + __pyx_v_i = __pyx_t_1; + + /* "View.MemoryView":1122 + * + * for i in range(ndim - 1, -1, -1): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * c_stride = mslice.strides[i] + * break + */ + __pyx_t_2 = ((__pyx_v_mslice->shape[__pyx_v_i]) > 1); + if (__pyx_t_2) { + + /* "View.MemoryView":1123 + * for i in range(ndim - 1, -1, -1): + * if mslice.shape[i] > 1: + * c_stride = mslice.strides[i] # <<<<<<<<<<<<<< + * break + * + */ + __pyx_v_c_stride = (__pyx_v_mslice->strides[__pyx_v_i]); + + /* "View.MemoryView":1124 + * if mslice.shape[i] > 1: + * c_stride = mslice.strides[i] + * break # <<<<<<<<<<<<<< + * + * for i in range(ndim): + */ + goto __pyx_L4_break; + + /* "View.MemoryView":1122 + * + * for i in range(ndim - 1, -1, -1): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * c_stride = mslice.strides[i] + * break + */ + } + } + __pyx_L4_break:; + + /* "View.MemoryView":1126 + * break + * + * for i in range(ndim): # <<<<<<<<<<<<<< + * if mslice.shape[i] > 1: + * f_stride = mslice.strides[i] + */ + __pyx_t_1 = __pyx_v_ndim; + __pyx_t_3 = __pyx_t_1; + for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) { + __pyx_v_i = __pyx_t_4; + + /* "View.MemoryView":1127 + * + * for i in range(ndim): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * f_stride = mslice.strides[i] + * break + */ + __pyx_t_2 = ((__pyx_v_mslice->shape[__pyx_v_i]) > 1); + if (__pyx_t_2) { + + /* "View.MemoryView":1128 + * for i in range(ndim): + * if mslice.shape[i] > 1: + * f_stride = mslice.strides[i] # <<<<<<<<<<<<<< + * break + * + */ + __pyx_v_f_stride = (__pyx_v_mslice->strides[__pyx_v_i]); + + /* "View.MemoryView":1129 + * if mslice.shape[i] > 1: + * f_stride = mslice.strides[i] + * break # <<<<<<<<<<<<<< + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): + */ + goto __pyx_L7_break; + + /* "View.MemoryView":1127 + * + * for i in range(ndim): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * f_stride = mslice.strides[i] + * break + */ + } + } + __pyx_L7_break:; + + /* "View.MemoryView":1131 + * break + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): # <<<<<<<<<<<<<< + * return 'C' + * else: + */ + __pyx_t_2 = (abs_py_ssize_t(__pyx_v_c_stride) <= abs_py_ssize_t(__pyx_v_f_stride)); + if (__pyx_t_2) { + + /* "View.MemoryView":1132 + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): + * return 'C' # <<<<<<<<<<<<<< + * else: + * return 'F' + */ + __pyx_r = 'C'; + goto __pyx_L0; + + /* "View.MemoryView":1131 + * break + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): # <<<<<<<<<<<<<< + * return 'C' + * else: + */ + } + + /* "View.MemoryView":1134 + * return 'C' + * else: + * return 'F' # <<<<<<<<<<<<<< + * + * @cython.cdivision(True) + */ + /*else*/ { + __pyx_r = 'F'; + goto __pyx_L0; + } + + /* "View.MemoryView":1113 + * + * @cname('__pyx_get_best_slice_order') + * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) noexcept nogil: # <<<<<<<<<<<<<< + * """ + * Figure out the best memory access order for a given slice. + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1137 + * + * @cython.cdivision(True) + * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides, # <<<<<<<<<<<<<< + * char *dst_data, Py_ssize_t *dst_strides, + * Py_ssize_t *src_shape, Py_ssize_t *dst_shape, + */ + +static void _copy_strided_to_strided(char *__pyx_v_src_data, Py_ssize_t *__pyx_v_src_strides, char *__pyx_v_dst_data, Py_ssize_t *__pyx_v_dst_strides, Py_ssize_t *__pyx_v_src_shape, Py_ssize_t *__pyx_v_dst_shape, int __pyx_v_ndim, size_t __pyx_v_itemsize) { + CYTHON_UNUSED Py_ssize_t __pyx_v_i; + CYTHON_UNUSED Py_ssize_t __pyx_v_src_extent; + Py_ssize_t __pyx_v_dst_extent; + Py_ssize_t __pyx_v_src_stride; + Py_ssize_t __pyx_v_dst_stride; + int __pyx_t_1; + int __pyx_t_2; + Py_ssize_t __pyx_t_3; + Py_ssize_t __pyx_t_4; + Py_ssize_t __pyx_t_5; + + /* "View.MemoryView":1144 + * + * cdef Py_ssize_t i + * cdef Py_ssize_t src_extent = src_shape[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t dst_extent = dst_shape[0] + * cdef Py_ssize_t src_stride = src_strides[0] + */ + __pyx_v_src_extent = (__pyx_v_src_shape[0]); + + /* "View.MemoryView":1145 + * cdef Py_ssize_t i + * cdef Py_ssize_t src_extent = src_shape[0] + * cdef Py_ssize_t dst_extent = dst_shape[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t src_stride = src_strides[0] + * cdef Py_ssize_t dst_stride = dst_strides[0] + */ + __pyx_v_dst_extent = (__pyx_v_dst_shape[0]); + + /* "View.MemoryView":1146 + * cdef Py_ssize_t src_extent = src_shape[0] + * cdef Py_ssize_t dst_extent = dst_shape[0] + * cdef Py_ssize_t src_stride = src_strides[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t dst_stride = dst_strides[0] + * + */ + __pyx_v_src_stride = (__pyx_v_src_strides[0]); + + /* "View.MemoryView":1147 + * cdef Py_ssize_t dst_extent = dst_shape[0] + * cdef Py_ssize_t src_stride = src_strides[0] + * cdef Py_ssize_t dst_stride = dst_strides[0] # <<<<<<<<<<<<<< + * + * if ndim == 1: + */ + __pyx_v_dst_stride = (__pyx_v_dst_strides[0]); + + /* "View.MemoryView":1149 + * cdef Py_ssize_t dst_stride = dst_strides[0] + * + * if ndim == 1: # <<<<<<<<<<<<<< + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): + */ + __pyx_t_1 = (__pyx_v_ndim == 1); + if (__pyx_t_1) { + + /* "View.MemoryView":1150 + * + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and # <<<<<<<<<<<<<< + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) + */ + __pyx_t_2 = (__pyx_v_src_stride > 0); + if (__pyx_t_2) { + } else { + __pyx_t_1 = __pyx_t_2; + goto __pyx_L5_bool_binop_done; + } + __pyx_t_2 = (__pyx_v_dst_stride > 0); + if (__pyx_t_2) { + } else { + __pyx_t_1 = __pyx_t_2; + goto __pyx_L5_bool_binop_done; + } + + /* "View.MemoryView":1151 + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): # <<<<<<<<<<<<<< + * memcpy(dst_data, src_data, itemsize * dst_extent) + * else: + */ + __pyx_t_2 = (((size_t)__pyx_v_src_stride) == __pyx_v_itemsize); + if (__pyx_t_2) { + __pyx_t_2 = (__pyx_v_itemsize == ((size_t)__pyx_v_dst_stride)); + } + __pyx_t_1 = __pyx_t_2; + __pyx_L5_bool_binop_done:; + + /* "View.MemoryView":1150 + * + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and # <<<<<<<<<<<<<< + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) + */ + if (__pyx_t_1) { + + /* "View.MemoryView":1152 + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) # <<<<<<<<<<<<<< + * else: + * for i in range(dst_extent): + */ + (void)(memcpy(__pyx_v_dst_data, __pyx_v_src_data, (__pyx_v_itemsize * __pyx_v_dst_extent))); + + /* "View.MemoryView":1150 + * + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and # <<<<<<<<<<<<<< + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) + */ + goto __pyx_L4; + } + + /* "View.MemoryView":1154 + * memcpy(dst_data, src_data, itemsize * dst_extent) + * else: + * for i in range(dst_extent): # <<<<<<<<<<<<<< + * memcpy(dst_data, src_data, itemsize) + * src_data += src_stride + */ + /*else*/ { + __pyx_t_3 = __pyx_v_dst_extent; + __pyx_t_4 = __pyx_t_3; + for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) { + __pyx_v_i = __pyx_t_5; + + /* "View.MemoryView":1155 + * else: + * for i in range(dst_extent): + * memcpy(dst_data, src_data, itemsize) # <<<<<<<<<<<<<< + * src_data += src_stride + * dst_data += dst_stride + */ + (void)(memcpy(__pyx_v_dst_data, __pyx_v_src_data, __pyx_v_itemsize)); + + /* "View.MemoryView":1156 + * for i in range(dst_extent): + * memcpy(dst_data, src_data, itemsize) + * src_data += src_stride # <<<<<<<<<<<<<< + * dst_data += dst_stride + * else: + */ + __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride); + + /* "View.MemoryView":1157 + * memcpy(dst_data, src_data, itemsize) + * src_data += src_stride + * dst_data += dst_stride # <<<<<<<<<<<<<< + * else: + * for i in range(dst_extent): + */ + __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride); + } + } + __pyx_L4:; + + /* "View.MemoryView":1149 + * cdef Py_ssize_t dst_stride = dst_strides[0] + * + * if ndim == 1: # <<<<<<<<<<<<<< + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): + */ + goto __pyx_L3; + } + + /* "View.MemoryView":1159 + * dst_data += dst_stride + * else: + * for i in range(dst_extent): # <<<<<<<<<<<<<< + * _copy_strided_to_strided(src_data, src_strides + 1, + * dst_data, dst_strides + 1, + */ + /*else*/ { + __pyx_t_3 = __pyx_v_dst_extent; + __pyx_t_4 = __pyx_t_3; + for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) { + __pyx_v_i = __pyx_t_5; + + /* "View.MemoryView":1160 + * else: + * for i in range(dst_extent): + * _copy_strided_to_strided(src_data, src_strides + 1, # <<<<<<<<<<<<<< + * dst_data, dst_strides + 1, + * src_shape + 1, dst_shape + 1, + */ + _copy_strided_to_strided(__pyx_v_src_data, (__pyx_v_src_strides + 1), __pyx_v_dst_data, (__pyx_v_dst_strides + 1), (__pyx_v_src_shape + 1), (__pyx_v_dst_shape + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize); + + /* "View.MemoryView":1164 + * src_shape + 1, dst_shape + 1, + * ndim - 1, itemsize) + * src_data += src_stride # <<<<<<<<<<<<<< + * dst_data += dst_stride + * + */ + __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride); + + /* "View.MemoryView":1165 + * ndim - 1, itemsize) + * src_data += src_stride + * dst_data += dst_stride # <<<<<<<<<<<<<< + * + * cdef void copy_strided_to_strided(__Pyx_memviewslice *src, + */ + __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride); + } + } + __pyx_L3:; + + /* "View.MemoryView":1137 + * + * @cython.cdivision(True) + * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides, # <<<<<<<<<<<<<< + * char *dst_data, Py_ssize_t *dst_strides, + * Py_ssize_t *src_shape, Py_ssize_t *dst_shape, + */ + + /* function exit code */ +} + +/* "View.MemoryView":1167 + * dst_data += dst_stride + * + * cdef void copy_strided_to_strided(__Pyx_memviewslice *src, # <<<<<<<<<<<<<< + * __Pyx_memviewslice *dst, + * int ndim, size_t itemsize) noexcept nogil: + */ + +static void copy_strided_to_strided(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize) { + + /* "View.MemoryView":1170 + * __Pyx_memviewslice *dst, + * int ndim, size_t itemsize) noexcept nogil: + * _copy_strided_to_strided(src.data, src.strides, dst.data, dst.strides, # <<<<<<<<<<<<<< + * src.shape, dst.shape, ndim, itemsize) + * + */ + _copy_strided_to_strided(__pyx_v_src->data, __pyx_v_src->strides, __pyx_v_dst->data, __pyx_v_dst->strides, __pyx_v_src->shape, __pyx_v_dst->shape, __pyx_v_ndim, __pyx_v_itemsize); + + /* "View.MemoryView":1167 + * dst_data += dst_stride + * + * cdef void copy_strided_to_strided(__Pyx_memviewslice *src, # <<<<<<<<<<<<<< + * __Pyx_memviewslice *dst, + * int ndim, size_t itemsize) noexcept nogil: + */ + + /* function exit code */ +} + +/* "View.MemoryView":1174 + * + * @cname('__pyx_memoryview_slice_get_size') + * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) noexcept nogil: # <<<<<<<<<<<<<< + * "Return the size of the memory occupied by the slice in number of bytes" + * cdef Py_ssize_t shape, size = src.memview.view.itemsize + */ + +static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *__pyx_v_src, int __pyx_v_ndim) { + Py_ssize_t __pyx_v_shape; + Py_ssize_t __pyx_v_size; + Py_ssize_t __pyx_r; + Py_ssize_t __pyx_t_1; + Py_ssize_t *__pyx_t_2; + Py_ssize_t *__pyx_t_3; + Py_ssize_t *__pyx_t_4; + + /* "View.MemoryView":1176 + * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) noexcept nogil: + * "Return the size of the memory occupied by the slice in number of bytes" + * cdef Py_ssize_t shape, size = src.memview.view.itemsize # <<<<<<<<<<<<<< + * + * for shape in src.shape[:ndim]: + */ + __pyx_t_1 = __pyx_v_src->memview->view.itemsize; + __pyx_v_size = __pyx_t_1; + + /* "View.MemoryView":1178 + * cdef Py_ssize_t shape, size = src.memview.view.itemsize + * + * for shape in src.shape[:ndim]: # <<<<<<<<<<<<<< + * size *= shape + * + */ + __pyx_t_3 = (__pyx_v_src->shape + __pyx_v_ndim); + for (__pyx_t_4 = __pyx_v_src->shape; __pyx_t_4 < __pyx_t_3; __pyx_t_4++) { + __pyx_t_2 = __pyx_t_4; + __pyx_v_shape = (__pyx_t_2[0]); + + /* "View.MemoryView":1179 + * + * for shape in src.shape[:ndim]: + * size *= shape # <<<<<<<<<<<<<< + * + * return size + */ + __pyx_v_size = (__pyx_v_size * __pyx_v_shape); + } + + /* "View.MemoryView":1181 + * size *= shape + * + * return size # <<<<<<<<<<<<<< + * + * @cname('__pyx_fill_contig_strides_array') + */ + __pyx_r = __pyx_v_size; + goto __pyx_L0; + + /* "View.MemoryView":1174 + * + * @cname('__pyx_memoryview_slice_get_size') + * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) noexcept nogil: # <<<<<<<<<<<<<< + * "Return the size of the memory occupied by the slice in number of bytes" + * cdef Py_ssize_t shape, size = src.memview.view.itemsize + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1184 + * + * @cname('__pyx_fill_contig_strides_array') + * cdef Py_ssize_t fill_contig_strides_array( # <<<<<<<<<<<<<< + * Py_ssize_t *shape, Py_ssize_t *strides, Py_ssize_t stride, + * int ndim, char order) noexcept nogil: + */ + +static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, Py_ssize_t __pyx_v_stride, int __pyx_v_ndim, char __pyx_v_order) { + int __pyx_v_idx; + Py_ssize_t __pyx_r; + int __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + int __pyx_t_4; + + /* "View.MemoryView":1193 + * cdef int idx + * + * if order == 'F': # <<<<<<<<<<<<<< + * for idx in range(ndim): + * strides[idx] = stride + */ + __pyx_t_1 = (__pyx_v_order == 'F'); + if (__pyx_t_1) { + + /* "View.MemoryView":1194 + * + * if order == 'F': + * for idx in range(ndim): # <<<<<<<<<<<<<< + * strides[idx] = stride + * stride *= shape[idx] + */ + __pyx_t_2 = __pyx_v_ndim; + __pyx_t_3 = __pyx_t_2; + for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) { + __pyx_v_idx = __pyx_t_4; + + /* "View.MemoryView":1195 + * if order == 'F': + * for idx in range(ndim): + * strides[idx] = stride # <<<<<<<<<<<<<< + * stride *= shape[idx] + * else: + */ + (__pyx_v_strides[__pyx_v_idx]) = __pyx_v_stride; + + /* "View.MemoryView":1196 + * for idx in range(ndim): + * strides[idx] = stride + * stride *= shape[idx] # <<<<<<<<<<<<<< + * else: + * for idx in range(ndim - 1, -1, -1): + */ + __pyx_v_stride = (__pyx_v_stride * (__pyx_v_shape[__pyx_v_idx])); + } + + /* "View.MemoryView":1193 + * cdef int idx + * + * if order == 'F': # <<<<<<<<<<<<<< + * for idx in range(ndim): + * strides[idx] = stride + */ + goto __pyx_L3; + } + + /* "View.MemoryView":1198 + * stride *= shape[idx] + * else: + * for idx in range(ndim - 1, -1, -1): # <<<<<<<<<<<<<< + * strides[idx] = stride + * stride *= shape[idx] + */ + /*else*/ { + for (__pyx_t_2 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<<<<<<<<<<<<<< + * __Pyx_memviewslice dst, + * int src_ndim, int dst_ndim, + */ + +static int __pyx_memoryview_copy_contents(__Pyx_memviewslice __pyx_v_src, __Pyx_memviewslice __pyx_v_dst, int __pyx_v_src_ndim, int __pyx_v_dst_ndim, int __pyx_v_dtype_is_object) { + void *__pyx_v_tmpdata; + size_t __pyx_v_itemsize; + int __pyx_v_i; + char __pyx_v_order; + int __pyx_v_broadcasting; + int __pyx_v_direct_copy; + __Pyx_memviewslice __pyx_v_tmp; + int __pyx_v_ndim; + int __pyx_r; + Py_ssize_t __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + int __pyx_t_4; + int __pyx_t_5; + int __pyx_t_6; + void *__pyx_t_7; + int __pyx_lineno = 0; + const char *__pyx_filename = NULL; + int __pyx_clineno = 0; + #ifdef WITH_THREAD + PyGILState_STATE __pyx_gilstate_save; + #endif + + /* "View.MemoryView":1273 + * Check for overlapping memory and verify the shapes. + * """ + * cdef void *tmpdata = NULL # <<<<<<<<<<<<<< + * cdef size_t itemsize = src.memview.view.itemsize + * cdef int i + */ + __pyx_v_tmpdata = NULL; + + /* "View.MemoryView":1274 + * """ + * cdef void *tmpdata = NULL + * cdef size_t itemsize = src.memview.view.itemsize # <<<<<<<<<<<<<< + * cdef int i + * cdef char order = get_best_order(&src, src_ndim) + */ + __pyx_t_1 = __pyx_v_src.memview->view.itemsize; + __pyx_v_itemsize = __pyx_t_1; + + /* "View.MemoryView":1276 + * cdef size_t itemsize = src.memview.view.itemsize + * cdef int i + * cdef char order = get_best_order(&src, src_ndim) # <<<<<<<<<<<<<< + * cdef bint broadcasting = False + * cdef bint direct_copy = False + */ + __pyx_v_order = __pyx_get_best_slice_order((&__pyx_v_src), __pyx_v_src_ndim); + + /* "View.MemoryView":1277 + * cdef int i + * cdef char order = get_best_order(&src, src_ndim) + * cdef bint broadcasting = False # <<<<<<<<<<<<<< + * cdef bint direct_copy = False + * cdef __Pyx_memviewslice tmp + */ + __pyx_v_broadcasting = 0; + + /* "View.MemoryView":1278 + * cdef char order = get_best_order(&src, src_ndim) + * cdef bint broadcasting = False + * cdef bint direct_copy = False # <<<<<<<<<<<<<< + * cdef __Pyx_memviewslice tmp + * + */ + __pyx_v_direct_copy = 0; + + /* "View.MemoryView":1281 + * cdef __Pyx_memviewslice tmp + * + * if src_ndim < dst_ndim: # <<<<<<<<<<<<<< + * broadcast_leading(&src, src_ndim, dst_ndim) + * elif dst_ndim < src_ndim: + */ + __pyx_t_2 = (__pyx_v_src_ndim < __pyx_v_dst_ndim); + if (__pyx_t_2) { + + /* "View.MemoryView":1282 + * + * if src_ndim < dst_ndim: + * broadcast_leading(&src, src_ndim, dst_ndim) # <<<<<<<<<<<<<< + * elif dst_ndim < src_ndim: + * broadcast_leading(&dst, dst_ndim, src_ndim) + */ + __pyx_memoryview_broadcast_leading((&__pyx_v_src), __pyx_v_src_ndim, __pyx_v_dst_ndim); + + /* "View.MemoryView":1281 + * cdef __Pyx_memviewslice tmp + * + * if src_ndim < dst_ndim: # <<<<<<<<<<<<<< + * broadcast_leading(&src, src_ndim, dst_ndim) + * elif dst_ndim < src_ndim: + */ + goto __pyx_L3; + } + + /* "View.MemoryView":1283 + * if src_ndim < dst_ndim: + * broadcast_leading(&src, src_ndim, dst_ndim) + * elif dst_ndim < src_ndim: # <<<<<<<<<<<<<< + * broadcast_leading(&dst, dst_ndim, src_ndim) + * + */ + __pyx_t_2 = (__pyx_v_dst_ndim < __pyx_v_src_ndim); + if (__pyx_t_2) { + + /* "View.MemoryView":1284 + * broadcast_leading(&src, src_ndim, dst_ndim) + * elif dst_ndim < src_ndim: + * broadcast_leading(&dst, dst_ndim, src_ndim) # <<<<<<<<<<<<<< + * + * cdef int ndim = max(src_ndim, dst_ndim) + */ + __pyx_memoryview_broadcast_leading((&__pyx_v_dst), __pyx_v_dst_ndim, __pyx_v_src_ndim); + + /* "View.MemoryView":1283 + * if src_ndim < dst_ndim: + * broadcast_leading(&src, src_ndim, dst_ndim) + * elif dst_ndim < src_ndim: # <<<<<<<<<<<<<< + * broadcast_leading(&dst, dst_ndim, src_ndim) + * + */ + } + __pyx_L3:; + + /* "View.MemoryView":1286 + * broadcast_leading(&dst, dst_ndim, src_ndim) + * + * cdef int ndim = max(src_ndim, dst_ndim) # <<<<<<<<<<<<<< + * + * for i in range(ndim): + */ + __pyx_t_3 = __pyx_v_dst_ndim; + __pyx_t_4 = __pyx_v_src_ndim; + __pyx_t_2 = (__pyx_t_3 > __pyx_t_4); + if (__pyx_t_2) { + __pyx_t_5 = __pyx_t_3; + } else { + __pyx_t_5 = __pyx_t_4; + } + __pyx_v_ndim = __pyx_t_5; + + /* "View.MemoryView":1288 + * cdef int ndim = max(src_ndim, dst_ndim) + * + * for i in range(ndim): # <<<<<<<<<<<<<< + * if src.shape[i] != dst.shape[i]: + * if src.shape[i] == 1: + */ + __pyx_t_5 = __pyx_v_ndim; + __pyx_t_3 = __pyx_t_5; + for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) { + __pyx_v_i = __pyx_t_4; + + /* "View.MemoryView":1289 + * + * for i in range(ndim): + * if src.shape[i] != dst.shape[i]: # <<<<<<<<<<<<<< + * if src.shape[i] == 1: + * broadcasting = True + */ + __pyx_t_2 = ((__pyx_v_src.shape[__pyx_v_i]) != (__pyx_v_dst.shape[__pyx_v_i])); + if (__pyx_t_2) { + + /* "View.MemoryView":1290 + * for i in range(ndim): + * if src.shape[i] != dst.shape[i]: + * if src.shape[i] == 1: # <<<<<<<<<<<<<< + * broadcasting = True + * src.strides[i] = 0 + */ + __pyx_t_2 = ((__pyx_v_src.shape[__pyx_v_i]) == 1); + if (__pyx_t_2) { + + /* "View.MemoryView":1291 + * if src.shape[i] != dst.shape[i]: + * if src.shape[i] == 1: + * broadcasting = True # <<<<<<<<<<<<<< + * src.strides[i] = 0 + * else: + */ + __pyx_v_broadcasting = 1; + + /* "View.MemoryView":1292 + * if src.shape[i] == 1: + * broadcasting = True + * src.strides[i] = 0 # <<<<<<<<<<<<<< + * else: + * _err_extents(i, dst.shape[i], src.shape[i]) + */ + (__pyx_v_src.strides[__pyx_v_i]) = 0; + + /* "View.MemoryView":1290 + * for i in range(ndim): + * if src.shape[i] != dst.shape[i]: + * if src.shape[i] == 1: # <<<<<<<<<<<<<< + * broadcasting = True + * src.strides[i] = 0 + */ + goto __pyx_L7; + } + + /* "View.MemoryView":1294 + * src.strides[i] = 0 + * else: + * _err_extents(i, dst.shape[i], src.shape[i]) # <<<<<<<<<<<<<< + * + * if src.suboffsets[i] >= 0: + */ + /*else*/ { + __pyx_t_6 = __pyx_memoryview_err_extents(__pyx_v_i, (__pyx_v_dst.shape[__pyx_v_i]), (__pyx_v_src.shape[__pyx_v_i])); if (unlikely(__pyx_t_6 == ((int)-1))) __PYX_ERR(1, 1294, __pyx_L1_error) + } + __pyx_L7:; + + /* "View.MemoryView":1289 + * + * for i in range(ndim): + * if src.shape[i] != dst.shape[i]: # <<<<<<<<<<<<<< + * if src.shape[i] == 1: + * broadcasting = True + */ + } + + /* "View.MemoryView":1296 + * _err_extents(i, dst.shape[i], src.shape[i]) + * + * if src.suboffsets[i] >= 0: # <<<<<<<<<<<<<< + * _err_dim(PyExc_ValueError, "Dimension %d is not direct", i) + * + */ + __pyx_t_2 = ((__pyx_v_src.suboffsets[__pyx_v_i]) >= 0); + if (__pyx_t_2) { + + /* "View.MemoryView":1297 + * + * if src.suboffsets[i] >= 0: + * _err_dim(PyExc_ValueError, "Dimension %d is not direct", i) # <<<<<<<<<<<<<< + * + * if slices_overlap(&src, &dst, ndim, itemsize): + */ + __pyx_t_6 = __pyx_memoryview_err_dim(PyExc_ValueError, __pyx_kp_s_Dimension_d_is_not_direct, __pyx_v_i); if (unlikely(__pyx_t_6 == ((int)-1))) __PYX_ERR(1, 1297, __pyx_L1_error) + + /* "View.MemoryView":1296 + * _err_extents(i, dst.shape[i], src.shape[i]) + * + * if src.suboffsets[i] >= 0: # <<<<<<<<<<<<<< + * _err_dim(PyExc_ValueError, "Dimension %d is not direct", i) + * + */ + } + } + + /* "View.MemoryView":1299 + * _err_dim(PyExc_ValueError, "Dimension %d is not direct", i) + * + * if slices_overlap(&src, &dst, ndim, itemsize): # <<<<<<<<<<<<<< + * + * if not slice_is_contig(src, order, ndim): + */ + __pyx_t_2 = __pyx_slices_overlap((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize); + if (__pyx_t_2) { + + /* "View.MemoryView":1301 + * if slices_overlap(&src, &dst, ndim, itemsize): + * + * if not slice_is_contig(src, order, ndim): # <<<<<<<<<<<<<< + * order = get_best_order(&dst, ndim) + * + */ + __pyx_t_2 = (!__pyx_memviewslice_is_contig(__pyx_v_src, __pyx_v_order, __pyx_v_ndim)); + if (__pyx_t_2) { + + /* "View.MemoryView":1302 + * + * if not slice_is_contig(src, order, ndim): + * order = get_best_order(&dst, ndim) # <<<<<<<<<<<<<< + * + * tmpdata = copy_data_to_temp(&src, &tmp, order, ndim) + */ + __pyx_v_order = __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim); + + /* "View.MemoryView":1301 + * if slices_overlap(&src, &dst, ndim, itemsize): + * + * if not slice_is_contig(src, order, ndim): # <<<<<<<<<<<<<< + * order = get_best_order(&dst, ndim) + * + */ + } + + /* "View.MemoryView":1304 + * order = get_best_order(&dst, ndim) + * + * tmpdata = copy_data_to_temp(&src, &tmp, order, ndim) # <<<<<<<<<<<<<< + * src = tmp + * + */ + __pyx_t_7 = __pyx_memoryview_copy_data_to_temp((&__pyx_v_src), (&__pyx_v_tmp), __pyx_v_order, __pyx_v_ndim); if (unlikely(__pyx_t_7 == ((void *)NULL))) __PYX_ERR(1, 1304, __pyx_L1_error) + __pyx_v_tmpdata = __pyx_t_7; + + /* "View.MemoryView":1305 + * + * tmpdata = copy_data_to_temp(&src, &tmp, order, ndim) + * src = tmp # <<<<<<<<<<<<<< + * + * if not broadcasting: + */ + __pyx_v_src = __pyx_v_tmp; + + /* "View.MemoryView":1299 + * _err_dim(PyExc_ValueError, "Dimension %d is not direct", i) + * + * if slices_overlap(&src, &dst, ndim, itemsize): # <<<<<<<<<<<<<< + * + * if not slice_is_contig(src, order, ndim): + */ + } + + /* "View.MemoryView":1307 + * src = tmp + * + * if not broadcasting: # <<<<<<<<<<<<<< + * + * + */ + __pyx_t_2 = (!__pyx_v_broadcasting); + if (__pyx_t_2) { + + /* "View.MemoryView":1310 + * + * + * if slice_is_contig(src, 'C', ndim): # <<<<<<<<<<<<<< + * direct_copy = slice_is_contig(dst, 'C', ndim) + * elif slice_is_contig(src, 'F', ndim): + */ + __pyx_t_2 = __pyx_memviewslice_is_contig(__pyx_v_src, 'C', __pyx_v_ndim); + if (__pyx_t_2) { + + /* "View.MemoryView":1311 + * + * if slice_is_contig(src, 'C', ndim): + * direct_copy = slice_is_contig(dst, 'C', ndim) # <<<<<<<<<<<<<< + * elif slice_is_contig(src, 'F', ndim): + * direct_copy = slice_is_contig(dst, 'F', ndim) + */ + __pyx_v_direct_copy = __pyx_memviewslice_is_contig(__pyx_v_dst, 'C', __pyx_v_ndim); + + /* "View.MemoryView":1310 + * + * + * if slice_is_contig(src, 'C', ndim): # <<<<<<<<<<<<<< + * direct_copy = slice_is_contig(dst, 'C', ndim) + * elif slice_is_contig(src, 'F', ndim): + */ + goto __pyx_L12; + } + + /* "View.MemoryView":1312 + * if slice_is_contig(src, 'C', ndim): + * direct_copy = slice_is_contig(dst, 'C', ndim) + * elif slice_is_contig(src, 'F', ndim): # <<<<<<<<<<<<<< + * direct_copy = slice_is_contig(dst, 'F', ndim) + * + */ + __pyx_t_2 = __pyx_memviewslice_is_contig(__pyx_v_src, 'F', __pyx_v_ndim); + if (__pyx_t_2) { + + /* "View.MemoryView":1313 + * direct_copy = slice_is_contig(dst, 'C', ndim) + * elif slice_is_contig(src, 'F', ndim): + * direct_copy = slice_is_contig(dst, 'F', ndim) # <<<<<<<<<<<<<< + * + * if direct_copy: + */ + __pyx_v_direct_copy = __pyx_memviewslice_is_contig(__pyx_v_dst, 'F', __pyx_v_ndim); + + /* "View.MemoryView":1312 + * if slice_is_contig(src, 'C', ndim): + * direct_copy = slice_is_contig(dst, 'C', ndim) + * elif slice_is_contig(src, 'F', ndim): # <<<<<<<<<<<<<< + * direct_copy = slice_is_contig(dst, 'F', ndim) + * + */ + } + __pyx_L12:; + + /* "View.MemoryView":1315 + * direct_copy = slice_is_contig(dst, 'F', ndim) + * + * if direct_copy: # <<<<<<<<<<<<<< + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + */ + if (__pyx_v_direct_copy) { + + /* "View.MemoryView":1317 + * if direct_copy: + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) # <<<<<<<<<<<<<< + * memcpy(dst.data, src.data, slice_get_size(&src, ndim)) + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + */ + __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0); + + /* "View.MemoryView":1318 + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + * memcpy(dst.data, src.data, slice_get_size(&src, ndim)) # <<<<<<<<<<<<<< + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + * free(tmpdata) + */ + (void)(memcpy(__pyx_v_dst.data, __pyx_v_src.data, __pyx_memoryview_slice_get_size((&__pyx_v_src), __pyx_v_ndim))); + + /* "View.MemoryView":1319 + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + * memcpy(dst.data, src.data, slice_get_size(&src, ndim)) + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) # <<<<<<<<<<<<<< + * free(tmpdata) + * return 0 + */ + __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1); + + /* "View.MemoryView":1320 + * memcpy(dst.data, src.data, slice_get_size(&src, ndim)) + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + * free(tmpdata) # <<<<<<<<<<<<<< + * return 0 + * + */ + free(__pyx_v_tmpdata); + + /* "View.MemoryView":1321 + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + * free(tmpdata) + * return 0 # <<<<<<<<<<<<<< + * + * if order == 'F' == get_best_order(&dst, ndim): + */ + __pyx_r = 0; + goto __pyx_L0; + + /* "View.MemoryView":1315 + * direct_copy = slice_is_contig(dst, 'F', ndim) + * + * if direct_copy: # <<<<<<<<<<<<<< + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + */ + } + + /* "View.MemoryView":1307 + * src = tmp + * + * if not broadcasting: # <<<<<<<<<<<<<< + * + * + */ + } + + /* "View.MemoryView":1323 + * return 0 + * + * if order == 'F' == get_best_order(&dst, ndim): # <<<<<<<<<<<<<< + * + * + */ + __pyx_t_2 = (__pyx_v_order == 'F'); + if (__pyx_t_2) { + __pyx_t_2 = ('F' == __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim)); + } + if (__pyx_t_2) { + + /* "View.MemoryView":1326 + * + * + * transpose_memslice(&src) # <<<<<<<<<<<<<< + * transpose_memslice(&dst) + * + */ + __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_src)); if (unlikely(__pyx_t_5 == ((int)-1))) __PYX_ERR(1, 1326, __pyx_L1_error) + + /* "View.MemoryView":1327 + * + * transpose_memslice(&src) + * transpose_memslice(&dst) # <<<<<<<<<<<<<< + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + */ + __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_dst)); if (unlikely(__pyx_t_5 == ((int)-1))) __PYX_ERR(1, 1327, __pyx_L1_error) + + /* "View.MemoryView":1323 + * return 0 + * + * if order == 'F' == get_best_order(&dst, ndim): # <<<<<<<<<<<<<< + * + * + */ + } + + /* "View.MemoryView":1329 + * transpose_memslice(&dst) + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) # <<<<<<<<<<<<<< + * copy_strided_to_strided(&src, &dst, ndim, itemsize) + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + */ + __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0); + + /* "View.MemoryView":1330 + * + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + * copy_strided_to_strided(&src, &dst, ndim, itemsize) # <<<<<<<<<<<<<< + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + * + */ + copy_strided_to_strided((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize); + + /* "View.MemoryView":1331 + * refcount_copying(&dst, dtype_is_object, ndim, inc=False) + * copy_strided_to_strided(&src, &dst, ndim, itemsize) + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) # <<<<<<<<<<<<<< + * + * free(tmpdata) + */ + __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1); + + /* "View.MemoryView":1333 + * refcount_copying(&dst, dtype_is_object, ndim, inc=True) + * + * free(tmpdata) # <<<<<<<<<<<<<< + * return 0 + * + */ + free(__pyx_v_tmpdata); + + /* "View.MemoryView":1334 + * + * free(tmpdata) + * return 0 # <<<<<<<<<<<<<< + * + * @cname('__pyx_memoryview_broadcast_leading') + */ + __pyx_r = 0; + goto __pyx_L0; + + /* "View.MemoryView":1265 + * + * @cname('__pyx_memoryview_copy_contents') + * cdef int memoryview_copy_contents(__Pyx_memviewslice src, # <<<<<<<<<<<<<< + * __Pyx_memviewslice dst, + * int src_ndim, int dst_ndim, + */ + + /* function exit code */ + __pyx_L1_error:; + #ifdef WITH_THREAD + __pyx_gilstate_save = __Pyx_PyGILState_Ensure(); + #endif + __Pyx_AddTraceback("View.MemoryView.memoryview_copy_contents", __pyx_clineno, __pyx_lineno, __pyx_filename); + __pyx_r = -1; + #ifdef WITH_THREAD + __Pyx_PyGILState_Release(__pyx_gilstate_save); + #endif + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1337 + * + * @cname('__pyx_memoryview_broadcast_leading') + * cdef void broadcast_leading(__Pyx_memviewslice *mslice, # <<<<<<<<<<<<<< + * int ndim, + * int ndim_other) noexcept nogil: + */ + +static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *__pyx_v_mslice, int __pyx_v_ndim, int __pyx_v_ndim_other) { + int __pyx_v_i; + int __pyx_v_offset; + int __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + + /* "View.MemoryView":1341 + * int ndim_other) noexcept nogil: + * cdef int i + * cdef int offset = ndim_other - ndim # <<<<<<<<<<<<<< + * + * for i in range(ndim - 1, -1, -1): + */ + __pyx_v_offset = (__pyx_v_ndim_other - __pyx_v_ndim); + + /* "View.MemoryView":1343 + * cdef int offset = ndim_other - ndim + * + * for i in range(ndim - 1, -1, -1): # <<<<<<<<<<<<<< + * mslice.shape[i + offset] = mslice.shape[i] + * mslice.strides[i + offset] = mslice.strides[i] + */ + for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) { + __pyx_v_i = __pyx_t_1; + + /* "View.MemoryView":1344 + * + * for i in range(ndim - 1, -1, -1): + * mslice.shape[i + offset] = mslice.shape[i] # <<<<<<<<<<<<<< + * mslice.strides[i + offset] = mslice.strides[i] + * mslice.suboffsets[i + offset] = mslice.suboffsets[i] + */ + (__pyx_v_mslice->shape[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->shape[__pyx_v_i]); + + /* "View.MemoryView":1345 + * for i in range(ndim - 1, -1, -1): + * mslice.shape[i + offset] = mslice.shape[i] + * mslice.strides[i + offset] = mslice.strides[i] # <<<<<<<<<<<<<< + * mslice.suboffsets[i + offset] = mslice.suboffsets[i] + * + */ + (__pyx_v_mslice->strides[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->strides[__pyx_v_i]); + + /* "View.MemoryView":1346 + * mslice.shape[i + offset] = mslice.shape[i] + * mslice.strides[i + offset] = mslice.strides[i] + * mslice.suboffsets[i + offset] = mslice.suboffsets[i] # <<<<<<<<<<<<<< + * + * for i in range(offset): + */ + (__pyx_v_mslice->suboffsets[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->suboffsets[__pyx_v_i]); + } + + /* "View.MemoryView":1348 + * mslice.suboffsets[i + offset] = mslice.suboffsets[i] + * + * for i in range(offset): # <<<<<<<<<<<<<< + * mslice.shape[i] = 1 + * mslice.strides[i] = mslice.strides[0] + */ + __pyx_t_1 = __pyx_v_offset; + __pyx_t_2 = __pyx_t_1; + for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) { + __pyx_v_i = __pyx_t_3; + + /* "View.MemoryView":1349 + * + * for i in range(offset): + * mslice.shape[i] = 1 # <<<<<<<<<<<<<< + * mslice.strides[i] = mslice.strides[0] + * mslice.suboffsets[i] = -1 + */ + (__pyx_v_mslice->shape[__pyx_v_i]) = 1; + + /* "View.MemoryView":1350 + * for i in range(offset): + * mslice.shape[i] = 1 + * mslice.strides[i] = mslice.strides[0] # <<<<<<<<<<<<<< + * mslice.suboffsets[i] = -1 + * + */ + (__pyx_v_mslice->strides[__pyx_v_i]) = (__pyx_v_mslice->strides[0]); + + /* "View.MemoryView":1351 + * mslice.shape[i] = 1 + * mslice.strides[i] = mslice.strides[0] + * mslice.suboffsets[i] = -1 # <<<<<<<<<<<<<< + * + * + */ + (__pyx_v_mslice->suboffsets[__pyx_v_i]) = -1L; + } + + /* "View.MemoryView":1337 + * + * @cname('__pyx_memoryview_broadcast_leading') + * cdef void broadcast_leading(__Pyx_memviewslice *mslice, # <<<<<<<<<<<<<< + * int ndim, + * int ndim_other) noexcept nogil: + */ + + /* function exit code */ +} + +/* "View.MemoryView":1359 + * + * @cname('__pyx_memoryview_refcount_copying') + * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil: # <<<<<<<<<<<<<< + * + * if dtype_is_object: + */ + +static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *__pyx_v_dst, int __pyx_v_dtype_is_object, int __pyx_v_ndim, int __pyx_v_inc) { + + /* "View.MemoryView":1361 + * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil: + * + * if dtype_is_object: # <<<<<<<<<<<<<< + * refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc) + * + */ + if (__pyx_v_dtype_is_object) { + + /* "View.MemoryView":1362 + * + * if dtype_is_object: + * refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc) # <<<<<<<<<<<<<< + * + * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil') + */ + __pyx_memoryview_refcount_objects_in_slice_with_gil(__pyx_v_dst->data, __pyx_v_dst->shape, __pyx_v_dst->strides, __pyx_v_ndim, __pyx_v_inc); + + /* "View.MemoryView":1361 + * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil: + * + * if dtype_is_object: # <<<<<<<<<<<<<< + * refcount_objects_in_slice_with_gil(dst.data, dst.shape, dst.strides, ndim, inc) + * + */ + } + + /* "View.MemoryView":1359 + * + * @cname('__pyx_memoryview_refcount_copying') + * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object, int ndim, bint inc) noexcept nogil: # <<<<<<<<<<<<<< + * + * if dtype_is_object: + */ + + /* function exit code */ +} + +/* "View.MemoryView":1365 + * + * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil') + * cdef void refcount_objects_in_slice_with_gil(char *data, Py_ssize_t *shape, # <<<<<<<<<<<<<< + * Py_ssize_t *strides, int ndim, + * bint inc) noexcept with gil: + */ + +static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, int __pyx_v_inc) { + #ifdef WITH_THREAD + PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure(); + #endif + + /* "View.MemoryView":1368 + * Py_ssize_t *strides, int ndim, + * bint inc) noexcept with gil: + * refcount_objects_in_slice(data, shape, strides, ndim, inc) # <<<<<<<<<<<<<< + * + * @cname('__pyx_memoryview_refcount_objects_in_slice') + */ + __pyx_memoryview_refcount_objects_in_slice(__pyx_v_data, __pyx_v_shape, __pyx_v_strides, __pyx_v_ndim, __pyx_v_inc); + + /* "View.MemoryView":1365 + * + * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil') + * cdef void refcount_objects_in_slice_with_gil(char *data, Py_ssize_t *shape, # <<<<<<<<<<<<<< + * Py_ssize_t *strides, int ndim, + * bint inc) noexcept with gil: + */ + + /* function exit code */ + #ifdef WITH_THREAD + __Pyx_PyGILState_Release(__pyx_gilstate_save); + #endif +} + +/* "View.MemoryView":1371 + * + * @cname('__pyx_memoryview_refcount_objects_in_slice') + * cdef void refcount_objects_in_slice(char *data, Py_ssize_t *shape, # <<<<<<<<<<<<<< + * Py_ssize_t *strides, int ndim, bint inc) noexcept: + * cdef Py_ssize_t i + */ + +static void __pyx_memoryview_refcount_objects_in_slice(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, int __pyx_v_inc) { + CYTHON_UNUSED Py_ssize_t __pyx_v_i; + Py_ssize_t __pyx_v_stride; + Py_ssize_t __pyx_t_1; + Py_ssize_t __pyx_t_2; + Py_ssize_t __pyx_t_3; + int __pyx_t_4; + + /* "View.MemoryView":1374 + * Py_ssize_t *strides, int ndim, bint inc) noexcept: + * cdef Py_ssize_t i + * cdef Py_ssize_t stride = strides[0] # <<<<<<<<<<<<<< + * + * for i in range(shape[0]): + */ + __pyx_v_stride = (__pyx_v_strides[0]); + + /* "View.MemoryView":1376 + * cdef Py_ssize_t stride = strides[0] + * + * for i in range(shape[0]): # <<<<<<<<<<<<<< + * if ndim == 1: + * if inc: + */ + __pyx_t_1 = (__pyx_v_shape[0]); + __pyx_t_2 = __pyx_t_1; + for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) { + __pyx_v_i = __pyx_t_3; + + /* "View.MemoryView":1377 + * + * for i in range(shape[0]): + * if ndim == 1: # <<<<<<<<<<<<<< + * if inc: + * Py_INCREF(( data)[0]) + */ + __pyx_t_4 = (__pyx_v_ndim == 1); + if (__pyx_t_4) { + + /* "View.MemoryView":1378 + * for i in range(shape[0]): + * if ndim == 1: + * if inc: # <<<<<<<<<<<<<< + * Py_INCREF(( data)[0]) + * else: + */ + if (__pyx_v_inc) { + + /* "View.MemoryView":1379 + * if ndim == 1: + * if inc: + * Py_INCREF(( data)[0]) # <<<<<<<<<<<<<< + * else: + * Py_DECREF(( data)[0]) + */ + Py_INCREF((((PyObject **)__pyx_v_data)[0])); + + /* "View.MemoryView":1378 + * for i in range(shape[0]): + * if ndim == 1: + * if inc: # <<<<<<<<<<<<<< + * Py_INCREF(( data)[0]) + * else: + */ + goto __pyx_L6; + } + + /* "View.MemoryView":1381 + * Py_INCREF(( data)[0]) + * else: + * Py_DECREF(( data)[0]) # <<<<<<<<<<<<<< + * else: + * refcount_objects_in_slice(data, shape + 1, strides + 1, ndim - 1, inc) + */ + /*else*/ { + Py_DECREF((((PyObject **)__pyx_v_data)[0])); + } + __pyx_L6:; + + /* "View.MemoryView":1377 + * + * for i in range(shape[0]): + * if ndim == 1: # <<<<<<<<<<<<<< + * if inc: + * Py_INCREF(( data)[0]) + */ + goto __pyx_L5; + } + + /* "View.MemoryView":1383 + * Py_DECREF(( data)[0]) + * else: + * refcount_objects_in_slice(data, shape + 1, strides + 1, ndim - 1, inc) # <<<<<<<<<<<<<< + * + * data += stride + */ + /*else*/ { + __pyx_memoryview_refcount_objects_in_slice(__pyx_v_data, (__pyx_v_shape + 1), (__pyx_v_strides + 1), (__pyx_v_ndim - 1), __pyx_v_inc); + } + __pyx_L5:; + + /* "View.MemoryView":1385 + * refcount_objects_in_slice(data, shape + 1, strides + 1, ndim - 1, inc) + * + * data += stride # <<<<<<<<<<<<<< + * + * + */ + __pyx_v_data = (__pyx_v_data + __pyx_v_stride); + } + + /* "View.MemoryView":1371 + * + * @cname('__pyx_memoryview_refcount_objects_in_slice') + * cdef void refcount_objects_in_slice(char *data, Py_ssize_t *shape, # <<<<<<<<<<<<<< + * Py_ssize_t *strides, int ndim, bint inc) noexcept: + * cdef Py_ssize_t i + */ + + /* function exit code */ +} + +/* "View.MemoryView":1391 + * + * @cname('__pyx_memoryview_slice_assign_scalar') + * cdef void slice_assign_scalar(__Pyx_memviewslice *dst, int ndim, # <<<<<<<<<<<<<< + * size_t itemsize, void *item, + * bint dtype_is_object) noexcept nogil: + */ + +static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize, void *__pyx_v_item, int __pyx_v_dtype_is_object) { + + /* "View.MemoryView":1394 + * size_t itemsize, void *item, + * bint dtype_is_object) noexcept nogil: + * refcount_copying(dst, dtype_is_object, ndim, inc=False) # <<<<<<<<<<<<<< + * _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim, itemsize, item) + * refcount_copying(dst, dtype_is_object, ndim, inc=True) + */ + __pyx_memoryview_refcount_copying(__pyx_v_dst, __pyx_v_dtype_is_object, __pyx_v_ndim, 0); + + /* "View.MemoryView":1395 + * bint dtype_is_object) noexcept nogil: + * refcount_copying(dst, dtype_is_object, ndim, inc=False) + * _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim, itemsize, item) # <<<<<<<<<<<<<< + * refcount_copying(dst, dtype_is_object, ndim, inc=True) + * + */ + __pyx_memoryview__slice_assign_scalar(__pyx_v_dst->data, __pyx_v_dst->shape, __pyx_v_dst->strides, __pyx_v_ndim, __pyx_v_itemsize, __pyx_v_item); + + /* "View.MemoryView":1396 + * refcount_copying(dst, dtype_is_object, ndim, inc=False) + * _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim, itemsize, item) + * refcount_copying(dst, dtype_is_object, ndim, inc=True) # <<<<<<<<<<<<<< + * + * + */ + __pyx_memoryview_refcount_copying(__pyx_v_dst, __pyx_v_dtype_is_object, __pyx_v_ndim, 1); + + /* "View.MemoryView":1391 + * + * @cname('__pyx_memoryview_slice_assign_scalar') + * cdef void slice_assign_scalar(__Pyx_memviewslice *dst, int ndim, # <<<<<<<<<<<<<< + * size_t itemsize, void *item, + * bint dtype_is_object) noexcept nogil: + */ + + /* function exit code */ +} + +/* "View.MemoryView":1400 + * + * @cname('__pyx_memoryview__slice_assign_scalar') + * cdef void _slice_assign_scalar(char *data, Py_ssize_t *shape, # <<<<<<<<<<<<<< + * Py_ssize_t *strides, int ndim, + * size_t itemsize, void *item) noexcept nogil: + */ + +static void __pyx_memoryview__slice_assign_scalar(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, size_t __pyx_v_itemsize, void *__pyx_v_item) { + CYTHON_UNUSED Py_ssize_t __pyx_v_i; + Py_ssize_t __pyx_v_stride; + Py_ssize_t __pyx_v_extent; + int __pyx_t_1; + Py_ssize_t __pyx_t_2; + Py_ssize_t __pyx_t_3; + Py_ssize_t __pyx_t_4; + + /* "View.MemoryView":1404 + * size_t itemsize, void *item) noexcept nogil: + * cdef Py_ssize_t i + * cdef Py_ssize_t stride = strides[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t extent = shape[0] + * + */ + __pyx_v_stride = (__pyx_v_strides[0]); + + /* "View.MemoryView":1405 + * cdef Py_ssize_t i + * cdef Py_ssize_t stride = strides[0] + * cdef Py_ssize_t extent = shape[0] # <<<<<<<<<<<<<< + * + * if ndim == 1: + */ + __pyx_v_extent = (__pyx_v_shape[0]); + + /* "View.MemoryView":1407 + * cdef Py_ssize_t extent = shape[0] + * + * if ndim == 1: # <<<<<<<<<<<<<< + * for i in range(extent): + * memcpy(data, item, itemsize) + */ + __pyx_t_1 = (__pyx_v_ndim == 1); + if (__pyx_t_1) { + + /* "View.MemoryView":1408 + * + * if ndim == 1: + * for i in range(extent): # <<<<<<<<<<<<<< + * memcpy(data, item, itemsize) + * data += stride + */ + __pyx_t_2 = __pyx_v_extent; + __pyx_t_3 = __pyx_t_2; + for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) { + __pyx_v_i = __pyx_t_4; + + /* "View.MemoryView":1409 + * if ndim == 1: + * for i in range(extent): + * memcpy(data, item, itemsize) # <<<<<<<<<<<<<< + * data += stride + * else: + */ + (void)(memcpy(__pyx_v_data, __pyx_v_item, __pyx_v_itemsize)); + + /* "View.MemoryView":1410 + * for i in range(extent): + * memcpy(data, item, itemsize) + * data += stride # <<<<<<<<<<<<<< + * else: + * for i in range(extent): + */ + __pyx_v_data = (__pyx_v_data + __pyx_v_stride); + } + + /* "View.MemoryView":1407 + * cdef Py_ssize_t extent = shape[0] + * + * if ndim == 1: # <<<<<<<<<<<<<< + * for i in range(extent): + * memcpy(data, item, itemsize) + */ + goto __pyx_L3; + } + + /* "View.MemoryView":1412 + * data += stride + * else: + * for i in range(extent): # <<<<<<<<<<<<<< + * _slice_assign_scalar(data, shape + 1, strides + 1, ndim - 1, itemsize, item) + * data += stride + */ + /*else*/ { + __pyx_t_2 = __pyx_v_extent; + __pyx_t_3 = __pyx_t_2; + for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) { + __pyx_v_i = __pyx_t_4; + + /* "View.MemoryView":1413 + * else: + * for i in range(extent): + * _slice_assign_scalar(data, shape + 1, strides + 1, ndim - 1, itemsize, item) # <<<<<<<<<<<<<< + * data += stride + * + */ + __pyx_memoryview__slice_assign_scalar(__pyx_v_data, (__pyx_v_shape + 1), (__pyx_v_strides + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize, __pyx_v_item); + + /* "View.MemoryView":1414 + * for i in range(extent): + * _slice_assign_scalar(data, shape + 1, strides + 1, ndim - 1, itemsize, item) + * data += stride # <<<<<<<<<<<<<< + * + * + */ + __pyx_v_data = (__pyx_v_data + __pyx_v_stride); + } + } + __pyx_L3:; + + /* "View.MemoryView":1400 + * + * @cname('__pyx_memoryview__slice_assign_scalar') + * cdef void _slice_assign_scalar(char *data, Py_ssize_t *shape, # <<<<<<<<<<<<<< + * Py_ssize_t *strides, int ndim, + * size_t itemsize, void *item) noexcept nogil: + */ + + /* function exit code */ +} + +/* "(tree fragment)":1 + * def __pyx_unpickle_Enum(__pyx_type, long __pyx_checksum, __pyx_state): # <<<<<<<<<<<<<< + * cdef object __pyx_PickleError + * cdef object __pyx_result + */ + +/* Python wrapper */ +static PyObject *__pyx_pw_15View_dot_MemoryView_1__pyx_unpickle_Enum(PyObject *__pyx_self, +#if CYTHON_METH_FASTCALL +PyObject *const *__pyx_args, Py_ssize_t __pyx_nargs, PyObject *__pyx_kwds +#else +PyObject *__pyx_args, PyObject *__pyx_kwds +#endif +); /*proto*/ +static PyMethodDef __pyx_mdef_15View_dot_MemoryView_1__pyx_unpickle_Enum = {"__pyx_unpickle_Enum", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw_15View_dot_MemoryView_1__pyx_unpickle_Enum, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}; +static PyObject *__pyx_pw_15View_dot_MemoryView_1__pyx_unpickle_Enum(PyObject *__pyx_self, +#if CYTHON_METH_FASTCALL +PyObject *const *__pyx_args, Py_ssize_t __pyx_nargs, PyObject *__pyx_kwds +#else +PyObject *__pyx_args, PyObject *__pyx_kwds +#endif +) { + PyObject *__pyx_v___pyx_type = 0; + long __pyx_v___pyx_checksum; + PyObject *__pyx_v___pyx_state = 0; + #if 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{"__getattr__", (PyCFunction)__pyx_array___getattr__, METH_O|METH_COEXIST, 0}, + {"__reduce_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_array_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"__setstate_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_array_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {0, 0, 0, 0} +}; + +static struct PyGetSetDef __pyx_getsets_array[] = { + {(char *)"memview", __pyx_getprop___pyx_array_memview, 0, (char *)0, 0}, + {0, 0, 0, 0, 0} +}; +#if CYTHON_USE_TYPE_SPECS +#if !CYTHON_COMPILING_IN_LIMITED_API + +static PyBufferProcs __pyx_tp_as_buffer_array = { + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getreadbuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getwritebuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getsegcount*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getcharbuffer*/ + #endif + __pyx_array_getbuffer, /*bf_getbuffer*/ + 0, /*bf_releasebuffer*/ +}; +#endif +static PyType_Slot __pyx_type___pyx_array_slots[] = { + {Py_tp_dealloc, (void *)__pyx_tp_dealloc_array}, + {Py_sq_length, (void *)__pyx_array___len__}, + {Py_sq_item, (void *)__pyx_sq_item_array}, + {Py_mp_length, (void *)__pyx_array___len__}, + {Py_mp_subscript, (void *)__pyx_array___getitem__}, + {Py_mp_ass_subscript, (void *)__pyx_mp_ass_subscript_array}, + {Py_tp_getattro, (void *)__pyx_tp_getattro_array}, + #if defined(Py_bf_getbuffer) + {Py_bf_getbuffer, (void *)__pyx_array_getbuffer}, + #endif + {Py_tp_methods, (void *)__pyx_methods_array}, + {Py_tp_getset, (void *)__pyx_getsets_array}, + {Py_tp_new, (void *)__pyx_tp_new_array}, + {0, 0}, +}; +static PyType_Spec __pyx_type___pyx_array_spec = { + "pygom.model._tau_leap.array", + sizeof(struct __pyx_array_obj), + 0, + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_SEQUENCE, + __pyx_type___pyx_array_slots, +}; +#else + +static PySequenceMethods __pyx_tp_as_sequence_array = { + __pyx_array___len__, /*sq_length*/ + 0, /*sq_concat*/ + 0, /*sq_repeat*/ + __pyx_sq_item_array, /*sq_item*/ + 0, /*sq_slice*/ + 0, /*sq_ass_item*/ + 0, /*sq_ass_slice*/ + 0, /*sq_contains*/ + 0, /*sq_inplace_concat*/ + 0, /*sq_inplace_repeat*/ +}; + +static PyMappingMethods __pyx_tp_as_mapping_array = { + __pyx_array___len__, /*mp_length*/ + __pyx_array___getitem__, /*mp_subscript*/ + __pyx_mp_ass_subscript_array, /*mp_ass_subscript*/ +}; + +static PyBufferProcs __pyx_tp_as_buffer_array = { + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getreadbuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getwritebuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getsegcount*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getcharbuffer*/ + #endif + __pyx_array_getbuffer, /*bf_getbuffer*/ + 0, /*bf_releasebuffer*/ +}; + +static PyTypeObject __pyx_type___pyx_array = { + PyVarObject_HEAD_INIT(0, 0) + "pygom.model._tau_leap.""array", /*tp_name*/ + sizeof(struct __pyx_array_obj), /*tp_basicsize*/ + 0, /*tp_itemsize*/ + __pyx_tp_dealloc_array, /*tp_dealloc*/ + #if PY_VERSION_HEX < 0x030800b4 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030800b4 + 0, /*tp_vectorcall_offset*/ + #endif + 0, /*tp_getattr*/ + 0, /*tp_setattr*/ + #if PY_MAJOR_VERSION < 3 + 0, /*tp_compare*/ + #endif + #if PY_MAJOR_VERSION >= 3 + 0, /*tp_as_async*/ + #endif + 0, /*tp_repr*/ + 0, /*tp_as_number*/ + &__pyx_tp_as_sequence_array, /*tp_as_sequence*/ + &__pyx_tp_as_mapping_array, /*tp_as_mapping*/ + 0, /*tp_hash*/ + 0, /*tp_call*/ + 0, /*tp_str*/ + __pyx_tp_getattro_array, /*tp_getattro*/ + 0, /*tp_setattro*/ + &__pyx_tp_as_buffer_array, /*tp_as_buffer*/ + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_SEQUENCE, /*tp_flags*/ + 0, /*tp_doc*/ + 0, /*tp_traverse*/ + 0, /*tp_clear*/ + 0, /*tp_richcompare*/ + 0, /*tp_weaklistoffset*/ + 0, /*tp_iter*/ + 0, /*tp_iternext*/ + __pyx_methods_array, /*tp_methods*/ + 0, /*tp_members*/ + __pyx_getsets_array, /*tp_getset*/ + 0, /*tp_base*/ + 0, /*tp_dict*/ + 0, /*tp_descr_get*/ + 0, /*tp_descr_set*/ + #if !CYTHON_USE_TYPE_SPECS + 0, /*tp_dictoffset*/ + #endif + 0, /*tp_init*/ + 0, /*tp_alloc*/ + __pyx_tp_new_array, /*tp_new*/ + 0, /*tp_free*/ + 0, /*tp_is_gc*/ + 0, /*tp_bases*/ + 0, /*tp_mro*/ + 0, /*tp_cache*/ + 0, /*tp_subclasses*/ + 0, /*tp_weaklist*/ + 0, /*tp_del*/ + 0, /*tp_version_tag*/ + #if PY_VERSION_HEX >= 0x030400a1 + #if CYTHON_USE_TP_FINALIZE + 0, /*tp_finalize*/ + #else + NULL, /*tp_finalize*/ + #endif + #endif + #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800) + 0, /*tp_vectorcall*/ + #endif + #if __PYX_NEED_TP_PRINT_SLOT == 1 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030C0000 + 0, /*tp_watched*/ + #endif + #if PY_VERSION_HEX >= 0x030d00A4 + 0, /*tp_versions_used*/ + #endif + #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000 + 0, /*tp_pypy_flags*/ + #endif +}; +#endif + +static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) { + struct __pyx_MemviewEnum_obj *p; + PyObject *o; + #if CYTHON_COMPILING_IN_LIMITED_API + allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc); + o = alloc_func(t, 0); + #else + if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) { + o = (*t->tp_alloc)(t, 0); + } else { + o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0); + } + if (unlikely(!o)) return 0; + #endif + p = ((struct __pyx_MemviewEnum_obj *)o); + p->name = Py_None; Py_INCREF(Py_None); + return o; +} + +static void __pyx_tp_dealloc_Enum(PyObject *o) { + struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o; + #if CYTHON_USE_TP_FINALIZE + if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) { + if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_Enum) { + if (PyObject_CallFinalizerFromDealloc(o)) return; + } + } + #endif + PyObject_GC_UnTrack(o); + Py_CLEAR(p->name); + #if CYTHON_USE_TYPE_SLOTS || CYTHON_COMPILING_IN_PYPY + (*Py_TYPE(o)->tp_free)(o); + #else + { + freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free); + if (tp_free) tp_free(o); + } + #endif +} + +static int __pyx_tp_traverse_Enum(PyObject *o, visitproc v, void *a) { + int e; + struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o; + if (p->name) { + e = (*v)(p->name, a); if (e) return e; + } + return 0; +} + +static int __pyx_tp_clear_Enum(PyObject *o) { + PyObject* tmp; + struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o; + tmp = ((PyObject*)p->name); + p->name = Py_None; Py_INCREF(Py_None); + Py_XDECREF(tmp); + return 0; +} + +static PyObject *__pyx_specialmethod___pyx_MemviewEnum___repr__(PyObject *self, CYTHON_UNUSED PyObject *arg) { + return __pyx_MemviewEnum___repr__(self); +} + +static PyMethodDef __pyx_methods_Enum[] = { + {"__repr__", (PyCFunction)__pyx_specialmethod___pyx_MemviewEnum___repr__, METH_NOARGS|METH_COEXIST, 0}, + {"__reduce_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_MemviewEnum_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"__setstate_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_MemviewEnum_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {0, 0, 0, 0} +}; +#if CYTHON_USE_TYPE_SPECS +static PyType_Slot __pyx_type___pyx_MemviewEnum_slots[] = { + {Py_tp_dealloc, (void *)__pyx_tp_dealloc_Enum}, + {Py_tp_repr, (void *)__pyx_MemviewEnum___repr__}, + {Py_tp_traverse, (void *)__pyx_tp_traverse_Enum}, + {Py_tp_clear, (void *)__pyx_tp_clear_Enum}, + {Py_tp_methods, (void *)__pyx_methods_Enum}, + {Py_tp_init, (void *)__pyx_MemviewEnum___init__}, + {Py_tp_new, (void *)__pyx_tp_new_Enum}, + {0, 0}, +}; +static PyType_Spec __pyx_type___pyx_MemviewEnum_spec = { + "pygom.model._tau_leap.Enum", + sizeof(struct __pyx_MemviewEnum_obj), + 0, + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, + __pyx_type___pyx_MemviewEnum_slots, +}; +#else + +static PyTypeObject __pyx_type___pyx_MemviewEnum = { + PyVarObject_HEAD_INIT(0, 0) + "pygom.model._tau_leap.""Enum", /*tp_name*/ + sizeof(struct __pyx_MemviewEnum_obj), /*tp_basicsize*/ + 0, /*tp_itemsize*/ + __pyx_tp_dealloc_Enum, /*tp_dealloc*/ + #if PY_VERSION_HEX < 0x030800b4 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030800b4 + 0, /*tp_vectorcall_offset*/ + #endif + 0, /*tp_getattr*/ + 0, /*tp_setattr*/ + #if PY_MAJOR_VERSION < 3 + 0, /*tp_compare*/ + #endif + #if PY_MAJOR_VERSION >= 3 + 0, /*tp_as_async*/ + #endif + __pyx_MemviewEnum___repr__, /*tp_repr*/ + 0, /*tp_as_number*/ + 0, /*tp_as_sequence*/ + 0, /*tp_as_mapping*/ + 0, /*tp_hash*/ + 0, /*tp_call*/ + 0, /*tp_str*/ + 0, /*tp_getattro*/ + 0, /*tp_setattro*/ + 0, /*tp_as_buffer*/ + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/ + 0, /*tp_doc*/ + __pyx_tp_traverse_Enum, /*tp_traverse*/ + __pyx_tp_clear_Enum, /*tp_clear*/ + 0, /*tp_richcompare*/ + 0, /*tp_weaklistoffset*/ + 0, /*tp_iter*/ + 0, /*tp_iternext*/ + __pyx_methods_Enum, /*tp_methods*/ + 0, /*tp_members*/ + 0, /*tp_getset*/ + 0, /*tp_base*/ + 0, /*tp_dict*/ + 0, /*tp_descr_get*/ + 0, /*tp_descr_set*/ + #if !CYTHON_USE_TYPE_SPECS + 0, /*tp_dictoffset*/ + #endif + __pyx_MemviewEnum___init__, /*tp_init*/ + 0, /*tp_alloc*/ + __pyx_tp_new_Enum, /*tp_new*/ + 0, /*tp_free*/ + 0, /*tp_is_gc*/ + 0, /*tp_bases*/ + 0, /*tp_mro*/ + 0, /*tp_cache*/ + 0, /*tp_subclasses*/ + 0, /*tp_weaklist*/ + 0, /*tp_del*/ + 0, /*tp_version_tag*/ + #if PY_VERSION_HEX >= 0x030400a1 + #if CYTHON_USE_TP_FINALIZE + 0, /*tp_finalize*/ + #else + NULL, /*tp_finalize*/ + #endif + #endif + #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800) + 0, /*tp_vectorcall*/ + #endif + #if __PYX_NEED_TP_PRINT_SLOT == 1 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030C0000 + 0, /*tp_watched*/ + #endif + #if PY_VERSION_HEX >= 0x030d00A4 + 0, /*tp_versions_used*/ + #endif + #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000 + 0, /*tp_pypy_flags*/ + #endif +}; +#endif +static struct __pyx_vtabstruct_memoryview __pyx_vtable_memoryview; + +static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k) { + struct __pyx_memoryview_obj *p; + PyObject *o; + #if CYTHON_COMPILING_IN_LIMITED_API + allocfunc alloc_func = (allocfunc)PyType_GetSlot(t, Py_tp_alloc); + o = alloc_func(t, 0); + #else + if (likely(!__Pyx_PyType_HasFeature(t, Py_TPFLAGS_IS_ABSTRACT))) { + o = (*t->tp_alloc)(t, 0); + } else { + o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0); + } + if (unlikely(!o)) return 0; + #endif + p = ((struct __pyx_memoryview_obj *)o); + p->__pyx_vtab = __pyx_vtabptr_memoryview; + p->obj = Py_None; Py_INCREF(Py_None); + p->_size = Py_None; Py_INCREF(Py_None); + p->_array_interface = Py_None; Py_INCREF(Py_None); + p->view.obj = NULL; + if (unlikely(__pyx_memoryview___cinit__(o, a, k) < 0)) goto bad; + return o; + bad: + Py_DECREF(o); o = 0; + return NULL; +} + +static void __pyx_tp_dealloc_memoryview(PyObject *o) { + struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o; + #if CYTHON_USE_TP_FINALIZE + if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) { + if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc_memoryview) { + if (PyObject_CallFinalizerFromDealloc(o)) return; + } + } + #endif + PyObject_GC_UnTrack(o); + { + PyObject *etype, *eval, *etb; + PyErr_Fetch(&etype, &eval, &etb); + __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1); + __pyx_memoryview___dealloc__(o); + __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1); + PyErr_Restore(etype, eval, etb); + } + Py_CLEAR(p->obj); + Py_CLEAR(p->_size); + Py_CLEAR(p->_array_interface); + #if CYTHON_USE_TYPE_SLOTS || CYTHON_COMPILING_IN_PYPY + (*Py_TYPE(o)->tp_free)(o); + #else + { + freefunc tp_free = (freefunc)PyType_GetSlot(Py_TYPE(o), Py_tp_free); + if (tp_free) tp_free(o); + } + #endif +} + +static int __pyx_tp_traverse_memoryview(PyObject *o, visitproc v, void *a) { + int e; + struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o; + if (p->obj) { + e = (*v)(p->obj, a); if (e) return e; + } + if (p->_size) { + e = (*v)(p->_size, a); if (e) return e; + } + if (p->_array_interface) { + e = (*v)(p->_array_interface, a); if (e) return e; + } + if (p->view.obj) { + e = (*v)(p->view.obj, a); if (e) return e; + } + return 0; +} + +static int __pyx_tp_clear_memoryview(PyObject *o) { + PyObject* tmp; + struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o; + tmp = ((PyObject*)p->obj); + p->obj = Py_None; Py_INCREF(Py_None); + Py_XDECREF(tmp); + tmp = ((PyObject*)p->_size); + p->_size = Py_None; Py_INCREF(Py_None); + Py_XDECREF(tmp); + tmp = ((PyObject*)p->_array_interface); + p->_array_interface = Py_None; Py_INCREF(Py_None); + Py_XDECREF(tmp); + Py_CLEAR(p->view.obj); + return 0; +} +static PyObject *__pyx_sq_item_memoryview(PyObject *o, Py_ssize_t i) { + PyObject *r; + PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0; + r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x); + Py_DECREF(x); + return r; +} + +static int __pyx_mp_ass_subscript_memoryview(PyObject *o, PyObject *i, PyObject *v) { + if (v) { + return __pyx_memoryview___setitem__(o, i, v); + } + else { + __Pyx_TypeName o_type_name; + o_type_name = __Pyx_PyType_GetName(Py_TYPE(o)); + PyErr_Format(PyExc_NotImplementedError, + "Subscript deletion not supported by " __Pyx_FMT_TYPENAME, o_type_name); + __Pyx_DECREF_TypeName(o_type_name); + return -1; + } +} + +static PyObject *__pyx_getprop___pyx_memoryview_T(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_1T_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_base(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_4base_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_shape(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_5shape_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_strides(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_7strides_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_suboffsets(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_10suboffsets_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_ndim(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_4ndim_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_itemsize(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_8itemsize_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_nbytes(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_6nbytes_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_size(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_4size_1__get__(o); +} + +static PyObject *__pyx_specialmethod___pyx_memoryview___repr__(PyObject *self, CYTHON_UNUSED PyObject *arg) { + return __pyx_memoryview___repr__(self); +} + +static PyMethodDef __pyx_methods_memoryview[] = { + {"__repr__", (PyCFunction)__pyx_specialmethod___pyx_memoryview___repr__, METH_NOARGS|METH_COEXIST, 0}, + {"is_c_contig", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_is_c_contig, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"is_f_contig", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_is_f_contig, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"copy", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_copy, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"copy_fortran", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_memoryview_copy_fortran, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"__reduce_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_memoryview_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"__setstate_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_memoryview_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {0, 0, 0, 0} +}; + +static struct PyGetSetDef __pyx_getsets_memoryview[] = { + {(char *)"T", __pyx_getprop___pyx_memoryview_T, 0, (char *)0, 0}, + {(char *)"base", __pyx_getprop___pyx_memoryview_base, 0, (char *)0, 0}, + {(char *)"shape", __pyx_getprop___pyx_memoryview_shape, 0, (char *)0, 0}, + {(char *)"strides", __pyx_getprop___pyx_memoryview_strides, 0, (char *)0, 0}, + {(char *)"suboffsets", __pyx_getprop___pyx_memoryview_suboffsets, 0, (char *)0, 0}, + {(char *)"ndim", __pyx_getprop___pyx_memoryview_ndim, 0, (char *)0, 0}, + {(char *)"itemsize", __pyx_getprop___pyx_memoryview_itemsize, 0, (char *)0, 0}, + {(char *)"nbytes", __pyx_getprop___pyx_memoryview_nbytes, 0, (char *)0, 0}, + {(char *)"size", __pyx_getprop___pyx_memoryview_size, 0, (char *)0, 0}, + {0, 0, 0, 0, 0} +}; +#if CYTHON_USE_TYPE_SPECS +#if !CYTHON_COMPILING_IN_LIMITED_API + +static PyBufferProcs __pyx_tp_as_buffer_memoryview = { + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getreadbuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getwritebuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getsegcount*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getcharbuffer*/ + #endif + __pyx_memoryview_getbuffer, /*bf_getbuffer*/ + 0, /*bf_releasebuffer*/ +}; +#endif +static PyType_Slot __pyx_type___pyx_memoryview_slots[] = { + {Py_tp_dealloc, (void *)__pyx_tp_dealloc_memoryview}, + {Py_tp_repr, (void *)__pyx_memoryview___repr__}, + {Py_sq_length, (void *)__pyx_memoryview___len__}, + {Py_sq_item, (void *)__pyx_sq_item_memoryview}, + {Py_mp_length, (void *)__pyx_memoryview___len__}, + {Py_mp_subscript, (void *)__pyx_memoryview___getitem__}, + {Py_mp_ass_subscript, (void *)__pyx_mp_ass_subscript_memoryview}, + {Py_tp_str, (void *)__pyx_memoryview___str__}, + #if defined(Py_bf_getbuffer) + {Py_bf_getbuffer, (void *)__pyx_memoryview_getbuffer}, + #endif + {Py_tp_traverse, (void *)__pyx_tp_traverse_memoryview}, + {Py_tp_clear, (void *)__pyx_tp_clear_memoryview}, + {Py_tp_methods, (void *)__pyx_methods_memoryview}, + {Py_tp_getset, (void *)__pyx_getsets_memoryview}, + {Py_tp_new, (void *)__pyx_tp_new_memoryview}, + {0, 0}, +}; +static PyType_Spec __pyx_type___pyx_memoryview_spec = { + "pygom.model._tau_leap.memoryview", + sizeof(struct __pyx_memoryview_obj), + 0, + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, + __pyx_type___pyx_memoryview_slots, +}; +#else + +static PySequenceMethods __pyx_tp_as_sequence_memoryview = { + __pyx_memoryview___len__, /*sq_length*/ + 0, /*sq_concat*/ + 0, /*sq_repeat*/ + __pyx_sq_item_memoryview, /*sq_item*/ + 0, /*sq_slice*/ + 0, /*sq_ass_item*/ + 0, /*sq_ass_slice*/ + 0, /*sq_contains*/ + 0, /*sq_inplace_concat*/ + 0, /*sq_inplace_repeat*/ +}; + +static PyMappingMethods __pyx_tp_as_mapping_memoryview = { + __pyx_memoryview___len__, /*mp_length*/ + __pyx_memoryview___getitem__, /*mp_subscript*/ + __pyx_mp_ass_subscript_memoryview, /*mp_ass_subscript*/ +}; + +static PyBufferProcs __pyx_tp_as_buffer_memoryview = { + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getreadbuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getwritebuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getsegcount*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getcharbuffer*/ + #endif + __pyx_memoryview_getbuffer, /*bf_getbuffer*/ + 0, /*bf_releasebuffer*/ +}; + +static PyTypeObject __pyx_type___pyx_memoryview = { + PyVarObject_HEAD_INIT(0, 0) + "pygom.model._tau_leap.""memoryview", /*tp_name*/ + sizeof(struct __pyx_memoryview_obj), /*tp_basicsize*/ + 0, /*tp_itemsize*/ + __pyx_tp_dealloc_memoryview, /*tp_dealloc*/ + #if PY_VERSION_HEX < 0x030800b4 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030800b4 + 0, /*tp_vectorcall_offset*/ + #endif + 0, /*tp_getattr*/ + 0, /*tp_setattr*/ + #if PY_MAJOR_VERSION < 3 + 0, /*tp_compare*/ + #endif + #if PY_MAJOR_VERSION >= 3 + 0, /*tp_as_async*/ + #endif + __pyx_memoryview___repr__, /*tp_repr*/ + 0, /*tp_as_number*/ + &__pyx_tp_as_sequence_memoryview, /*tp_as_sequence*/ + &__pyx_tp_as_mapping_memoryview, /*tp_as_mapping*/ + 0, /*tp_hash*/ + 0, /*tp_call*/ + __pyx_memoryview___str__, /*tp_str*/ + 0, /*tp_getattro*/ + 0, /*tp_setattro*/ + &__pyx_tp_as_buffer_memoryview, /*tp_as_buffer*/ + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/ + 0, /*tp_doc*/ + __pyx_tp_traverse_memoryview, /*tp_traverse*/ + __pyx_tp_clear_memoryview, /*tp_clear*/ + 0, /*tp_richcompare*/ + 0, /*tp_weaklistoffset*/ + 0, /*tp_iter*/ + 0, /*tp_iternext*/ + __pyx_methods_memoryview, /*tp_methods*/ + 0, /*tp_members*/ + __pyx_getsets_memoryview, /*tp_getset*/ + 0, /*tp_base*/ + 0, /*tp_dict*/ + 0, /*tp_descr_get*/ + 0, /*tp_descr_set*/ + #if !CYTHON_USE_TYPE_SPECS + 0, /*tp_dictoffset*/ + #endif + 0, /*tp_init*/ + 0, /*tp_alloc*/ + __pyx_tp_new_memoryview, /*tp_new*/ + 0, /*tp_free*/ + 0, /*tp_is_gc*/ + 0, /*tp_bases*/ + 0, /*tp_mro*/ + 0, /*tp_cache*/ + 0, /*tp_subclasses*/ + 0, /*tp_weaklist*/ + 0, /*tp_del*/ + 0, /*tp_version_tag*/ + #if PY_VERSION_HEX >= 0x030400a1 + #if CYTHON_USE_TP_FINALIZE + 0, /*tp_finalize*/ + #else + NULL, /*tp_finalize*/ + #endif + #endif + #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800) + 0, /*tp_vectorcall*/ + #endif + #if __PYX_NEED_TP_PRINT_SLOT == 1 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030C0000 + 0, /*tp_watched*/ + #endif + #if PY_VERSION_HEX >= 0x030d00A4 + 0, /*tp_versions_used*/ + #endif + #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000 + 0, /*tp_pypy_flags*/ + #endif +}; +#endif +static struct __pyx_vtabstruct__memoryviewslice __pyx_vtable__memoryviewslice; + +static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k) { + struct __pyx_memoryviewslice_obj *p; + PyObject *o = __pyx_tp_new_memoryview(t, a, k); + if (unlikely(!o)) return 0; + p = ((struct __pyx_memoryviewslice_obj *)o); + p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_memoryview*)__pyx_vtabptr__memoryviewslice; + p->from_object = Py_None; Py_INCREF(Py_None); + p->from_slice.memview = NULL; + return o; +} + +static void __pyx_tp_dealloc__memoryviewslice(PyObject *o) { + struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o; + #if CYTHON_USE_TP_FINALIZE + if (unlikely((PY_VERSION_HEX >= 0x03080000 || __Pyx_PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE)) && __Pyx_PyObject_GetSlot(o, tp_finalize, destructor)) && !__Pyx_PyObject_GC_IsFinalized(o)) { + if (__Pyx_PyObject_GetSlot(o, tp_dealloc, destructor) == __pyx_tp_dealloc__memoryviewslice) { + if (PyObject_CallFinalizerFromDealloc(o)) return; + } + } + #endif + PyObject_GC_UnTrack(o); + { + PyObject *etype, *eval, *etb; + PyErr_Fetch(&etype, &eval, &etb); + __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1); + __pyx_memoryviewslice___dealloc__(o); + __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1); + PyErr_Restore(etype, eval, etb); + } + Py_CLEAR(p->from_object); + PyObject_GC_Track(o); + __pyx_tp_dealloc_memoryview(o); +} + +static int __pyx_tp_traverse__memoryviewslice(PyObject *o, visitproc v, void *a) { + int e; + struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o; + e = __pyx_tp_traverse_memoryview(o, v, a); if (e) return e; + if (p->from_object) { + e = (*v)(p->from_object, a); if (e) return e; + } + return 0; +} + +static int __pyx_tp_clear__memoryviewslice(PyObject *o) { + PyObject* tmp; + struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o; + __pyx_tp_clear_memoryview(o); + tmp = ((PyObject*)p->from_object); + p->from_object = Py_None; Py_INCREF(Py_None); + Py_XDECREF(tmp); + __PYX_XCLEAR_MEMVIEW(&p->from_slice, 1); + return 0; +} + +static PyMethodDef __pyx_methods__memoryviewslice[] = { + {"__reduce_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_memoryviewslice_1__reduce_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {"__setstate_cython__", (PyCFunction)(void*)(__Pyx_PyCFunction_FastCallWithKeywords)__pyx_pw___pyx_memoryviewslice_3__setstate_cython__, __Pyx_METH_FASTCALL|METH_KEYWORDS, 0}, + {0, 0, 0, 0} +}; +#if CYTHON_USE_TYPE_SPECS +static PyType_Slot __pyx_type___pyx_memoryviewslice_slots[] = { + {Py_tp_dealloc, (void *)__pyx_tp_dealloc__memoryviewslice}, + {Py_tp_doc, (void *)PyDoc_STR("Internal class for passing memoryview slices to Python")}, + {Py_tp_traverse, (void *)__pyx_tp_traverse__memoryviewslice}, + {Py_tp_clear, (void *)__pyx_tp_clear__memoryviewslice}, + {Py_tp_methods, (void *)__pyx_methods__memoryviewslice}, + {Py_tp_new, (void *)__pyx_tp_new__memoryviewslice}, + {0, 0}, +}; +static PyType_Spec __pyx_type___pyx_memoryviewslice_spec = { + "pygom.model._tau_leap._memoryviewslice", + sizeof(struct __pyx_memoryviewslice_obj), + 0, + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC|Py_TPFLAGS_SEQUENCE, + __pyx_type___pyx_memoryviewslice_slots, +}; +#else + +static PyTypeObject __pyx_type___pyx_memoryviewslice = { + PyVarObject_HEAD_INIT(0, 0) + "pygom.model._tau_leap.""_memoryviewslice", /*tp_name*/ + sizeof(struct __pyx_memoryviewslice_obj), /*tp_basicsize*/ + 0, /*tp_itemsize*/ + __pyx_tp_dealloc__memoryviewslice, /*tp_dealloc*/ + #if PY_VERSION_HEX < 0x030800b4 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030800b4 + 0, /*tp_vectorcall_offset*/ + #endif + 0, /*tp_getattr*/ + 0, /*tp_setattr*/ + #if PY_MAJOR_VERSION < 3 + 0, /*tp_compare*/ + #endif + #if PY_MAJOR_VERSION >= 3 + 0, /*tp_as_async*/ + #endif + #if CYTHON_COMPILING_IN_PYPY || 0 + __pyx_memoryview___repr__, /*tp_repr*/ + #else + 0, /*tp_repr*/ + #endif + 0, /*tp_as_number*/ + 0, /*tp_as_sequence*/ + 0, /*tp_as_mapping*/ + 0, /*tp_hash*/ + 0, /*tp_call*/ + #if CYTHON_COMPILING_IN_PYPY || 0 + __pyx_memoryview___str__, /*tp_str*/ + #else + 0, /*tp_str*/ + #endif + 0, /*tp_getattro*/ + 0, /*tp_setattro*/ + 0, /*tp_as_buffer*/ + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC|Py_TPFLAGS_SEQUENCE, /*tp_flags*/ + PyDoc_STR("Internal class for passing memoryview slices to Python"), /*tp_doc*/ + __pyx_tp_traverse__memoryviewslice, /*tp_traverse*/ + __pyx_tp_clear__memoryviewslice, /*tp_clear*/ + 0, /*tp_richcompare*/ + 0, /*tp_weaklistoffset*/ + 0, /*tp_iter*/ + 0, /*tp_iternext*/ + __pyx_methods__memoryviewslice, /*tp_methods*/ + 0, /*tp_members*/ + 0, /*tp_getset*/ + 0, /*tp_base*/ + 0, /*tp_dict*/ + 0, /*tp_descr_get*/ + 0, /*tp_descr_set*/ + #if !CYTHON_USE_TYPE_SPECS + 0, /*tp_dictoffset*/ + #endif + 0, /*tp_init*/ + 0, /*tp_alloc*/ + __pyx_tp_new__memoryviewslice, /*tp_new*/ + 0, /*tp_free*/ + 0, /*tp_is_gc*/ + 0, /*tp_bases*/ + 0, /*tp_mro*/ + 0, /*tp_cache*/ + 0, /*tp_subclasses*/ + 0, /*tp_weaklist*/ + 0, /*tp_del*/ + 0, /*tp_version_tag*/ + #if PY_VERSION_HEX >= 0x030400a1 + #if CYTHON_USE_TP_FINALIZE + 0, /*tp_finalize*/ + #else + NULL, /*tp_finalize*/ + #endif + #endif + #if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800) + 0, /*tp_vectorcall*/ + #endif + #if __PYX_NEED_TP_PRINT_SLOT == 1 + 0, /*tp_print*/ + #endif + #if PY_VERSION_HEX >= 0x030C0000 + 0, /*tp_watched*/ + #endif + #if PY_VERSION_HEX >= 0x030d00A4 + 0, /*tp_versions_used*/ + #endif + #if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000 + 0, /*tp_pypy_flags*/ + #endif +}; +#endif + +static PyMethodDef __pyx_methods[] = { + {0, 0, 0, 0} +}; +#ifndef CYTHON_SMALL_CODE +#if defined(__clang__) + #define CYTHON_SMALL_CODE +#elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) + #define CYTHON_SMALL_CODE __attribute__((cold)) +#else + #define CYTHON_SMALL_CODE +#endif +#endif +/* #### Code section: pystring_table ### */ + +static int __Pyx_CreateStringTabAndInitStrings(void) { + __Pyx_StringTabEntry __pyx_string_tab[] = { + {&__pyx_kp_u_, __pyx_k_, sizeof(__pyx_k_), 0, 1, 0, 0}, + {&__pyx_n_s_ASCII, __pyx_k_ASCII, sizeof(__pyx_k_ASCII), 0, 0, 1, 1}, + {&__pyx_kp_s_All_dimensions_preceding_dimensi, __pyx_k_All_dimensions_preceding_dimensi, sizeof(__pyx_k_All_dimensions_preceding_dimensi), 0, 0, 1, 0}, + {&__pyx_n_s_AssertionError, __pyx_k_AssertionError, sizeof(__pyx_k_AssertionError), 0, 0, 1, 1}, + {&__pyx_kp_s_Buffer_view_does_not_expose_stri, __pyx_k_Buffer_view_does_not_expose_stri, sizeof(__pyx_k_Buffer_view_does_not_expose_stri), 0, 0, 1, 0}, + {&__pyx_kp_s_Can_only_create_a_buffer_that_is, __pyx_k_Can_only_create_a_buffer_that_is, sizeof(__pyx_k_Can_only_create_a_buffer_that_is), 0, 0, 1, 0}, + {&__pyx_kp_s_Cannot_assign_to_read_only_memor, __pyx_k_Cannot_assign_to_read_only_memor, sizeof(__pyx_k_Cannot_assign_to_read_only_memor), 0, 0, 1, 0}, + {&__pyx_kp_s_Cannot_create_writable_memory_vi, __pyx_k_Cannot_create_writable_memory_vi, sizeof(__pyx_k_Cannot_create_writable_memory_vi), 0, 0, 1, 0}, + {&__pyx_kp_u_Cannot_index_with_type, __pyx_k_Cannot_index_with_type, sizeof(__pyx_k_Cannot_index_with_type), 0, 1, 0, 0}, + {&__pyx_kp_s_Cannot_transpose_memoryview_with, __pyx_k_Cannot_transpose_memoryview_with, sizeof(__pyx_k_Cannot_transpose_memoryview_with), 0, 0, 1, 0}, + {&__pyx_kp_s_Dimension_d_is_not_direct, __pyx_k_Dimension_d_is_not_direct, sizeof(__pyx_k_Dimension_d_is_not_direct), 0, 0, 1, 0}, + {&__pyx_n_s_Ellipsis, __pyx_k_Ellipsis, sizeof(__pyx_k_Ellipsis), 0, 0, 1, 1}, + {&__pyx_kp_s_Empty_shape_tuple_for_cython_arr, __pyx_k_Empty_shape_tuple_for_cython_arr, sizeof(__pyx_k_Empty_shape_tuple_for_cython_arr), 0, 0, 1, 0}, + {&__pyx_n_s_ImportError, __pyx_k_ImportError, 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+#else + if (s1 == s2) { + return (equals == Py_EQ); + } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) { + const char *ps1, *ps2; + Py_ssize_t length = PyBytes_GET_SIZE(s1); + if (length != PyBytes_GET_SIZE(s2)) + return (equals == Py_NE); + ps1 = PyBytes_AS_STRING(s1); + ps2 = PyBytes_AS_STRING(s2); + if (ps1[0] != ps2[0]) { + return (equals == Py_NE); + } else if (length == 1) { + return (equals == Py_EQ); + } else { + int result; +#if CYTHON_USE_UNICODE_INTERNALS && (PY_VERSION_HEX < 0x030B0000) + Py_hash_t hash1, hash2; + hash1 = ((PyBytesObject*)s1)->ob_shash; + hash2 = ((PyBytesObject*)s2)->ob_shash; + if (hash1 != hash2 && hash1 != -1 && hash2 != -1) { + return (equals == Py_NE); + } +#endif + result = memcmp(ps1, ps2, (size_t)length); + return (equals == Py_EQ) ? (result == 0) : (result != 0); + } + } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) { + return (equals == Py_NE); + } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) { + return (equals == Py_NE); + } else { + int result; + PyObject* py_result = PyObject_RichCompare(s1, s2, equals); + if (!py_result) + return -1; + result = __Pyx_PyObject_IsTrue(py_result); + Py_DECREF(py_result); + return result; + } +#endif +} + +/* UnicodeEquals */ +static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) { +#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API + return PyObject_RichCompareBool(s1, s2, equals); +#else +#if PY_MAJOR_VERSION < 3 + PyObject* owned_ref = NULL; +#endif + int s1_is_unicode, s2_is_unicode; + if (s1 == s2) { + goto return_eq; + } + s1_is_unicode = PyUnicode_CheckExact(s1); + s2_is_unicode = PyUnicode_CheckExact(s2); +#if PY_MAJOR_VERSION < 3 + if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) { + owned_ref = PyUnicode_FromObject(s2); + if (unlikely(!owned_ref)) + return -1; + s2 = owned_ref; + s2_is_unicode = 1; + } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) { + owned_ref = PyUnicode_FromObject(s1); + if (unlikely(!owned_ref)) + return -1; + s1 = owned_ref; + s1_is_unicode = 1; + } else if (((!s2_is_unicode) & (!s1_is_unicode))) { + return __Pyx_PyBytes_Equals(s1, s2, equals); + } +#endif + if (s1_is_unicode & s2_is_unicode) { + Py_ssize_t length; + int kind; + void *data1, *data2; + if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0)) + return -1; + length = __Pyx_PyUnicode_GET_LENGTH(s1); + if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) { + goto return_ne; + } +#if CYTHON_USE_UNICODE_INTERNALS + { + Py_hash_t hash1, hash2; + #if CYTHON_PEP393_ENABLED + hash1 = ((PyASCIIObject*)s1)->hash; + hash2 = ((PyASCIIObject*)s2)->hash; + #else + hash1 = ((PyUnicodeObject*)s1)->hash; + hash2 = ((PyUnicodeObject*)s2)->hash; + #endif + if (hash1 != hash2 && hash1 != -1 && hash2 != -1) { + goto return_ne; + } + } +#endif + kind = __Pyx_PyUnicode_KIND(s1); + if (kind != __Pyx_PyUnicode_KIND(s2)) { + goto return_ne; + } + data1 = __Pyx_PyUnicode_DATA(s1); + data2 = __Pyx_PyUnicode_DATA(s2); + if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) { + goto return_ne; + } else if (length == 1) { + goto return_eq; + } else { + int result = memcmp(data1, data2, (size_t)(length * kind)); + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + return (equals == Py_EQ) ? (result == 0) : (result != 0); + } + } else if ((s1 == Py_None) & s2_is_unicode) { + goto return_ne; + } else if ((s2 == Py_None) & s1_is_unicode) { + goto return_ne; + } else { + int result; + PyObject* py_result = PyObject_RichCompare(s1, s2, equals); + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + if (!py_result) + return -1; + result = __Pyx_PyObject_IsTrue(py_result); + Py_DECREF(py_result); + return result; + } +return_eq: + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + return (equals == Py_EQ); +return_ne: + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + return (equals == Py_NE); +#endif +} + +/* fastcall */ +#if CYTHON_METH_FASTCALL +static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s) +{ + Py_ssize_t i, n = PyTuple_GET_SIZE(kwnames); + for (i = 0; i < n; i++) + { + if (s == PyTuple_GET_ITEM(kwnames, i)) return kwvalues[i]; + } + for (i = 0; i < n; i++) + { + int eq = __Pyx_PyUnicode_Equals(s, PyTuple_GET_ITEM(kwnames, i), Py_EQ); + if (unlikely(eq != 0)) { + if (unlikely(eq < 0)) return NULL; + return kwvalues[i]; + } + } + return NULL; +} +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000 +CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues) { + Py_ssize_t i, nkwargs = PyTuple_GET_SIZE(kwnames); + PyObject *dict; + dict = PyDict_New(); + if (unlikely(!dict)) + return NULL; + for (i=0; i= 3 + "%s() got multiple values for keyword argument '%U'", func_name, kw_name); + #else + "%s() got multiple values for keyword argument '%s'", func_name, + PyString_AsString(kw_name)); + #endif +} + +/* ParseKeywords */ +static int __Pyx_ParseOptionalKeywords( + PyObject *kwds, + PyObject *const *kwvalues, + PyObject **argnames[], + PyObject *kwds2, + PyObject *values[], + Py_ssize_t num_pos_args, + const char* function_name) +{ + PyObject *key = 0, *value = 0; + Py_ssize_t pos = 0; + PyObject*** name; + PyObject*** first_kw_arg = argnames + num_pos_args; + int kwds_is_tuple = CYTHON_METH_FASTCALL && likely(PyTuple_Check(kwds)); + while (1) { + Py_XDECREF(key); key = NULL; + Py_XDECREF(value); value = NULL; + if (kwds_is_tuple) { + Py_ssize_t size; +#if CYTHON_ASSUME_SAFE_MACROS + size = PyTuple_GET_SIZE(kwds); +#else + size = PyTuple_Size(kwds); + if (size < 0) goto bad; +#endif + if (pos >= size) break; +#if CYTHON_AVOID_BORROWED_REFS + key = __Pyx_PySequence_ITEM(kwds, pos); + if (!key) goto bad; +#elif CYTHON_ASSUME_SAFE_MACROS + key = PyTuple_GET_ITEM(kwds, pos); +#else + key = PyTuple_GetItem(kwds, pos); + if (!key) goto bad; +#endif + value = kwvalues[pos]; + pos++; + } + else + { + if (!PyDict_Next(kwds, &pos, &key, &value)) break; +#if CYTHON_AVOID_BORROWED_REFS + Py_INCREF(key); +#endif + } + name = first_kw_arg; + while (*name && (**name != key)) name++; + if (*name) { + values[name-argnames] = value; +#if CYTHON_AVOID_BORROWED_REFS + Py_INCREF(value); + Py_DECREF(key); +#endif + key = NULL; + value = NULL; + continue; + } +#if !CYTHON_AVOID_BORROWED_REFS + Py_INCREF(key); +#endif + Py_INCREF(value); + name = first_kw_arg; + #if PY_MAJOR_VERSION < 3 + if (likely(PyString_Check(key))) { + while (*name) { + if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key)) + && _PyString_Eq(**name, key)) { + values[name-argnames] = value; +#if CYTHON_AVOID_BORROWED_REFS + value = NULL; +#endif + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + if ((**argname == key) || ( + (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key)) + && _PyString_Eq(**argname, key))) { + goto arg_passed_twice; + } + argname++; + } + } + } else + #endif + if (likely(PyUnicode_Check(key))) { + while (*name) { + int cmp = ( + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 : + #endif + PyUnicode_Compare(**name, key) + ); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) { + values[name-argnames] = value; +#if CYTHON_AVOID_BORROWED_REFS + value = NULL; +#endif + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + int cmp = (**argname == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 : + #endif + PyUnicode_Compare(**argname, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) goto arg_passed_twice; + argname++; + } + } + } else + goto invalid_keyword_type; + if (kwds2) { + if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad; + } else { + goto invalid_keyword; + } + } + Py_XDECREF(key); + Py_XDECREF(value); + return 0; +arg_passed_twice: + __Pyx_RaiseDoubleKeywordsError(function_name, key); + goto bad; +invalid_keyword_type: + PyErr_Format(PyExc_TypeError, + "%.200s() keywords must be strings", function_name); + goto bad; +invalid_keyword: + #if PY_MAJOR_VERSION < 3 + PyErr_Format(PyExc_TypeError, + "%.200s() got an unexpected keyword argument '%.200s'", + function_name, PyString_AsString(key)); + #else + PyErr_Format(PyExc_TypeError, + "%s() got an unexpected keyword argument '%U'", + function_name, key); + #endif +bad: + Py_XDECREF(key); + Py_XDECREF(value); + return -1; +} + +/* ArgTypeTest */ +static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact) +{ + __Pyx_TypeName type_name; + __Pyx_TypeName obj_type_name; + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + else if (exact) { + #if PY_MAJOR_VERSION == 2 + if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1; + #endif + } + else { + if (likely(__Pyx_TypeCheck(obj, type))) return 1; + } + type_name = __Pyx_PyType_GetName(type); + obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj)); + PyErr_Format(PyExc_TypeError, + "Argument '%.200s' has incorrect type (expected " __Pyx_FMT_TYPENAME + ", got " __Pyx_FMT_TYPENAME ")", name, type_name, obj_type_name); + __Pyx_DECREF_TypeName(type_name); + __Pyx_DECREF_TypeName(obj_type_name); + return 0; +} + +/* RaiseException */ +#if PY_MAJOR_VERSION < 3 +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) { + __Pyx_PyThreadState_declare + CYTHON_UNUSED_VAR(cause); + Py_XINCREF(type); + if (!value || value == Py_None) + value = NULL; + else + Py_INCREF(value); + if (!tb || tb == Py_None) + tb = NULL; + else { + Py_INCREF(tb); + if (!PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto raise_error; + } + } + if (PyType_Check(type)) { +#if CYTHON_COMPILING_IN_PYPY + if (!value) { + Py_INCREF(Py_None); + value = Py_None; + } +#endif + PyErr_NormalizeException(&type, &value, &tb); + } else { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto raise_error; + } + value = type; + type = (PyObject*) Py_TYPE(type); + Py_INCREF(type); + if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto raise_error; + } + } + __Pyx_PyThreadState_assign + __Pyx_ErrRestore(type, value, tb); + return; +raise_error: + Py_XDECREF(value); + Py_XDECREF(type); + Py_XDECREF(tb); + return; +} +#else +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) { + PyObject* owned_instance = NULL; + if (tb == Py_None) { + tb = 0; + } else if (tb && !PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto bad; + } + if (value == Py_None) + value = 0; + if (PyExceptionInstance_Check(type)) { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto bad; + } + value = type; + type = (PyObject*) Py_TYPE(value); + } else if (PyExceptionClass_Check(type)) { + PyObject *instance_class = NULL; + if (value && PyExceptionInstance_Check(value)) { + instance_class = (PyObject*) Py_TYPE(value); + if (instance_class != type) { + int is_subclass = PyObject_IsSubclass(instance_class, type); + if (!is_subclass) { + instance_class = NULL; + } else if (unlikely(is_subclass == -1)) { + goto bad; + } else { + type = instance_class; + } + } + } + if (!instance_class) { + PyObject *args; + if (!value) + args = PyTuple_New(0); + else if (PyTuple_Check(value)) { + Py_INCREF(value); + args = value; + } else + args = PyTuple_Pack(1, value); + if (!args) + goto bad; + owned_instance = PyObject_Call(type, args, NULL); + Py_DECREF(args); + if (!owned_instance) + goto bad; + value = owned_instance; + if (!PyExceptionInstance_Check(value)) { + PyErr_Format(PyExc_TypeError, + "calling %R should have returned an instance of " + "BaseException, not %R", + type, Py_TYPE(value)); + goto bad; + } + } + } else { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto bad; + } + if (cause) { + PyObject *fixed_cause; + if (cause == Py_None) { + fixed_cause = NULL; + } else if (PyExceptionClass_Check(cause)) { + fixed_cause = PyObject_CallObject(cause, NULL); + if (fixed_cause == NULL) + goto bad; + } else if (PyExceptionInstance_Check(cause)) { + fixed_cause = cause; + Py_INCREF(fixed_cause); + } else { + PyErr_SetString(PyExc_TypeError, + "exception causes must derive from " + "BaseException"); + goto bad; + } + PyException_SetCause(value, fixed_cause); + } + PyErr_SetObject(type, value); + if (tb) { + #if PY_VERSION_HEX >= 0x030C00A6 + PyException_SetTraceback(value, tb); + #elif CYTHON_FAST_THREAD_STATE + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject* tmp_tb = tstate->curexc_traceback; + if (tb != tmp_tb) { + Py_INCREF(tb); + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_tb); + } +#else + PyObject *tmp_type, *tmp_value, *tmp_tb; + PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb); + Py_INCREF(tb); + PyErr_Restore(tmp_type, tmp_value, tb); + Py_XDECREF(tmp_tb); +#endif + } +bad: + Py_XDECREF(owned_instance); + return; +} +#endif + +/* PyFunctionFastCall */ +#if CYTHON_FAST_PYCALL && !CYTHON_VECTORCALL +static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na, + PyObject *globals) { + PyFrameObject *f; + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject **fastlocals; + Py_ssize_t i; + PyObject *result; + assert(globals != NULL); + /* XXX Perhaps we should create a specialized + PyFrame_New() that doesn't take locals, but does + take builtins without sanity checking them. + */ + assert(tstate != NULL); + f = PyFrame_New(tstate, co, globals, NULL); + if (f == NULL) { + return NULL; + } + fastlocals = __Pyx_PyFrame_GetLocalsplus(f); + for (i = 0; i < na; i++) { + Py_INCREF(*args); + fastlocals[i] = *args++; + } + result = PyEval_EvalFrameEx(f,0); + ++tstate->recursion_depth; + Py_DECREF(f); + --tstate->recursion_depth; + return result; +} +static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs) { + PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func); + PyObject *globals = PyFunction_GET_GLOBALS(func); + PyObject *argdefs = PyFunction_GET_DEFAULTS(func); + PyObject *closure; +#if PY_MAJOR_VERSION >= 3 + PyObject *kwdefs; +#endif + PyObject *kwtuple, **k; + PyObject **d; + Py_ssize_t nd; + Py_ssize_t nk; + PyObject *result; + assert(kwargs == NULL || PyDict_Check(kwargs)); + nk = kwargs ? PyDict_Size(kwargs) : 0; + #if PY_MAJOR_VERSION < 3 + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) { + return NULL; + } + #else + if (unlikely(Py_EnterRecursiveCall(" while calling a Python object"))) { + return NULL; + } + #endif + if ( +#if PY_MAJOR_VERSION >= 3 + co->co_kwonlyargcount == 0 && +#endif + likely(kwargs == NULL || nk == 0) && + co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) { + if (argdefs == NULL && co->co_argcount == nargs) { + result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals); + goto done; + } + else if (nargs == 0 && argdefs != NULL + && co->co_argcount == Py_SIZE(argdefs)) { + /* function called with no arguments, but all parameters have + a default value: use default values as arguments .*/ + args = &PyTuple_GET_ITEM(argdefs, 0); + result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals); + goto done; + } + } + if (kwargs != NULL) { + Py_ssize_t pos, i; + kwtuple = PyTuple_New(2 * nk); + if (kwtuple == NULL) { + result = NULL; + goto done; + } + k = &PyTuple_GET_ITEM(kwtuple, 0); + pos = i = 0; + while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) { + Py_INCREF(k[i]); + Py_INCREF(k[i+1]); + i += 2; + } + nk = i / 2; + } + else { + kwtuple = NULL; + k = NULL; + } + closure = PyFunction_GET_CLOSURE(func); +#if PY_MAJOR_VERSION >= 3 + kwdefs = PyFunction_GET_KW_DEFAULTS(func); +#endif + if (argdefs != NULL) { + d = &PyTuple_GET_ITEM(argdefs, 0); + nd = Py_SIZE(argdefs); + } + else { + d = NULL; + nd = 0; + } +#if PY_MAJOR_VERSION >= 3 + result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL, + args, (int)nargs, + k, (int)nk, + d, (int)nd, kwdefs, closure); +#else + result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL, + args, (int)nargs, + k, (int)nk, + d, (int)nd, closure); +#endif + Py_XDECREF(kwtuple); +done: + Py_LeaveRecursiveCall(); + return result; +} +#endif + +/* PyObjectCall */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { + PyObject *result; + ternaryfunc call = Py_TYPE(func)->tp_call; + if (unlikely(!call)) + return PyObject_Call(func, arg, kw); + #if PY_MAJOR_VERSION < 3 + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + #else + if (unlikely(Py_EnterRecursiveCall(" while calling a Python object"))) + return NULL; + #endif + result = (*call)(func, arg, kw); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* PyObjectCallMethO */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) { + PyObject *self, *result; + PyCFunction cfunc; + cfunc = __Pyx_CyOrPyCFunction_GET_FUNCTION(func); + self = __Pyx_CyOrPyCFunction_GET_SELF(func); + #if PY_MAJOR_VERSION < 3 + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + #else + if (unlikely(Py_EnterRecursiveCall(" while calling a Python object"))) + return NULL; + #endif + result = cfunc(self, arg); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* PyObjectFastCall */ +#if PY_VERSION_HEX < 0x03090000 || CYTHON_COMPILING_IN_LIMITED_API +static PyObject* __Pyx_PyObject_FastCall_fallback(PyObject *func, PyObject **args, size_t nargs, PyObject *kwargs) { + PyObject *argstuple; + PyObject *result = 0; + size_t i; + argstuple = PyTuple_New((Py_ssize_t)nargs); + if (unlikely(!argstuple)) return NULL; + for (i = 0; i < nargs; i++) { + Py_INCREF(args[i]); + if (__Pyx_PyTuple_SET_ITEM(argstuple, (Py_ssize_t)i, args[i]) < 0) goto bad; + } + result = __Pyx_PyObject_Call(func, argstuple, kwargs); + bad: + Py_DECREF(argstuple); + return result; +} +#endif +static CYTHON_INLINE PyObject* __Pyx_PyObject_FastCallDict(PyObject *func, PyObject **args, size_t _nargs, PyObject *kwargs) { + Py_ssize_t nargs = __Pyx_PyVectorcall_NARGS(_nargs); +#if CYTHON_COMPILING_IN_CPYTHON + if (nargs == 0 && kwargs == NULL) { + if (__Pyx_CyOrPyCFunction_Check(func) && likely( __Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_NOARGS)) + return __Pyx_PyObject_CallMethO(func, NULL); + } + else if (nargs == 1 && kwargs == NULL) { + if (__Pyx_CyOrPyCFunction_Check(func) && likely( __Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_O)) + return __Pyx_PyObject_CallMethO(func, args[0]); + } +#endif + #if PY_VERSION_HEX < 0x030800B1 + #if CYTHON_FAST_PYCCALL + if (PyCFunction_Check(func)) { + if (kwargs) { + return _PyCFunction_FastCallDict(func, args, nargs, kwargs); + } else { + return _PyCFunction_FastCallKeywords(func, args, nargs, NULL); + } + } + #if PY_VERSION_HEX >= 0x030700A1 + if (!kwargs && __Pyx_IS_TYPE(func, &PyMethodDescr_Type)) { + return _PyMethodDescr_FastCallKeywords(func, args, nargs, NULL); + } + #endif + #endif + #if CYTHON_FAST_PYCALL + if (PyFunction_Check(func)) { + return __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs); + } + #endif + #endif + if (kwargs == NULL) { + #if CYTHON_VECTORCALL + #if PY_VERSION_HEX < 0x03090000 + vectorcallfunc f = _PyVectorcall_Function(func); + #else + vectorcallfunc f = PyVectorcall_Function(func); + #endif + if (f) { + return f(func, args, (size_t)nargs, NULL); + } + #elif defined(__Pyx_CyFunction_USED) && CYTHON_BACKPORT_VECTORCALL + if (__Pyx_CyFunction_CheckExact(func)) { + __pyx_vectorcallfunc f = __Pyx_CyFunction_func_vectorcall(func); + if (f) return f(func, args, (size_t)nargs, NULL); + } + #endif + } + if (nargs == 0) { + return __Pyx_PyObject_Call(func, __pyx_empty_tuple, kwargs); + } + #if PY_VERSION_HEX >= 0x03090000 && !CYTHON_COMPILING_IN_LIMITED_API + return PyObject_VectorcallDict(func, args, (size_t)nargs, kwargs); + #else + return __Pyx_PyObject_FastCall_fallback(func, args, (size_t)nargs, kwargs); + #endif +} + +/* RaiseUnexpectedTypeError */ +static int +__Pyx_RaiseUnexpectedTypeError(const char *expected, PyObject *obj) +{ + __Pyx_TypeName obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj)); + PyErr_Format(PyExc_TypeError, "Expected %s, got " __Pyx_FMT_TYPENAME, + expected, obj_type_name); + __Pyx_DECREF_TypeName(obj_type_name); + return 0; +} + +/* CIntToDigits */ +static const char DIGIT_PAIRS_10[2*10*10+1] = { + "00010203040506070809" + "10111213141516171819" + "20212223242526272829" + "30313233343536373839" + "40414243444546474849" + "50515253545556575859" + "60616263646566676869" + "70717273747576777879" + "80818283848586878889" + "90919293949596979899" +}; +static const char DIGIT_PAIRS_8[2*8*8+1] = { + "0001020304050607" + "1011121314151617" + "2021222324252627" + "3031323334353637" + "4041424344454647" + "5051525354555657" + "6061626364656667" + "7071727374757677" +}; +static const char DIGITS_HEX[2*16+1] = { + "0123456789abcdef" + "0123456789ABCDEF" +}; + +/* BuildPyUnicode */ +static PyObject* __Pyx_PyUnicode_BuildFromAscii(Py_ssize_t ulength, char* chars, int clength, + int prepend_sign, char padding_char) { + PyObject *uval; + Py_ssize_t uoffset = ulength - clength; +#if CYTHON_USE_UNICODE_INTERNALS + Py_ssize_t i; +#if CYTHON_PEP393_ENABLED + void *udata; + uval = PyUnicode_New(ulength, 127); + if (unlikely(!uval)) return NULL; + udata = PyUnicode_DATA(uval); +#else + Py_UNICODE *udata; + uval = PyUnicode_FromUnicode(NULL, ulength); + if (unlikely(!uval)) return NULL; + udata = PyUnicode_AS_UNICODE(uval); +#endif + if (uoffset > 0) { + i = 0; + if (prepend_sign) { + __Pyx_PyUnicode_WRITE(PyUnicode_1BYTE_KIND, udata, 0, '-'); + i++; + } + for (; i < uoffset; i++) { + __Pyx_PyUnicode_WRITE(PyUnicode_1BYTE_KIND, udata, i, padding_char); + } + } + for (i=0; i < clength; i++) { + __Pyx_PyUnicode_WRITE(PyUnicode_1BYTE_KIND, udata, uoffset+i, chars[i]); + } +#else + { + PyObject *sign = NULL, *padding = NULL; + uval = NULL; + if (uoffset > 0) { + prepend_sign = !!prepend_sign; + if (uoffset > prepend_sign) { + padding = PyUnicode_FromOrdinal(padding_char); + if (likely(padding) && uoffset > prepend_sign + 1) { + PyObject *tmp; + PyObject *repeat = PyInt_FromSsize_t(uoffset - prepend_sign); + if (unlikely(!repeat)) goto done_or_error; + tmp = PyNumber_Multiply(padding, repeat); + Py_DECREF(repeat); + Py_DECREF(padding); + padding = tmp; + } + if (unlikely(!padding)) goto done_or_error; + } + if (prepend_sign) { + sign = PyUnicode_FromOrdinal('-'); + if (unlikely(!sign)) goto done_or_error; + } + } + uval = PyUnicode_DecodeASCII(chars, clength, NULL); + if (likely(uval) && padding) { + PyObject *tmp = PyNumber_Add(padding, uval); + Py_DECREF(uval); + uval = tmp; + } + if (likely(uval) && sign) { + PyObject *tmp = PyNumber_Add(sign, uval); + Py_DECREF(uval); + uval = tmp; + } +done_or_error: + Py_XDECREF(padding); + Py_XDECREF(sign); + } +#endif + return uval; +} + +/* CIntToPyUnicode */ +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_int(int value, Py_ssize_t width, char padding_char, char format_char) { + char digits[sizeof(int)*3+2]; + char *dpos, *end = digits + sizeof(int)*3+2; + const char *hex_digits = DIGITS_HEX; + Py_ssize_t length, ulength; + int prepend_sign, last_one_off; + int remaining; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const int neg_one = (int) -1, const_zero = (int) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; + if (format_char == 'X') { + hex_digits += 16; + format_char = 'x'; + } + remaining = value; + last_one_off = 0; + dpos = end; + do { + int digit_pos; + switch (format_char) { + case 'o': + digit_pos = abs((int)(remaining % (8*8))); + remaining = (int) (remaining / (8*8)); + dpos -= 2; + memcpy(dpos, DIGIT_PAIRS_8 + digit_pos * 2, 2); + last_one_off = (digit_pos < 8); + break; + case 'd': + digit_pos = abs((int)(remaining % (10*10))); + remaining = (int) (remaining / (10*10)); + dpos -= 2; + memcpy(dpos, DIGIT_PAIRS_10 + digit_pos * 2, 2); + last_one_off = (digit_pos < 10); + break; + case 'x': + *(--dpos) = hex_digits[abs((int)(remaining % 16))]; + remaining = (int) (remaining / 16); + break; + default: + assert(0); + break; + } + } while (unlikely(remaining != 0)); + assert(!last_one_off || *dpos == '0'); + dpos += last_one_off; + length = end - dpos; + ulength = length; + prepend_sign = 0; + if (!is_unsigned && value <= neg_one) { + if (padding_char == ' ' || width <= length + 1) { + *(--dpos) = '-'; + ++length; + } else { + prepend_sign = 1; + } + ++ulength; + } + if (width > ulength) { + ulength = width; + } + if (ulength == 1) { + return PyUnicode_FromOrdinal(*dpos); + } + return __Pyx_PyUnicode_BuildFromAscii(ulength, dpos, (int) length, prepend_sign, padding_char); +} + +/* CIntToPyUnicode */ +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_From_Py_ssize_t(Py_ssize_t value, Py_ssize_t width, char padding_char, char format_char) { + char digits[sizeof(Py_ssize_t)*3+2]; + char *dpos, *end = digits + sizeof(Py_ssize_t)*3+2; + const char *hex_digits = DIGITS_HEX; + Py_ssize_t length, ulength; + int prepend_sign, last_one_off; + Py_ssize_t remaining; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const Py_ssize_t neg_one = (Py_ssize_t) -1, const_zero = (Py_ssize_t) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; + if (format_char == 'X') { + hex_digits += 16; + format_char = 'x'; + } + remaining = value; + last_one_off = 0; + dpos = end; + do { + int digit_pos; + switch (format_char) { + case 'o': + digit_pos = abs((int)(remaining % (8*8))); + remaining = (Py_ssize_t) (remaining / (8*8)); + dpos -= 2; + memcpy(dpos, DIGIT_PAIRS_8 + digit_pos * 2, 2); + last_one_off = (digit_pos < 8); + break; + case 'd': + digit_pos = abs((int)(remaining % (10*10))); + remaining = (Py_ssize_t) (remaining / (10*10)); + dpos -= 2; + memcpy(dpos, DIGIT_PAIRS_10 + digit_pos * 2, 2); + last_one_off = (digit_pos < 10); + break; + case 'x': + *(--dpos) = hex_digits[abs((int)(remaining % 16))]; + remaining = (Py_ssize_t) (remaining / 16); + break; + default: + assert(0); + break; + } + } while (unlikely(remaining != 0)); + assert(!last_one_off || *dpos == '0'); + dpos += last_one_off; + length = end - dpos; + ulength = length; + prepend_sign = 0; + if (!is_unsigned && value <= neg_one) { + if (padding_char == ' ' || width <= length + 1) { + *(--dpos) = '-'; + ++length; + } else { + prepend_sign = 1; + } + ++ulength; + } + if (width > ulength) { + ulength = width; + } + if (ulength == 1) { + return PyUnicode_FromOrdinal(*dpos); + } + return __Pyx_PyUnicode_BuildFromAscii(ulength, dpos, (int) length, prepend_sign, padding_char); +} + +/* JoinPyUnicode */ +static PyObject* __Pyx_PyUnicode_Join(PyObject* value_tuple, Py_ssize_t value_count, Py_ssize_t result_ulength, + Py_UCS4 max_char) { +#if CYTHON_USE_UNICODE_INTERNALS && CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + PyObject *result_uval; + int result_ukind, kind_shift; + Py_ssize_t i, char_pos; + void *result_udata; + CYTHON_MAYBE_UNUSED_VAR(max_char); +#if CYTHON_PEP393_ENABLED + result_uval = PyUnicode_New(result_ulength, max_char); + if (unlikely(!result_uval)) return NULL; + result_ukind = (max_char <= 255) ? PyUnicode_1BYTE_KIND : (max_char <= 65535) ? PyUnicode_2BYTE_KIND : PyUnicode_4BYTE_KIND; + kind_shift = (result_ukind == PyUnicode_4BYTE_KIND) ? 2 : result_ukind - 1; + result_udata = PyUnicode_DATA(result_uval); +#else + result_uval = PyUnicode_FromUnicode(NULL, result_ulength); + if (unlikely(!result_uval)) return NULL; + result_ukind = sizeof(Py_UNICODE); + kind_shift = (result_ukind == 4) ? 2 : result_ukind - 1; + result_udata = PyUnicode_AS_UNICODE(result_uval); +#endif + assert(kind_shift == 2 || kind_shift == 1 || kind_shift == 0); + char_pos = 0; + for (i=0; i < value_count; i++) { + int ukind; + Py_ssize_t ulength; + void *udata; + PyObject *uval = PyTuple_GET_ITEM(value_tuple, i); + if (unlikely(__Pyx_PyUnicode_READY(uval))) + goto bad; + ulength = __Pyx_PyUnicode_GET_LENGTH(uval); + if (unlikely(!ulength)) + continue; + if (unlikely((PY_SSIZE_T_MAX >> kind_shift) - ulength < char_pos)) + goto overflow; + ukind = __Pyx_PyUnicode_KIND(uval); + udata = __Pyx_PyUnicode_DATA(uval); + if (!CYTHON_PEP393_ENABLED || ukind == result_ukind) { + memcpy((char *)result_udata + (char_pos << kind_shift), udata, (size_t) (ulength << kind_shift)); + } else { + #if PY_VERSION_HEX >= 0x030d0000 + if (unlikely(PyUnicode_CopyCharacters(result_uval, char_pos, uval, 0, ulength) < 0)) goto bad; + #elif CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030300F0 || defined(_PyUnicode_FastCopyCharacters) + _PyUnicode_FastCopyCharacters(result_uval, char_pos, uval, 0, ulength); + #else + Py_ssize_t j; + for (j=0; j < ulength; j++) { + Py_UCS4 uchar = __Pyx_PyUnicode_READ(ukind, udata, j); + __Pyx_PyUnicode_WRITE(result_ukind, result_udata, char_pos+j, uchar); + } + #endif + } + char_pos += ulength; + } + return result_uval; +overflow: + PyErr_SetString(PyExc_OverflowError, "join() result is too long for a Python string"); +bad: + Py_DECREF(result_uval); + return NULL; +#else + CYTHON_UNUSED_VAR(max_char); + CYTHON_UNUSED_VAR(result_ulength); + CYTHON_UNUSED_VAR(value_count); + return PyUnicode_Join(__pyx_empty_unicode, value_tuple); +#endif +} + +/* GetAttr */ +static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) { +#if CYTHON_USE_TYPE_SLOTS +#if PY_MAJOR_VERSION >= 3 + if (likely(PyUnicode_Check(n))) +#else + if (likely(PyString_Check(n))) +#endif + return __Pyx_PyObject_GetAttrStr(o, n); +#endif + return PyObject_GetAttr(o, n); +} + +/* GetItemInt */ +static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) { + PyObject *r; + if (unlikely(!j)) return NULL; + r = PyObject_GetItem(o, j); + Py_DECREF(j); + return r; +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + Py_ssize_t wrapped_i = i; + if (wraparound & unlikely(i < 0)) { + wrapped_i += PyList_GET_SIZE(o); + } + if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) { + PyObject *r = PyList_GET_ITEM(o, wrapped_i); + Py_INCREF(r); + return r; + } + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +#else + return PySequence_GetItem(o, i); +#endif +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + Py_ssize_t wrapped_i = i; + if (wraparound & unlikely(i < 0)) { + wrapped_i += PyTuple_GET_SIZE(o); + } + if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) { + PyObject *r = PyTuple_GET_ITEM(o, wrapped_i); + Py_INCREF(r); + return r; + } + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +#else + return PySequence_GetItem(o, i); +#endif +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS + if (is_list || PyList_CheckExact(o)) { + Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o); + if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) { + PyObject *r = PyList_GET_ITEM(o, n); + Py_INCREF(r); + return r; + } + } + else if (PyTuple_CheckExact(o)) { + Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o); + if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) { + PyObject *r = PyTuple_GET_ITEM(o, n); + Py_INCREF(r); + return r; + } + } else { + PyMappingMethods *mm = Py_TYPE(o)->tp_as_mapping; + PySequenceMethods *sm = Py_TYPE(o)->tp_as_sequence; + if (mm && mm->mp_subscript) { + PyObject *r, *key = PyInt_FromSsize_t(i); + if (unlikely(!key)) return NULL; + r = mm->mp_subscript(o, key); + Py_DECREF(key); + return r; + } + if (likely(sm && sm->sq_item)) { + if (wraparound && unlikely(i < 0) && likely(sm->sq_length)) { + Py_ssize_t l = sm->sq_length(o); + if (likely(l >= 0)) { + i += l; + } else { + if (!PyErr_ExceptionMatches(PyExc_OverflowError)) + return NULL; + PyErr_Clear(); + } + } + return sm->sq_item(o, i); + } + } +#else + if (is_list || !PyMapping_Check(o)) { + return PySequence_GetItem(o, i); + } +#endif + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +} + +/* PyObjectCallOneArg */ +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *args[2] = {NULL, arg}; + return __Pyx_PyObject_FastCall(func, args+1, 1 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET); +} + +/* ObjectGetItem */ +#if CYTHON_USE_TYPE_SLOTS +static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject *index) { + PyObject *runerr = NULL; + Py_ssize_t key_value; + key_value = __Pyx_PyIndex_AsSsize_t(index); + if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) { + return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1); + } + if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) { + __Pyx_TypeName index_type_name = __Pyx_PyType_GetName(Py_TYPE(index)); + PyErr_Clear(); + PyErr_Format(PyExc_IndexError, + "cannot fit '" __Pyx_FMT_TYPENAME "' into an index-sized integer", index_type_name); + __Pyx_DECREF_TypeName(index_type_name); + } + return NULL; +} +static PyObject *__Pyx_PyObject_GetItem_Slow(PyObject *obj, PyObject *key) { + __Pyx_TypeName obj_type_name; + if (likely(PyType_Check(obj))) { + PyObject *meth = __Pyx_PyObject_GetAttrStrNoError(obj, __pyx_n_s_class_getitem); + if (!meth) { + PyErr_Clear(); + } else { + PyObject *result = __Pyx_PyObject_CallOneArg(meth, key); + Py_DECREF(meth); + return result; + } + } + obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj)); + PyErr_Format(PyExc_TypeError, + "'" __Pyx_FMT_TYPENAME "' object is not subscriptable", obj_type_name); + __Pyx_DECREF_TypeName(obj_type_name); + return NULL; +} +static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject *key) { + PyTypeObject *tp = Py_TYPE(obj); + PyMappingMethods *mm = tp->tp_as_mapping; + PySequenceMethods *sm = tp->tp_as_sequence; + if (likely(mm && mm->mp_subscript)) { + return mm->mp_subscript(obj, key); + } + if (likely(sm && sm->sq_item)) { + return __Pyx_PyObject_GetIndex(obj, key); + } + return __Pyx_PyObject_GetItem_Slow(obj, key); +} +#endif + +/* KeywordStringCheck */ +static int __Pyx_CheckKeywordStrings( + PyObject *kw, + const char* function_name, + int kw_allowed) +{ + PyObject* key = 0; + Py_ssize_t pos = 0; +#if CYTHON_COMPILING_IN_PYPY + if (!kw_allowed && PyDict_Next(kw, &pos, &key, 0)) + goto invalid_keyword; + return 1; +#else + if (CYTHON_METH_FASTCALL && likely(PyTuple_Check(kw))) { + Py_ssize_t kwsize; +#if CYTHON_ASSUME_SAFE_MACROS + kwsize = PyTuple_GET_SIZE(kw); +#else + kwsize = PyTuple_Size(kw); + if (kwsize < 0) return 0; +#endif + if (unlikely(kwsize == 0)) + return 1; + if (!kw_allowed) { +#if CYTHON_ASSUME_SAFE_MACROS + key = PyTuple_GET_ITEM(kw, 0); +#else + key = PyTuple_GetItem(kw, pos); + if (!key) return 0; +#endif + goto invalid_keyword; + } +#if PY_VERSION_HEX < 0x03090000 + for (pos = 0; pos < kwsize; pos++) { +#if CYTHON_ASSUME_SAFE_MACROS + key = PyTuple_GET_ITEM(kw, pos); +#else + key = PyTuple_GetItem(kw, pos); + if (!key) return 0; +#endif + if (unlikely(!PyUnicode_Check(key))) + goto invalid_keyword_type; + } +#endif + return 1; + } + while (PyDict_Next(kw, &pos, &key, 0)) { + #if PY_MAJOR_VERSION < 3 + if (unlikely(!PyString_Check(key))) + #endif + if (unlikely(!PyUnicode_Check(key))) + goto invalid_keyword_type; + } + if (!kw_allowed && unlikely(key)) + goto invalid_keyword; + return 1; +invalid_keyword_type: + PyErr_Format(PyExc_TypeError, + "%.200s() keywords must be strings", function_name); + return 0; +#endif +invalid_keyword: + #if PY_MAJOR_VERSION < 3 + PyErr_Format(PyExc_TypeError, + "%.200s() got an unexpected keyword argument '%.200s'", + function_name, PyString_AsString(key)); + #else + PyErr_Format(PyExc_TypeError, + "%s() got an unexpected keyword argument '%U'", + function_name, key); + #endif + return 0; +} + +/* DivInt[Py_ssize_t] */ +static CYTHON_INLINE Py_ssize_t __Pyx_div_Py_ssize_t(Py_ssize_t a, Py_ssize_t b) { + Py_ssize_t q = a / b; + Py_ssize_t r = a - q*b; + q -= ((r != 0) & ((r ^ b) < 0)); + return q; +} + +/* GetAttr3 */ +#if __PYX_LIMITED_VERSION_HEX < 0x030d00A1 +static PyObject *__Pyx_GetAttr3Default(PyObject *d) { + __Pyx_PyThreadState_declare + __Pyx_PyThreadState_assign + if (unlikely(!__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError))) + return NULL; + __Pyx_PyErr_Clear(); + Py_INCREF(d); + return d; +} +#endif +static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject *d) { + PyObject *r; +#if __PYX_LIMITED_VERSION_HEX >= 0x030d00A1 + int res = PyObject_GetOptionalAttr(o, n, &r); + return (res != 0) ? r : __Pyx_NewRef(d); +#else + #if CYTHON_USE_TYPE_SLOTS + if (likely(PyString_Check(n))) { + r = __Pyx_PyObject_GetAttrStrNoError(o, n); + if (unlikely(!r) && likely(!PyErr_Occurred())) { + r = __Pyx_NewRef(d); + } + return r; + } + #endif + r = PyObject_GetAttr(o, n); + return (likely(r)) ? r : __Pyx_GetAttr3Default(d); +#endif +} + +/* PyDictVersioning */ +#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) { + PyObject *dict = Py_TYPE(obj)->tp_dict; + return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0; +} +static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) { + PyObject **dictptr = NULL; + Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset; + if (offset) { +#if CYTHON_COMPILING_IN_CPYTHON + dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj); +#else + dictptr = _PyObject_GetDictPtr(obj); +#endif + } + return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0; +} +static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) { + PyObject *dict = Py_TYPE(obj)->tp_dict; + if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict))) + return 0; + return obj_dict_version == __Pyx_get_object_dict_version(obj); +} +#endif + +/* GetModuleGlobalName */ +#if CYTHON_USE_DICT_VERSIONS +static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value) +#else +static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name) +#endif +{ + PyObject *result; +#if !CYTHON_AVOID_BORROWED_REFS +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && PY_VERSION_HEX < 0x030d0000 + result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } else if (unlikely(PyErr_Occurred())) { + return NULL; + } +#elif CYTHON_COMPILING_IN_LIMITED_API + if (unlikely(!__pyx_m)) { + return NULL; + } + result = PyObject_GetAttr(__pyx_m, name); + if (likely(result)) { + return result; + } +#else + result = PyDict_GetItem(__pyx_d, name); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } +#endif +#else + result = PyObject_GetItem(__pyx_d, name); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } + PyErr_Clear(); +#endif + return __Pyx_GetBuiltinName(name); +} + +/* RaiseTooManyValuesToUnpack */ +static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) { + PyErr_Format(PyExc_ValueError, + "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected); +} + +/* RaiseNeedMoreValuesToUnpack */ +static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) { + PyErr_Format(PyExc_ValueError, + "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack", + index, (index == 1) ? "" : "s"); +} + +/* RaiseNoneIterError */ +static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) { + PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable"); +} + +/* ExtTypeTest */ +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { + __Pyx_TypeName obj_type_name; + __Pyx_TypeName type_name; + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + if (likely(__Pyx_TypeCheck(obj, type))) + return 1; + obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj)); + type_name = __Pyx_PyType_GetName(type); + PyErr_Format(PyExc_TypeError, + "Cannot convert " __Pyx_FMT_TYPENAME " to " __Pyx_FMT_TYPENAME, + obj_type_name, type_name); + __Pyx_DECREF_TypeName(obj_type_name); + __Pyx_DECREF_TypeName(type_name); + return 0; +} + +/* GetTopmostException */ +#if CYTHON_USE_EXC_INFO_STACK && CYTHON_FAST_THREAD_STATE +static _PyErr_StackItem * +__Pyx_PyErr_GetTopmostException(PyThreadState *tstate) +{ + _PyErr_StackItem *exc_info = tstate->exc_info; + while ((exc_info->exc_value == NULL || exc_info->exc_value == Py_None) && + exc_info->previous_item != NULL) + { + exc_info = exc_info->previous_item; + } + return exc_info; +} +#endif + +/* SaveResetException */ +#if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4 + _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate); + PyObject *exc_value = exc_info->exc_value; + if (exc_value == NULL || exc_value == Py_None) { + *value = NULL; + *type = NULL; + *tb = NULL; + } else { + *value = exc_value; + Py_INCREF(*value); + *type = (PyObject*) Py_TYPE(exc_value); + Py_INCREF(*type); + *tb = PyException_GetTraceback(exc_value); + } + #elif CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate); + *type = exc_info->exc_type; + *value = exc_info->exc_value; + *tb = exc_info->exc_traceback; + Py_XINCREF(*type); + Py_XINCREF(*value); + Py_XINCREF(*tb); + #else + *type = tstate->exc_type; + *value = tstate->exc_value; + *tb = tstate->exc_traceback; + Py_XINCREF(*type); + Py_XINCREF(*value); + Py_XINCREF(*tb); + #endif +} +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4 + _PyErr_StackItem *exc_info = tstate->exc_info; + PyObject *tmp_value = exc_info->exc_value; + exc_info->exc_value = value; + Py_XDECREF(tmp_value); + Py_XDECREF(type); + Py_XDECREF(tb); + #else + PyObject *tmp_type, *tmp_value, *tmp_tb; + #if CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = type; + exc_info->exc_value = value; + exc_info->exc_traceback = tb; + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = type; + tstate->exc_value = value; + tstate->exc_traceback = tb; + #endif + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); + #endif +} +#endif + +/* GetException */ +#if CYTHON_FAST_THREAD_STATE +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) +#endif +{ + PyObject *local_type = NULL, *local_value, *local_tb = NULL; +#if CYTHON_FAST_THREAD_STATE + PyObject *tmp_type, *tmp_value, *tmp_tb; + #if PY_VERSION_HEX >= 0x030C00A6 + local_value = tstate->current_exception; + tstate->current_exception = 0; + if (likely(local_value)) { + local_type = (PyObject*) Py_TYPE(local_value); + Py_INCREF(local_type); + local_tb = PyException_GetTraceback(local_value); + } + #else + local_type = tstate->curexc_type; + local_value = tstate->curexc_value; + local_tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; + #endif +#else + PyErr_Fetch(&local_type, &local_value, &local_tb); +#endif + PyErr_NormalizeException(&local_type, &local_value, &local_tb); +#if CYTHON_FAST_THREAD_STATE && PY_VERSION_HEX >= 0x030C00A6 + if (unlikely(tstate->current_exception)) +#elif CYTHON_FAST_THREAD_STATE + if (unlikely(tstate->curexc_type)) +#else + if (unlikely(PyErr_Occurred())) +#endif + goto bad; + #if PY_MAJOR_VERSION >= 3 + if (local_tb) { + if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0)) + goto bad; + } + #endif + Py_XINCREF(local_tb); + Py_XINCREF(local_type); + Py_XINCREF(local_value); + *type = local_type; + *value = local_value; + *tb = local_tb; +#if CYTHON_FAST_THREAD_STATE + #if CYTHON_USE_EXC_INFO_STACK + { + _PyErr_StackItem *exc_info = tstate->exc_info; + #if PY_VERSION_HEX >= 0x030B00a4 + tmp_value = exc_info->exc_value; + exc_info->exc_value = local_value; + tmp_type = NULL; + tmp_tb = NULL; + Py_XDECREF(local_type); + Py_XDECREF(local_tb); + #else + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = local_type; + exc_info->exc_value = local_value; + exc_info->exc_traceback = local_tb; + #endif + } + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = local_type; + tstate->exc_value = local_value; + tstate->exc_traceback = local_tb; + #endif + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +#else + PyErr_SetExcInfo(local_type, local_value, local_tb); +#endif + return 0; +bad: + *type = 0; + *value = 0; + *tb = 0; + Py_XDECREF(local_type); + Py_XDECREF(local_value); + Py_XDECREF(local_tb); + return -1; +} + +/* SwapException */ +#if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4 + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_value = exc_info->exc_value; + exc_info->exc_value = *value; + if (tmp_value == NULL || tmp_value == Py_None) { + Py_XDECREF(tmp_value); + tmp_value = NULL; + tmp_type = NULL; + tmp_tb = NULL; + } else { + tmp_type = (PyObject*) Py_TYPE(tmp_value); + Py_INCREF(tmp_type); + #if CYTHON_COMPILING_IN_CPYTHON + tmp_tb = ((PyBaseExceptionObject*) tmp_value)->traceback; + Py_XINCREF(tmp_tb); + #else + tmp_tb = PyException_GetTraceback(tmp_value); + #endif + } + #elif CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = *type; + exc_info->exc_value = *value; + exc_info->exc_traceback = *tb; + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = *type; + tstate->exc_value = *value; + tstate->exc_traceback = *tb; + #endif + *type = tmp_type; + *value = tmp_value; + *tb = tmp_tb; +} +#else +static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb); + PyErr_SetExcInfo(*type, *value, *tb); + *type = tmp_type; + *value = tmp_value; + *tb = tmp_tb; +} +#endif + +/* Import */ +static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) { + PyObject *module = 0; + PyObject *empty_dict = 0; + PyObject *empty_list = 0; + #if PY_MAJOR_VERSION < 3 + PyObject *py_import; + py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import); + if (unlikely(!py_import)) + goto bad; + if (!from_list) { + empty_list = PyList_New(0); + if (unlikely(!empty_list)) + goto bad; + from_list = empty_list; + } + #endif + empty_dict = PyDict_New(); + if (unlikely(!empty_dict)) + goto bad; + { + #if PY_MAJOR_VERSION >= 3 + if (level == -1) { + if (strchr(__Pyx_MODULE_NAME, '.') != NULL) { + module = PyImport_ImportModuleLevelObject( + name, __pyx_d, empty_dict, from_list, 1); + if (unlikely(!module)) { + if (unlikely(!PyErr_ExceptionMatches(PyExc_ImportError))) + goto bad; + PyErr_Clear(); + } + } + level = 0; + } + #endif + if (!module) { + #if PY_MAJOR_VERSION < 3 + PyObject *py_level = PyInt_FromLong(level); + if (unlikely(!py_level)) + goto bad; + module = PyObject_CallFunctionObjArgs(py_import, + name, __pyx_d, empty_dict, from_list, py_level, (PyObject *)NULL); + Py_DECREF(py_level); + #else + module = PyImport_ImportModuleLevelObject( + name, __pyx_d, empty_dict, from_list, level); + #endif + } + } +bad: + Py_XDECREF(empty_dict); + Py_XDECREF(empty_list); + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(py_import); + #endif + return module; +} + +/* ImportDottedModule */ +#if PY_MAJOR_VERSION >= 3 +static PyObject *__Pyx__ImportDottedModule_Error(PyObject *name, PyObject *parts_tuple, Py_ssize_t count) { + PyObject *partial_name = NULL, *slice = NULL, *sep = NULL; + if (unlikely(PyErr_Occurred())) { + PyErr_Clear(); + } + if (likely(PyTuple_GET_SIZE(parts_tuple) == count)) { + partial_name = name; + } else { + slice = PySequence_GetSlice(parts_tuple, 0, count); + if (unlikely(!slice)) + goto bad; + sep = PyUnicode_FromStringAndSize(".", 1); + if (unlikely(!sep)) + goto bad; + partial_name = PyUnicode_Join(sep, slice); + } + PyErr_Format( +#if PY_MAJOR_VERSION < 3 + PyExc_ImportError, + "No module named '%s'", PyString_AS_STRING(partial_name)); +#else +#if PY_VERSION_HEX >= 0x030600B1 + PyExc_ModuleNotFoundError, +#else + PyExc_ImportError, +#endif + "No module named '%U'", partial_name); +#endif +bad: + Py_XDECREF(sep); + Py_XDECREF(slice); + Py_XDECREF(partial_name); + return NULL; +} +#endif +#if PY_MAJOR_VERSION >= 3 +static PyObject *__Pyx__ImportDottedModule_Lookup(PyObject *name) { + PyObject *imported_module; +#if PY_VERSION_HEX < 0x030700A1 || (CYTHON_COMPILING_IN_PYPY && PYPY_VERSION_NUM < 0x07030400) + PyObject *modules = PyImport_GetModuleDict(); + if (unlikely(!modules)) + return NULL; + imported_module = __Pyx_PyDict_GetItemStr(modules, name); + Py_XINCREF(imported_module); +#else + imported_module = PyImport_GetModule(name); +#endif + return imported_module; +} +#endif +#if PY_MAJOR_VERSION >= 3 +static PyObject *__Pyx_ImportDottedModule_WalkParts(PyObject *module, PyObject *name, PyObject *parts_tuple) { + Py_ssize_t i, nparts; + nparts = PyTuple_GET_SIZE(parts_tuple); + for (i=1; i < nparts && module; i++) { + PyObject *part, *submodule; +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + part = PyTuple_GET_ITEM(parts_tuple, i); +#else + part = PySequence_ITEM(parts_tuple, i); +#endif + submodule = __Pyx_PyObject_GetAttrStrNoError(module, part); +#if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS) + Py_DECREF(part); +#endif + Py_DECREF(module); + module = submodule; + } + if (unlikely(!module)) { + return __Pyx__ImportDottedModule_Error(name, parts_tuple, i); + } + return module; +} +#endif +static PyObject *__Pyx__ImportDottedModule(PyObject *name, PyObject *parts_tuple) { +#if PY_MAJOR_VERSION < 3 + PyObject *module, *from_list, *star = __pyx_n_s__3; + CYTHON_UNUSED_VAR(parts_tuple); + from_list = PyList_New(1); + if (unlikely(!from_list)) + return NULL; + Py_INCREF(star); + PyList_SET_ITEM(from_list, 0, star); + module = __Pyx_Import(name, from_list, 0); + Py_DECREF(from_list); + return module; +#else + PyObject *imported_module; + PyObject *module = __Pyx_Import(name, NULL, 0); + if (!parts_tuple || unlikely(!module)) + return module; + imported_module = __Pyx__ImportDottedModule_Lookup(name); + if (likely(imported_module)) { + Py_DECREF(module); + return imported_module; + } + PyErr_Clear(); + return __Pyx_ImportDottedModule_WalkParts(module, name, parts_tuple); +#endif +} +static PyObject *__Pyx_ImportDottedModule(PyObject *name, PyObject *parts_tuple) { +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030400B1 + PyObject *module = __Pyx__ImportDottedModule_Lookup(name); + if (likely(module)) { + PyObject *spec = __Pyx_PyObject_GetAttrStrNoError(module, __pyx_n_s_spec); + if (likely(spec)) { + PyObject *unsafe = __Pyx_PyObject_GetAttrStrNoError(spec, __pyx_n_s_initializing); + if (likely(!unsafe || !__Pyx_PyObject_IsTrue(unsafe))) { + Py_DECREF(spec); + spec = NULL; + } + Py_XDECREF(unsafe); + } + if (likely(!spec)) { + PyErr_Clear(); + return module; + } + Py_DECREF(spec); + Py_DECREF(module); + } else if (PyErr_Occurred()) { + PyErr_Clear(); + } +#endif + return __Pyx__ImportDottedModule(name, parts_tuple); +} + +/* FastTypeChecks */ +#if CYTHON_COMPILING_IN_CPYTHON +static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) { + while (a) { + a = __Pyx_PyType_GetSlot(a, tp_base, PyTypeObject*); + if (a == b) + return 1; + } + return b == &PyBaseObject_Type; +} +static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) { + PyObject *mro; + if (a == b) return 1; + mro = a->tp_mro; + if (likely(mro)) { + Py_ssize_t i, n; + n = PyTuple_GET_SIZE(mro); + for (i = 0; i < n; i++) { + if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b) + return 1; + } + return 0; + } + return __Pyx_InBases(a, b); +} +static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b) { + PyObject *mro; + if (cls == a || cls == b) return 1; + mro = cls->tp_mro; + if (likely(mro)) { + Py_ssize_t i, n; + n = PyTuple_GET_SIZE(mro); + for (i = 0; i < n; i++) { + PyObject *base = PyTuple_GET_ITEM(mro, i); + if (base == (PyObject *)a || base == (PyObject *)b) + return 1; + } + return 0; + } + return __Pyx_InBases(cls, a) || __Pyx_InBases(cls, b); +} +#if PY_MAJOR_VERSION == 2 +static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) { + PyObject *exception, *value, *tb; + int res; + __Pyx_PyThreadState_declare + __Pyx_PyThreadState_assign + __Pyx_ErrFetch(&exception, &value, &tb); + res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0; + if (unlikely(res == -1)) { + PyErr_WriteUnraisable(err); + res = 0; + } + if (!res) { + res = PyObject_IsSubclass(err, exc_type2); + if (unlikely(res == -1)) { + PyErr_WriteUnraisable(err); + res = 0; + } + } + __Pyx_ErrRestore(exception, value, tb); + return res; +} +#else +static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) { + if (exc_type1) { + return __Pyx_IsAnySubtype2((PyTypeObject*)err, (PyTypeObject*)exc_type1, (PyTypeObject*)exc_type2); + } else { + return __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2); + } +} +#endif +static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { + Py_ssize_t i, n; + assert(PyExceptionClass_Check(exc_type)); + n = PyTuple_GET_SIZE(tuple); +#if PY_MAJOR_VERSION >= 3 + for (i=0; itp_as_sequence && type->tp_as_sequence->sq_repeat)) { + return type->tp_as_sequence->sq_repeat(seq, mul); + } else +#endif + { + return __Pyx_PySequence_Multiply_Generic(seq, mul); + } +} + +/* SetItemInt */ +static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) { + int r; + if (unlikely(!j)) return -1; + r = PyObject_SetItem(o, j, v); + Py_DECREF(j); + return r; +} +static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list, + CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS + if (is_list || PyList_CheckExact(o)) { + Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o)); + if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o)))) { + PyObject* old = PyList_GET_ITEM(o, n); + Py_INCREF(v); + PyList_SET_ITEM(o, n, v); + Py_DECREF(old); + return 1; + } + } else { + PyMappingMethods *mm = Py_TYPE(o)->tp_as_mapping; + PySequenceMethods *sm = Py_TYPE(o)->tp_as_sequence; + if (mm && mm->mp_ass_subscript) { + int r; + PyObject *key = PyInt_FromSsize_t(i); + if (unlikely(!key)) return -1; + r = mm->mp_ass_subscript(o, key, v); + Py_DECREF(key); + return r; + } + if (likely(sm && sm->sq_ass_item)) { + if (wraparound && unlikely(i < 0) && likely(sm->sq_length)) { + Py_ssize_t l = sm->sq_length(o); + if (likely(l >= 0)) { + i += l; + } else { + if (!PyErr_ExceptionMatches(PyExc_OverflowError)) + return -1; + PyErr_Clear(); + } + } + return sm->sq_ass_item(o, i, v); + } + } +#else + if (is_list || !PyMapping_Check(o)) + { + return PySequence_SetItem(o, i, v); + } +#endif + return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v); +} + +/* RaiseUnboundLocalError */ +static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) { + PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname); +} + +/* DivInt[long] */ +static CYTHON_INLINE long __Pyx_div_long(long a, long b) { + long q = a / b; + long r = a - q*b; + q -= ((r != 0) & ((r ^ b) < 0)); + return q; +} + +/* ImportFrom */ +static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) { + PyObject* value = __Pyx_PyObject_GetAttrStr(module, name); + if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) { + const char* module_name_str = 0; + PyObject* module_name = 0; + PyObject* module_dot = 0; + PyObject* full_name = 0; + PyErr_Clear(); + module_name_str = PyModule_GetName(module); + if (unlikely(!module_name_str)) { goto modbad; } + module_name = PyUnicode_FromString(module_name_str); + if (unlikely(!module_name)) { goto modbad; } + module_dot = PyUnicode_Concat(module_name, __pyx_kp_u__2); + if (unlikely(!module_dot)) { goto modbad; } + full_name = PyUnicode_Concat(module_dot, name); + if (unlikely(!full_name)) { goto modbad; } + #if PY_VERSION_HEX < 0x030700A1 || (CYTHON_COMPILING_IN_PYPY && PYPY_VERSION_NUM < 0x07030400) + { + PyObject *modules = PyImport_GetModuleDict(); + if (unlikely(!modules)) + goto modbad; + value = PyObject_GetItem(modules, full_name); + } + #else + value = PyImport_GetModule(full_name); + #endif + modbad: + Py_XDECREF(full_name); + Py_XDECREF(module_dot); + Py_XDECREF(module_name); + } + if (unlikely(!value)) { + PyErr_Format(PyExc_ImportError, + #if PY_MAJOR_VERSION < 3 + "cannot import name %.230s", PyString_AS_STRING(name)); + #else + "cannot import name %S", name); + #endif + } + return value; +} + +/* HasAttr */ +static CYTHON_INLINE int __Pyx_HasAttr(PyObject *o, PyObject *n) { + PyObject *r; + if (unlikely(!__Pyx_PyBaseString_Check(n))) { + PyErr_SetString(PyExc_TypeError, + "hasattr(): attribute name must be string"); + return -1; + } + r = __Pyx_GetAttr(o, n); + if (!r) { + PyErr_Clear(); + return 0; + } else { + Py_DECREF(r); + return 1; + } +} + +/* IsLittleEndian */ +static CYTHON_INLINE int __Pyx_Is_Little_Endian(void) +{ + union { + uint32_t u32; + uint8_t u8[4]; + } S; + S.u32 = 0x01020304; + return S.u8[0] == 4; +} + +/* BufferFormatCheck */ +static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx, + __Pyx_BufFmt_StackElem* stack, + __Pyx_TypeInfo* type) { + stack[0].field = &ctx->root; + stack[0].parent_offset = 0; + ctx->root.type = type; + ctx->root.name = "buffer dtype"; + ctx->root.offset = 0; + ctx->head = stack; + ctx->head->field = &ctx->root; + ctx->fmt_offset = 0; + ctx->head->parent_offset = 0; + ctx->new_packmode = '@'; + ctx->enc_packmode = '@'; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->is_complex = 0; + ctx->is_valid_array = 0; + ctx->struct_alignment = 0; + while (type->typegroup == 'S') { + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = 0; + type = type->fields->type; + } +} +static int __Pyx_BufFmt_ParseNumber(const char** ts) { + int count; + const char* t = *ts; + if (*t < '0' || *t > '9') { + return -1; + } else { + count = *t++ - '0'; + while (*t >= '0' && *t <= '9') { + count *= 10; + count += *t++ - '0'; + } + } + *ts = t; + return count; +} +static int __Pyx_BufFmt_ExpectNumber(const char **ts) { + int number = __Pyx_BufFmt_ParseNumber(ts); + if (number == -1) + PyErr_Format(PyExc_ValueError,\ + "Does not understand character buffer dtype format string ('%c')", **ts); + return number; +} +static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) { + PyErr_Format(PyExc_ValueError, + "Unexpected format string character: '%c'", ch); +} +static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) { + switch (ch) { + case '?': return "'bool'"; + case 'c': return "'char'"; + case 'b': return "'signed char'"; + case 'B': return "'unsigned char'"; + case 'h': return "'short'"; + case 'H': return "'unsigned short'"; + case 'i': return "'int'"; + case 'I': return "'unsigned int'"; + case 'l': return "'long'"; + case 'L': return "'unsigned long'"; + case 'q': return "'long long'"; + case 'Q': return "'unsigned long long'"; + case 'f': return (is_complex ? "'complex float'" : "'float'"); + case 'd': return (is_complex ? "'complex double'" : "'double'"); + case 'g': return (is_complex ? "'complex long double'" : "'long double'"); + case 'T': return "a struct"; + case 'O': return "Python object"; + case 'P': return "a pointer"; + case 's': case 'p': return "a string"; + case 0: return "end"; + default: return "unparsable format string"; + } +} +static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return 2; + case 'i': case 'I': case 'l': case 'L': return 4; + case 'q': case 'Q': return 8; + case 'f': return (is_complex ? 8 : 4); + case 'd': return (is_complex ? 16 : 8); + case 'g': { + PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g').."); + return 0; + } + case 'O': case 'P': return sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(short); + case 'i': case 'I': return sizeof(int); + case 'l': case 'L': return sizeof(long); + #ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(PY_LONG_LONG); + #endif + case 'f': return sizeof(float) * (is_complex ? 2 : 1); + case 'd': return sizeof(double) * (is_complex ? 2 : 1); + case 'g': return sizeof(long double) * (is_complex ? 2 : 1); + case 'O': case 'P': return sizeof(void*); + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +typedef struct { char c; short x; } __Pyx_st_short; +typedef struct { char c; int x; } __Pyx_st_int; +typedef struct { char c; long x; } __Pyx_st_long; +typedef struct { char c; float x; } __Pyx_st_float; +typedef struct { char c; double x; } __Pyx_st_double; +typedef struct { char c; long double x; } __Pyx_st_longdouble; +typedef struct { char c; void *x; } __Pyx_st_void_p; +#ifdef HAVE_LONG_LONG +typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong; +#endif +static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, int is_complex) { + CYTHON_UNUSED_VAR(is_complex); + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short); + case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int); + case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long); +#ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG); +#endif + case 'f': return sizeof(__Pyx_st_float) - sizeof(float); + case 'd': return sizeof(__Pyx_st_double) - sizeof(double); + case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double); + case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +/* These are for computing the padding at the end of the struct to align + on the first member of the struct. This will probably the same as above, + but we don't have any guarantees. + */ +typedef struct { short x; char c; } __Pyx_pad_short; +typedef struct { int x; char c; } __Pyx_pad_int; +typedef struct { long x; char c; } __Pyx_pad_long; +typedef struct { float x; char c; } __Pyx_pad_float; +typedef struct { double x; char c; } __Pyx_pad_double; +typedef struct { long double x; char c; } __Pyx_pad_longdouble; +typedef struct { void *x; char c; } __Pyx_pad_void_p; +#ifdef HAVE_LONG_LONG +typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong; +#endif +static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, int is_complex) { + CYTHON_UNUSED_VAR(is_complex); + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short); + case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int); + case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long); +#ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG); +#endif + case 'f': return sizeof(__Pyx_pad_float) - sizeof(float); + case 'd': return sizeof(__Pyx_pad_double) - sizeof(double); + case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double); + case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) { + switch (ch) { + case 'c': + return 'H'; + case 'b': case 'h': case 'i': + case 'l': case 'q': case 's': case 'p': + return 'I'; + case '?': case 'B': case 'H': case 'I': case 'L': case 'Q': + return 'U'; + case 'f': case 'd': case 'g': + return (is_complex ? 'C' : 'R'); + case 'O': + return 'O'; + case 'P': + return 'P'; + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) { + if (ctx->head == NULL || ctx->head->field == &ctx->root) { + const char* expected; + const char* quote; + if (ctx->head == NULL) { + expected = "end"; + quote = ""; + } else { + expected = ctx->head->field->type->name; + quote = "'"; + } + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch, expected %s%s%s but got %s", + quote, expected, quote, + __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex)); + } else { + __Pyx_StructField* field = ctx->head->field; + __Pyx_StructField* parent = (ctx->head - 1)->field; + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'", + field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex), + parent->type->name, field->name); + } +} +static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) { + char group; + size_t size, offset, arraysize = 1; + if (ctx->enc_type == 0) return 0; + if (ctx->head->field->type->arraysize[0]) { + int i, ndim = 0; + if (ctx->enc_type == 's' || ctx->enc_type == 'p') { + ctx->is_valid_array = ctx->head->field->type->ndim == 1; + ndim = 1; + if (ctx->enc_count != ctx->head->field->type->arraysize[0]) { + PyErr_Format(PyExc_ValueError, + "Expected a dimension of size %zu, got %zu", + ctx->head->field->type->arraysize[0], ctx->enc_count); + return -1; + } + } + if (!ctx->is_valid_array) { + PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d", + ctx->head->field->type->ndim, ndim); + return -1; + } + for (i = 0; i < ctx->head->field->type->ndim; i++) { + arraysize *= ctx->head->field->type->arraysize[i]; + } + ctx->is_valid_array = 0; + ctx->enc_count = 1; + } + group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex); + do { + __Pyx_StructField* field = ctx->head->field; + __Pyx_TypeInfo* type = field->type; + if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') { + size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex); + } else { + size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex); + } + if (ctx->enc_packmode == '@') { + size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex); + size_t align_mod_offset; + if (align_at == 0) return -1; + align_mod_offset = ctx->fmt_offset % align_at; + if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset; + if (ctx->struct_alignment == 0) + ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type, + ctx->is_complex); + } + if (type->size != size || type->typegroup != group) { + if (type->typegroup == 'C' && type->fields != NULL) { + size_t parent_offset = ctx->head->parent_offset + field->offset; + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = parent_offset; + continue; + } + if ((type->typegroup == 'H' || group == 'H') && type->size == size) { + } else { + __Pyx_BufFmt_RaiseExpected(ctx); + return -1; + } + } + offset = ctx->head->parent_offset + field->offset; + if (ctx->fmt_offset != offset) { + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected", + (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset); + return -1; + } + ctx->fmt_offset += size; + if (arraysize) + ctx->fmt_offset += (arraysize - 1) * size; + --ctx->enc_count; + while (1) { + if (field == &ctx->root) { + ctx->head = NULL; + if (ctx->enc_count != 0) { + __Pyx_BufFmt_RaiseExpected(ctx); + return -1; + } + break; + } + ctx->head->field = ++field; + if (field->type == NULL) { + --ctx->head; + field = ctx->head->field; + continue; + } else if (field->type->typegroup == 'S') { + size_t parent_offset = ctx->head->parent_offset + field->offset; + if (field->type->fields->type == NULL) continue; + field = field->type->fields; + ++ctx->head; + ctx->head->field = field; + ctx->head->parent_offset = parent_offset; + break; + } else { + break; + } + } + } while (ctx->enc_count); + ctx->enc_type = 0; + ctx->is_complex = 0; + return 0; +} +static int +__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp) +{ + const char *ts = *tsp; + int i = 0, number, ndim; + ++ts; + if (ctx->new_count != 1) { + PyErr_SetString(PyExc_ValueError, + "Cannot handle repeated arrays in format string"); + return -1; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return -1; + ndim = ctx->head->field->type->ndim; + while (*ts && *ts != ')') { + switch (*ts) { + case ' ': case '\f': case '\r': case '\n': case '\t': case '\v': continue; + default: break; + } + number = __Pyx_BufFmt_ExpectNumber(&ts); + if (number == -1) return -1; + if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i]) { + PyErr_Format(PyExc_ValueError, + "Expected a dimension of size %zu, got %d", + ctx->head->field->type->arraysize[i], number); + return -1; + } + if (*ts != ',' && *ts != ')') { + PyErr_Format(PyExc_ValueError, + "Expected a comma in format string, got '%c'", *ts); + return -1; + } + if (*ts == ',') ts++; + i++; + } + if (i != ndim) { + PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d", + ctx->head->field->type->ndim, i); + return -1; + } + if (!*ts) { + PyErr_SetString(PyExc_ValueError, + "Unexpected end of format string, expected ')'"); + return -1; + } + ctx->is_valid_array = 1; + ctx->new_count = 1; + *tsp = ++ts; + return 0; +} +static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) { + int got_Z = 0; + while (1) { + switch(*ts) { + case 0: + if (ctx->enc_type != 0 && ctx->head == NULL) { + __Pyx_BufFmt_RaiseExpected(ctx); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + if (ctx->head != NULL) { + __Pyx_BufFmt_RaiseExpected(ctx); + return NULL; + } + return ts; + case ' ': + case '\r': + case '\n': + ++ts; + break; + case '<': + if (!__Pyx_Is_Little_Endian()) { + PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler"); + return NULL; + } + ctx->new_packmode = '='; + ++ts; + break; + case '>': + case '!': + if (__Pyx_Is_Little_Endian()) { + PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler"); + return NULL; + } + ctx->new_packmode = '='; + ++ts; + break; + case '=': + case '@': + case '^': + ctx->new_packmode = *ts++; + break; + case 'T': + { + const char* ts_after_sub; + size_t i, struct_count = ctx->new_count; + size_t struct_alignment = ctx->struct_alignment; + ctx->new_count = 1; + ++ts; + if (*ts != '{') { + PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'"); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_type = 0; + ctx->enc_count = 0; + ctx->struct_alignment = 0; + ++ts; + ts_after_sub = ts; + for (i = 0; i != struct_count; ++i) { + ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts); + if (!ts_after_sub) return NULL; + } + ts = ts_after_sub; + if (struct_alignment) ctx->struct_alignment = struct_alignment; + } + break; + case '}': + { + size_t alignment = ctx->struct_alignment; + ++ts; + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_type = 0; + if (alignment && ctx->fmt_offset % alignment) { + ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment); + } + } + return ts; + case 'x': + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->fmt_offset += ctx->new_count; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->enc_packmode = ctx->new_packmode; + ++ts; + break; + case 'Z': + got_Z = 1; + ++ts; + if (*ts != 'f' && *ts != 'd' && *ts != 'g') { + __Pyx_BufFmt_RaiseUnexpectedChar('Z'); + return NULL; + } + CYTHON_FALLTHROUGH; + case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I': + case 'l': case 'L': case 'q': case 'Q': + case 'f': case 'd': case 'g': + case 'O': case 'p': + if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) && + (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) { + ctx->enc_count += ctx->new_count; + ctx->new_count = 1; + got_Z = 0; + ++ts; + break; + } + CYTHON_FALLTHROUGH; + case 's': + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_count = ctx->new_count; + ctx->enc_packmode = ctx->new_packmode; + ctx->enc_type = *ts; + ctx->is_complex = got_Z; + ++ts; + ctx->new_count = 1; + got_Z = 0; + break; + case ':': + ++ts; + while(*ts != ':') ++ts; + ++ts; + break; + case '(': + if (__pyx_buffmt_parse_array(ctx, &ts) < 0) return NULL; + break; + default: + { + int number = __Pyx_BufFmt_ExpectNumber(&ts); + if (number == -1) return NULL; + ctx->new_count = (size_t)number; + } + } + } +} + +/* BufferGetAndValidate */ + static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) { + if (unlikely(info->buf == NULL)) return; + if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL; + __Pyx_ReleaseBuffer(info); +} +static void __Pyx_ZeroBuffer(Py_buffer* buf) { + buf->buf = NULL; + buf->obj = NULL; + buf->strides = __Pyx_zeros; + buf->shape = __Pyx_zeros; + buf->suboffsets = __Pyx_minusones; +} +static int __Pyx__GetBufferAndValidate( + Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, + int nd, int cast, __Pyx_BufFmt_StackElem* stack) +{ + buf->buf = NULL; + if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) { + __Pyx_ZeroBuffer(buf); + return -1; + } + if (unlikely(buf->ndim != nd)) { + PyErr_Format(PyExc_ValueError, + "Buffer has wrong number of dimensions (expected %d, got %d)", + nd, buf->ndim); + goto fail; + } + if (!cast) { + __Pyx_BufFmt_Context ctx; + __Pyx_BufFmt_Init(&ctx, stack, dtype); + if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail; + } + if (unlikely((size_t)buf->itemsize != dtype->size)) { + PyErr_Format(PyExc_ValueError, + "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)", + buf->itemsize, (buf->itemsize > 1) ? "s" : "", + dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : ""); + goto fail; + } + if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones; + return 0; +fail:; + __Pyx_SafeReleaseBuffer(buf); + return -1; +} + +/* PyObject_GenericGetAttrNoDict */ + #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000 +static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) { + __Pyx_TypeName type_name = __Pyx_PyType_GetName(tp); + PyErr_Format(PyExc_AttributeError, +#if PY_MAJOR_VERSION >= 3 + "'" __Pyx_FMT_TYPENAME "' object has no attribute '%U'", + type_name, attr_name); +#else + "'" __Pyx_FMT_TYPENAME "' object has no attribute '%.400s'", + type_name, PyString_AS_STRING(attr_name)); +#endif + __Pyx_DECREF_TypeName(type_name); + return NULL; +} +static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) { + PyObject *descr; + PyTypeObject *tp = Py_TYPE(obj); + if (unlikely(!PyString_Check(attr_name))) { + return PyObject_GenericGetAttr(obj, attr_name); + } + assert(!tp->tp_dictoffset); + descr = _PyType_Lookup(tp, attr_name); + if (unlikely(!descr)) { + return __Pyx_RaiseGenericGetAttributeError(tp, attr_name); + } + Py_INCREF(descr); + #if PY_MAJOR_VERSION < 3 + if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS))) + #endif + { + descrgetfunc f = Py_TYPE(descr)->tp_descr_get; + if (unlikely(f)) { + PyObject *res = f(descr, obj, (PyObject *)tp); + Py_DECREF(descr); + return res; + } + } + return descr; +} +#endif + +/* PyObject_GenericGetAttr */ + #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000 +static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) { + if (unlikely(Py_TYPE(obj)->tp_dictoffset)) { + return PyObject_GenericGetAttr(obj, attr_name); + } + return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name); +} +#endif + +/* FixUpExtensionType */ + #if CYTHON_USE_TYPE_SPECS +static int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type) { +#if PY_VERSION_HEX > 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API + CYTHON_UNUSED_VAR(spec); + CYTHON_UNUSED_VAR(type); +#else + const PyType_Slot *slot = spec->slots; + while (slot && slot->slot && slot->slot != Py_tp_members) + slot++; + if (slot && slot->slot == Py_tp_members) { + int changed = 0; +#if !(PY_VERSION_HEX <= 0x030900b1 && CYTHON_COMPILING_IN_CPYTHON) + const +#endif + PyMemberDef *memb = (PyMemberDef*) slot->pfunc; + while (memb && memb->name) { + if (memb->name[0] == '_' && memb->name[1] == '_') { +#if PY_VERSION_HEX < 0x030900b1 + if (strcmp(memb->name, "__weaklistoffset__") == 0) { + assert(memb->type == T_PYSSIZET); + assert(memb->flags == READONLY); + type->tp_weaklistoffset = memb->offset; + changed = 1; + } + else if (strcmp(memb->name, "__dictoffset__") == 0) { + assert(memb->type == T_PYSSIZET); + assert(memb->flags == READONLY); + type->tp_dictoffset = memb->offset; + changed = 1; + } +#if CYTHON_METH_FASTCALL + else if (strcmp(memb->name, "__vectorcalloffset__") == 0) { + assert(memb->type == T_PYSSIZET); + assert(memb->flags == READONLY); +#if PY_VERSION_HEX >= 0x030800b4 + type->tp_vectorcall_offset = memb->offset; +#else + type->tp_print = (printfunc) memb->offset; +#endif + changed = 1; + } +#endif +#else + if ((0)); +#endif +#if PY_VERSION_HEX <= 0x030900b1 && CYTHON_COMPILING_IN_CPYTHON + else if (strcmp(memb->name, "__module__") == 0) { + PyObject *descr; + assert(memb->type == T_OBJECT); + assert(memb->flags == 0 || memb->flags == READONLY); + descr = PyDescr_NewMember(type, memb); + if (unlikely(!descr)) + return -1; + if (unlikely(PyDict_SetItem(type->tp_dict, PyDescr_NAME(descr), descr) < 0)) { + Py_DECREF(descr); + return -1; + } + Py_DECREF(descr); + changed = 1; + } +#endif + } + memb++; + } + if (changed) + PyType_Modified(type); + } +#endif + return 0; +} +#endif + +/* PyObjectCallNoArg */ + static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) { + PyObject *arg[2] = {NULL, NULL}; + return __Pyx_PyObject_FastCall(func, arg + 1, 0 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET); +} + +/* PyObjectGetMethod */ + static int __Pyx_PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method) { + PyObject *attr; +#if CYTHON_UNPACK_METHODS && CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_PYTYPE_LOOKUP + __Pyx_TypeName type_name; + PyTypeObject *tp = Py_TYPE(obj); + PyObject *descr; + descrgetfunc f = NULL; + PyObject **dictptr, *dict; + int meth_found = 0; + assert (*method == NULL); + if (unlikely(tp->tp_getattro != PyObject_GenericGetAttr)) { + attr = __Pyx_PyObject_GetAttrStr(obj, name); + goto try_unpack; + } + if (unlikely(tp->tp_dict == NULL) && unlikely(PyType_Ready(tp) < 0)) { + return 0; + } + descr = _PyType_Lookup(tp, name); + if (likely(descr != NULL)) { + Py_INCREF(descr); +#if defined(Py_TPFLAGS_METHOD_DESCRIPTOR) && Py_TPFLAGS_METHOD_DESCRIPTOR + if (__Pyx_PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_METHOD_DESCRIPTOR)) +#elif PY_MAJOR_VERSION >= 3 + #ifdef __Pyx_CyFunction_USED + if (likely(PyFunction_Check(descr) || __Pyx_IS_TYPE(descr, &PyMethodDescr_Type) || __Pyx_CyFunction_Check(descr))) + #else + if (likely(PyFunction_Check(descr) || __Pyx_IS_TYPE(descr, &PyMethodDescr_Type))) + #endif +#else + #ifdef __Pyx_CyFunction_USED + if (likely(PyFunction_Check(descr) || __Pyx_CyFunction_Check(descr))) + #else + if (likely(PyFunction_Check(descr))) + #endif +#endif + { + meth_found = 1; + } else { + f = Py_TYPE(descr)->tp_descr_get; + if (f != NULL && PyDescr_IsData(descr)) { + attr = f(descr, obj, (PyObject *)Py_TYPE(obj)); + Py_DECREF(descr); + goto try_unpack; + } + } + } + dictptr = _PyObject_GetDictPtr(obj); + if (dictptr != NULL && (dict = *dictptr) != NULL) { + Py_INCREF(dict); + attr = __Pyx_PyDict_GetItemStr(dict, name); + if (attr != NULL) { + Py_INCREF(attr); + Py_DECREF(dict); + Py_XDECREF(descr); + goto try_unpack; + } + Py_DECREF(dict); + } + if (meth_found) { + *method = descr; + return 1; + } + if (f != NULL) { + attr = f(descr, obj, (PyObject *)Py_TYPE(obj)); + Py_DECREF(descr); + goto try_unpack; + } + if (likely(descr != NULL)) { + *method = descr; + return 0; + } + type_name = __Pyx_PyType_GetName(tp); + PyErr_Format(PyExc_AttributeError, +#if PY_MAJOR_VERSION >= 3 + "'" __Pyx_FMT_TYPENAME "' object has no attribute '%U'", + type_name, name); +#else + "'" __Pyx_FMT_TYPENAME "' object has no attribute '%.400s'", + type_name, PyString_AS_STRING(name)); +#endif + __Pyx_DECREF_TypeName(type_name); + return 0; +#else + attr = __Pyx_PyObject_GetAttrStr(obj, name); + goto try_unpack; +#endif +try_unpack: +#if CYTHON_UNPACK_METHODS + if (likely(attr) && PyMethod_Check(attr) && likely(PyMethod_GET_SELF(attr) == obj)) { + PyObject *function = PyMethod_GET_FUNCTION(attr); + Py_INCREF(function); + Py_DECREF(attr); + *method = function; + return 1; + } +#endif + *method = attr; + return 0; +} + +/* PyObjectCallMethod0 */ + static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name) { + PyObject *method = NULL, *result = NULL; + int is_method = __Pyx_PyObject_GetMethod(obj, method_name, &method); + if (likely(is_method)) { + result = __Pyx_PyObject_CallOneArg(method, obj); + Py_DECREF(method); + return result; + } + if (unlikely(!method)) goto bad; + result = __Pyx_PyObject_CallNoArg(method); + Py_DECREF(method); +bad: + return result; +} + +/* ValidateBasesTuple */ + #if CYTHON_COMPILING_IN_CPYTHON || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_USE_TYPE_SPECS +static int __Pyx_validate_bases_tuple(const char *type_name, Py_ssize_t dictoffset, PyObject *bases) { + Py_ssize_t i, n; +#if CYTHON_ASSUME_SAFE_MACROS + n = PyTuple_GET_SIZE(bases); +#else + n = PyTuple_Size(bases); + if (n < 0) return -1; +#endif + for (i = 1; i < n; i++) + { +#if CYTHON_AVOID_BORROWED_REFS + PyObject *b0 = PySequence_GetItem(bases, i); + if (!b0) return -1; +#elif CYTHON_ASSUME_SAFE_MACROS + PyObject *b0 = PyTuple_GET_ITEM(bases, i); +#else + PyObject *b0 = PyTuple_GetItem(bases, i); + if (!b0) return -1; +#endif + PyTypeObject *b; +#if PY_MAJOR_VERSION < 3 + if (PyClass_Check(b0)) + { + PyErr_Format(PyExc_TypeError, "base class '%.200s' is an old-style class", + PyString_AS_STRING(((PyClassObject*)b0)->cl_name)); +#if CYTHON_AVOID_BORROWED_REFS + Py_DECREF(b0); +#endif + return -1; + } +#endif + b = (PyTypeObject*) b0; + if (!__Pyx_PyType_HasFeature(b, Py_TPFLAGS_HEAPTYPE)) + { + __Pyx_TypeName b_name = __Pyx_PyType_GetName(b); + PyErr_Format(PyExc_TypeError, + "base class '" __Pyx_FMT_TYPENAME "' is not a heap type", b_name); + __Pyx_DECREF_TypeName(b_name); +#if CYTHON_AVOID_BORROWED_REFS + Py_DECREF(b0); +#endif + return -1; + } + if (dictoffset == 0) + { + Py_ssize_t b_dictoffset = 0; +#if CYTHON_USE_TYPE_SLOTS || CYTHON_COMPILING_IN_PYPY + b_dictoffset = b->tp_dictoffset; +#else + PyObject *py_b_dictoffset = PyObject_GetAttrString((PyObject*)b, "__dictoffset__"); + if (!py_b_dictoffset) goto dictoffset_return; + b_dictoffset = PyLong_AsSsize_t(py_b_dictoffset); + Py_DECREF(py_b_dictoffset); + if (b_dictoffset == -1 && PyErr_Occurred()) goto dictoffset_return; +#endif + if (b_dictoffset) { + { + __Pyx_TypeName b_name = __Pyx_PyType_GetName(b); + PyErr_Format(PyExc_TypeError, + "extension type '%.200s' has no __dict__ slot, " + "but base type '" __Pyx_FMT_TYPENAME "' has: " + "either add 'cdef dict __dict__' to the extension type " + "or add '__slots__ = [...]' to the base type", + type_name, b_name); + __Pyx_DECREF_TypeName(b_name); + } +#if !(CYTHON_USE_TYPE_SLOTS || CYTHON_COMPILING_IN_PYPY) + dictoffset_return: +#endif +#if CYTHON_AVOID_BORROWED_REFS + Py_DECREF(b0); +#endif + return -1; + } + } +#if CYTHON_AVOID_BORROWED_REFS + Py_DECREF(b0); +#endif + } + return 0; +} +#endif + +/* PyType_Ready */ + static int __Pyx_PyType_Ready(PyTypeObject *t) { +#if CYTHON_USE_TYPE_SPECS || !(CYTHON_COMPILING_IN_CPYTHON || CYTHON_COMPILING_IN_LIMITED_API) || defined(PYSTON_MAJOR_VERSION) + (void)__Pyx_PyObject_CallMethod0; +#if CYTHON_USE_TYPE_SPECS + (void)__Pyx_validate_bases_tuple; +#endif + return PyType_Ready(t); +#else + int r; + PyObject *bases = __Pyx_PyType_GetSlot(t, tp_bases, PyObject*); + if (bases && unlikely(__Pyx_validate_bases_tuple(t->tp_name, t->tp_dictoffset, bases) == -1)) + return -1; +#if PY_VERSION_HEX >= 0x03050000 && !defined(PYSTON_MAJOR_VERSION) + { + int gc_was_enabled; + #if PY_VERSION_HEX >= 0x030A00b1 + gc_was_enabled = PyGC_Disable(); + (void)__Pyx_PyObject_CallMethod0; + #else + PyObject *ret, *py_status; + PyObject *gc = NULL; + #if PY_VERSION_HEX >= 0x030700a1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM+0 >= 0x07030400) + gc = PyImport_GetModule(__pyx_kp_u_gc); + #endif + if (unlikely(!gc)) gc = PyImport_Import(__pyx_kp_u_gc); + if (unlikely(!gc)) return -1; + py_status = __Pyx_PyObject_CallMethod0(gc, __pyx_kp_u_isenabled); + if (unlikely(!py_status)) { + Py_DECREF(gc); + return -1; + } + gc_was_enabled = __Pyx_PyObject_IsTrue(py_status); + Py_DECREF(py_status); + if (gc_was_enabled > 0) { + ret = __Pyx_PyObject_CallMethod0(gc, __pyx_kp_u_disable); + if (unlikely(!ret)) { + Py_DECREF(gc); + return -1; + } + Py_DECREF(ret); + } else if (unlikely(gc_was_enabled == -1)) { + Py_DECREF(gc); + return -1; + } + #endif + t->tp_flags |= Py_TPFLAGS_HEAPTYPE; +#if PY_VERSION_HEX >= 0x030A0000 + t->tp_flags |= Py_TPFLAGS_IMMUTABLETYPE; +#endif +#else + (void)__Pyx_PyObject_CallMethod0; +#endif + r = PyType_Ready(t); +#if PY_VERSION_HEX >= 0x03050000 && !defined(PYSTON_MAJOR_VERSION) + t->tp_flags &= ~Py_TPFLAGS_HEAPTYPE; + #if PY_VERSION_HEX >= 0x030A00b1 + if (gc_was_enabled) + PyGC_Enable(); + #else + if (gc_was_enabled) { + PyObject *tp, *v, *tb; + PyErr_Fetch(&tp, &v, &tb); + ret = __Pyx_PyObject_CallMethod0(gc, __pyx_kp_u_enable); + if (likely(ret || r == -1)) { + Py_XDECREF(ret); + PyErr_Restore(tp, v, tb); + } else { + Py_XDECREF(tp); + Py_XDECREF(v); + Py_XDECREF(tb); + r = -1; + } + } + Py_DECREF(gc); + #endif + } +#endif + return r; +#endif +} + +/* SetVTable */ + static int __Pyx_SetVtable(PyTypeObject *type, void *vtable) { + PyObject *ob = PyCapsule_New(vtable, 0, 0); + if (unlikely(!ob)) + goto bad; +#if CYTHON_COMPILING_IN_LIMITED_API + if (unlikely(PyObject_SetAttr((PyObject *) type, __pyx_n_s_pyx_vtable, ob) < 0)) +#else + if (unlikely(PyDict_SetItem(type->tp_dict, __pyx_n_s_pyx_vtable, ob) < 0)) +#endif + goto bad; + Py_DECREF(ob); + return 0; +bad: + Py_XDECREF(ob); + return -1; +} + +/* GetVTable */ + static void* __Pyx_GetVtable(PyTypeObject *type) { + void* ptr; +#if CYTHON_COMPILING_IN_LIMITED_API + PyObject *ob = PyObject_GetAttr((PyObject *)type, __pyx_n_s_pyx_vtable); +#else + PyObject *ob = PyObject_GetItem(type->tp_dict, __pyx_n_s_pyx_vtable); +#endif + if (!ob) + goto bad; + ptr = PyCapsule_GetPointer(ob, 0); + if (!ptr && !PyErr_Occurred()) + PyErr_SetString(PyExc_RuntimeError, "invalid vtable found for imported type"); + Py_DECREF(ob); + return ptr; +bad: + Py_XDECREF(ob); + return NULL; +} + +/* MergeVTables */ + #if !CYTHON_COMPILING_IN_LIMITED_API +static int __Pyx_MergeVtables(PyTypeObject *type) { + int i; + void** base_vtables; + __Pyx_TypeName tp_base_name; + __Pyx_TypeName base_name; + void* unknown = (void*)-1; + PyObject* bases = type->tp_bases; + int base_depth = 0; + { + PyTypeObject* base = type->tp_base; + while (base) { + base_depth += 1; + base = base->tp_base; + } + } + base_vtables = (void**) malloc(sizeof(void*) * (size_t)(base_depth + 1)); + base_vtables[0] = unknown; + for (i = 1; i < PyTuple_GET_SIZE(bases); i++) { + void* base_vtable = __Pyx_GetVtable(((PyTypeObject*)PyTuple_GET_ITEM(bases, i))); + if (base_vtable != NULL) { + int j; + PyTypeObject* base = type->tp_base; + for (j = 0; j < base_depth; j++) { + if (base_vtables[j] == unknown) { + base_vtables[j] = __Pyx_GetVtable(base); + base_vtables[j + 1] = unknown; + } + if (base_vtables[j] == base_vtable) { + break; + } else if (base_vtables[j] == NULL) { + goto bad; + } + base = base->tp_base; + } + } + } + PyErr_Clear(); + free(base_vtables); + return 0; +bad: + tp_base_name = __Pyx_PyType_GetName(type->tp_base); + base_name = __Pyx_PyType_GetName((PyTypeObject*)PyTuple_GET_ITEM(bases, i)); + PyErr_Format(PyExc_TypeError, + "multiple bases have vtable conflict: '" __Pyx_FMT_TYPENAME "' and '" __Pyx_FMT_TYPENAME "'", tp_base_name, base_name); + __Pyx_DECREF_TypeName(tp_base_name); + __Pyx_DECREF_TypeName(base_name); + free(base_vtables); + return -1; +} +#endif + +/* SetupReduce */ + #if !CYTHON_COMPILING_IN_LIMITED_API +static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) { + int ret; + PyObject *name_attr; + name_attr = __Pyx_PyObject_GetAttrStrNoError(meth, __pyx_n_s_name_2); + if (likely(name_attr)) { + ret = PyObject_RichCompareBool(name_attr, name, Py_EQ); + } else { + ret = -1; + } + if (unlikely(ret < 0)) { + PyErr_Clear(); + ret = 0; + } + Py_XDECREF(name_attr); + return ret; +} +static int __Pyx_setup_reduce(PyObject* type_obj) { + int ret = 0; + PyObject *object_reduce = NULL; + PyObject *object_getstate = NULL; + PyObject *object_reduce_ex = NULL; + PyObject *reduce = NULL; + PyObject *reduce_ex = NULL; + PyObject *reduce_cython = NULL; + PyObject *setstate = NULL; + PyObject *setstate_cython = NULL; + PyObject *getstate = NULL; +#if CYTHON_USE_PYTYPE_LOOKUP + getstate = _PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate); +#else + getstate = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_getstate); + if (!getstate && PyErr_Occurred()) { + goto __PYX_BAD; + } +#endif + if (getstate) { +#if CYTHON_USE_PYTYPE_LOOKUP + object_getstate = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_getstate); +#else + object_getstate = __Pyx_PyObject_GetAttrStrNoError((PyObject*)&PyBaseObject_Type, __pyx_n_s_getstate); + if (!object_getstate && PyErr_Occurred()) { + goto __PYX_BAD; + } +#endif + if (object_getstate != getstate) { + goto __PYX_GOOD; + } + } +#if CYTHON_USE_PYTYPE_LOOKUP + object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD; +#else + object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD; +#endif + reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto __PYX_BAD; + if (reduce_ex == object_reduce_ex) { +#if CYTHON_USE_PYTYPE_LOOKUP + object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto __PYX_BAD; +#else + object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto __PYX_BAD; +#endif + reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto __PYX_BAD; + if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) { + reduce_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_reduce_cython); + if (likely(reduce_cython)) { + ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD; + ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD; + } else if (reduce == object_reduce || PyErr_Occurred()) { + goto __PYX_BAD; + } + setstate = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_setstate); + if (!setstate) PyErr_Clear(); + if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) { + setstate_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_setstate_cython); + if (likely(setstate_cython)) { + ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD; + ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD; + } else if (!setstate || PyErr_Occurred()) { + goto __PYX_BAD; + } + } + PyType_Modified((PyTypeObject*)type_obj); + } + } + goto __PYX_GOOD; +__PYX_BAD: + if (!PyErr_Occurred()) { + __Pyx_TypeName type_obj_name = + __Pyx_PyType_GetName((PyTypeObject*)type_obj); + PyErr_Format(PyExc_RuntimeError, + "Unable to initialize pickling for " __Pyx_FMT_TYPENAME, type_obj_name); + __Pyx_DECREF_TypeName(type_obj_name); + } + ret = -1; +__PYX_GOOD: +#if !CYTHON_USE_PYTYPE_LOOKUP + Py_XDECREF(object_reduce); + Py_XDECREF(object_reduce_ex); + Py_XDECREF(object_getstate); + Py_XDECREF(getstate); +#endif + Py_XDECREF(reduce); + Py_XDECREF(reduce_ex); + Py_XDECREF(reduce_cython); + Py_XDECREF(setstate); + Py_XDECREF(setstate_cython); + return ret; +} +#endif + +/* TypeImport */ + #ifndef __PYX_HAVE_RT_ImportType_3_0_11 +#define __PYX_HAVE_RT_ImportType_3_0_11 +static PyTypeObject *__Pyx_ImportType_3_0_11(PyObject *module, const char *module_name, const char *class_name, + size_t size, size_t alignment, enum __Pyx_ImportType_CheckSize_3_0_11 check_size) +{ + PyObject *result = 0; + char warning[200]; + Py_ssize_t basicsize; + Py_ssize_t itemsize; +#if CYTHON_COMPILING_IN_LIMITED_API + PyObject *py_basicsize; + PyObject *py_itemsize; +#endif + result = PyObject_GetAttrString(module, class_name); + if (!result) + goto bad; + if (!PyType_Check(result)) { + PyErr_Format(PyExc_TypeError, + "%.200s.%.200s is not a type object", + module_name, class_name); + goto bad; + } +#if !CYTHON_COMPILING_IN_LIMITED_API + basicsize = ((PyTypeObject *)result)->tp_basicsize; + itemsize = ((PyTypeObject *)result)->tp_itemsize; +#else + py_basicsize = PyObject_GetAttrString(result, "__basicsize__"); + if (!py_basicsize) + goto bad; + basicsize = PyLong_AsSsize_t(py_basicsize); + Py_DECREF(py_basicsize); + py_basicsize = 0; + if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred()) + goto bad; + py_itemsize = PyObject_GetAttrString(result, "__itemsize__"); + if (!py_itemsize) + goto bad; + itemsize = PyLong_AsSsize_t(py_itemsize); + Py_DECREF(py_itemsize); + py_itemsize = 0; + if (itemsize == (Py_ssize_t)-1 && PyErr_Occurred()) + goto bad; +#endif + if (itemsize) { + if (size % alignment) { + alignment = size % alignment; + } + if (itemsize < (Py_ssize_t)alignment) + itemsize = (Py_ssize_t)alignment; + } + if ((size_t)(basicsize + itemsize) < size) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize+itemsize); + goto bad; + } + if (check_size == __Pyx_ImportType_CheckSize_Error_3_0_11 && + ((size_t)basicsize > size || (size_t)(basicsize + itemsize) < size)) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd-%zd from PyObject", + module_name, class_name, size, basicsize, basicsize+itemsize); + goto bad; + } + else if (check_size == __Pyx_ImportType_CheckSize_Warn_3_0_11 && (size_t)basicsize > size) { + PyOS_snprintf(warning, sizeof(warning), + "%s.%s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad; + } + return (PyTypeObject *)result; +bad: + Py_XDECREF(result); + return NULL; +} +#endif + +/* FetchSharedCythonModule */ + static PyObject *__Pyx_FetchSharedCythonABIModule(void) { + return __Pyx_PyImport_AddModuleRef((char*) __PYX_ABI_MODULE_NAME); +} + +/* FetchCommonType */ + static int __Pyx_VerifyCachedType(PyObject *cached_type, + const char *name, + Py_ssize_t basicsize, + Py_ssize_t expected_basicsize) { + if (!PyType_Check(cached_type)) { + PyErr_Format(PyExc_TypeError, + "Shared Cython type %.200s is not a type object", name); + return -1; + } + if (basicsize != expected_basicsize) { + PyErr_Format(PyExc_TypeError, + "Shared Cython type %.200s has the wrong size, try recompiling", + name); + return -1; + } + return 0; +} +#if !CYTHON_USE_TYPE_SPECS +static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) { + PyObject* abi_module; + const char* object_name; + PyTypeObject *cached_type = NULL; + abi_module = __Pyx_FetchSharedCythonABIModule(); + if (!abi_module) return NULL; + object_name = strrchr(type->tp_name, '.'); + object_name = object_name ? object_name+1 : type->tp_name; + cached_type = (PyTypeObject*) PyObject_GetAttrString(abi_module, object_name); + if (cached_type) { + if (__Pyx_VerifyCachedType( + (PyObject *)cached_type, + object_name, + cached_type->tp_basicsize, + type->tp_basicsize) < 0) { + goto bad; + } + goto done; + } + if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad; + PyErr_Clear(); + if (PyType_Ready(type) < 0) goto bad; + if (PyObject_SetAttrString(abi_module, object_name, (PyObject *)type) < 0) + goto bad; + Py_INCREF(type); + cached_type = type; +done: + Py_DECREF(abi_module); + return cached_type; +bad: + Py_XDECREF(cached_type); + cached_type = NULL; + goto done; +} +#else +static PyTypeObject *__Pyx_FetchCommonTypeFromSpec(PyObject *module, PyType_Spec *spec, PyObject *bases) { + PyObject *abi_module, *cached_type = NULL; + const char* object_name = strrchr(spec->name, '.'); + object_name = object_name ? object_name+1 : spec->name; + abi_module = __Pyx_FetchSharedCythonABIModule(); + if (!abi_module) return NULL; + cached_type = PyObject_GetAttrString(abi_module, object_name); + if (cached_type) { + Py_ssize_t basicsize; +#if CYTHON_COMPILING_IN_LIMITED_API + PyObject *py_basicsize; + py_basicsize = PyObject_GetAttrString(cached_type, "__basicsize__"); + if (unlikely(!py_basicsize)) goto bad; + basicsize = PyLong_AsSsize_t(py_basicsize); + Py_DECREF(py_basicsize); + py_basicsize = 0; + if (unlikely(basicsize == (Py_ssize_t)-1) && PyErr_Occurred()) goto bad; +#else + basicsize = likely(PyType_Check(cached_type)) ? ((PyTypeObject*) cached_type)->tp_basicsize : -1; +#endif + if (__Pyx_VerifyCachedType( + cached_type, + object_name, + basicsize, + spec->basicsize) < 0) { + goto bad; + } + goto done; + } + if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad; + PyErr_Clear(); + CYTHON_UNUSED_VAR(module); + cached_type = __Pyx_PyType_FromModuleAndSpec(abi_module, spec, bases); + if (unlikely(!cached_type)) goto bad; + if (unlikely(__Pyx_fix_up_extension_type_from_spec(spec, (PyTypeObject *) cached_type) < 0)) goto bad; + if (PyObject_SetAttrString(abi_module, object_name, cached_type) < 0) goto bad; +done: + Py_DECREF(abi_module); + assert(cached_type == NULL || PyType_Check(cached_type)); + return (PyTypeObject *) cached_type; +bad: + Py_XDECREF(cached_type); + cached_type = NULL; + goto done; +} +#endif + +/* PyVectorcallFastCallDict */ + #if CYTHON_METH_FASTCALL +static PyObject *__Pyx_PyVectorcall_FastCallDict_kw(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw) +{ + PyObject *res = NULL; + PyObject *kwnames; + PyObject **newargs; + PyObject **kwvalues; + Py_ssize_t i, pos; + size_t j; + PyObject *key, *value; + unsigned long keys_are_strings; + Py_ssize_t nkw = PyDict_GET_SIZE(kw); + newargs = (PyObject **)PyMem_Malloc((nargs + (size_t)nkw) * sizeof(args[0])); + if (unlikely(newargs == NULL)) { + PyErr_NoMemory(); + return NULL; + } + for (j = 0; j < nargs; j++) newargs[j] = args[j]; + kwnames = PyTuple_New(nkw); + if (unlikely(kwnames == NULL)) { + PyMem_Free(newargs); + return NULL; + } + kwvalues = newargs + nargs; + pos = i = 0; + keys_are_strings = Py_TPFLAGS_UNICODE_SUBCLASS; + while (PyDict_Next(kw, &pos, &key, &value)) { + keys_are_strings &= Py_TYPE(key)->tp_flags; + Py_INCREF(key); + Py_INCREF(value); + PyTuple_SET_ITEM(kwnames, i, key); + kwvalues[i] = value; + i++; + } + if (unlikely(!keys_are_strings)) { + PyErr_SetString(PyExc_TypeError, "keywords must be strings"); + goto cleanup; + } + res = vc(func, newargs, nargs, kwnames); +cleanup: + Py_DECREF(kwnames); + for (i = 0; i < nkw; i++) + Py_DECREF(kwvalues[i]); + PyMem_Free(newargs); + return res; +} +static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw) +{ + if (likely(kw == NULL) || PyDict_GET_SIZE(kw) == 0) { + return vc(func, args, nargs, NULL); + } + return __Pyx_PyVectorcall_FastCallDict_kw(func, vc, args, nargs, kw); +} +#endif + +/* CythonFunctionShared */ + #if CYTHON_COMPILING_IN_LIMITED_API +static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void *cfunc) { + if (__Pyx_CyFunction_Check(func)) { + return PyCFunction_GetFunction(((__pyx_CyFunctionObject*)func)->func) == (PyCFunction) cfunc; + } else if (PyCFunction_Check(func)) { + return PyCFunction_GetFunction(func) == (PyCFunction) cfunc; + } + return 0; +} +#else +static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void *cfunc) { + return __Pyx_CyOrPyCFunction_Check(func) && __Pyx_CyOrPyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc; +} +#endif +static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj) { +#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API + __Pyx_Py_XDECREF_SET( + __Pyx_CyFunction_GetClassObj(f), + ((classobj) ? __Pyx_NewRef(classobj) : NULL)); +#else + __Pyx_Py_XDECREF_SET( + ((PyCMethodObject *) (f))->mm_class, + (PyTypeObject*)((classobj) ? __Pyx_NewRef(classobj) : NULL)); +#endif +} +static PyObject * +__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, void *closure) +{ + CYTHON_UNUSED_VAR(closure); + if (unlikely(op->func_doc == NULL)) { +#if CYTHON_COMPILING_IN_LIMITED_API + op->func_doc = PyObject_GetAttrString(op->func, "__doc__"); + if (unlikely(!op->func_doc)) return NULL; +#else + if (((PyCFunctionObject*)op)->m_ml->ml_doc) { +#if PY_MAJOR_VERSION >= 3 + op->func_doc = PyUnicode_FromString(((PyCFunctionObject*)op)->m_ml->ml_doc); +#else + op->func_doc = PyString_FromString(((PyCFunctionObject*)op)->m_ml->ml_doc); +#endif + if (unlikely(op->func_doc == NULL)) + return NULL; + } else { + Py_INCREF(Py_None); + return Py_None; + } +#endif + } + Py_INCREF(op->func_doc); + return op->func_doc; +} +static int +__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value, void *context) +{ + CYTHON_UNUSED_VAR(context); + if (value == NULL) { + value = Py_None; + } + Py_INCREF(value); + __Pyx_Py_XDECREF_SET(op->func_doc, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op, void *context) +{ + CYTHON_UNUSED_VAR(context); + if (unlikely(op->func_name == NULL)) { +#if CYTHON_COMPILING_IN_LIMITED_API + op->func_name = PyObject_GetAttrString(op->func, "__name__"); +#elif PY_MAJOR_VERSION >= 3 + op->func_name = PyUnicode_InternFromString(((PyCFunctionObject*)op)->m_ml->ml_name); +#else + op->func_name = PyString_InternFromString(((PyCFunctionObject*)op)->m_ml->ml_name); +#endif + if (unlikely(op->func_name == NULL)) + return NULL; + } + Py_INCREF(op->func_name); + return op->func_name; +} +static int +__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value, void *context) +{ + CYTHON_UNUSED_VAR(context); +#if PY_MAJOR_VERSION >= 3 + if (unlikely(value == NULL || !PyUnicode_Check(value))) +#else + if (unlikely(value == NULL || !PyString_Check(value))) +#endif + { + PyErr_SetString(PyExc_TypeError, + "__name__ must be set to a string object"); + return -1; + } + Py_INCREF(value); + __Pyx_Py_XDECREF_SET(op->func_name, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op, void *context) +{ + CYTHON_UNUSED_VAR(context); + Py_INCREF(op->func_qualname); + return op->func_qualname; +} +static int +__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value, void *context) +{ + CYTHON_UNUSED_VAR(context); +#if PY_MAJOR_VERSION >= 3 + if (unlikely(value == NULL || !PyUnicode_Check(value))) +#else + if (unlikely(value == NULL || !PyString_Check(value))) +#endif + { + PyErr_SetString(PyExc_TypeError, + "__qualname__ must be set to a string object"); + return -1; + } + Py_INCREF(value); + __Pyx_Py_XDECREF_SET(op->func_qualname, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op, void *context) +{ + CYTHON_UNUSED_VAR(context); + if (unlikely(op->func_dict == NULL)) { + op->func_dict = PyDict_New(); + if (unlikely(op->func_dict == NULL)) + return NULL; + } + Py_INCREF(op->func_dict); + return op->func_dict; +} +static int +__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value, void *context) +{ + CYTHON_UNUSED_VAR(context); + if (unlikely(value == NULL)) { + PyErr_SetString(PyExc_TypeError, + "function's dictionary may not be deleted"); + return -1; + } + if (unlikely(!PyDict_Check(value))) { + PyErr_SetString(PyExc_TypeError, + "setting function's dictionary to a non-dict"); + return -1; + } + Py_INCREF(value); + __Pyx_Py_XDECREF_SET(op->func_dict, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op, void *context) +{ + CYTHON_UNUSED_VAR(context); + Py_INCREF(op->func_globals); + return op->func_globals; +} +static PyObject * +__Pyx_CyFunction_get_closure(__pyx_CyFunctionObject *op, void *context) +{ + CYTHON_UNUSED_VAR(op); + CYTHON_UNUSED_VAR(context); + Py_INCREF(Py_None); + return Py_None; +} +static PyObject * +__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op, void *context) +{ + PyObject* result = (op->func_code) ? op->func_code : Py_None; + CYTHON_UNUSED_VAR(context); + Py_INCREF(result); + return result; +} +static int +__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) { + int result = 0; + PyObject *res = op->defaults_getter((PyObject *) op); + if (unlikely(!res)) + return -1; + #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + op->defaults_tuple = PyTuple_GET_ITEM(res, 0); + Py_INCREF(op->defaults_tuple); + op->defaults_kwdict = PyTuple_GET_ITEM(res, 1); + Py_INCREF(op->defaults_kwdict); + #else + op->defaults_tuple = __Pyx_PySequence_ITEM(res, 0); + if (unlikely(!op->defaults_tuple)) result = -1; + else { + op->defaults_kwdict = __Pyx_PySequence_ITEM(res, 1); + if (unlikely(!op->defaults_kwdict)) result = -1; + } + #endif + Py_DECREF(res); + return result; +} +static int +__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) { + CYTHON_UNUSED_VAR(context); + if (!value) { + value = Py_None; + } else if (unlikely(value != Py_None && !PyTuple_Check(value))) { + PyErr_SetString(PyExc_TypeError, + "__defaults__ must be set to a tuple object"); + return -1; + } + PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__defaults__ will not " + "currently affect the values used in function calls", 1); + Py_INCREF(value); + __Pyx_Py_XDECREF_SET(op->defaults_tuple, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op, void *context) { + PyObject* result = op->defaults_tuple; + CYTHON_UNUSED_VAR(context); + if (unlikely(!result)) { + if (op->defaults_getter) { + if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL; + result = op->defaults_tuple; + } else { + result = Py_None; + } + } + Py_INCREF(result); + return result; +} +static int +__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) { + CYTHON_UNUSED_VAR(context); + if (!value) { + value = Py_None; + } else if (unlikely(value != Py_None && !PyDict_Check(value))) { + PyErr_SetString(PyExc_TypeError, + "__kwdefaults__ must be set to a dict object"); + return -1; + } + PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__kwdefaults__ will not " + "currently affect the values used in function calls", 1); + Py_INCREF(value); + __Pyx_Py_XDECREF_SET(op->defaults_kwdict, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op, void *context) { + PyObject* result = op->defaults_kwdict; + CYTHON_UNUSED_VAR(context); + if (unlikely(!result)) { + if (op->defaults_getter) { + if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL; + result = op->defaults_kwdict; + } else { + result = Py_None; + } + } + Py_INCREF(result); + return result; +} +static int +__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value, void *context) { + CYTHON_UNUSED_VAR(context); + if (!value || value == Py_None) { + value = NULL; + } else if (unlikely(!PyDict_Check(value))) { + PyErr_SetString(PyExc_TypeError, + "__annotations__ must be set to a dict object"); + return -1; + } + Py_XINCREF(value); + __Pyx_Py_XDECREF_SET(op->func_annotations, value); + return 0; +} +static PyObject * +__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op, void *context) { + PyObject* result = op->func_annotations; + CYTHON_UNUSED_VAR(context); + if (unlikely(!result)) { + result = PyDict_New(); + if (unlikely(!result)) return NULL; + op->func_annotations = result; + } + Py_INCREF(result); + return result; +} +static PyObject * +__Pyx_CyFunction_get_is_coroutine(__pyx_CyFunctionObject *op, void *context) { + int is_coroutine; + CYTHON_UNUSED_VAR(context); + if (op->func_is_coroutine) { + return __Pyx_NewRef(op->func_is_coroutine); + } + is_coroutine = op->flags & __Pyx_CYFUNCTION_COROUTINE; +#if PY_VERSION_HEX >= 0x03050000 + if (is_coroutine) { + PyObject *module, *fromlist, *marker = __pyx_n_s_is_coroutine; + fromlist = PyList_New(1); + if (unlikely(!fromlist)) return NULL; + Py_INCREF(marker); +#if CYTHON_ASSUME_SAFE_MACROS + PyList_SET_ITEM(fromlist, 0, marker); +#else + if (unlikely(PyList_SetItem(fromlist, 0, marker) < 0)) { + Py_DECREF(marker); + Py_DECREF(fromlist); + return NULL; + } +#endif + module = PyImport_ImportModuleLevelObject(__pyx_n_s_asyncio_coroutines, NULL, NULL, fromlist, 0); + Py_DECREF(fromlist); + if (unlikely(!module)) goto ignore; + op->func_is_coroutine = __Pyx_PyObject_GetAttrStr(module, marker); + Py_DECREF(module); + if (likely(op->func_is_coroutine)) { + return __Pyx_NewRef(op->func_is_coroutine); + } +ignore: + PyErr_Clear(); + } +#endif + op->func_is_coroutine = __Pyx_PyBool_FromLong(is_coroutine); + return __Pyx_NewRef(op->func_is_coroutine); +} +#if CYTHON_COMPILING_IN_LIMITED_API +static PyObject * +__Pyx_CyFunction_get_module(__pyx_CyFunctionObject *op, void *context) { + CYTHON_UNUSED_VAR(context); + return PyObject_GetAttrString(op->func, "__module__"); +} +static int +__Pyx_CyFunction_set_module(__pyx_CyFunctionObject *op, PyObject* value, void *context) { + CYTHON_UNUSED_VAR(context); + return PyObject_SetAttrString(op->func, "__module__", value); +} +#endif +static PyGetSetDef __pyx_CyFunction_getsets[] = { + {(char *) "func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0}, + {(char *) "__doc__", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0}, + {(char *) "func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0}, + {(char *) "__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0}, + {(char *) "__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0}, + {(char *) "func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0}, + {(char *) "__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0}, + {(char *) "func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0}, + {(char *) "__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0}, + {(char *) "func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0}, + {(char *) "__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0}, + {(char *) "func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0}, + {(char *) "__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0}, + {(char *) "func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0}, + {(char *) "__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0}, + {(char *) "__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0}, + {(char *) "__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0}, + {(char *) "_is_coroutine", (getter)__Pyx_CyFunction_get_is_coroutine, 0, 0, 0}, +#if CYTHON_COMPILING_IN_LIMITED_API + {"__module__", (getter)__Pyx_CyFunction_get_module, (setter)__Pyx_CyFunction_set_module, 0, 0}, +#endif + {0, 0, 0, 0, 0} +}; +static PyMemberDef __pyx_CyFunction_members[] = { +#if !CYTHON_COMPILING_IN_LIMITED_API + {(char *) "__module__", T_OBJECT, offsetof(PyCFunctionObject, m_module), 0, 0}, +#endif +#if CYTHON_USE_TYPE_SPECS + {(char *) "__dictoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_dict), READONLY, 0}, +#if CYTHON_METH_FASTCALL +#if CYTHON_BACKPORT_VECTORCALL + {(char *) "__vectorcalloffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_vectorcall), READONLY, 0}, +#else +#if !CYTHON_COMPILING_IN_LIMITED_API + {(char *) "__vectorcalloffset__", T_PYSSIZET, offsetof(PyCFunctionObject, vectorcall), READONLY, 0}, +#endif +#endif +#endif +#if PY_VERSION_HEX < 0x030500A0 || CYTHON_COMPILING_IN_LIMITED_API + {(char *) "__weaklistoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_weakreflist), READONLY, 0}, +#else + {(char *) "__weaklistoffset__", T_PYSSIZET, offsetof(PyCFunctionObject, m_weakreflist), READONLY, 0}, +#endif +#endif + {0, 0, 0, 0, 0} +}; +static PyObject * +__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, PyObject *args) +{ + CYTHON_UNUSED_VAR(args); +#if PY_MAJOR_VERSION >= 3 + Py_INCREF(m->func_qualname); + return m->func_qualname; +#else + return PyString_FromString(((PyCFunctionObject*)m)->m_ml->ml_name); +#endif +} +static PyMethodDef __pyx_CyFunction_methods[] = { + {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0}, + {0, 0, 0, 0} +}; +#if PY_VERSION_HEX < 0x030500A0 || CYTHON_COMPILING_IN_LIMITED_API +#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist) +#else +#define __Pyx_CyFunction_weakreflist(cyfunc) (((PyCFunctionObject*)cyfunc)->m_weakreflist) +#endif +static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject *op, PyMethodDef *ml, int flags, PyObject* qualname, + PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) { +#if !CYTHON_COMPILING_IN_LIMITED_API + PyCFunctionObject *cf = (PyCFunctionObject*) op; +#endif + if (unlikely(op == NULL)) + return NULL; +#if CYTHON_COMPILING_IN_LIMITED_API + op->func = PyCFunction_NewEx(ml, (PyObject*)op, module); + if (unlikely(!op->func)) return NULL; +#endif + op->flags = flags; + __Pyx_CyFunction_weakreflist(op) = NULL; +#if !CYTHON_COMPILING_IN_LIMITED_API + cf->m_ml = ml; + cf->m_self = (PyObject *) op; +#endif + Py_XINCREF(closure); + op->func_closure = closure; +#if !CYTHON_COMPILING_IN_LIMITED_API + Py_XINCREF(module); + cf->m_module = module; +#endif + op->func_dict = NULL; + op->func_name = NULL; + Py_INCREF(qualname); + op->func_qualname = qualname; + op->func_doc = NULL; +#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API + op->func_classobj = NULL; +#else + ((PyCMethodObject*)op)->mm_class = NULL; +#endif + op->func_globals = globals; + Py_INCREF(op->func_globals); + Py_XINCREF(code); + op->func_code = code; + op->defaults_pyobjects = 0; + op->defaults_size = 0; + op->defaults = NULL; + op->defaults_tuple = NULL; + op->defaults_kwdict = NULL; + op->defaults_getter = NULL; + op->func_annotations = NULL; + op->func_is_coroutine = NULL; +#if CYTHON_METH_FASTCALL + switch (ml->ml_flags & (METH_VARARGS | METH_FASTCALL | METH_NOARGS | METH_O | METH_KEYWORDS | METH_METHOD)) { + case METH_NOARGS: + __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_NOARGS; + break; + case METH_O: + __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_O; + break; + case METH_METHOD | METH_FASTCALL | METH_KEYWORDS: + __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD; + break; + case METH_FASTCALL | METH_KEYWORDS: + __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS; + break; + case METH_VARARGS | METH_KEYWORDS: + __Pyx_CyFunction_func_vectorcall(op) = NULL; + break; + default: + PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction"); + Py_DECREF(op); + return NULL; + } +#endif + return (PyObject *) op; +} +static int +__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m) +{ + Py_CLEAR(m->func_closure); +#if CYTHON_COMPILING_IN_LIMITED_API + Py_CLEAR(m->func); +#else + Py_CLEAR(((PyCFunctionObject*)m)->m_module); +#endif + Py_CLEAR(m->func_dict); + Py_CLEAR(m->func_name); + Py_CLEAR(m->func_qualname); + Py_CLEAR(m->func_doc); + Py_CLEAR(m->func_globals); + Py_CLEAR(m->func_code); +#if !CYTHON_COMPILING_IN_LIMITED_API +#if PY_VERSION_HEX < 0x030900B1 + Py_CLEAR(__Pyx_CyFunction_GetClassObj(m)); +#else + { + PyObject *cls = (PyObject*) ((PyCMethodObject *) (m))->mm_class; + ((PyCMethodObject *) (m))->mm_class = NULL; + Py_XDECREF(cls); + } +#endif +#endif + Py_CLEAR(m->defaults_tuple); + Py_CLEAR(m->defaults_kwdict); + Py_CLEAR(m->func_annotations); + Py_CLEAR(m->func_is_coroutine); + if (m->defaults) { + PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m); + int i; + for (i = 0; i < m->defaults_pyobjects; i++) + Py_XDECREF(pydefaults[i]); + PyObject_Free(m->defaults); + m->defaults = NULL; + } + return 0; +} +static void __Pyx__CyFunction_dealloc(__pyx_CyFunctionObject *m) +{ + if (__Pyx_CyFunction_weakreflist(m) != NULL) + PyObject_ClearWeakRefs((PyObject *) m); + __Pyx_CyFunction_clear(m); + __Pyx_PyHeapTypeObject_GC_Del(m); +} +static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m) +{ + PyObject_GC_UnTrack(m); + __Pyx__CyFunction_dealloc(m); +} +static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg) +{ + Py_VISIT(m->func_closure); +#if CYTHON_COMPILING_IN_LIMITED_API + Py_VISIT(m->func); +#else + Py_VISIT(((PyCFunctionObject*)m)->m_module); +#endif + Py_VISIT(m->func_dict); + Py_VISIT(m->func_name); + Py_VISIT(m->func_qualname); + Py_VISIT(m->func_doc); + Py_VISIT(m->func_globals); + Py_VISIT(m->func_code); +#if !CYTHON_COMPILING_IN_LIMITED_API + Py_VISIT(__Pyx_CyFunction_GetClassObj(m)); +#endif + Py_VISIT(m->defaults_tuple); + Py_VISIT(m->defaults_kwdict); + Py_VISIT(m->func_is_coroutine); + if (m->defaults) { + PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m); + int i; + for (i = 0; i < m->defaults_pyobjects; i++) + Py_VISIT(pydefaults[i]); + } + return 0; +} +static PyObject* +__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op) +{ +#if PY_MAJOR_VERSION >= 3 + return PyUnicode_FromFormat("", + op->func_qualname, (void *)op); +#else + return PyString_FromFormat("", + PyString_AsString(op->func_qualname), (void *)op); +#endif +} +static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) { +#if CYTHON_COMPILING_IN_LIMITED_API + PyObject *f = ((__pyx_CyFunctionObject*)func)->func; + PyObject *py_name = NULL; + PyCFunction meth; + int flags; + meth = PyCFunction_GetFunction(f); + if (unlikely(!meth)) return NULL; + flags = PyCFunction_GetFlags(f); + if (unlikely(flags < 0)) return NULL; +#else + PyCFunctionObject* f = (PyCFunctionObject*)func; + PyCFunction meth = f->m_ml->ml_meth; + int flags = f->m_ml->ml_flags; +#endif + Py_ssize_t size; + switch (flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) { + case METH_VARARGS: + if (likely(kw == NULL || PyDict_Size(kw) == 0)) + return (*meth)(self, arg); + break; + case METH_VARARGS | METH_KEYWORDS: + return (*(PyCFunctionWithKeywords)(void*)meth)(self, arg, kw); + case METH_NOARGS: + if (likely(kw == NULL || PyDict_Size(kw) == 0)) { +#if CYTHON_ASSUME_SAFE_MACROS + size = PyTuple_GET_SIZE(arg); +#else + size = PyTuple_Size(arg); + if (unlikely(size < 0)) return NULL; +#endif + if (likely(size == 0)) + return (*meth)(self, NULL); +#if CYTHON_COMPILING_IN_LIMITED_API + py_name = __Pyx_CyFunction_get_name((__pyx_CyFunctionObject*)func, NULL); + if (!py_name) return NULL; + PyErr_Format(PyExc_TypeError, + "%.200S() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)", + py_name, size); + Py_DECREF(py_name); +#else + PyErr_Format(PyExc_TypeError, + "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)", + f->m_ml->ml_name, size); +#endif + return NULL; + } + break; + case METH_O: + if (likely(kw == NULL || PyDict_Size(kw) == 0)) { +#if CYTHON_ASSUME_SAFE_MACROS + size = PyTuple_GET_SIZE(arg); +#else + size = PyTuple_Size(arg); + if (unlikely(size < 0)) return NULL; +#endif + if (likely(size == 1)) { + PyObject *result, *arg0; + #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + arg0 = PyTuple_GET_ITEM(arg, 0); + #else + arg0 = __Pyx_PySequence_ITEM(arg, 0); if (unlikely(!arg0)) return NULL; + #endif + result = (*meth)(self, arg0); + #if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS) + Py_DECREF(arg0); + #endif + return result; + } +#if CYTHON_COMPILING_IN_LIMITED_API + py_name = __Pyx_CyFunction_get_name((__pyx_CyFunctionObject*)func, NULL); + if (!py_name) return NULL; + PyErr_Format(PyExc_TypeError, + "%.200S() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)", + py_name, size); + Py_DECREF(py_name); +#else + PyErr_Format(PyExc_TypeError, + "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)", + f->m_ml->ml_name, size); +#endif + return NULL; + } + break; + default: + PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction"); + return NULL; + } +#if CYTHON_COMPILING_IN_LIMITED_API + py_name = __Pyx_CyFunction_get_name((__pyx_CyFunctionObject*)func, NULL); + if (!py_name) return NULL; + PyErr_Format(PyExc_TypeError, "%.200S() takes no keyword arguments", + py_name); + Py_DECREF(py_name); +#else + PyErr_Format(PyExc_TypeError, "%.200s() takes no keyword arguments", + f->m_ml->ml_name); +#endif + return NULL; +} +static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) { + PyObject *self, *result; +#if CYTHON_COMPILING_IN_LIMITED_API + self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)func)->func); + if (unlikely(!self) && PyErr_Occurred()) return NULL; +#else + self = ((PyCFunctionObject*)func)->m_self; +#endif + result = __Pyx_CyFunction_CallMethod(func, self, arg, kw); + return result; +} +static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) { + PyObject *result; + __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func; +#if CYTHON_METH_FASTCALL + __pyx_vectorcallfunc vc = __Pyx_CyFunction_func_vectorcall(cyfunc); + if (vc) { +#if CYTHON_ASSUME_SAFE_MACROS + return __Pyx_PyVectorcall_FastCallDict(func, vc, &PyTuple_GET_ITEM(args, 0), (size_t)PyTuple_GET_SIZE(args), kw); +#else + (void) &__Pyx_PyVectorcall_FastCallDict; + return PyVectorcall_Call(func, args, kw); +#endif + } +#endif + if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) { + Py_ssize_t argc; + PyObject *new_args; + PyObject *self; +#if CYTHON_ASSUME_SAFE_MACROS + argc = PyTuple_GET_SIZE(args); +#else + argc = PyTuple_Size(args); + if (unlikely(!argc) < 0) return NULL; +#endif + new_args = PyTuple_GetSlice(args, 1, argc); + if (unlikely(!new_args)) + return NULL; + self = PyTuple_GetItem(args, 0); + if (unlikely(!self)) { + Py_DECREF(new_args); +#if PY_MAJOR_VERSION > 2 + PyErr_Format(PyExc_TypeError, + "unbound method %.200S() needs an argument", + cyfunc->func_qualname); +#else + PyErr_SetString(PyExc_TypeError, + "unbound method needs an argument"); +#endif + return NULL; + } + result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw); + Py_DECREF(new_args); + } else { + result = __Pyx_CyFunction_Call(func, args, kw); + } + return result; +} +#if CYTHON_METH_FASTCALL +static CYTHON_INLINE int __Pyx_CyFunction_Vectorcall_CheckArgs(__pyx_CyFunctionObject *cyfunc, Py_ssize_t nargs, PyObject *kwnames) +{ + int ret = 0; + if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) { + if (unlikely(nargs < 1)) { + PyErr_Format(PyExc_TypeError, "%.200s() needs an argument", + ((PyCFunctionObject*)cyfunc)->m_ml->ml_name); + return -1; + } + ret = 1; + } + if (unlikely(kwnames) && unlikely(PyTuple_GET_SIZE(kwnames))) { + PyErr_Format(PyExc_TypeError, + "%.200s() takes no keyword arguments", ((PyCFunctionObject*)cyfunc)->m_ml->ml_name); + return -1; + } + return ret; +} +static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames) +{ + __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func; + PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml; +#if CYTHON_BACKPORT_VECTORCALL + Py_ssize_t nargs = (Py_ssize_t)nargsf; +#else + Py_ssize_t nargs = PyVectorcall_NARGS(nargsf); +#endif + PyObject *self; + switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) { + case 1: + self = args[0]; + args += 1; + nargs -= 1; + break; + case 0: + self = ((PyCFunctionObject*)cyfunc)->m_self; + break; + default: + return NULL; + } + if (unlikely(nargs != 0)) { + PyErr_Format(PyExc_TypeError, + "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)", + def->ml_name, nargs); + return NULL; + } + return def->ml_meth(self, NULL); +} +static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames) +{ + __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func; + PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml; +#if CYTHON_BACKPORT_VECTORCALL + Py_ssize_t nargs = (Py_ssize_t)nargsf; +#else + Py_ssize_t nargs = PyVectorcall_NARGS(nargsf); +#endif + PyObject *self; + switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) { + case 1: + self = args[0]; + args += 1; + nargs -= 1; + break; + case 0: + self = ((PyCFunctionObject*)cyfunc)->m_self; + break; + default: + return NULL; + } + if (unlikely(nargs != 1)) { + PyErr_Format(PyExc_TypeError, + "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)", + def->ml_name, nargs); + return NULL; + } + return def->ml_meth(self, args[0]); +} +static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames) +{ + __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func; + PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml; +#if CYTHON_BACKPORT_VECTORCALL + Py_ssize_t nargs = (Py_ssize_t)nargsf; +#else + Py_ssize_t nargs = PyVectorcall_NARGS(nargsf); +#endif + PyObject *self; + switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) { + case 1: + self = args[0]; + args += 1; + nargs -= 1; + break; + case 0: + self = ((PyCFunctionObject*)cyfunc)->m_self; + break; + default: + return NULL; + } + return ((__Pyx_PyCFunctionFastWithKeywords)(void(*)(void))def->ml_meth)(self, args, nargs, kwnames); +} +static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames) +{ + __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func; + PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml; + PyTypeObject *cls = (PyTypeObject *) __Pyx_CyFunction_GetClassObj(cyfunc); +#if CYTHON_BACKPORT_VECTORCALL + Py_ssize_t nargs = (Py_ssize_t)nargsf; +#else + Py_ssize_t nargs = PyVectorcall_NARGS(nargsf); +#endif + PyObject *self; + switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) { + case 1: + self = args[0]; + args += 1; + nargs -= 1; + break; + case 0: + self = ((PyCFunctionObject*)cyfunc)->m_self; + break; + default: + return NULL; + } + return ((__Pyx_PyCMethod)(void(*)(void))def->ml_meth)(self, cls, args, (size_t)nargs, kwnames); +} +#endif +#if CYTHON_USE_TYPE_SPECS +static PyType_Slot __pyx_CyFunctionType_slots[] = { + {Py_tp_dealloc, (void *)__Pyx_CyFunction_dealloc}, + {Py_tp_repr, (void *)__Pyx_CyFunction_repr}, + {Py_tp_call, (void *)__Pyx_CyFunction_CallAsMethod}, + {Py_tp_traverse, (void *)__Pyx_CyFunction_traverse}, + {Py_tp_clear, (void *)__Pyx_CyFunction_clear}, + {Py_tp_methods, (void *)__pyx_CyFunction_methods}, + {Py_tp_members, (void *)__pyx_CyFunction_members}, + {Py_tp_getset, (void *)__pyx_CyFunction_getsets}, + {Py_tp_descr_get, (void *)__Pyx_PyMethod_New}, + {0, 0}, +}; +static PyType_Spec __pyx_CyFunctionType_spec = { + __PYX_TYPE_MODULE_PREFIX "cython_function_or_method", + sizeof(__pyx_CyFunctionObject), + 0, +#ifdef Py_TPFLAGS_METHOD_DESCRIPTOR + Py_TPFLAGS_METHOD_DESCRIPTOR | +#endif +#if (defined(_Py_TPFLAGS_HAVE_VECTORCALL) && CYTHON_METH_FASTCALL) + _Py_TPFLAGS_HAVE_VECTORCALL | +#endif + Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_BASETYPE, + __pyx_CyFunctionType_slots +}; +#else +static PyTypeObject __pyx_CyFunctionType_type = { + PyVarObject_HEAD_INIT(0, 0) + __PYX_TYPE_MODULE_PREFIX "cython_function_or_method", + sizeof(__pyx_CyFunctionObject), + 0, + (destructor) __Pyx_CyFunction_dealloc, +#if !CYTHON_METH_FASTCALL + 0, +#elif CYTHON_BACKPORT_VECTORCALL + (printfunc)offsetof(__pyx_CyFunctionObject, func_vectorcall), +#else + offsetof(PyCFunctionObject, vectorcall), +#endif + 0, + 0, +#if PY_MAJOR_VERSION < 3 + 0, +#else + 0, +#endif + (reprfunc) __Pyx_CyFunction_repr, + 0, + 0, + 0, + 0, + __Pyx_CyFunction_CallAsMethod, + 0, + 0, + 0, + 0, +#ifdef Py_TPFLAGS_METHOD_DESCRIPTOR + Py_TPFLAGS_METHOD_DESCRIPTOR | +#endif +#if defined(_Py_TPFLAGS_HAVE_VECTORCALL) && CYTHON_METH_FASTCALL + _Py_TPFLAGS_HAVE_VECTORCALL | +#endif + Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_BASETYPE, + 0, + (traverseproc) __Pyx_CyFunction_traverse, + (inquiry) __Pyx_CyFunction_clear, + 0, +#if PY_VERSION_HEX < 0x030500A0 + offsetof(__pyx_CyFunctionObject, func_weakreflist), +#else + offsetof(PyCFunctionObject, m_weakreflist), +#endif + 0, + 0, + __pyx_CyFunction_methods, + __pyx_CyFunction_members, + __pyx_CyFunction_getsets, + 0, + 0, + __Pyx_PyMethod_New, + 0, + offsetof(__pyx_CyFunctionObject, func_dict), + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, +#if PY_VERSION_HEX >= 0x030400a1 + 0, +#endif +#if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800) + 0, +#endif +#if __PYX_NEED_TP_PRINT_SLOT + 0, +#endif +#if PY_VERSION_HEX >= 0x030C0000 + 0, +#endif +#if PY_VERSION_HEX >= 0x030d00A4 + 0, +#endif +#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000 + 0, +#endif +}; +#endif +static int __pyx_CyFunction_init(PyObject *module) { +#if CYTHON_USE_TYPE_SPECS + __pyx_CyFunctionType = __Pyx_FetchCommonTypeFromSpec(module, &__pyx_CyFunctionType_spec, NULL); +#else + CYTHON_UNUSED_VAR(module); + __pyx_CyFunctionType = __Pyx_FetchCommonType(&__pyx_CyFunctionType_type); +#endif + if (unlikely(__pyx_CyFunctionType == NULL)) { + return -1; + } + return 0; +} +static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *func, size_t size, int pyobjects) { + __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func; + m->defaults = PyObject_Malloc(size); + if (unlikely(!m->defaults)) + return PyErr_NoMemory(); + memset(m->defaults, 0, size); + m->defaults_pyobjects = pyobjects; + m->defaults_size = size; + return m->defaults; +} +static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) { + __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func; + m->defaults_tuple = tuple; + Py_INCREF(tuple); +} +static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) { + __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func; + m->defaults_kwdict = dict; + Py_INCREF(dict); +} +static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) { + __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func; + m->func_annotations = dict; + Py_INCREF(dict); +} + +/* CythonFunction */ + static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml, int flags, PyObject* qualname, + PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) { + PyObject *op = __Pyx_CyFunction_Init( + PyObject_GC_New(__pyx_CyFunctionObject, __pyx_CyFunctionType), + ml, flags, qualname, closure, module, globals, code + ); + if (likely(op)) { + PyObject_GC_Track(op); + } + return op; +} + +/* CLineInTraceback */ + #ifndef CYTHON_CLINE_IN_TRACEBACK +static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) { + PyObject *use_cline; + PyObject *ptype, *pvalue, *ptraceback; +#if CYTHON_COMPILING_IN_CPYTHON + PyObject **cython_runtime_dict; +#endif + CYTHON_MAYBE_UNUSED_VAR(tstate); + if (unlikely(!__pyx_cython_runtime)) { + return c_line; + } + __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback); +#if CYTHON_COMPILING_IN_CPYTHON + cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime); + if (likely(cython_runtime_dict)) { + __PYX_PY_DICT_LOOKUP_IF_MODIFIED( + use_cline, *cython_runtime_dict, + __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback)) + } else +#endif + { + PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStrNoError(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback); + if (use_cline_obj) { + use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True; + Py_DECREF(use_cline_obj); + } else { + PyErr_Clear(); + use_cline = NULL; + } + } + if (!use_cline) { + c_line = 0; + (void) PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False); + } + else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) { + c_line = 0; + } + __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback); + return c_line; +} +#endif + +/* CodeObjectCache */ + #if !CYTHON_COMPILING_IN_LIMITED_API +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { + int start = 0, mid = 0, end = count - 1; + if (end >= 0 && code_line > entries[end].code_line) { + return count; + } + while (start < end) { + mid = start + (end - start) / 2; + if (code_line < entries[mid].code_line) { + end = mid; + } else if (code_line > entries[mid].code_line) { + start = mid + 1; + } else { + return mid; + } + } + if (code_line <= entries[mid].code_line) { + return mid; + } else { + return mid + 1; + } +} +static PyCodeObject *__pyx_find_code_object(int code_line) { + PyCodeObject* code_object; + int pos; + if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { + return NULL; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { + return NULL; + } + code_object = __pyx_code_cache.entries[pos].code_object; + Py_INCREF(code_object); + return code_object; +} +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { + int pos, i; + __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; + if (unlikely(!code_line)) { + return; + } + if (unlikely(!entries)) { + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); + if (likely(entries)) { + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = 64; + __pyx_code_cache.count = 1; + entries[0].code_line = code_line; + entries[0].code_object = code_object; + Py_INCREF(code_object); + } + return; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { + PyCodeObject* tmp = entries[pos].code_object; + entries[pos].code_object = code_object; + Py_DECREF(tmp); + return; + } + if (__pyx_code_cache.count == __pyx_code_cache.max_count) { + int new_max = __pyx_code_cache.max_count + 64; + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( + __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry)); + if (unlikely(!entries)) { + return; + } + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = new_max; + } + for (i=__pyx_code_cache.count; i>pos; i--) { + entries[i] = entries[i-1]; + } + entries[pos].code_line = code_line; + entries[pos].code_object = code_object; + __pyx_code_cache.count++; + Py_INCREF(code_object); +} +#endif + +/* AddTraceback */ + #include "compile.h" +#include "frameobject.h" +#include "traceback.h" +#if PY_VERSION_HEX >= 0x030b00a6 && !CYTHON_COMPILING_IN_LIMITED_API + #ifndef Py_BUILD_CORE + #define Py_BUILD_CORE 1 + #endif + #include "internal/pycore_frame.h" +#endif +#if CYTHON_COMPILING_IN_LIMITED_API +static PyObject *__Pyx_PyCode_Replace_For_AddTraceback(PyObject *code, PyObject *scratch_dict, + PyObject *firstlineno, PyObject *name) { + PyObject *replace = NULL; + if (unlikely(PyDict_SetItemString(scratch_dict, "co_firstlineno", firstlineno))) return NULL; + if (unlikely(PyDict_SetItemString(scratch_dict, "co_name", name))) return NULL; + replace = PyObject_GetAttrString(code, "replace"); + if (likely(replace)) { + PyObject *result; + result = PyObject_Call(replace, __pyx_empty_tuple, scratch_dict); + Py_DECREF(replace); + return result; + } + PyErr_Clear(); + #if __PYX_LIMITED_VERSION_HEX < 0x030780000 + { + PyObject *compiled = NULL, *result = NULL; + if (unlikely(PyDict_SetItemString(scratch_dict, "code", code))) return NULL; + if (unlikely(PyDict_SetItemString(scratch_dict, "type", (PyObject*)(&PyType_Type)))) return NULL; + compiled = Py_CompileString( + "out = type(code)(\n" + " code.co_argcount, code.co_kwonlyargcount, code.co_nlocals, code.co_stacksize,\n" + " code.co_flags, code.co_code, code.co_consts, code.co_names,\n" + " code.co_varnames, code.co_filename, co_name, co_firstlineno,\n" + " code.co_lnotab)\n", "", Py_file_input); + if (!compiled) return NULL; + result = PyEval_EvalCode(compiled, scratch_dict, scratch_dict); + Py_DECREF(compiled); + if (!result) PyErr_Print(); + Py_DECREF(result); + result = PyDict_GetItemString(scratch_dict, "out"); + if (result) Py_INCREF(result); + return result; + } + #else + return NULL; + #endif +} +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename) { + PyObject *code_object = NULL, *py_py_line = NULL, *py_funcname = NULL, *dict = NULL; + PyObject *replace = NULL, *getframe = NULL, *frame = NULL; + PyObject *exc_type, *exc_value, *exc_traceback; + int success = 0; + if (c_line) { + (void) __pyx_cfilenm; + (void) __Pyx_CLineForTraceback(__Pyx_PyThreadState_Current, c_line); + } + PyErr_Fetch(&exc_type, &exc_value, &exc_traceback); + code_object = Py_CompileString("_getframe()", filename, Py_eval_input); + if (unlikely(!code_object)) goto bad; + py_py_line = PyLong_FromLong(py_line); + if (unlikely(!py_py_line)) goto bad; + py_funcname = PyUnicode_FromString(funcname); + if (unlikely(!py_funcname)) goto bad; + dict = PyDict_New(); + if (unlikely(!dict)) goto bad; + { + PyObject *old_code_object = code_object; + code_object = __Pyx_PyCode_Replace_For_AddTraceback(code_object, dict, py_py_line, py_funcname); + Py_DECREF(old_code_object); + } + if (unlikely(!code_object)) goto bad; + getframe = PySys_GetObject("_getframe"); + if (unlikely(!getframe)) goto bad; + if (unlikely(PyDict_SetItemString(dict, "_getframe", getframe))) goto bad; + frame = PyEval_EvalCode(code_object, dict, dict); + if (unlikely(!frame) || frame == Py_None) goto bad; + success = 1; + bad: + PyErr_Restore(exc_type, exc_value, exc_traceback); + Py_XDECREF(code_object); + Py_XDECREF(py_py_line); + Py_XDECREF(py_funcname); + Py_XDECREF(dict); + Py_XDECREF(replace); + if (success) { + PyTraceBack_Here( + (struct _frame*)frame); + } + Py_XDECREF(frame); +} +#else +static PyCodeObject* __Pyx_CreateCodeObjectForTraceback( + const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = NULL; + PyObject *py_funcname = NULL; + #if PY_MAJOR_VERSION < 3 + PyObject *py_srcfile = NULL; + py_srcfile = PyString_FromString(filename); + if (!py_srcfile) goto bad; + #endif + if (c_line) { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + if (!py_funcname) goto bad; + #else + py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + if (!py_funcname) goto bad; + funcname = PyUnicode_AsUTF8(py_funcname); + if (!funcname) goto bad; + #endif + } + else { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromString(funcname); + if (!py_funcname) goto bad; + #endif + } + #if PY_MAJOR_VERSION < 3 + py_code = __Pyx_PyCode_New( + 0, + 0, + 0, + 0, + 0, + 0, + __pyx_empty_bytes, /*PyObject *code,*/ + __pyx_empty_tuple, /*PyObject *consts,*/ + __pyx_empty_tuple, /*PyObject *names,*/ + __pyx_empty_tuple, /*PyObject *varnames,*/ + __pyx_empty_tuple, /*PyObject *freevars,*/ + __pyx_empty_tuple, /*PyObject *cellvars,*/ + py_srcfile, /*PyObject *filename,*/ + py_funcname, /*PyObject *name,*/ + py_line, + __pyx_empty_bytes /*PyObject *lnotab*/ + ); + Py_DECREF(py_srcfile); + #else + py_code = PyCode_NewEmpty(filename, funcname, py_line); + #endif + Py_XDECREF(py_funcname); + return py_code; +bad: + Py_XDECREF(py_funcname); + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(py_srcfile); + #endif + return NULL; +} +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyFrameObject *py_frame = 0; + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject *ptype, *pvalue, *ptraceback; + if (c_line) { + c_line = __Pyx_CLineForTraceback(tstate, c_line); + } + py_code = __pyx_find_code_object(c_line ? -c_line : py_line); + if (!py_code) { + __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback); + py_code = __Pyx_CreateCodeObjectForTraceback( + funcname, c_line, py_line, filename); + if (!py_code) { + /* If the code object creation fails, then we should clear the + fetched exception references and propagate the new exception */ + Py_XDECREF(ptype); + Py_XDECREF(pvalue); + Py_XDECREF(ptraceback); + goto bad; + } + __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback); + __pyx_insert_code_object(c_line ? -c_line : py_line, py_code); + } + py_frame = PyFrame_New( + tstate, /*PyThreadState *tstate,*/ + py_code, /*PyCodeObject *code,*/ + __pyx_d, /*PyObject *globals,*/ + 0 /*PyObject *locals*/ + ); + if (!py_frame) goto bad; + __Pyx_PyFrame_SetLineNumber(py_frame, py_line); + PyTraceBack_Here(py_frame); +bad: + Py_XDECREF(py_code); + Py_XDECREF(py_frame); +} +#endif + +#if PY_MAJOR_VERSION < 3 +static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) { + __Pyx_TypeName obj_type_name; + if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags); + if (__Pyx_TypeCheck(obj, __pyx_array_type)) return __pyx_array_getbuffer(obj, view, flags); + if (__Pyx_TypeCheck(obj, __pyx_memoryview_type)) return __pyx_memoryview_getbuffer(obj, view, flags); + obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj)); + PyErr_Format(PyExc_TypeError, + "'" __Pyx_FMT_TYPENAME "' does not have the buffer interface", + obj_type_name); + __Pyx_DECREF_TypeName(obj_type_name); + return -1; +} +static void __Pyx_ReleaseBuffer(Py_buffer *view) { + PyObject *obj = view->obj; + if (!obj) return; + if (PyObject_CheckBuffer(obj)) { + PyBuffer_Release(view); + return; + } + if ((0)) {} + view->obj = NULL; + Py_DECREF(obj); +} +#endif + + + /* MemviewSliceIsContig */ + static int +__pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, char order, int ndim) +{ + int i, index, step, start; + Py_ssize_t itemsize = mvs.memview->view.itemsize; + if (order == 'F') { + step = 1; + start = 0; + } else { + step = -1; + start = ndim - 1; + } + for (i = 0; i < ndim; i++) { + index = start + step * i; + if (mvs.suboffsets[index] >= 0 || mvs.strides[index] != itemsize) + return 0; + itemsize *= mvs.shape[index]; + } + return 1; +} + +/* OverlappingSlices */ + static void +__pyx_get_array_memory_extents(__Pyx_memviewslice *slice, + void **out_start, void **out_end, + int ndim, size_t itemsize) +{ + char *start, *end; + int i; + start = end = slice->data; + for (i = 0; i < ndim; i++) { + Py_ssize_t stride = slice->strides[i]; + Py_ssize_t extent = slice->shape[i]; + if (extent == 0) { + *out_start = *out_end = start; + return; + } else { + if (stride > 0) + end += stride * (extent - 1); + else + start += stride * (extent - 1); + } + } + *out_start = start; + *out_end = end + itemsize; +} +static int +__pyx_slices_overlap(__Pyx_memviewslice *slice1, + __Pyx_memviewslice *slice2, + int ndim, size_t itemsize) +{ + void *start1, *end1, *start2, *end2; + __pyx_get_array_memory_extents(slice1, &start1, &end1, ndim, itemsize); + __pyx_get_array_memory_extents(slice2, &start2, &end2, ndim, itemsize); + return (start1 < end2) && (start2 < end1); +} + +/* TypeInfoCompare */ + static int +__pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b) +{ + int i; + if (!a || !b) + return 0; + if (a == b) + return 1; + if (a->size != b->size || a->typegroup != b->typegroup || + a->is_unsigned != b->is_unsigned || a->ndim != b->ndim) { + if (a->typegroup == 'H' || b->typegroup == 'H') { + return a->size == b->size; + } else { + return 0; + } + } + if (a->ndim) { + for (i = 0; i < a->ndim; i++) + if (a->arraysize[i] != b->arraysize[i]) + return 0; + } + if (a->typegroup == 'S') { + if (a->flags != b->flags) + return 0; + if (a->fields || b->fields) { + if (!(a->fields && b->fields)) + return 0; + for (i = 0; a->fields[i].type && b->fields[i].type; i++) { + __Pyx_StructField *field_a = a->fields + i; + __Pyx_StructField *field_b = b->fields + i; + if (field_a->offset != field_b->offset || + !__pyx_typeinfo_cmp(field_a->type, field_b->type)) + return 0; + } + return !a->fields[i].type && !b->fields[i].type; + } + } + return 1; +} + +/* MemviewSliceValidateAndInit */ + static int +__pyx_check_strides(Py_buffer *buf, int dim, int ndim, int spec) +{ + if (buf->shape[dim] <= 1) + return 1; + if (buf->strides) { + if (spec & __Pyx_MEMVIEW_CONTIG) { + if (spec & (__Pyx_MEMVIEW_PTR|__Pyx_MEMVIEW_FULL)) { + if (unlikely(buf->strides[dim] != sizeof(void *))) { + PyErr_Format(PyExc_ValueError, + "Buffer is not indirectly contiguous " + "in dimension %d.", dim); + goto fail; + } + } else if (unlikely(buf->strides[dim] != buf->itemsize)) { + PyErr_SetString(PyExc_ValueError, + "Buffer and memoryview are not contiguous " + "in the same dimension."); + goto fail; + } + } + if (spec & __Pyx_MEMVIEW_FOLLOW) { + Py_ssize_t stride = buf->strides[dim]; + if (stride < 0) + stride = -stride; + if (unlikely(stride < buf->itemsize)) { + PyErr_SetString(PyExc_ValueError, + "Buffer and memoryview are not contiguous " + "in the same dimension."); + goto fail; + } + } + } else { + if (unlikely(spec & __Pyx_MEMVIEW_CONTIG && dim != ndim - 1)) { + PyErr_Format(PyExc_ValueError, + "C-contiguous buffer is not contiguous in " + "dimension %d", dim); + goto fail; + } else if (unlikely(spec & (__Pyx_MEMVIEW_PTR))) { + PyErr_Format(PyExc_ValueError, + "C-contiguous buffer is not indirect in " + "dimension %d", dim); + goto fail; + } else if (unlikely(buf->suboffsets)) { + PyErr_SetString(PyExc_ValueError, + "Buffer exposes suboffsets but no strides"); + goto fail; + } + } + return 1; +fail: + return 0; +} +static int +__pyx_check_suboffsets(Py_buffer *buf, int dim, int ndim, int spec) +{ + CYTHON_UNUSED_VAR(ndim); + if (spec & __Pyx_MEMVIEW_DIRECT) { + if (unlikely(buf->suboffsets && buf->suboffsets[dim] >= 0)) { + PyErr_Format(PyExc_ValueError, + "Buffer not compatible with direct access " + "in dimension %d.", dim); + goto fail; + } + } + if (spec & __Pyx_MEMVIEW_PTR) { + if (unlikely(!buf->suboffsets || (buf->suboffsets[dim] < 0))) { + PyErr_Format(PyExc_ValueError, + "Buffer is not indirectly accessible " + "in dimension %d.", dim); + goto fail; + } + } + return 1; +fail: + return 0; +} +static int +__pyx_verify_contig(Py_buffer *buf, int ndim, int c_or_f_flag) +{ + int i; + if (c_or_f_flag & __Pyx_IS_F_CONTIG) { + Py_ssize_t stride = 1; + for (i = 0; i < ndim; i++) { + if (unlikely(stride * buf->itemsize != buf->strides[i] && buf->shape[i] > 1)) { + PyErr_SetString(PyExc_ValueError, + "Buffer not fortran contiguous."); + goto fail; + } + stride = stride * buf->shape[i]; + } + } else if (c_or_f_flag & __Pyx_IS_C_CONTIG) { + Py_ssize_t stride = 1; + for (i = ndim - 1; i >- 1; i--) { + if (unlikely(stride * buf->itemsize != buf->strides[i] && buf->shape[i] > 1)) { + PyErr_SetString(PyExc_ValueError, + "Buffer not C contiguous."); + goto fail; + } + stride = stride * buf->shape[i]; + } + } + return 1; +fail: + return 0; +} +static int __Pyx_ValidateAndInit_memviewslice( + int *axes_specs, + int c_or_f_flag, + int buf_flags, + int ndim, + __Pyx_TypeInfo *dtype, + __Pyx_BufFmt_StackElem stack[], + __Pyx_memviewslice *memviewslice, + PyObject *original_obj) +{ + struct __pyx_memoryview_obj *memview, *new_memview; + __Pyx_RefNannyDeclarations + Py_buffer *buf; + int i, spec = 0, retval = -1; + __Pyx_BufFmt_Context ctx; + int from_memoryview = __pyx_memoryview_check(original_obj); + __Pyx_RefNannySetupContext("ValidateAndInit_memviewslice", 0); + if (from_memoryview && __pyx_typeinfo_cmp(dtype, ((struct __pyx_memoryview_obj *) + original_obj)->typeinfo)) { + memview = (struct __pyx_memoryview_obj *) original_obj; + new_memview = NULL; + } else { + memview = (struct __pyx_memoryview_obj *) __pyx_memoryview_new( + original_obj, buf_flags, 0, dtype); + new_memview = memview; + if (unlikely(!memview)) + goto fail; + } + buf = &memview->view; + if (unlikely(buf->ndim != ndim)) { + PyErr_Format(PyExc_ValueError, + "Buffer has wrong number of dimensions (expected %d, got %d)", + ndim, buf->ndim); + goto fail; + } + if (new_memview) { + __Pyx_BufFmt_Init(&ctx, stack, dtype); + if (unlikely(!__Pyx_BufFmt_CheckString(&ctx, buf->format))) goto fail; + } + if (unlikely((unsigned) buf->itemsize != dtype->size)) { + PyErr_Format(PyExc_ValueError, + "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "u byte%s) " + "does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "u byte%s)", + buf->itemsize, + (buf->itemsize > 1) ? "s" : "", + dtype->name, + dtype->size, + (dtype->size > 1) ? "s" : ""); + goto fail; + } + if (buf->len > 0) { + for (i = 0; i < ndim; i++) { + spec = axes_specs[i]; + if (unlikely(!__pyx_check_strides(buf, i, ndim, spec))) + goto fail; + if (unlikely(!__pyx_check_suboffsets(buf, i, ndim, spec))) + goto fail; + } + if (unlikely(buf->strides && !__pyx_verify_contig(buf, ndim, c_or_f_flag))) + goto fail; + } + if (unlikely(__Pyx_init_memviewslice(memview, ndim, memviewslice, + new_memview != NULL) == -1)) { + goto fail; + } + retval = 0; + goto no_fail; +fail: + Py_XDECREF(new_memview); + retval = -1; +no_fail: + __Pyx_RefNannyFinishContext(); + return retval; +} + +/* ObjectToMemviewSlice */ + static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_double(PyObject *obj, int writable_flag) { + __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } }; + __Pyx_BufFmt_StackElem stack[1]; + int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) }; + int retcode; + if (obj == Py_None) { + result.memview = (struct __pyx_memoryview_obj *) Py_None; + return result; + } + retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0, + PyBUF_RECORDS_RO | writable_flag, 1, + &__Pyx_TypeInfo_double, stack, + &result, obj); + if (unlikely(retcode == -1)) + goto __pyx_fail; + return result; +__pyx_fail: + result.memview = NULL; + result.data = NULL; + return result; +} + +/* ObjectToMemviewSlice */ + static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_nn___pyx_t_5numpy_int64_t(PyObject *obj, int writable_flag) { + __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } }; + __Pyx_BufFmt_StackElem stack[1]; + int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED), (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) }; + int retcode; + if (obj == Py_None) { + result.memview = (struct __pyx_memoryview_obj *) Py_None; + return result; + } + retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0, + PyBUF_RECORDS_RO | writable_flag, 2, + &__Pyx_TypeInfo_nn___pyx_t_5numpy_int64_t, stack, + &result, obj); + if (unlikely(retcode == -1)) + goto __pyx_fail; + return result; +__pyx_fail: + result.memview = NULL; + result.data = NULL; + return result; +} + +/* CIntFromPyVerify */ + #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) +#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) +#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ + {\ + func_type value = func_value;\ + if (sizeof(target_type) < sizeof(func_type)) {\ + if (unlikely(value != (func_type) (target_type) value)) {\ + func_type zero = 0;\ + if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ + return (target_type) -1;\ + if (is_unsigned && unlikely(value < zero))\ + goto raise_neg_overflow;\ + else\ + goto raise_overflow;\ + }\ + }\ + return (target_type) value;\ + } + +/* Declarations */ + #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return ::std::complex< float >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return x + y*(__pyx_t_float_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + __pyx_t_float_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabsf(b.real) >= fabsf(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + float r = b.imag / b.real; + float s = (float)(1.0) / (b.real + b.imag * r); + return __pyx_t_float_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + float r = b.real / b.imag; + float s = (float)(1.0) / (b.imag + b.real * r); + return __pyx_t_float_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + float denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_float_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrtf(z.real*z.real + z.imag*z.imag); + #else + return hypotf(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + float r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + float denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + return __Pyx_c_prod_float(a, a); + case 3: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, a); + case 4: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if ((b.imag == 0) && (a.real >= 0)) { + z.real = powf(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2f(0.0, -1.0); + } + } else { + r = __Pyx_c_abs_float(a); + theta = atan2f(a.imag, a.real); + } + lnr = logf(r); + z_r = expf(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cosf(z_theta); + z.imag = z_r * sinf(z_theta); + return z; + } + #endif +#endif + +/* Declarations */ + #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return ::std::complex< double >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return x + y*(__pyx_t_double_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + __pyx_t_double_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabs(b.real) >= fabs(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + double r = b.imag / b.real; + double s = (double)(1.0) / (b.real + b.imag * r); + return __pyx_t_double_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + double r = b.real / b.imag; + double s = (double)(1.0) / (b.imag + b.real * r); + return __pyx_t_double_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + double denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_double_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrt(z.real*z.real + z.imag*z.imag); + #else + return hypot(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + double r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + double denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + return __Pyx_c_prod_double(a, a); + case 3: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, a); + case 4: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if ((b.imag == 0) && (a.real >= 0)) { + z.real = pow(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2(0.0, -1.0); + } + } else { + r = __Pyx_c_abs_double(a); + theta = atan2(a.imag, a.real); + } + lnr = log(r); + z_r = exp(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cos(z_theta); + z.imag = z_r * sin(z_theta); + return z; + } + #endif +#endif + +/* Declarations */ + #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) { + return ::std::complex< long double >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) { + return x + y*(__pyx_t_long_double_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) { + __pyx_t_long_double_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus) +#else + static CYTHON_INLINE int __Pyx_c_eq_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_sum_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + __pyx_t_long_double_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_diff_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + __pyx_t_long_double_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_prod_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + __pyx_t_long_double_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + if (b.imag == 0) { + return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabsl(b.real) >= fabsl(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + long double r = b.imag / b.real; + long double s = (long double)(1.0) / (b.real + b.imag * r); + return __pyx_t_long_double_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + long double r = b.real / b.imag; + long double s = (long double)(1.0) / (b.imag + b.real * r); + return __pyx_t_long_double_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + if (b.imag == 0) { + return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + long double denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_long_double_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_neg_long__double(__pyx_t_long_double_complex a) { + __pyx_t_long_double_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_long__double(__pyx_t_long_double_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_conj_long__double(__pyx_t_long_double_complex a) { + __pyx_t_long_double_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE long double __Pyx_c_abs_long__double(__pyx_t_long_double_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrtl(z.real*z.real + z.imag*z.imag); + #else + return hypotl(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_pow_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) { + __pyx_t_long_double_complex z; + long double r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + long double denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + return __Pyx_c_prod_long__double(a, a); + case 3: + z = __Pyx_c_prod_long__double(a, a); + return __Pyx_c_prod_long__double(z, a); + case 4: + z = __Pyx_c_prod_long__double(a, a); + return __Pyx_c_prod_long__double(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if ((b.imag == 0) && (a.real >= 0)) { + z.real = powl(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2l(0.0, -1.0); + } + } else { + r = __Pyx_c_abs_long__double(a); + theta = atan2l(a.imag, a.real); + } + lnr = logl(r); + z_r = expl(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cosl(z_theta); + z.imag = z_r * sinl(z_theta); + return z; + } + #endif +#endif + +/* MemviewSliceCopyTemplate */ + static __Pyx_memviewslice +__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs, + const char *mode, int ndim, + size_t sizeof_dtype, int contig_flag, + int dtype_is_object) +{ + __Pyx_RefNannyDeclarations + int i; + __Pyx_memviewslice new_mvs = { 0, 0, { 0 }, { 0 }, { 0 } }; + struct __pyx_memoryview_obj *from_memview = from_mvs->memview; + Py_buffer *buf = &from_memview->view; + PyObject *shape_tuple = NULL; + PyObject *temp_int = NULL; + struct __pyx_array_obj *array_obj = NULL; + struct __pyx_memoryview_obj *memview_obj = NULL; + __Pyx_RefNannySetupContext("__pyx_memoryview_copy_new_contig", 0); + for (i = 0; i < ndim; i++) { + if (unlikely(from_mvs->suboffsets[i] >= 0)) { + PyErr_Format(PyExc_ValueError, "Cannot copy memoryview slice with " + "indirect dimensions (axis %d)", i); + goto fail; + } + } + shape_tuple = PyTuple_New(ndim); + if (unlikely(!shape_tuple)) { + goto fail; + } + __Pyx_GOTREF(shape_tuple); + for(i = 0; i < ndim; i++) { + temp_int = PyInt_FromSsize_t(from_mvs->shape[i]); + if(unlikely(!temp_int)) { + goto fail; + } else { + PyTuple_SET_ITEM(shape_tuple, i, temp_int); + temp_int = NULL; + } + } + array_obj = __pyx_array_new(shape_tuple, sizeof_dtype, buf->format, (char *) mode, NULL); + if (unlikely(!array_obj)) { + goto fail; + } + __Pyx_GOTREF(array_obj); + memview_obj = (struct __pyx_memoryview_obj *) __pyx_memoryview_new( + (PyObject *) array_obj, contig_flag, + dtype_is_object, + from_mvs->memview->typeinfo); + if (unlikely(!memview_obj)) + goto fail; + if (unlikely(__Pyx_init_memviewslice(memview_obj, ndim, &new_mvs, 1) < 0)) + goto fail; + if (unlikely(__pyx_memoryview_copy_contents(*from_mvs, new_mvs, ndim, ndim, + dtype_is_object) < 0)) + goto fail; + goto no_fail; +fail: + __Pyx_XDECREF(new_mvs.memview); + new_mvs.memview = NULL; + new_mvs.data = NULL; +no_fail: + __Pyx_XDECREF(shape_tuple); + __Pyx_XDECREF(temp_int); + __Pyx_XDECREF(array_obj); + __Pyx_RefNannyFinishContext(); + return new_mvs; +} + +/* MemviewSliceInit */ + static int +__Pyx_init_memviewslice(struct __pyx_memoryview_obj *memview, + int ndim, + __Pyx_memviewslice *memviewslice, + int memview_is_new_reference) +{ + __Pyx_RefNannyDeclarations + int i, retval=-1; + Py_buffer *buf = &memview->view; + __Pyx_RefNannySetupContext("init_memviewslice", 0); + if (unlikely(memviewslice->memview || memviewslice->data)) { + PyErr_SetString(PyExc_ValueError, + "memviewslice is already initialized!"); + goto fail; + } + if (buf->strides) { + for (i = 0; i < ndim; i++) { + memviewslice->strides[i] = buf->strides[i]; + } + } else { + Py_ssize_t stride = buf->itemsize; + for (i = ndim - 1; i >= 0; i--) { + memviewslice->strides[i] = stride; + stride *= buf->shape[i]; + } + } + for (i = 0; i < ndim; i++) { + memviewslice->shape[i] = buf->shape[i]; + if (buf->suboffsets) { + memviewslice->suboffsets[i] = buf->suboffsets[i]; + } else { + memviewslice->suboffsets[i] = -1; + } + } + memviewslice->memview = memview; + memviewslice->data = (char *)buf->buf; + if (__pyx_add_acquisition_count(memview) == 0 && !memview_is_new_reference) { + Py_INCREF(memview); + } + retval = 0; + goto no_fail; +fail: + memviewslice->memview = 0; + memviewslice->data = 0; + retval = -1; +no_fail: + __Pyx_RefNannyFinishContext(); + return retval; +} +#ifndef Py_NO_RETURN +#define Py_NO_RETURN +#endif +static void __pyx_fatalerror(const char *fmt, ...) Py_NO_RETURN { + va_list vargs; + char msg[200]; +#if PY_VERSION_HEX >= 0x030A0000 || defined(HAVE_STDARG_PROTOTYPES) + va_start(vargs, fmt); +#else + va_start(vargs); +#endif + vsnprintf(msg, 200, fmt, vargs); + va_end(vargs); + Py_FatalError(msg); +} +static CYTHON_INLINE int +__pyx_add_acquisition_count_locked(__pyx_atomic_int_type *acquisition_count, + PyThread_type_lock lock) +{ + int result; + PyThread_acquire_lock(lock, 1); + result = (*acquisition_count)++; + PyThread_release_lock(lock); + return result; +} +static CYTHON_INLINE int +__pyx_sub_acquisition_count_locked(__pyx_atomic_int_type *acquisition_count, + PyThread_type_lock lock) +{ + int result; + PyThread_acquire_lock(lock, 1); + result = (*acquisition_count)--; + PyThread_release_lock(lock); + return result; +} +static CYTHON_INLINE void +__Pyx_INC_MEMVIEW(__Pyx_memviewslice *memslice, int have_gil, int lineno) +{ + __pyx_nonatomic_int_type old_acquisition_count; + struct __pyx_memoryview_obj *memview = memslice->memview; + if (unlikely(!memview || (PyObject *) memview == Py_None)) { + return; + } + old_acquisition_count = __pyx_add_acquisition_count(memview); + if (unlikely(old_acquisition_count <= 0)) { + if (likely(old_acquisition_count == 0)) { + if (have_gil) { + Py_INCREF((PyObject *) memview); + } else { + PyGILState_STATE _gilstate = PyGILState_Ensure(); + Py_INCREF((PyObject *) memview); + PyGILState_Release(_gilstate); + } + } else { + __pyx_fatalerror("Acquisition count is %d (line %d)", + old_acquisition_count+1, lineno); + } + } +} +static CYTHON_INLINE void __Pyx_XCLEAR_MEMVIEW(__Pyx_memviewslice *memslice, + int have_gil, int lineno) { + __pyx_nonatomic_int_type old_acquisition_count; + struct __pyx_memoryview_obj *memview = memslice->memview; + if (unlikely(!memview || (PyObject *) memview == Py_None)) { + memslice->memview = NULL; + return; + } + old_acquisition_count = __pyx_sub_acquisition_count(memview); + memslice->data = NULL; + if (likely(old_acquisition_count > 1)) { + memslice->memview = NULL; + } else if (likely(old_acquisition_count == 1)) { + if (have_gil) { + Py_CLEAR(memslice->memview); + } else { + PyGILState_STATE _gilstate = PyGILState_Ensure(); + Py_CLEAR(memslice->memview); + PyGILState_Release(_gilstate); + } + } else { + __pyx_fatalerror("Acquisition count is %d (line %d)", + old_acquisition_count-1, lineno); + } +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_npy_int64(npy_int64 value) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const npy_int64 neg_one = (npy_int64) -1, const_zero = (npy_int64) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(npy_int64) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(npy_int64) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(npy_int64) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(npy_int64) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(npy_int64) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + unsigned char *bytes = (unsigned char *)&value; +#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4 + if (is_unsigned) { + return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1); + } else { + return PyLong_FromNativeBytes(bytes, sizeof(value), -1); + } +#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000 + int one = 1; int little = (int)*(unsigned char *)&one; + return _PyLong_FromByteArray(bytes, sizeof(npy_int64), + little, !is_unsigned); +#else + int one = 1; int little = (int)*(unsigned char *)&one; + PyObject *from_bytes, *result = NULL; + PyObject *py_bytes = NULL, *arg_tuple = NULL, *kwds = NULL, *order_str = NULL; + from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes"); + if (!from_bytes) return NULL; + py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(npy_int64)); + if (!py_bytes) goto limited_bad; + order_str = PyUnicode_FromString(little ? "little" : "big"); + if (!order_str) goto limited_bad; + arg_tuple = PyTuple_Pack(2, py_bytes, order_str); + if (!arg_tuple) goto limited_bad; + if (!is_unsigned) { + kwds = PyDict_New(); + if (!kwds) goto limited_bad; + if (PyDict_SetItemString(kwds, "signed", __Pyx_NewRef(Py_True))) goto limited_bad; + } + result = PyObject_Call(from_bytes, arg_tuple, kwds); + limited_bad: + Py_XDECREF(kwds); + Py_XDECREF(arg_tuple); + Py_XDECREF(order_str); + Py_XDECREF(py_bytes); + Py_XDECREF(from_bytes); + return result; +#endif + } +} + +/* CIntFromPy */ + static CYTHON_INLINE npy_int64 __Pyx_PyInt_As_npy_int64(PyObject *x) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const npy_int64 neg_one = (npy_int64) -1, const_zero = (npy_int64) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if ((sizeof(npy_int64) < sizeof(long))) { + __PYX_VERIFY_RETURN_INT(npy_int64, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (npy_int64) val; + } + } +#endif + if (unlikely(!PyLong_Check(x))) { + npy_int64 val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (npy_int64) -1; + val = __Pyx_PyInt_As_npy_int64(tmp); + Py_DECREF(tmp); + return val; + } + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + if (unlikely(__Pyx_PyLong_IsNeg(x))) { + goto raise_neg_overflow; + } else if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(npy_int64, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_DigitCount(x)) { + case 2: + if ((8 * sizeof(npy_int64) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) >= 2 * PyLong_SHIFT)) { + return (npy_int64) (((((npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])); + } + } + break; + case 3: + if ((8 * sizeof(npy_int64) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) >= 3 * PyLong_SHIFT)) { + return (npy_int64) (((((((npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])); + } + } + break; + case 4: + if ((8 * sizeof(npy_int64) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) >= 4 * PyLong_SHIFT)) { + return (npy_int64) (((((((((npy_int64)digits[3]) << PyLong_SHIFT) | (npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0])); + } + } + break; + } + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7 + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (npy_int64) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if ((sizeof(npy_int64) <= sizeof(unsigned long))) { + __PYX_VERIFY_RETURN_INT_EXC(npy_int64, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(npy_int64) <= sizeof(unsigned PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(npy_int64, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(npy_int64, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_SignedDigitCount(x)) { + case -2: + if ((8 * sizeof(npy_int64) - 1 > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) - 1 > 2 * PyLong_SHIFT)) { + return (npy_int64) (((npy_int64)-1)*(((((npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]))); + } + } + break; + case 2: + if ((8 * sizeof(npy_int64) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) - 1 > 2 * PyLong_SHIFT)) { + return (npy_int64) ((((((npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]))); + } + } + break; + case -3: + if ((8 * sizeof(npy_int64) - 1 > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) - 1 > 3 * PyLong_SHIFT)) { + return (npy_int64) (((npy_int64)-1)*(((((((npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]))); + } + } + break; + case 3: + if ((8 * sizeof(npy_int64) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) - 1 > 3 * PyLong_SHIFT)) { + return (npy_int64) ((((((((npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]))); + } + } + break; + case -4: + if ((8 * sizeof(npy_int64) - 1 > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) - 1 > 4 * PyLong_SHIFT)) { + return (npy_int64) (((npy_int64)-1)*(((((((((npy_int64)digits[3]) << PyLong_SHIFT) | (npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]))); + } + } + break; + case 4: + if ((8 * sizeof(npy_int64) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(npy_int64, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(npy_int64) - 1 > 4 * PyLong_SHIFT)) { + return (npy_int64) ((((((((((npy_int64)digits[3]) << PyLong_SHIFT) | (npy_int64)digits[2]) << PyLong_SHIFT) | (npy_int64)digits[1]) << PyLong_SHIFT) | (npy_int64)digits[0]))); + } + } + break; + } + } +#endif + if ((sizeof(npy_int64) <= sizeof(long))) { + __PYX_VERIFY_RETURN_INT_EXC(npy_int64, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(npy_int64) <= sizeof(PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(npy_int64, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { + npy_int64 val; + int ret = -1; +#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API + Py_ssize_t bytes_copied = PyLong_AsNativeBytes( + x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0)); + if (unlikely(bytes_copied == -1)) { + } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) { + goto raise_overflow; + } else { + ret = 0; + } +#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray) + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + ret = _PyLong_AsByteArray((PyLongObject *)x, + bytes, sizeof(val), + is_little, !is_unsigned); +#else + PyObject *v; + PyObject *stepval = NULL, *mask = NULL, *shift = NULL; + int bits, remaining_bits, is_negative = 0; + int chunk_size = (sizeof(long) < 8) ? 30 : 62; + if (likely(PyLong_CheckExact(x))) { + v = __Pyx_NewRef(x); + } else { + v = PyNumber_Long(x); + if (unlikely(!v)) return (npy_int64) -1; + assert(PyLong_CheckExact(v)); + } + { + int result = PyObject_RichCompareBool(v, Py_False, Py_LT); + if (unlikely(result < 0)) { + Py_DECREF(v); + return (npy_int64) -1; + } + is_negative = result == 1; + } + if (is_unsigned && unlikely(is_negative)) { + Py_DECREF(v); + goto raise_neg_overflow; + } else if (is_negative) { + stepval = PyNumber_Invert(v); + Py_DECREF(v); + if (unlikely(!stepval)) + return (npy_int64) -1; + } else { + stepval = v; + } + v = NULL; + val = (npy_int64) 0; + mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done; + shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done; + for (bits = 0; bits < (int) sizeof(npy_int64) * 8 - chunk_size; bits += chunk_size) { + PyObject *tmp, *digit; + long idigit; + digit = PyNumber_And(stepval, mask); + if (unlikely(!digit)) goto done; + idigit = PyLong_AsLong(digit); + Py_DECREF(digit); + if (unlikely(idigit < 0)) goto done; + val |= ((npy_int64) idigit) << bits; + tmp = PyNumber_Rshift(stepval, shift); + if (unlikely(!tmp)) goto done; + Py_DECREF(stepval); stepval = tmp; + } + Py_DECREF(shift); shift = NULL; + Py_DECREF(mask); mask = NULL; + { + long idigit = PyLong_AsLong(stepval); + if (unlikely(idigit < 0)) goto done; + remaining_bits = ((int) sizeof(npy_int64) * 8) - bits - (is_unsigned ? 0 : 1); + if (unlikely(idigit >= (1L << remaining_bits))) + goto raise_overflow; + val |= ((npy_int64) idigit) << bits; + } + if (!is_unsigned) { + if (unlikely(val & (((npy_int64) 1) << (sizeof(npy_int64) * 8 - 1)))) + goto raise_overflow; + if (is_negative) + val = ~val; + } + ret = 0; + done: + Py_XDECREF(shift); + Py_XDECREF(mask); + Py_XDECREF(stepval); +#endif + if (unlikely(ret)) + return (npy_int64) -1; + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to npy_int64"); + return (npy_int64) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to npy_int64"); + return (npy_int64) -1; +} + +/* CIntFromPy */ + static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const int neg_one = (int) -1, const_zero = (int) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if ((sizeof(int) < sizeof(long))) { + __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (int) val; + } + } +#endif + if (unlikely(!PyLong_Check(x))) { + int val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (int) -1; + val = __Pyx_PyInt_As_int(tmp); + Py_DECREF(tmp); + return val; + } + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + if (unlikely(__Pyx_PyLong_IsNeg(x))) { + goto raise_neg_overflow; + } else if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_DigitCount(x)) { + case 2: + if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) >= 2 * PyLong_SHIFT)) { + return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 3: + if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) >= 3 * PyLong_SHIFT)) { + return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 4: + if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) >= 4 * PyLong_SHIFT)) { + return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + } + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7 + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (int) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if ((sizeof(int) <= sizeof(unsigned long))) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(int) <= sizeof(unsigned PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_SignedDigitCount(x)) { + case -2: + if ((8 * sizeof(int) - 1 > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) { + return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 2: + if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) { + return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -3: + if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) { + return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 3: + if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) { + return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -4: + if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) { + return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 4: + if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) { + return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + } + } +#endif + if ((sizeof(int) <= sizeof(long))) { + __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(int) <= sizeof(PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { + int val; + int ret = -1; +#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API + Py_ssize_t bytes_copied = PyLong_AsNativeBytes( + x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0)); + if (unlikely(bytes_copied == -1)) { + } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) { + goto raise_overflow; + } else { + ret = 0; + } +#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray) + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + ret = _PyLong_AsByteArray((PyLongObject *)x, + bytes, sizeof(val), + is_little, !is_unsigned); +#else + PyObject *v; + PyObject *stepval = NULL, *mask = NULL, *shift = NULL; + int bits, remaining_bits, is_negative = 0; + int chunk_size = (sizeof(long) < 8) ? 30 : 62; + if (likely(PyLong_CheckExact(x))) { + v = __Pyx_NewRef(x); + } else { + v = PyNumber_Long(x); + if (unlikely(!v)) return (int) -1; + assert(PyLong_CheckExact(v)); + } + { + int result = PyObject_RichCompareBool(v, Py_False, Py_LT); + if (unlikely(result < 0)) { + Py_DECREF(v); + return (int) -1; + } + is_negative = result == 1; + } + if (is_unsigned && unlikely(is_negative)) { + Py_DECREF(v); + goto raise_neg_overflow; + } else if (is_negative) { + stepval = PyNumber_Invert(v); + Py_DECREF(v); + if (unlikely(!stepval)) + return (int) -1; + } else { + stepval = v; + } + v = NULL; + val = (int) 0; + mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done; + shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done; + for (bits = 0; bits < (int) sizeof(int) * 8 - chunk_size; bits += chunk_size) { + PyObject *tmp, *digit; + long idigit; + digit = PyNumber_And(stepval, mask); + if (unlikely(!digit)) goto done; + idigit = PyLong_AsLong(digit); + Py_DECREF(digit); + if (unlikely(idigit < 0)) goto done; + val |= ((int) idigit) << bits; + tmp = PyNumber_Rshift(stepval, shift); + if (unlikely(!tmp)) goto done; + Py_DECREF(stepval); stepval = tmp; + } + Py_DECREF(shift); shift = NULL; + Py_DECREF(mask); mask = NULL; + { + long idigit = PyLong_AsLong(stepval); + if (unlikely(idigit < 0)) goto done; + remaining_bits = ((int) sizeof(int) * 8) - bits - (is_unsigned ? 0 : 1); + if (unlikely(idigit >= (1L << remaining_bits))) + goto raise_overflow; + val |= ((int) idigit) << bits; + } + if (!is_unsigned) { + if (unlikely(val & (((int) 1) << (sizeof(int) * 8 - 1)))) + goto raise_overflow; + if (is_negative) + val = ~val; + } + ret = 0; + done: + Py_XDECREF(shift); + Py_XDECREF(mask); + Py_XDECREF(stepval); +#endif + if (unlikely(ret)) + return (int) -1; + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to int"); + return (int) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to int"); + return (int) -1; +} + +/* CIntFromPy */ + static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const long neg_one = (long) -1, const_zero = (long) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if ((sizeof(long) < sizeof(long))) { + __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (long) val; + } + } +#endif + if (unlikely(!PyLong_Check(x))) { + long val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (long) -1; + val = __Pyx_PyInt_As_long(tmp); + Py_DECREF(tmp); + return val; + } + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + if (unlikely(__Pyx_PyLong_IsNeg(x))) { + goto raise_neg_overflow; + } else if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_DigitCount(x)) { + case 2: + if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) >= 2 * PyLong_SHIFT)) { + return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 3: + if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) >= 3 * PyLong_SHIFT)) { + return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 4: + if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) >= 4 * PyLong_SHIFT)) { + return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + } + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7 + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (long) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if ((sizeof(long) <= sizeof(unsigned long))) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(long) <= sizeof(unsigned PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_SignedDigitCount(x)) { + case -2: + if ((8 * sizeof(long) - 1 > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) { + return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 2: + if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) { + return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -3: + if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) { + return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 3: + if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) { + return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -4: + if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) { + return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 4: + if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) { + return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + } + } +#endif + if ((sizeof(long) <= sizeof(long))) { + __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(long) <= sizeof(PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { + long val; + int ret = -1; +#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API + Py_ssize_t bytes_copied = PyLong_AsNativeBytes( + x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0)); + if (unlikely(bytes_copied == -1)) { + } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) { + goto raise_overflow; + } else { + ret = 0; + } +#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray) + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + ret = _PyLong_AsByteArray((PyLongObject *)x, + bytes, sizeof(val), + is_little, !is_unsigned); +#else + PyObject *v; + PyObject *stepval = NULL, *mask = NULL, *shift = NULL; + int bits, remaining_bits, is_negative = 0; + int chunk_size = (sizeof(long) < 8) ? 30 : 62; + if (likely(PyLong_CheckExact(x))) { + v = __Pyx_NewRef(x); + } else { + v = PyNumber_Long(x); + if (unlikely(!v)) return (long) -1; + assert(PyLong_CheckExact(v)); + } + { + int result = PyObject_RichCompareBool(v, Py_False, Py_LT); + if (unlikely(result < 0)) { + Py_DECREF(v); + return (long) -1; + } + is_negative = result == 1; + } + if (is_unsigned && unlikely(is_negative)) { + Py_DECREF(v); + goto raise_neg_overflow; + } else if (is_negative) { + stepval = PyNumber_Invert(v); + Py_DECREF(v); + if (unlikely(!stepval)) + return (long) -1; + } else { + stepval = v; + } + v = NULL; + val = (long) 0; + mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done; + shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done; + for (bits = 0; bits < (int) sizeof(long) * 8 - chunk_size; bits += chunk_size) { + PyObject *tmp, *digit; + long idigit; + digit = PyNumber_And(stepval, mask); + if (unlikely(!digit)) goto done; + idigit = PyLong_AsLong(digit); + Py_DECREF(digit); + if (unlikely(idigit < 0)) goto done; + val |= ((long) idigit) << bits; + tmp = PyNumber_Rshift(stepval, shift); + if (unlikely(!tmp)) goto done; + Py_DECREF(stepval); stepval = tmp; + } + Py_DECREF(shift); shift = NULL; + Py_DECREF(mask); mask = NULL; + { + long idigit = PyLong_AsLong(stepval); + if (unlikely(idigit < 0)) goto done; + remaining_bits = ((int) sizeof(long) * 8) - bits - (is_unsigned ? 0 : 1); + if (unlikely(idigit >= (1L << remaining_bits))) + goto raise_overflow; + val |= ((long) idigit) << bits; + } + if (!is_unsigned) { + if (unlikely(val & (((long) 1) << (sizeof(long) * 8 - 1)))) + goto raise_overflow; + if (is_negative) + val = ~val; + } + ret = 0; + done: + Py_XDECREF(shift); + Py_XDECREF(mask); + Py_XDECREF(stepval); +#endif + if (unlikely(ret)) + return (long) -1; + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to long"); + return (long) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to long"); + return (long) -1; +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const int neg_one = (int) -1, const_zero = (int) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(int) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(int) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(int) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + unsigned char *bytes = (unsigned char *)&value; +#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4 + if (is_unsigned) { + return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1); + } else { + return PyLong_FromNativeBytes(bytes, sizeof(value), -1); + } +#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000 + int one = 1; int little = (int)*(unsigned char *)&one; + return _PyLong_FromByteArray(bytes, sizeof(int), + little, !is_unsigned); +#else + int one = 1; int little = (int)*(unsigned char *)&one; + PyObject *from_bytes, *result = NULL; + PyObject *py_bytes = NULL, *arg_tuple = NULL, *kwds = NULL, *order_str = NULL; + from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes"); + if (!from_bytes) return NULL; + py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(int)); + if (!py_bytes) goto limited_bad; + order_str = PyUnicode_FromString(little ? "little" : "big"); + if (!order_str) goto limited_bad; + arg_tuple = PyTuple_Pack(2, py_bytes, order_str); + if (!arg_tuple) goto limited_bad; + if (!is_unsigned) { + kwds = PyDict_New(); + if (!kwds) goto limited_bad; + if (PyDict_SetItemString(kwds, "signed", __Pyx_NewRef(Py_True))) goto limited_bad; + } + result = PyObject_Call(from_bytes, arg_tuple, kwds); + limited_bad: + Py_XDECREF(kwds); + Py_XDECREF(arg_tuple); + Py_XDECREF(order_str); + Py_XDECREF(py_bytes); + Py_XDECREF(from_bytes); + return result; +#endif + } +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const long neg_one = (long) -1, const_zero = (long) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(long) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(long) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(long) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + unsigned char *bytes = (unsigned char *)&value; +#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4 + if (is_unsigned) { + return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1); + } else { + return PyLong_FromNativeBytes(bytes, sizeof(value), -1); + } +#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000 + int one = 1; int little = (int)*(unsigned char *)&one; + return _PyLong_FromByteArray(bytes, sizeof(long), + little, !is_unsigned); +#else + int one = 1; int little = (int)*(unsigned char *)&one; + PyObject *from_bytes, *result = NULL; + PyObject *py_bytes = NULL, *arg_tuple = NULL, *kwds = NULL, *order_str = NULL; + from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes"); + if (!from_bytes) return NULL; + py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(long)); + if (!py_bytes) goto limited_bad; + order_str = PyUnicode_FromString(little ? "little" : "big"); + if (!order_str) goto limited_bad; + arg_tuple = PyTuple_Pack(2, py_bytes, order_str); + if (!arg_tuple) goto limited_bad; + if (!is_unsigned) { + kwds = PyDict_New(); + if (!kwds) goto limited_bad; + if (PyDict_SetItemString(kwds, "signed", __Pyx_NewRef(Py_True))) goto limited_bad; + } + result = PyObject_Call(from_bytes, arg_tuple, kwds); + limited_bad: + Py_XDECREF(kwds); + Py_XDECREF(arg_tuple); + Py_XDECREF(order_str); + Py_XDECREF(py_bytes); + Py_XDECREF(from_bytes); + return result; +#endif + } +} + +/* CIntFromPy */ + static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *x) { +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wconversion" +#endif + const char neg_one = (char) -1, const_zero = (char) 0; +#ifdef __Pyx_HAS_GCC_DIAGNOSTIC +#pragma GCC diagnostic pop +#endif + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if ((sizeof(char) < sizeof(long))) { + __PYX_VERIFY_RETURN_INT(char, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (char) val; + } + } +#endif + if (unlikely(!PyLong_Check(x))) { + char val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (char) -1; + val = __Pyx_PyInt_As_char(tmp); + Py_DECREF(tmp); + return val; + } + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + if (unlikely(__Pyx_PyLong_IsNeg(x))) { + goto raise_neg_overflow; + } else if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(char, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_DigitCount(x)) { + case 2: + if ((8 * sizeof(char) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) >= 2 * PyLong_SHIFT)) { + return (char) (((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0])); + } + } + break; + case 3: + if ((8 * sizeof(char) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) >= 3 * PyLong_SHIFT)) { + return (char) (((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])); + } + } + break; + case 4: + if ((8 * sizeof(char) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) >= 4 * PyLong_SHIFT)) { + return (char) (((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])); + } + } + break; + } + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7 + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (char) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if ((sizeof(char) <= sizeof(unsigned long))) { + __PYX_VERIFY_RETURN_INT_EXC(char, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(char) <= sizeof(unsigned PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(char, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + if (__Pyx_PyLong_IsCompact(x)) { + __PYX_VERIFY_RETURN_INT(char, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x)) + } else { + const digit* digits = __Pyx_PyLong_Digits(x); + assert(__Pyx_PyLong_DigitCount(x) > 1); + switch (__Pyx_PyLong_SignedDigitCount(x)) { + case -2: + if ((8 * sizeof(char) - 1 > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) - 1 > 2 * PyLong_SHIFT)) { + return (char) (((char)-1)*(((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case 2: + if ((8 * sizeof(char) > 1 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) - 1 > 2 * PyLong_SHIFT)) { + return (char) ((((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case -3: + if ((8 * sizeof(char) - 1 > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) - 1 > 3 * PyLong_SHIFT)) { + return (char) (((char)-1)*(((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case 3: + if ((8 * sizeof(char) > 2 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) - 1 > 3 * PyLong_SHIFT)) { + return (char) ((((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case -4: + if ((8 * sizeof(char) - 1 > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) - 1 > 4 * PyLong_SHIFT)) { + return (char) (((char)-1)*(((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case 4: + if ((8 * sizeof(char) > 3 * PyLong_SHIFT)) { + if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if ((8 * sizeof(char) - 1 > 4 * PyLong_SHIFT)) { + return (char) ((((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + } + } +#endif + if ((sizeof(char) <= sizeof(long))) { + __PYX_VERIFY_RETURN_INT_EXC(char, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if ((sizeof(char) <= sizeof(PY_LONG_LONG))) { + __PYX_VERIFY_RETURN_INT_EXC(char, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { + char val; + int ret = -1; +#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API + Py_ssize_t bytes_copied = PyLong_AsNativeBytes( + x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0)); + if (unlikely(bytes_copied == -1)) { + } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) { + goto raise_overflow; + } else { + ret = 0; + } +#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray) + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + ret = _PyLong_AsByteArray((PyLongObject *)x, + bytes, sizeof(val), + is_little, !is_unsigned); +#else + PyObject *v; + PyObject *stepval = NULL, *mask = NULL, *shift = NULL; + int bits, remaining_bits, is_negative = 0; + int chunk_size = (sizeof(long) < 8) ? 30 : 62; + if (likely(PyLong_CheckExact(x))) { + v = __Pyx_NewRef(x); + } else { + v = PyNumber_Long(x); + if (unlikely(!v)) return (char) -1; + assert(PyLong_CheckExact(v)); + } + { + int result = PyObject_RichCompareBool(v, Py_False, Py_LT); + if (unlikely(result < 0)) { + Py_DECREF(v); + return (char) -1; + } + is_negative = result == 1; + } + if (is_unsigned && unlikely(is_negative)) { + Py_DECREF(v); + goto raise_neg_overflow; + } else if (is_negative) { + stepval = PyNumber_Invert(v); + Py_DECREF(v); + if (unlikely(!stepval)) + return (char) -1; + } else { + stepval = v; + } + v = NULL; + val = (char) 0; + mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done; + shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done; + for (bits = 0; bits < (int) sizeof(char) * 8 - chunk_size; bits += chunk_size) { + PyObject *tmp, *digit; + long idigit; + digit = PyNumber_And(stepval, mask); + if (unlikely(!digit)) goto done; + idigit = PyLong_AsLong(digit); + Py_DECREF(digit); + if (unlikely(idigit < 0)) goto done; + val |= ((char) idigit) << bits; + tmp = PyNumber_Rshift(stepval, shift); + if (unlikely(!tmp)) goto done; + Py_DECREF(stepval); stepval = tmp; + } + Py_DECREF(shift); shift = NULL; + Py_DECREF(mask); mask = NULL; + { + long idigit = PyLong_AsLong(stepval); + if (unlikely(idigit < 0)) goto done; + remaining_bits = ((int) sizeof(char) * 8) - bits - (is_unsigned ? 0 : 1); + if (unlikely(idigit >= (1L << remaining_bits))) + goto raise_overflow; + val |= ((char) idigit) << bits; + } + if (!is_unsigned) { + if (unlikely(val & (((char) 1) << (sizeof(char) * 8 - 1)))) + goto raise_overflow; + if (is_negative) + val = ~val; + } + ret = 0; + done: + Py_XDECREF(shift); + Py_XDECREF(mask); + Py_XDECREF(stepval); +#endif + if (unlikely(ret)) + return (char) -1; + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to char"); + return (char) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to char"); + return (char) -1; +} + +/* FormatTypeName */ + #if CYTHON_COMPILING_IN_LIMITED_API +static __Pyx_TypeName +__Pyx_PyType_GetName(PyTypeObject* tp) +{ + PyObject *name = __Pyx_PyObject_GetAttrStr((PyObject *)tp, + __pyx_n_s_name_2); + if (unlikely(name == NULL) || unlikely(!PyUnicode_Check(name))) { + PyErr_Clear(); + Py_XDECREF(name); + name = __Pyx_NewRef(__pyx_n_s__25); + } + return name; +} +#endif + +/* CheckBinaryVersion */ + static unsigned long __Pyx_get_runtime_version(void) { +#if __PYX_LIMITED_VERSION_HEX >= 0x030B00A4 + return Py_Version & ~0xFFUL; +#else + const char* rt_version = Py_GetVersion(); + unsigned long version = 0; + unsigned long factor = 0x01000000UL; + unsigned int digit = 0; + int i = 0; + while (factor) { + while ('0' <= rt_version[i] && rt_version[i] <= '9') { + digit = digit * 10 + (unsigned int) (rt_version[i] - '0'); + ++i; + } + version += factor * digit; + if (rt_version[i] != '.') + break; + digit = 0; + factor >>= 8; + ++i; + } + return version; +#endif +} +static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer) { + const unsigned long MAJOR_MINOR = 0xFFFF0000UL; + if ((rt_version & MAJOR_MINOR) == (ct_version & MAJOR_MINOR)) + return 0; + if (likely(allow_newer && (rt_version & MAJOR_MINOR) > (ct_version & MAJOR_MINOR))) + return 1; + { + char message[200]; + PyOS_snprintf(message, sizeof(message), + "compile time Python version %d.%d " + "of module '%.100s' " + "%s " + "runtime version %d.%d", + (int) (ct_version >> 24), (int) ((ct_version >> 16) & 0xFF), + __Pyx_MODULE_NAME, + (allow_newer) ? "was newer than" : "does not match", + (int) (rt_version >> 24), (int) ((rt_version >> 16) & 0xFF) + ); + return PyErr_WarnEx(NULL, message, 1); + } +} + +/* FunctionImport */ + #ifndef __PYX_HAVE_RT_ImportFunction_3_0_11 +#define __PYX_HAVE_RT_ImportFunction_3_0_11 +static int __Pyx_ImportFunction_3_0_11(PyObject *module, const char *funcname, void (**f)(void), const char *sig) { + PyObject *d = 0; + PyObject *cobj = 0; + union { + void (*fp)(void); + void *p; + } tmp; + d = PyObject_GetAttrString(module, (char *)"__pyx_capi__"); + if (!d) + goto bad; + cobj = PyDict_GetItemString(d, funcname); + if (!cobj) { + PyErr_Format(PyExc_ImportError, + "%.200s does not export expected C function %.200s", + PyModule_GetName(module), funcname); + goto bad; + } + if (!PyCapsule_IsValid(cobj, sig)) { + PyErr_Format(PyExc_TypeError, + "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)", + PyModule_GetName(module), funcname, sig, PyCapsule_GetName(cobj)); + goto bad; + } + tmp.p = PyCapsule_GetPointer(cobj, sig); + *f = tmp.fp; + if (!(*f)) + goto bad; + Py_DECREF(d); + return 0; +bad: + Py_XDECREF(d); + return -1; +} +#endif + +/* InitStrings */ + #if PY_MAJOR_VERSION >= 3 +static int __Pyx_InitString(__Pyx_StringTabEntry t, PyObject **str) { + if (t.is_unicode | t.is_str) { + if (t.intern) { + *str = PyUnicode_InternFromString(t.s); + } else if (t.encoding) { + *str = PyUnicode_Decode(t.s, t.n - 1, t.encoding, NULL); + } else { + *str = PyUnicode_FromStringAndSize(t.s, t.n - 1); + } + } else { + *str = PyBytes_FromStringAndSize(t.s, t.n - 1); + } + if (!*str) + return -1; + if (PyObject_Hash(*str) == -1) + return -1; + return 0; +} +#endif +static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) { + while (t->p) { + #if PY_MAJOR_VERSION >= 3 + __Pyx_InitString(*t, t->p); + #else + if (t->is_unicode) { + *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL); + } else if (t->intern) { + *t->p = PyString_InternFromString(t->s); + } else { + *t->p = PyString_FromStringAndSize(t->s, t->n - 1); + } + if (!*t->p) + return -1; + if (PyObject_Hash(*t->p) == -1) + return -1; + #endif + ++t; + } + return 0; +} + +#include +static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s) { + size_t len = strlen(s); + if (unlikely(len > (size_t) PY_SSIZE_T_MAX)) { + PyErr_SetString(PyExc_OverflowError, "byte string is too long"); + return -1; + } + return (Py_ssize_t) len; +} +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) { + Py_ssize_t len = __Pyx_ssize_strlen(c_str); + if (unlikely(len < 0)) return NULL; + return __Pyx_PyUnicode_FromStringAndSize(c_str, len); +} +static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char* c_str) { + Py_ssize_t len = __Pyx_ssize_strlen(c_str); + if (unlikely(len < 0)) return NULL; + return PyByteArray_FromStringAndSize(c_str, len); +} +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) { + Py_ssize_t ignore; + return __Pyx_PyObject_AsStringAndSize(o, &ignore); +} +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +#if !CYTHON_PEP393_ENABLED +static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { + char* defenc_c; + PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL); + if (!defenc) return NULL; + defenc_c = PyBytes_AS_STRING(defenc); +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + { + char* end = defenc_c + PyBytes_GET_SIZE(defenc); + char* c; + for (c = defenc_c; c < end; c++) { + if ((unsigned char) (*c) >= 128) { + PyUnicode_AsASCIIString(o); + return NULL; + } + } + } +#endif + *length = PyBytes_GET_SIZE(defenc); + return defenc_c; +} +#else +static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { + if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL; +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + if (likely(PyUnicode_IS_ASCII(o))) { + *length = PyUnicode_GET_LENGTH(o); + return PyUnicode_AsUTF8(o); + } else { + PyUnicode_AsASCIIString(o); + return NULL; + } +#else + return PyUnicode_AsUTF8AndSize(o, length); +#endif +} +#endif +#endif +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) { +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT + if ( +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + __Pyx_sys_getdefaultencoding_not_ascii && +#endif + PyUnicode_Check(o)) { + return __Pyx_PyUnicode_AsStringAndSize(o, length); + } else +#endif +#if (!CYTHON_COMPILING_IN_PYPY && !CYTHON_COMPILING_IN_LIMITED_API) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) + if (PyByteArray_Check(o)) { + *length = PyByteArray_GET_SIZE(o); + return PyByteArray_AS_STRING(o); + } else +#endif + { + char* result; + int r = PyBytes_AsStringAndSize(o, &result, length); + if (unlikely(r < 0)) { + return NULL; + } else { + return result; + } + } +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { + int is_true = x == Py_True; + if (is_true | (x == Py_False) | (x == Py_None)) return is_true; + else return PyObject_IsTrue(x); +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) { + int retval; + if (unlikely(!x)) return -1; + retval = __Pyx_PyObject_IsTrue(x); + Py_DECREF(x); + return retval; +} +static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) { + __Pyx_TypeName result_type_name = __Pyx_PyType_GetName(Py_TYPE(result)); +#if PY_MAJOR_VERSION >= 3 + if (PyLong_Check(result)) { + if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1, + "__int__ returned non-int (type " __Pyx_FMT_TYPENAME "). " + "The ability to return an instance of a strict subclass of int is deprecated, " + "and may be removed in a future version of Python.", + result_type_name)) { + __Pyx_DECREF_TypeName(result_type_name); + Py_DECREF(result); + return NULL; + } + __Pyx_DECREF_TypeName(result_type_name); + return result; + } +#endif + PyErr_Format(PyExc_TypeError, + "__%.4s__ returned non-%.4s (type " __Pyx_FMT_TYPENAME ")", + type_name, type_name, result_type_name); + __Pyx_DECREF_TypeName(result_type_name); + Py_DECREF(result); + return NULL; +} +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) { +#if CYTHON_USE_TYPE_SLOTS + PyNumberMethods *m; +#endif + const char *name = NULL; + PyObject *res = NULL; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x) || PyLong_Check(x))) +#else + if (likely(PyLong_Check(x))) +#endif + return __Pyx_NewRef(x); +#if CYTHON_USE_TYPE_SLOTS + m = Py_TYPE(x)->tp_as_number; + #if PY_MAJOR_VERSION < 3 + if (m && m->nb_int) { + name = "int"; + res = m->nb_int(x); + } + else if (m && m->nb_long) { + name = "long"; + res = m->nb_long(x); + } + #else + if (likely(m && m->nb_int)) { + name = "int"; + res = m->nb_int(x); + } + #endif +#else + if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) { + res = PyNumber_Int(x); + } +#endif + if (likely(res)) { +#if PY_MAJOR_VERSION < 3 + if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) { +#else + if (unlikely(!PyLong_CheckExact(res))) { +#endif + return __Pyx_PyNumber_IntOrLongWrongResultType(res, name); + } + } + else if (!PyErr_Occurred()) { + PyErr_SetString(PyExc_TypeError, + "an integer is required"); + } + return res; +} +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) { + Py_ssize_t ival; + PyObject *x; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(b))) { + if (sizeof(Py_ssize_t) >= sizeof(long)) + return PyInt_AS_LONG(b); + else + return PyInt_AsSsize_t(b); + } +#endif + if (likely(PyLong_CheckExact(b))) { + #if CYTHON_USE_PYLONG_INTERNALS + if (likely(__Pyx_PyLong_IsCompact(b))) { + return __Pyx_PyLong_CompactValue(b); + } else { + const digit* digits = __Pyx_PyLong_Digits(b); + const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(b); + switch (size) { + case 2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + } + } + #endif + return PyLong_AsSsize_t(b); + } + x = PyNumber_Index(b); + if (!x) return -1; + ival = PyInt_AsSsize_t(x); + Py_DECREF(x); + return ival; +} +static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject* o) { + if (sizeof(Py_hash_t) == sizeof(Py_ssize_t)) { + return (Py_hash_t) __Pyx_PyIndex_AsSsize_t(o); +#if PY_MAJOR_VERSION < 3 + } else if (likely(PyInt_CheckExact(o))) { + return PyInt_AS_LONG(o); +#endif + } else { + Py_ssize_t ival; + PyObject *x; + x = PyNumber_Index(o); + if (!x) return -1; + ival = PyInt_AsLong(x); + Py_DECREF(x); + return ival; + } +} +static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) { + return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False); +} +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { + return PyInt_FromSize_t(ival); +} + + +/* #### Code section: utility_code_pragmas_end ### */ +#ifdef _MSC_VER +#pragma warning( pop ) +#endif + + + +/* #### Code section: end ### */ +#endif /* Py_PYTHON_H */ diff --git a/src/pygom/model/_transition_graph.py b/src/pygom/model/_transition_graph.py index 048b3ff6..a2e3ebc0 100644 --- a/src/pygom/model/_transition_graph.py +++ b/src/pygom/model/_transition_graph.py @@ -4,6 +4,9 @@ from .transition import TransitionType from sympy.matrices import MatrixBase from ._ode_composition import getMatchingExpressionVector, _hasExpression +import matplotlib.pyplot as plt +import sympy +from ._model_verification import checkEquation # Functions to produce transition graph @@ -11,6 +14,7 @@ 'iota', 'kappa', 'lambda', 'mu', 'nu', 'xi', 'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon', 'phi', 'chi', 'psi', 'omega') + def generateTransitionGraph(ode_model, file_name=None): """ Generates the transition graph in graphviz given an ode model with transitions @@ -43,29 +47,79 @@ def generateTransitionGraph(ode_model, file_name=None): for s in states: dot.node(s) - transition = ode_model.transition_list - bd_list = ode_model.birth_death_list - - for transition in (transition + bd_list): - s1 = transition.origin - eq = _makeEquationPretty(transition.equation, param) - - if transition.transition_type is TransitionType.T: - s2 = transition.destination - dot.edge(s1, s2, label=eq) - elif transition.transition_type is TransitionType.B: - # when we have a birth or death process, do not make the box - dot.node(eq, shape="plaintext", width="0", height="0", margin="0") - dot.edge(eq, s1) - elif transition.transition_type is TransitionType.D: - dot.node(eq, shape="plaintext", width="0", height="0", margin="0") - dot.edge(s1, eq) - else: - pass + events=ode_model.event_list + + # get colors, TODO: limited to 9 colours, also experiment with linetype to assist + # with colourblind users + # pallette from: https://gist.github.com/thriveth/8560036 + + cols = ['#377eb8', '#ff7f00', '#4daf4a', '#f781bf', '#a65628', '#984ea3', '#999999', '#e41a1c', '#dede00'] + + i=0 + for e_number, event in enumerate(events): + + col="black" + linetype="solid" + + if len(event.transition_list)>1: + col=cols[i] + i+=1 + + rate=_makeEquationPretty(event.rate, param) + for transition in event.transition_list: + mag_lab="" + if transition._magnitude!='1': + mag_lab=_makeEquationPretty(transition._magnitude, param) + + if transition.transition_type==TransitionType.B: + destination=transition.destination + s1=destination + n0="birth"+s1+str(e_number) + dot.node(n0, label="", shape="none", height="0", width="0") + dot.edge(n0, s1, label=rate, headlabel=mag_lab, color=col, style=linetype) + + elif transition.transition_type==TransitionType.D: + origin=transition.origin + s1=origin + n0="death"+s1+str(e_number) + dot.node(n0, label=mag_lab, shape="none", height="0", width="0") + dot.edge(s1, n0, label=rate, headlabel=mag_lab, color=col, style=linetype) + + elif transition.transition_type==TransitionType.T: + origin=transition.origin + destination=transition.destination + s1=origin + s2=destination + + dot.edge(s1, s2, label=rate, headlabel=mag_lab, color=col, style=linetype) + else: + pass + + for ode in ode_model.ode_list: + col="black" + linetype="dashed" + + origin=ode.origin + s1=origin + + n0="ode"+s1 + + equation=ode.equation + + dot.node(n0, label="", shape="none", height="0", width="0") + + # # If there is one term and it's negative, make it a death process. + # if equation[0]=="-" and len(sympy.Add.make_args(sympy.sympify(equation)))==1: + # equation=equation[1:] + # dot.edge(s1, n0, label=equation, color=col, style=linetype) + # else: + # dot.edge(n0, s1, label=equation, color=col, style=linetype) + dot.edge(n0, s1, label=equation, color=col, style=linetype) return dot + def _makeEquationPretty(eq, param): """ Make the equation suitable for graphviz format by converting diff --git a/src/pygom/model/base_ode_model.py b/src/pygom/model/base_ode_model.py index dea78f0d..eac60baf 100644 --- a/src/pygom/model/base_ode_model.py +++ b/src/pygom/model/base_ode_model.py @@ -15,7 +15,7 @@ from sympy import symbols from scipy.stats._distn_infrastructure import rv_frozen -from .transition import Transition, TransitionType +from .transition import Event, Transition, TransitionType from ._model_errors import InputError, OutputError from ._model_verification import checkEquation from .ode_variable import ODEVariable @@ -44,6 +44,8 @@ class BaseOdeModel(object): A list of the derived parameters (tuple of (string, string)) transition: list A list of transition (:class:`.Transition`) + event: list + A list of events (:class:`.Transition`) birth_death: list A list of birth or death process (:class:`.Transition`) ode: list @@ -56,65 +58,71 @@ def __init__(self, param=None, derived_param=None, transition=None, + event=None, birth_death=None, ode=None): """ Constructor - """ - # the 3 required inputs when doing evaluation - self._state = None - self._param = None - self._time = None - # we always need time to be a symbol and it should be denoted as t + # """ + + # TODO: This is probably cluttered with definitions that are unnecessary. + # Need to comb through. + + # # the 3 required inputs when doing evaluation + # self._state = None + # self._param = None + # self._time = None + # self._state_lims=None + + # # we always need time to be a symbol and it should be denoted as t self._t = symbols('t') self._isDifficult = False - # allows the system to be defined directly - self._ode = None + + # # allows the system to be defined directly + # self._ode = None self._odeList = list() - self._explicitOde = False + # self._explicitOde = False - # book keeping parameters/states and etc + # # book keeping parameters/states and etc self._paramList = list() - # holder for the values of the parameters + # # holder for the values of the parameters self._paramValue = None self._stateList = list() self._derivedParamList = list() self._derivedParamEqn = list() - # this three is not actually that useful - # but lets leave it here for now - self._parameters = None - self._stochasticParam = None + # # Derived states: + # # these differ from params since we know the d/dt but not algebraic forms + # # this three is not actually that useful + # # but lets leave it here for now + #self._parameters = None + self._stochasticParam = None self._hasNewTransition = HasNewTransition() - # dictionary for mapping + # # dictionary for mapping self._paramDict = dict() - # although time is not defined as a parameter, we want to keep - # record of it existence + # # although time is not defined as a parameter, we want to keep + # # record of it existence self._paramDict['t'] = self._t self._stateDict = dict() self._derivedParamDict = dict() - # dictionary to store vector symbols + # # dictionary to store vector symbols self._vectorStateDict = dict() - # holders for the actual equations + # # holders for the actual equations self._transitionList = list() - self._transitionMatrix = None + self._eventList = list() + # self._transitionMatrix = None self._birthDeathList = list() self._birthDeathVector = list() - # information about the ode in general - # reactant, state change and the dependency graph matrix - self._lambdaMat = None - self._vMat = None - self._GMat = None - self._lambdaMatOD = None # also trialing this matrix indicating if a state is an origin or destination in a transition + # self.tstep=False - self._add_list_attr(state, "state_list") + self._add_list_attr_with_limits(state, "state_list") self._add_list_attr(param, "param_list") # this has to go after adding the parameters @@ -124,69 +132,26 @@ def __init__(self, # difference when inferring the parameters of the variables if not ode_utils.none_or_empty_list(derived_param): self.derived_param_list = derived_param - # if derived_param is not None: - # if transition is not None: + if not ode_utils.none_or_empty_list(event): + self.event_list = event + if not ode_utils.none_or_empty_list(transition): self.transition_list = transition - # if birth_death is not None: if not ode_utils.none_or_empty_list(birth_death): self.birth_death_list = birth_death - # if ode is not None: if not ode_utils.none_or_empty_list(ode): - # we have a set of ode explicitly defined! - if len(ode) > 0: - # tests on validity of using ode - # if transition is not None: - if not ode_utils.none_or_empty_list(transition): - raise InputError("Transition equations detected even " + - "though the set of ode is explicitly " + - "defined") - # if birth_death is not None: - if not ode_utils.none_or_empty_list(birth_death): - raise InputError("Birth Death equations detected even " + - "though the set of ode is explicitly " + - "defined") - - # set equations - self.ode_list = ode - else: - pass - - self._transitionVector = self._computeTransitionVector() + self.ode_list = ode - def _get_model_str(self): - model_str = "(%s, %s, %s, %s, %s, %s)" % (self._stateList, - self._paramList, - self._derivedParamEqn, - self._transitionList, - self._birthDeathList, - self._odeList) - if self._parameters is not None: - model_str += ".setParameters(%s)" % \ - {str(k): v for k, v in self._parameters.items()} - return model_str - - def _add_list_attr(self, attr, attr_list_name): - """ - Given an attribute (name attr_name), which is a string of comma - or space separated values, create a new attribute (name attr_name_list) - which is a list of those separated values. - e.g. "a,b,c d ef" returns [a, b, c, d, ef] - """ - if attr is not None: - if isinstance(attr, str): - attr = re_split_string.split(attr) - attr = filter(lambda x: not len(x.strip()) == 0, attr) - self.__setattr__(attr_list_name, list(attr)) + #self._computeEventRateVector() - ######################################################################## + ########################################################################### # # Getters and setters # - ######################################################################## + ########################################################################### @property def parameters(self): @@ -198,6 +163,8 @@ def parameters(self): (:mod:`sympy.core.symbol`, numeric) """ + if not hasattr(self, "_parameters"): + return None return self._parameters @parameters.setter @@ -220,6 +187,7 @@ def parameters(self, parameters): f = self._extractParamSymbol # A stupid and complicated type checking procedure. Someone please # kill me when you read this. + # TODO: Would be good to clean this up. param_out = dict() if parameters is not None: # currently only accept 3 main types here, obviously apart @@ -268,7 +236,7 @@ def parameters(self, parameters): # TODO: change this properly so that there are two different # types of parameter input. One is when we initialize and # another when we set new ones - if self._parameters is not None: + if hasattr(self, "_parameters"): param_out = self._parameters # extra the key from the parameters dictionary @@ -339,6 +307,8 @@ def parameters(self, parameters): index = self.get_param_index(key) self._paramValue[index] = val + self.set_sp() + @property def state(self): """ @@ -380,6 +350,8 @@ def state(self, state): self._state = self._unrollState(state) else: raise InputError(err_str) + + self.set_sp() else: raise InputError(err_str) @@ -518,11 +490,12 @@ def transition_list(self): with elements as :class:`.Transition` """ - if self._explicitOde is False: - return self._transitionList - else: - raise OutputError("ode was defined explicitly, no " + - "transition available") + return self._transitionList + # if self._explicitOde is False: + # return self._transitionList + # else: + # raise OutputError("ode was defined explicitly, no " + + # "transition available") # also need to make it transitionScript class @transition_list.setter @@ -536,12 +509,48 @@ def transition_list(self, transition_list): list of :class:`.Transition` of type transition in :class:`.transition_type` """ + + # TODO: This warning can be really annoying, I want it to just appear once. + # print("Update: In the latest version, between state transitions should be passed to SimulateODE"+ + # " via the Event objects.") + if isinstance(transition_list, (list, tuple)): for t in transition_list: self.add_transition(t) else: raise InputError("Expecting a list") + @property + def event_list(self): + """ + Returns a list of the events + + Returns + ------- + list + with elements as :class:`.Transition` + + """ + return self._eventList + + # also need to make it transitionScript class + @event_list.setter + def event_list(self, event_list): + """ + Set the set of events for the ode system + + Parameters + ---------- + event: list + list of :class:`.Event` + """ + if isinstance(event_list, (list, tuple)): + for event in event_list: + self.add_event(event) + else: + raise InputError("Expecting a list") + + @property def birth_death_list(self): """ @@ -571,6 +580,11 @@ def birth_death_list(self, birth_death_list): :class:`.transition_type` """ + + # TODO: This warning can be really annoying, I want it to just appear once. + # print("Update: In the latest version, birth/death transitions should be passed to SimulateODE"+ + # " via the Event objects.") + if isinstance(birth_death_list, (list, tuple)): for bd in birth_death_list: self.add_birth_death(bd) @@ -591,10 +605,11 @@ def ode_list(self): with elements as :class:`.Transition` """ - if self._explicitOde is True: - return self._odeList - else: - raise OutputError("ode was not defined explicitly") + return self._odeList + # if self._explicitOde is True: + # return self._odeList + # else: + # raise OutputError("ode was not defined explicitly") @ode_list.setter def ode_list(self, ode_list): @@ -658,8 +673,20 @@ def num_derived_param(self): """ return len(self._derivedParamList) + # @property + # def num_pure_transitions(self): + # """ + # Returns the total number of pure transition objects + + # Returns + # ------- + # int + # total number of pure transitions + # """ + # return len(self._transitionList) + @property - def num_pure_transitions(self): + def num_events(self): """ Returns the total number of pure transition objects @@ -668,7 +695,7 @@ def num_pure_transitions(self): int total number of pure transitions """ - return len(self._transitionList) + return len(self.event_list) @property def num_birth_deaths(self): @@ -696,6 +723,112 @@ def num_transitions(self): return self.num_pure_transitions + self.num_birth_deaths + ########################################################################### + + + def _get_model_str(self): + model_str = "(%s, %s, %s, %s, %s, %s)" % (self._stateList, + self._paramList, + self._derivedParamEqn, + self._transitionList, + self._birthDeathList, + self._odeList) + if hasattr(self, "_parameters"): + model_str += ".setParameters(%s)" % \ + {str(k): v for k, v in self._parameters.items()} + return model_str + + def _add_list_attr(self, attr, attr_list_name): + """ + Given an attribute (name attr_name), which is a string of comma + or space separated values, create a new attribute (name attr_name_list) + which is a list of those separated values. + e.g. "a,b,c d ef" returns [a, b, c, d, ef] + """ + if attr is not None: + if isinstance(attr, str): + attr = re_split_string.split(attr) + attr = filter(lambda x: not len(x.strip()) == 0, attr) + self.__setattr__(attr_list_name, list(attr)) + else: + raise InputError("No attribute passed to function") + + def _add_list_attr_with_limits(self, attr, attr_list_name): + """ + Given an attribute (name attr), which is a list + , create a new attribute (name attr_list_name) + which is a list of those separated values. + e.g. "a,b,c d ef" returns [a, b, c, d, ef] + """ + if attr is not None: + if isinstance(attr, str): + attr = re_split_string.split(attr) + attr = filter(lambda x: not len(x.strip()) == 0, attr) + attr_list=list(attr) + lim_list=[(0, None)]*len(attr_list) + elif isinstance(attr, list): + attr_list=[] + lim_list=[] + for att in attr: + if isinstance(att, tuple): + if len(att)!=2: + raise InputError("Variable must be tuple of length 2") + else: + if not isinstance(att[0], str): + raise InputError("Variable must be of type string") + elif len(att[0].strip()) == 0: + raise InputError("Variable has no name") + elif not isinstance(att[1], tuple): + raise InputError("Limits must be type tuple") + elif len(att[1])!=2: + raise InputError("Limit tuple must be length 2") + else: + attr_list.append(att[0]) + lim_list.append(att[1]) + elif isinstance(att, str): + if len(att.strip()) == 0: + raise InputError("Variable has no name") + else: + attr_list.append(att) + lim_list.append( (0, None) ) # We assume that the minimum value of each variable is zero + elif isinstance(att, ODEVariable): + attr_list.append(att) + lim_list.append( (0, None) ) + else: + raise InputError("List elements should be tuple, string or ODEVariable") + # else: + # raise InputError("Input type should either be a string or list") + + self._state_lims=lim_list # TODO: maybe assigning limits via a dict is tidier/safer + self.__setattr__(attr_list_name, list(attr_list)) + + else: + raise InputError("No attribute passed to function") + + def set_sp(self): + ''' + Set sp attribute, which is collection of all states and vars + TODO: testing this out still + ''' + self._s = self._stateList + [self._t] + self._sp = self._s + self._paramList + + # Calls to the autowrap method can't take ODEVariable class objects + # Better to convert the objects in self._sp back to sympy objects + # This code will convert any ODEVariable object in either the stateDict + # or paramDict dictonary + for i, item in enumerate(self._sp): + try: + self._sp[i] = self._stateDict[item.ID] + except Exception: + pass + try: + self._sp[i] = self._paramDict[item.ID] + except Exception: + pass + + return None + def get_state_index(self, input_str): """ Finds the index of the state @@ -792,15 +925,11 @@ def _addStateSymbol(self, input_str): if isinstance(symbol_name, sympy.Symbol): if str(symbol_name) not in self._paramList: - self._addVariable(symbol_name, var_obj, - self._stateList, - self._stateDict) + self._addVariable(symbol_name, var_obj, self._stateList, self._stateDict) else: for sym in symbol_name: self._addStateSymbol(str(sym)) - return None - def _addParamSymbol(self, input_str): # turn input_str into a ODEVarialbe if required if isinstance(input_str, str): @@ -812,21 +941,15 @@ def _addParamSymbol(self, input_str): if isinstance(symbol_name, sympy.Symbol): if str(symbol_name) not in self._paramList: - self._addVariable(symbol_name, var_obj, - self._paramList, - self._paramDict) + self._addVariable(symbol_name, var_obj, self._paramList, self._paramDict) else: for sym in symbol_name: self._addParamSymbol(str(sym)) - return - def _addDerivedParam(self, name, eqn): var_obj = ODEVariable(name, name) fixed_eqn = checkEquation(eqn, *self._getListOfVariablesDict()) - self._addVariable(fixed_eqn, var_obj, - self._derivedParamList, - self._derivedParamDict) + self._addVariable(fixed_eqn, var_obj, self._derivedParamList, self._derivedParamDict) self._hasNewTransition.trip() self._derivedParamEqn += [(name, eqn)] @@ -847,8 +970,20 @@ def add_transition(self, transition): The transition object that contains all the information regarding the transition """ + + # Manipulate transitions into events, to allow backwards compatibility. + if isinstance(transition, Transition): if transition.transition_type is TransitionType.T: + + trans=Transition(origin=transition.origin, + destination=transition.destination, + transition_type="T") + + event=Event(rate=transition.equation, + transition_list=[trans]) + + self._eventList.append(event) self._transitionList.append(transition) self._hasNewTransition.trip() else: @@ -857,22 +992,24 @@ def add_transition(self, transition): raise InputError("Input %s is not a Transition." % type(transition)) return None - - def _computeTransitionMatrix(self): - """ - Computes the transition matrix given the transitions + + def add_event(self, event): """ - # holders - self._transitionMatrix = sympy.zeros(self.num_state, self.num_state) - # going through the list of transitions - pure_trans = self._getAllTransition(pureTransitions=True) - from_list, to, eqn = self._unrollTransitionList(pure_trans) - for k, eqn in enumerate(eqn): - for i in from_list[k]: - for j in to[k]: - self._transitionMatrix[i, j] += eqn + Add an event - return self._transitionMatrix + """ + if isinstance(event, Event): + self._eventList.append(event) + self._hasNewTransition.trip() + elif isinstance(event, Transition): # Convert single transition into event + rate=event.equation + event._equation=None + derived_event=Event(rate=rate, + transition_list=[event]) + self._eventList.append(derived_event) + self._hasNewTransition.trip() + else: + raise InputError("Input %s is not an Event or Transition." % type(event)) def add_birth_death(self, birth_death): """ @@ -885,11 +1022,29 @@ def add_birth_death(self, birth_death): regarding the process """ + + # Manipulate transitions into events, to allow backwards compatibility. + if isinstance(birth_death, Transition): t = birth_death.transition_type - if t is TransitionType.B or t is TransitionType.D: - self._birthDeathList.append(birth_death) - self._hasNewTransition.trip() + if t is TransitionType.B: + trans_birth=Transition(destination=birth_death.destination, transition_type="B") + + birth_event=Event(rate=birth_death.equation, + transition_list=[trans_birth]) + + self._eventList.append(birth_event) + self._birthDeathList.append(birth_event) + self._hasNewTransition.trip() + elif t is TransitionType.D: + trans_death=Transition(origin=birth_death.origin, transition_type="D") + + death_event=Event(rate=birth_death.equation, + transition_list=[trans_death]) + + self._eventList.append(death_event) + self._birthDeathList.append(death_event) + self._hasNewTransition.trip() else: raise InputError("Input is not a birth death process") else: @@ -897,20 +1052,6 @@ def add_birth_death(self, birth_death): return None - def _computeBirthDeathVector(self): - # holder - self._birthDeathVector = sympy.zeros(self.num_state, 1) - # go through all the transition objects - for bdObj in self._birthDeathList: - fromIndex, _toIndex, eqn = self._unrollTransition(bdObj) - for i in fromIndex: - if bdObj.transition_type is TransitionType.B: - self._birthDeathVector[i] += eqn - elif bdObj.transition_type is TransitionType.D: - self._birthDeathVector[i] -= eqn - - return self._birthDeathVector - def add_ode(self, eqn): """ Add an ode @@ -937,44 +1078,124 @@ def add_ode(self, eqn): return None - def _computeOdeVector(self): - # we are only testing it here because we want to be flexible and - # allow the end user to input more state than initially desired - if len(self.ode_list) <= self.num_state: - self._ode = sympy.zeros(self.num_state, 1) - fromList, _t, eqn = self._unrollTransitionList(self.ode_list) - for i, eqn in enumerate(eqn): - if len(fromList[i]) > 1: - raise InputError("An explicit ode cannot describe more " + - "than a single state") - else: - self._ode[fromList[i][0]] = eqn - else: - raise InputError("The total number of ode is %s " + - "where the number of state is %s" % - len(self.ode_list), self.num_state) + def get_TransitionMatrix(self): + """ + Computes the pure transition matrix given the transitions + """ + # holders + self._transitionMatrix = sympy.zeros(self.num_state, self.num_state) - return None + # Loop through event transitions and only consider pure ones between 2 states + for event in self.event_list: + rate=checkEquation(event.rate, *self._getListOfVariablesDict()) + for transition in event.transition_list: + magnitude=checkEquation(transition._magnitude, *self._getListOfVariablesDict()) + rate_of_change=magnitude*rate + if transition.transition_type==TransitionType.T: + origin_index=self.state_list.index(transition.origin) + destination_index=self.state_list.index(transition.destination) + self._transitionMatrix[origin_index, destination_index] += rate_of_change + + return self._transitionMatrix + + def get_BirthDeathVector(self): + # holder + self._birthDeathVector = sympy.zeros(self.num_state, 1) + # Extract all info from events + for event in self.event_list: + rate=checkEquation(event.rate, *self._getListOfVariablesDict()) + for transition in event.transition_list: + magnitude=checkEquation(transition._magnitude, *self._getListOfVariablesDict()) + rate_of_change=magnitude*rate + if transition.transition_type==TransitionType.B: + destination_index=self.state_list.index(transition.destination) + self._birthDeathVector[destination_index] += rate_of_change + elif transition.transition_type==TransitionType.D: + origin_index=self.state_list.index(transition.origin) + self._birthDeathVector[origin_index] -= rate_of_change + + return self._birthDeathVector + + # def _computeOdeVector(self): + # # we are only testing it here because we want to be flexible and + # # allow the end user to input more state than initially desired + # if len(self.ode_list) <= self.num_state: + # self._ode = sympy.zeros(self.num_state, 1) + # #fromList, _t, eqn, sec = self._unrollTransitionList(self.ode_list) + + # unrolled_trans_list= self._unrollTransitionList(self.ode_list) + # from_list = unrolled_trans_list["from_list"] + # eqn_list = unrolled_trans_list["eqn_list"] + + # for i, eqn in enumerate(eqn_list): + # if len(from_list[i]) > 1: + # raise InputError("An explicit ode cannot describe more " + + # "than a single state") + # else: + # self._ode[from_list[i][0]] = eqn + # else: + # raise InputError("The total number of ode is %s " + + # "where the number of state is %s" % + # len(self.ode_list), self.num_state) - def _computeTransitionVector(self): + # return None + + def get_EventRateVector(self): """ Get all the transitions into a vector, arranged by state to state transition then the birth death processes """ - self._transitionVector = sympy.zeros(self.num_transitions, 1) - _f, _t, eqn = self._unrollTransitionList(self._getAllTransition()) - for i, eqn in enumerate(eqn): - self._transitionVector[i] = eqn - return self._transitionVector + self._eventRateVector = sympy.zeros(self.num_events, 1) + # Extract all info from events + for i, event in enumerate(self.event_list): + self._eventRateVector[i]=checkEquation(event.rate, *self._getListOfVariablesDict()) - ######################################################################## - # - # Other type of matrices - # - ######################################################################## + return self._eventRateVector - def _computeReactantMatrix(self): + def get_StateChangeMatrix(self): + """ + The state change matrix, where + .. math:: + v_{i,j} = change in state i if transition j occurs + (this could still be in symbolic form at this stage) + """ + # container for output + self._vMat = sympy.zeros(self.num_state, self.num_events) + + for event_index, event in enumerate(self.event_list): + for transition in event.transition_list: + magnitude=checkEquation(transition._magnitude, *self._getListOfVariablesDict()) + if transition.transition_type==TransitionType.B: + destination_index=self.state_list.index(transition.destination) + self._vMat[destination_index, event_index] += magnitude + elif transition.transition_type==TransitionType.D: + origin_index=self.state_list.index(transition.origin) + self._vMat[origin_index, event_index] -= magnitude + elif transition.transition_type==TransitionType.T: + origin_index=self.state_list.index(transition.origin) + destination_index=self.state_list.index(transition.destination) + self._vMat[origin_index, event_index] -= magnitude + self._vMat[destination_index, event_index] += magnitude + + return self._vMat + + def get_pureOdeVector(self): + ''' + non transition terms + ''' + + pure_ode = sympy.zeros(self.num_state, 1) + # Now extract any ODE contributions from ODE type transitions + for ode in self.ode_list: + origin_index=self.state_list.index(ode.origin) + pure_ode[origin_index] += checkEquation(ode.equation, *self._getListOfVariablesDict()) + + self._pureOdeVector=pure_ode + + return self._pureOdeVector + + def get_ReactantMatrix(self): """ The reactant matrix, where @@ -983,92 +1204,102 @@ def _computeReactantMatrix(self): 0, &otherwise \\right. """ # declare holder - self._lambdaMat = np.zeros((self.num_state, self.num_transitions), int) - - _f, _t, eqn = self._unrollTransitionList(self._getAllTransition()) - for j, eqn in enumerate(eqn): - for i, state in enumerate(self._stateList): - if type(eqn)==int: - self._lambdaMat[i, j] = 0 - elif self._stateDict[state.ID] in eqn.atoms(): - self._lambdaMat[i, j] = 1 + self._lambdaMat = np.zeros((self.num_state, self.num_events), int) + + for event_index, event in enumerate(self.event_list): + for transition in event.transition_list: + if transition.transition_type==TransitionType.B: + destination_index=self.state_list.index(transition.destination) + self._lambdaMat[destination_index, event_index] = 1 + elif transition.transition_type==TransitionType.D: + origin_index=self.state_list.index(transition.origin) + self._lambdaMat[origin_index, event_index] = 1 + elif transition.transition_type==TransitionType.T: + origin_index=self.state_list.index(transition.origin) + destination_index=self.state_list.index(transition.destination) + self._lambdaMat[origin_index, event_index] = 1 + self._lambdaMat[destination_index, event_index] = 1 return self._lambdaMat - def _computeStateChangeMatrix(self): - """ - The state change matrix, where - .. math:: - v_{i,j} = \\left\\{ 1, &if transition j cause state i to lose a particle, \\\\ - -1, &if transition j cause state i to gain a particle, \\\\ - 0, &otherwise \\right. - """ - self._vMat = np.zeros((self.num_state, self.num_transitions), int) - - f, t, eqn = self._unrollTransitionList(self._getAllTransition()) - for j, _eqn in enumerate(eqn): - if j < self.num_pure_transitions: - for k1 in f[j]: - self._vMat[k1, j] += -1 - for k2 in t[j]: - self._vMat[k2, j] += 1 - else: - bdObj = self._birthDeathList[j - self.num_pure_transitions] - if bdObj.transition_type is TransitionType.B: - for k1 in f[j]: - self._vMat[k1, j] += 1 - elif bdObj.transition_type is TransitionType.D: - for k2 in f[j]: - self._vMat[k2, j] += -1 - - return self._vMat - - # Might replace _computeReactantMatrix. This function gives a matrix - def _computeReactantMatrixOD(self): - """ - The alternative reactant matrix, where - - .. math:: - \\lambda_{i,j} = \\left\\{ 1, &if state i is an origin or destination in transition j, \\\\ - 0, &otherwise \\right. + ######################################################################## + # + # State change matrix + # + ######################################################################## - OD imples this refers to origin and destination - """ + # TODO: The folloiwng commented out matrices are not used + # consider removing if they are just providing clutter + + # def _computeReactantMatrix(self): + # """ + # The reactant matrix, where + + # .. math:: + # \\lambda_{i,j} = \\left\\{ 1, &if state i is involved in transition j, \\\\ + # 0, &otherwise \\right. + # """ + # # declare holder + # self._lambdaMat = np.zeros((self.num_state, self.num_transitions), int) + + # _f, _t, eqn = self._unrollTransitionList(self._getAllTransition()) + # for j, eqn in enumerate(eqn): + # for i, state in enumerate(self._stateList): + # if type(eqn)==int: + # self._lambdaMat[i, j] = 0 + # elif self._stateDict[state.ID] in eqn.atoms(): + # self._lambdaMat[i, j] = 1 + + # return self._lambdaMat + + # # Might replace _computeReactantMatrix. This function gives a matrix + # def _computeReactantMatrixOD(self): + # """ + # The alternative reactant matrix, where + + # .. math:: + # \\lambda_{i,j} = \\left\\{ 1, &if state i is an origin or destination in transition j, \\\\ + # 0, &otherwise \\right. + + # OD imples this refers to origin and destination + # """ - x=self._vMat!=0 - x=x.astype(int) - self._lambdaMatOD=x + # x=self._vMat!=0 + # x=x.astype(int) + # self._lambdaMatOD=x - return self._lambdaMatOD + # return self._lambdaMatOD - def _computeDependencyMatrix(self): - """ - Obtain the dependency matrix/graph. G_{i,j} indicate whether invoking - the transition j will cause the rate to change for transition j - """ - if self._lambdaMat is None: - self._computeReactantMatrix() - if self._vMat is None: - self._computeStateChangeMatrix() - if self._lambdaMatOD is None: - self._computeReactantMatrixOD() + # def _computeDependencyMatrix(self): + # """ + # Obtain the dependency matrix/graph. G_{i,j} indicate whether invoking + # the transition j will cause the rate to change for transition j + # """ + # # if self._lambdaMat is None: + # # self._computeReactantMatrix() + # # if self._lambdaMatOD is None: + # # self._computeReactantMatrixOD() + # if self._vMat is None: + # self._computeStateChangeMatrix() - nt = self.num_transitions - self._GMat = np.zeros((nt, nt), int) + # nt = self.num_transitions + # self._GMat = np.zeros((nt, nt), int) - for i in range(nt): - for j in range(nt): - d = 0 - for k in range(self.num_state): - d = d or (self._lambdaMat[k, i] and self._vMat[k, j]) - self._GMat[i, j] = d + # for i in range(nt): + # for j in range(nt): + # d = 0 + # for k in range(self.num_state): + # d = d or (self._lambdaMat[k, i] and self._vMat[k, j]) + # self._GMat[i, j] = d - return self._GMat + # return self._GMat ######################################################################## # Unrolling of the information # state + # TODO: This unrolling is probably not useful anymore if we are + # basing the system on events rather than transitions. ######################################################################## def _unrollState(self, state): @@ -1097,44 +1328,55 @@ def _unrollTransition(self, transition_obj): """ from_index = self._extractStateIndex(transition_obj.origin) to_index = self._extractStateIndex(transition_obj.destination) + eqn = checkEquation(transition_obj.equation, *self._getListOfVariablesDict()) - eqn = checkEquation(transition_obj.equation, - *self._getListOfVariablesDict()) + + # Try returning as dict (should improve modularity over tuple output) + + out= {"from_index": from_index, + "to_index": to_index, + "eqn": eqn} - return from_index, to_index, eqn + return out def _unrollTransitionList(self, transition_list): + ''' + ...describe... + ''' + from_list = list() to_list = list() eqn_list = list() - for t in transition_list: - from_list.append(self._extractStateIndex(t.origin)) - to_list.append(self._extractStateIndex(t.destination)) - eqn_list.append(t.equation) + type_list = list() + + for transition_obj in transition_list: + unrolled_transition=self._unrollTransition(transition_obj) + from_list.append(unrolled_transition["from_index"]) + to_list.append(unrolled_transition["to_index"]) + eqn_list.append(unrolled_transition["eqn"]) - eqn_list = checkEquation(eqn_list, *self._getListOfVariablesDict()) eqn_list = eqn_list if hasattr(eqn_list, '__iter__') else [eqn_list] - return from_list, to_list, eqn_list + out= { + "from_list": from_list, + "to_list": to_list, + "eqn_list": eqn_list, + } + + return out def _getAllTransition(self, pureTransitions=False): - assert isinstance(pureTransitions, bool), \ - "requires type(pureTransitions) = bool" + ''' + Get all transitions into a list + If pureTransitions==True just transitions between states + If pureTransitions==False between states plus birth deaths + ''' + assert isinstance(pureTransitions, bool), "requires type(pureTransitions) = bool" if pureTransitions: - n = self.num_pure_transitions + return self._transitionList else: - n = self.num_transitions - - all_transition = list() - for j in range(n): - if j < self.num_pure_transitions: - all_transition.append(self._transitionList[j]) - else: - i = j - self.num_pure_transitions - all_transition.append(self._birthDeathList[i]) - - return all_transition + return self._transitionList+self._birthDeathList def _iterStateList(self): """ @@ -1178,12 +1420,16 @@ def _extractParamSymbol(self, input_str): else: raise InputError("Input parameter: %s does not exist" % input_str) + # TODO: figure out why this is so awkward def _extractStateIndex(self, input_str): + ''' + Find the index of the string or sympy.Symbol 'input_str' + ''' if input_str is None: return list() else: if isinstance(input_str, (str, sympy.Symbol)): - input_str = [input_str] # make this an iterable + input_str = [input_str] # make this an iterable TODO: why? if hasattr(input_str, '__iter__'): return [self._extractStateIndexSingle(i) for i in input_str] @@ -1192,6 +1438,9 @@ def _extractStateIndex(self, input_str): "object of string") def _extractStateIndexSingle(self, input_str): + ''' + Find the index of the string or sympy.Symbol 'input_str' + ''' if isinstance(input_str, ODEVariable): return self._stateList.index(input_str) else: @@ -1253,4 +1502,4 @@ def _extractUpperTriangle(self, A, nrow=None, ncol=None): for j in range(i, ncol): B[i,j] = A[i, j] - return B \ No newline at end of file + return B diff --git a/src/pygom/model/common_models.py b/src/pygom/model/common_models.py index 91960683..56cfecb0 100644 --- a/src/pygom/model/common_models.py +++ b/src/pygom/model/common_models.py @@ -7,7 +7,7 @@ from collections import OrderedDict -from .transition import TransitionType, Transition +from .transition import TransitionType, Transition, Event #from .deterministic import DeterministicOde from .simulate import SimulateOde @@ -32,23 +32,24 @@ def SIS(param=None): >>> ode.plot() """ - state = ['S', 'I'] + state_list = [('S', (0,None)), ('I', (0, None))] param_list = ['beta', 'gamma', 'N'] - transition = [ - Transition(origin='S', destination='I', equation='beta*S*I/N',transition_type=TransitionType.T), - Transition(origin='I', destination='S', equation='gamma*I',transition_type=TransitionType.T) - ] - # initialize the model - ode = SimulateOde(state, - param_list, - transition=transition) - # set return, depending on whether we have input the parameters + trans_inf=Transition(origin='S', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='beta*S*I/N', transition_list=[trans_inf]) + + trans_rec=Transition(origin='I', destination='S',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) + + model = SimulateOde(state=state_list, + param=param_list, + event=[event_inf, event_rec]) + if param is None: - return ode + return model else: - ode.parameters = param - return ode + model.parameters = param + return model def SIS_Periodic(param=None): @@ -77,31 +78,26 @@ def SIS_Periodic(param=None): >>> ode.plot() """ - state = ['I', 'tau'] + state_list = [('S', (0,None)), ('I', (0, None))] param_list = ['gamma', 'beta0', 'delta', 'period', 'N'] - # derived_param = [('betaT', '2 - 1.8*cos(5*tau)')] - derived_param = [('betaT', 'beta0*(1-delta*cos(2*3.14159*tau/period))')] - ode = [ - Transition(origin='I', - equation='(betaT - gamma)*I - (betaT*I*I/N)', - transition_type=TransitionType.ODE), - Transition(origin='tau', - equation='1', - transition_type=TransitionType.ODE) - ] - # initialize the model - ode_obj = SimulateOde(state, - param_list, - derived_param=derived_param, - ode=ode) + derived_param = [('betaT', 'beta0*(1-delta*cos(2*3.14159*t/period))')] + + trans_inf=Transition(origin='S', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='betaT*S*I/N', transition_list=[trans_inf]) + + trans_rec=Transition(origin='I', destination='S',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) + + model = SimulateOde(state=state_list, + param=param_list, + derived_param=derived_param, + event=[event_inf, event_rec]) - # set return, depending on whether we have input the parameters if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj - + model.parameters = param + return model def SIR(param=None): """ @@ -130,188 +126,55 @@ def SIR(param=None): >>> ode.plot() """ - state = ['S', 'I', 'R'] - param_list = ['beta', 'gamma', 'N'] - transition = [ - Transition(origin='S', destination='I', equation='beta*S*I/N', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T) - ] - # initialize the model - ode_obj = SimulateOde(state, param_list, transition=transition) - - # set return, depending on whether we have input the parameters - if param is None: - return ode_obj - else: - ode_obj.parameters = param - return ode_obj - - -def SIR_norm(param=None): - """ - A normalized SIR model: - - .. math:: - \\frac{dS}{dt} &= -\\beta SI \\\\ - \\frac{dI}{dt} &= \\beta SI - \\gamma I \\\\ - \\frac{dR}{dt} &= \\gamma I - - - Examples - -------- - The model that produced top two graph in Figure 1.3 of the reference above. - First, when everyone is susceptible and only one individual was infected. - >>> import numpy as np - >>> from pygom import common_models - >>> ode = common_models.SIR({'beta':3.6, 'gamma':0.2}) - >>> t = np.linspace(0, 730, 1001) - >>> N = 7781984.0 - >>> x0 = [1.0, 10/N, 0.0] - >>> ode.initial_values = (x0, t[0]) - >>> solution = ode.integrate(t[1::]) - >>> ode.plot() + state_list = [('S', (0,None)), ('I', (0, None)), ('R', (0, None))] + param_list = ['beta', 'gamma', 'N'] - Second model with a more *realistic* scenario + trans_inf=Transition(origin='S', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='beta*S*I/N', transition_list=[trans_inf]) - >>> import numpy as np - >>> from pygom import common_models - >>> ode = common_models.SIR({'beta':3.6, 'gamma':0.2}) - >>> t = np.linspace(0, 730, 1001) - >>> N = 7781984.0 - >>> x0 = [0.065, 123*(5.0/30.0)/N, 0.0] - >>> ode.initial_values = (x0, t[0]) - >>> solution = ode.integrate(t[1::]) - >>> ode.plot() + trans_rec=Transition(origin='I', destination='R',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) - """ - state = ['S', 'I', 'R'] - param_list = ['beta', 'gamma'] - transition = [ - Transition(origin='S', destination='I', equation='beta*S*I', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T) - ] - # initialize the model - ode_obj = SimulateOde(state, param_list, transition=transition) + model = SimulateOde(state=state_list, + param=param_list, + event=[event_inf, event_rec]) - # set return, depending on whether we have input the parameters if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj - -# def SIR_N(param=None, init=None): -# """ -# A standard SIR model [Brauer2008]_ with population N - -# .. math:: -# \\frac{dS}{dt} &= -\\beta SI/N \\\\ -# \\frac{dI}{dt} &= \\beta SI/N- \\gamma I \\\\ -# \\frac{dR}{dt} &= \\gamma I - -# """ -# stateList = ['S', 'I', 'R'] -# paramList = ['beta', 'gamma', 'N'] -# transitionList = [Transition(origin='S', destination='I', equation='beta*S*I/N', transition_type=TransitionType.T), -# Transition(origin='I', destination='R', equation='gamma*I', transition_type=TransitionType.T)] - -# # initialize the model -# ode_obj = SimulateOde(stateList, paramList, transition=transitionList) - -# # set return, depending on whether we have input the parameters - -# if param is not None: -# ode_obj.parameters = param - -# if init is not None: -# ode_obj.initial_values = init + model.parameters = param + return model -# return ode_obj - - -def SEIR_N(param=None, init=None): +def SEIR(param=None, init=None): """ A standard SIR model [Brauer2008]_ with population N """ - stateList = ['S', 'E', 'I', 'R'] - paramList = ['beta', 'alpha', 'gamma', 'N'] - transitionList = [Transition(origin='S', destination='E', equation='beta*S*I/N', transition_type=TransitionType.T), - Transition(origin='E', destination='I', equation='alpha*E', transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', transition_type=TransitionType.T)] - - # initialize the model - ode_obj = SimulateOde(stateList, paramList, transition=transitionList) - - # set return, depending on whether we have input the parameters - if param is not None: - ode_obj.parameters = param - - if init is not None: - ode_obj.initial_values = init - - return ode_obj -# def SIR_N(param=None): -# """ -# A standard SIR model [Brauer2008]_ with population N. This is the unnormalized -# version of the SIR model. - -# .. math:: -# \\frac{dS}{dt} &= -\\beta SI/N \\\\ -# \\frac{dI}{dt} &= \\beta SI/N- \\gamma I \\\\ -# \\frac{dR}{dt} &= \\gamma I + state_list = [('S', (0,None)), ('E', (0,None)), ('I', (0, None)), ('R', (0, None))] + param_list = ['beta', 'alpha', 'gamma', 'N'] -# Examples -# -------- -# The model that produced top two graph in Figure 1.3 of the reference above. -# First, when everyone is susceptible and only one individual was infected. + trans_exp=Transition(origin='S', destination='E',transition_type=TransitionType.T) + event_exp=Event(rate='beta*S*I/N', transition_list=[trans_exp]) -# >>> import numpy as np -# >>> from pygom import common_models -# >>> ode = common_models.SIR({'beta':3.6, 'gamma':0.2}) -# >>> t = np.linspace(0, 730, 1001) -# >>> N = 7781984.0 -# >>> x0 = [N, 1.0, 0.0] -# >>> ode.initial_values = (x0, t[0]) -# >>> solution = ode.integrate(t[1::]) -# >>> ode.plot() + trans_inf=Transition(origin='E', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='alpha*E', transition_list=[trans_inf]) -# Second model with a more *realistic* scenario + trans_rec=Transition(origin='I', destination='R',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) -# >>> import numpy as np -# >>> from pygom import common_models -# >>> ode = common_models.SIR({'beta':3.6, 'gamma':0.2}) -# >>> t = np.linspace(0, 730, 1001) -# >>> N = 7781984.0 -# >>> x0 = [int(0.065*N), 21.0, 0.0] -# >>> ode.initial_values = (x0, t[0]) -# >>> solution = ode.integrate(t[1::]) -# >>> ode.plot() -# """ -# state = ['S', 'I', 'R'] -# param_list = ['beta', 'gamma', 'N'] -# transition = [ -# Transition(origin='S', destination='I', equation='beta*S*I/N', -# transition_type=TransitionType.T), -# Transition(origin='I', destination='R', equation='gamma*I', -# transition_type=TransitionType.T) -# ] -# # initialize the model -# ode_obj = SimulateOde(state, param_list, transition=transition) - -# # set return, depending on whether we have input the parameters -# if param is None: -# return ode_obj -# else: -# ode_obj.parameters = param -# return ode_obj + model = SimulateOde(state=state_list, + param=param_list, + event=[event_exp, + event_inf, + event_rec]) + if param is None: + return model + else: + model.parameters = param + return model def SIR_Birth_Death(param=None): """ @@ -343,87 +206,54 @@ def SIR_Birth_Death(param=None): -------- :func:`.SIR` """ - state = ['S', 'I', 'R'] - param_list = ['beta', 'gamma', 'mu', 'N'] - transition = [ - Transition(origin='S', destination='I', equation='beta*S*I/N', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T) - ] - # our birth and deaths - birth_death = [ - Transition(origin='S', equation='mu*N', - transition_type=TransitionType.B), - Transition(origin='S', equation='mu*S', - transition_type=TransitionType.D), - Transition(origin='I', equation='mu*I', - transition_type=TransitionType.D), - Transition(origin='R', equation='mu*R', - transition_type=TransitionType.D) - ] - # initialize the model - ode_obj = SimulateOde(state, - param_list, - birth_death=birth_death, - transition=transition) + state_list = [('S', (0,None)), ('I', (0, None)), ('R', (0, None)), ('N', (0, None))] + param_list=['beta', 'gamma', 'mu'] - # set return, depending on whether we have input the parameters - if param is None: - return ode_obj - else: - ode_obj.parameters = param - return ode_obj + # Infection + trans_inf=Transition(origin='S', destination='I', transition_type='T') + event_inf=Event(transition_list=[trans_inf], rate='beta*S*I/N') + # Recovery + trans_rec=Transition(origin='I', destination='R', transition_type='T') + event_rec=Event(transition_list=[trans_rec], rate='gamma*I') -def SEIR(param=None): - """ - A standard SEIR model [Brauer2008]_, defined by the ode - - .. math:: - \\frac{dS}{dt} &= -\\beta SI \\\\ - \\frac{dE}{dt} &= \\beta SI - \\alpha E \\\\ - \\frac{dI}{dt} &= \\alpha E - \\gamma I \\\\ - \\frac{dR}{dt} &= \\gamma I + # Transitions in and out of total population count + # These will be used in the following event definitions + birth_N=Transition(destination="N", transition_type="B") + death_N=Transition(origin="N", transition_type="D") - Examples - -------- + # 1) Birth event into S + birth=Transition(destination="S", transition_type="B") + event_birth=Event(transition_list=[birth, birth_N], rate='mu*N') - >>> import numpy as np - >>> from pygom import common_models - >>> ode = common_models.SEIR({'beta':1800, 'gamma':100, 'alpha':35.84}) - >>> t = np.linspace(0, 50, 1001) - >>> x0 = [0.0658, 0.0007, 0.0002, 0.0] - >>> ode.initial_values = (x0, t[0]) - >>> solution,output = ode.integrate(t[1::], full_output=True) - >>> ode.plot() + # 2) Death event of an S + death_S=Transition(origin="S", transition_type="D") + event_death_S=Event(transition_list=[death_S, death_N], rate='mu*S') - See also - -------- - :func:`.SEIR_Birth_Death` - """ + # 3) Death event of an I + death_I=Transition(origin="I", transition_type="D") + event_death_I=Event(transition_list=[death_I, death_N], rate='mu*I') - state = ['S', 'E', 'I', 'R'] - param_list = ['beta', 'alpha', 'gamma', 'N'] + # 4) Death event of an R + death_R=Transition(origin="R", transition_type="D") + event_death_R=Event(transition_list=[death_R, death_N], rate='mu*R') - transition = [ - Transition(origin='S', destination='E', equation='beta*S*I/N', - transition_type=TransitionType.T), - Transition(origin='E', destination='I', equation='alpha*E', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T) - ] - ode_obj = SimulateOde(state, param_list, transition=transition) + model=SimulateOde(state=state_list, + param=param_list, + event=[event_inf, + event_rec, + event_birth, + event_death_S, + event_death_I, + event_death_R]) if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj - + model.parameters = param + return model def SEIR_Birth_Death(param=None): """ @@ -455,38 +285,63 @@ def SEIR_Birth_Death(param=None): :func:`.SEIR` """ - state = ['S', 'E', 'I', 'R'] - param_list = ['beta', 'alpha', 'gamma', 'mu', 'N'] + state_list = [('S', (0,None)), ('E', (0,None)), ('I', (0, None)), ('R', (0, None)), ('N', (0, None))] + param_list = ['beta', 'alpha', 'gamma', 'mu'] - transition = [ - Transition(origin='S', destination='E', equation='beta*S*I/N', - transition_type=TransitionType.T), - Transition(origin='E', destination='I', equation='alpha*E', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T) - ] + # Exposure + trans_exp=Transition(origin='S', destination='E',transition_type=TransitionType.T) + event_exp=Event(rate='beta*S*I/N', transition_list=[trans_exp]) - bd_list = [ - Transition(origin='S', equation='mu*S', - transition_type=TransitionType.D), - Transition(origin='E', equation='mu*E', - transition_type=TransitionType.D), - Transition(origin='I', equation='mu*I', - transition_type=TransitionType.D), - Transition(origin='S', equation='mu*N', - transition_type=TransitionType.B) - ] + # Infectious + trans_inf=Transition(origin='E', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='alpha*E', transition_list=[trans_inf]) - ode_obj = SimulateOde(state, param_list, - transition=transition, - birth_death=bd_list) + # Recovery + trans_rec=Transition(origin='I', destination='R',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) + + # Transitions in and out of total population count + # These will be used in the following event definitions + birth_N=Transition(destination="N", transition_type="B") + death_N=Transition(origin="N", transition_type="D") + + # 1) Birth event into S + birth=Transition(destination="S", transition_type="B") + event_birth=Event(transition_list=[birth, birth_N], rate='mu*N') + + # 2) Death event of an S + death_S=Transition(origin="S", transition_type="D") + event_death_S=Event(transition_list=[death_S, death_N], rate='mu*S') + + # 3) Death event of an E + death_E=Transition(origin="E", transition_type="D") + event_death_E=Event(transition_list=[death_E, death_N], rate='mu*E') + + # 4) Death event of an I + death_I=Transition(origin="I", transition_type="D") + event_death_I=Event(transition_list=[death_I, death_N], rate='mu*I') + + # 5) Death event of an R + death_R=Transition(origin="R", transition_type="D") + event_death_R=Event(transition_list=[death_R, death_N], rate='mu*R') + + + model=SimulateOde(state=state_list, + param=param_list, + event=[event_exp, + event_inf, + event_rec, + event_birth, + event_death_S, + event_death_E, + event_death_I, + event_death_R]) if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj + model.parameters = param + return model def SEIR_Birth_Death_Periodic(param=None): """ @@ -531,74 +386,139 @@ def SEIR_Birth_Death_Periodic(param=None): :func:`.SEIR`, :func:`.SEIR_Birth_Death`, :func:`.SIR_Periodic` """ - state = ['S', 'E', 'I', 'tau'] - param_list = ['mu', 'alpha', 'gamma', 'beta_0', 'beta_1'] - derived_param = [('beta_S', 'beta_0 * (1 + beta_1*cos(2*pi*tau))')] - ode = [ - Transition(origin='S', equation='mu - beta_S*S*I - mu*S', - transition_type=TransitionType.ODE), - Transition(origin='E', equation='beta_S*S*I - (mu + alpha)*E', - transition_type=TransitionType.ODE), - Transition(origin='I', equation='alpha*E - (mu + gamma)*I', - transition_type=TransitionType.ODE), - Transition(origin='tau', equation='1', - transition_type=TransitionType.ODE) - ] - # initialize the model - ode_obj = SimulateOde(state, param_list, - derived_param=derived_param, - ode=ode) + state_list = [('S', (0,None)), ('E', (0,None)), ('I', (0, None)), ('R', (0, None)), ('N', (0, None))] + param_list = ['beta0', 'delta', 'period', 'alpha', 'gamma', 'mu'] + derived_param = [('betaT', 'beta0*(1-delta*cos(2*3.14159*t/period))')] + + # Exposure + trans_exp=Transition(origin='S', destination='E',transition_type=TransitionType.T) + event_exp=Event(rate='betaT*S*I/N', transition_list=[trans_exp]) + + # Infectious + trans_inf=Transition(origin='E', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='alpha*E', transition_list=[trans_inf]) + + # Recovery + trans_rec=Transition(origin='I', destination='R',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) + + # Transitions in and out of total population count + # These will be used in the following event definitions + birth_N=Transition(destination="N", transition_type="B") + death_N=Transition(origin="N", transition_type="D") + + # 1) Birth event into S + birth=Transition(destination="S", transition_type="B") + event_birth=Event(transition_list=[birth, birth_N], rate='mu*N') + + # 2) Death event of an S + death_S=Transition(origin="S", transition_type="D") + event_death_S=Event(transition_list=[death_S, death_N], rate='mu*S') + + # 3) Death event of an E + death_E=Transition(origin="E", transition_type="D") + event_death_E=Event(transition_list=[death_E, death_N], rate='mu*E') + + # 4) Death event of an I + death_I=Transition(origin="I", transition_type="D") + event_death_I=Event(transition_list=[death_I, death_N], rate='mu*I') + + # 5) Death event of an R + death_R=Transition(origin="R", transition_type="D") + event_death_R=Event(transition_list=[death_R, death_N], rate='mu*R') + + model=SimulateOde(state=state_list, + param=param_list, + derived_param=derived_param, + event=[event_exp, + event_inf, + event_rec, + event_birth, + event_death_S, + event_death_E, + event_death_I, + event_death_R]) if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj + model.parameters = param + return model def SEIR_Birth_Death_Periodic_Waning_Intro(param=None): - state = ['S', 'E', 'I', 'R', 'tau'] - param_list = ['mu', 'alpha', 'gamma', 'epsilon', 'w', 'beta0', 'delta', 'period', 'N'] - - derived_param = [('betaT', 'beta0*(1-delta*cos(2*3.14159*tau/period))')] - - transition = [ - Transition(origin='S', destination='E', equation='betaT*S*I/N', - transition_type=TransitionType.T), - Transition(origin='S', destination='E', equation='epsilon*S', - transition_type=TransitionType.T), - Transition(origin='E', destination='I', equation='alpha*E', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T), - Transition(origin='R', destination='S', equation='w*R', - transition_type=TransitionType.T) - ] - - bd_list = [ - Transition(origin='S', equation='mu*S', - transition_type=TransitionType.D), - Transition(origin='E', equation='mu*E', - transition_type=TransitionType.D), - Transition(origin='I', equation='mu*I', - transition_type=TransitionType.D), - Transition(origin='R', equation='mu*R', - transition_type=TransitionType.D), - Transition(origin='S', equation='mu*N', - transition_type=TransitionType.B), - Transition(origin='tau', equation='1', - transition_type=TransitionType.B) - ] - - ode_obj = SimulateOde(state, param_list, derived_param=derived_param, - transition=transition, - birth_death=bd_list) + ''' + SEIR model with vital dynamics, periodic infectivity, immune waning and + external introductions + ''' + state_list = [('S', (0,None)), ('E', (0,None)), ('I', (0, None)), ('R', (0, None)), ('N', (0, None))] + param_list = ['beta0', 'delta', 'period', 'alpha', 'gamma', 'mu', 'w', 'ar'] + derived_param = [('betaT', 'beta0*(1-delta*cos(2*3.14159*t/period))')] + + # Exposure, internal transmission + trans_exp=Transition(origin='S', destination='E',transition_type=TransitionType.T) + event_exp=Event(rate='betaT*S*I/N', transition_list=[trans_exp]) + + # Exposure, external attack rate (ar) + trans_exp_ext=Transition(origin='S', destination='E',transition_type=TransitionType.T) + event_exp_ext=Event(rate='S*ar', transition_list=[trans_exp_ext]) + + # Infectious + trans_inf=Transition(origin='E', destination='I',transition_type=TransitionType.T) + event_inf=Event(rate='alpha*E', transition_list=[trans_inf]) + + # Recovery + trans_rec=Transition(origin='I', destination='R',transition_type=TransitionType.T) + event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) + + # Waning + trans_wan=Transition(origin='R', destination='S',transition_type=TransitionType.T) + event_wan=Event(rate='w*R', transition_list=[trans_wan]) + + # Transitions in and out of total population count + # These will be used in the following event definitions + birth_N=Transition(destination="N", transition_type="B") + death_N=Transition(origin="N", transition_type="D") + + # 1) Birth event into S + birth=Transition(destination="S", transition_type="B") + event_birth=Event(transition_list=[birth, birth_N], rate='mu*N') + + # 2) Death event of an S + death_S=Transition(origin="S", transition_type="D") + event_death_S=Event(transition_list=[death_S, death_N], rate='mu*S') + + # 3) Death event of an E + death_E=Transition(origin="E", transition_type="D") + event_death_E=Event(transition_list=[death_E, death_N], rate='mu*E') + + # 4) Death event of an I + death_I=Transition(origin="I", transition_type="D") + event_death_I=Event(transition_list=[death_I, death_N], rate='mu*I') + + # 5) Death event of an R + death_R=Transition(origin="R", transition_type="D") + event_death_R=Event(transition_list=[death_R, death_N], rate='mu*R') + + model=SimulateOde(state=state_list, + param=param_list, + derived_param=derived_param, + event=[event_exp, + event_exp_ext, + event_inf, + event_rec, + event_wan, + event_birth, + event_death_S, + event_death_E, + event_death_I, + event_death_R]) if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj + model.parameters = param + return model def SEIR_Multiple(n=2, param=None): """ @@ -707,7 +627,7 @@ def SEIR_Multiple(n=2, param=None): ode_obj.parameters = param return ode_obj -def Influenza_SLIARN(param=None): +def Influenza_SLIARD(param=None): """ A simple influenza model from [Brauer2008]_, page 323. @@ -717,33 +637,59 @@ def Influenza_SLIARN(param=None): \\frac{dI}{dt} &= p \\kappa L - \\alpha I \\\\ \\frac{dA}{dt} &= (1 - p) \\kappa L - \\eta A \\\\ \\frac{dR}{dt} &= f \\alpha I + \\eta A \\\\ - \\frac{dN}{dt} &= -(1 - f) \\alpha I + \\frac{dD}{dt} &= (1 - f) \\alpha I """ - state = ['S', 'L', 'I', 'A', 'R', 'N'] - param_list = ['beta', 'p', 'kappa', 'alpha', 'f', 'delta', 'epsilon'] - ode = [ - Transition(origin='S', equation='-beta*S*(I + delta*A)', - transition_type=TransitionType.ODE), - Transition(origin='L', equation='beta*S*(I + delta*A) - kappa*L', - transition_type=TransitionType.ODE), - Transition(origin='I', equation='p*kappa*L - alpha*I', - transition_type=TransitionType.ODE), - Transition(origin='A', equation='(1 - p)*kappa*L - epsilon*A', - transition_type=TransitionType.ODE), - Transition(origin='R', equation='f*alpha*I + epsilon*A', - transition_type=TransitionType.ODE), - Transition(origin='N', equation='-(1 - f)*alpha*I', - transition_type=TransitionType.ODE) - ] - # initialize the model - ode_obj = SimulateOde(state, param_list, ode=ode) + + state_list = [('S', (0,None)), + ('L', (0,None)), + ('I', (0, None)), + ('A', (0, None)), + ('R', (0, None)), + ('D', (0, None))] + + param_list = ['beta', 'delta', 'N', 'kappa', 'p', 'epsilon', 'alpha', 'f'] + + # 1) Susceptibles enter latent phase through: + ## (i) Encounters with symptomatic infectious, I + trans_exp_I=Transition(origin='S', destination='L',transition_type=TransitionType.T) + event_exp_I=Event(rate='beta*S*I/N', transition_list=[trans_exp_I]) + ## (ii) Encounters with asymptomatic infectious, A + trans_exp_A=Transition(origin='S', destination='L',transition_type=TransitionType.T) + event_exp_A=Event(rate='beta*S*delta*A/N', transition_list=[trans_exp_A]) + # 2) Latent phase ends + ## (i) A fraction, p, go on to become symptomatic infectious, I + trans_inf_I=Transition(origin='L', destination='I',transition_type=TransitionType.T) + event_inf_I=Event(rate='p*kappa*L', transition_list=[trans_inf_I]) + ## (ii) The remaining (1-p) become asymptomatic infectious, A + trans_inf_A=Transition(origin='L', destination='A',transition_type=TransitionType.T) + event_inf_A=Event(rate='(1 - p)*kappa*L', transition_list=[trans_inf_A]) + # 3) All asymptomatics recover + trans_rec_A=Transition(origin='A', destination='R',transition_type=TransitionType.T) + event_rec_A=Event(rate='epsilon*A', transition_list=[trans_rec_A]) + # 4) For the symptomatics: + ## (i) A fraction, f, recover + trans_rec_I=Transition(origin='I', destination='R',transition_type=TransitionType.T) + event_rec_I=Event(rate='f*alpha*I', transition_list=[trans_rec_I]) + ## (ii) The remaining 1-f die + trans_death_I=Transition(origin='I', destination='D',transition_type=TransitionType.T) + event_death_I=Event(rate='(1-f)*alpha*I', transition_list=[trans_death_I]) + + model = SimulateOde(state=state_list, + param=param_list, + event=[event_exp_I, + event_exp_A, + event_inf_I, + event_inf_A, + event_rec_A, + event_rec_I, + event_death_I]) if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj + model.parameters = param + return model def Legrand_Ebola_SEIHFR(param=None): @@ -853,7 +799,6 @@ def Legrand_Ebola_SEIHFR(param=None): ode_obj.parameters = param return ode_obj - def Lotka_Volterra(param=None): """ Standard Lotka-Volterra model with two states and four parameters [Lotka1920]_ @@ -874,88 +819,191 @@ def Lotka_Volterra(param=None): >>> ode.plot() """ - # our two state and four parameters - state = ['x', 'y'] - # while these 4 are - param_list = ['alpha', 'beta', 'gamma', 'delta', 'A'] - # then define the set of ode - # ode = [ - # Transition(origin='x', equation='alpha*x - c*x*y', - # transition_type=TransitionType.ODE), - # Transition(origin='y', equation='-delta*y + gamma*x*y', - # transition_type=TransitionType.ODE) - # ] - # ode_obj = SimulateOde(state, param_list, ode=ode) - - # Defining via transitions allows us to solve stochastically too - birth_death = [ - Transition(origin='x', equation='alpha*x', - transition_type=TransitionType.B), - Transition(origin='x', equation='beta*x*y/A', - transition_type=TransitionType.D), - Transition(origin='y', equation='gamma*x*y/A', - transition_type=TransitionType.B), - Transition(origin='y', equation='delta*y', - transition_type=TransitionType.D) - ] + state_list = [('x', (0,None)), ('y', (0,None))] # x=prey, y=pred + param_list = ['alpha', 'beta', 'gamma', 'delta'] - # initialize the model - ode_obj = SimulateOde(state, - param_list, - birth_death=birth_death) + # 1) Birth of prey + birth_prey=Transition(destination="x", transition_type="B") + event_birth_prey=Event(transition_list=[birth_prey], rate='alpha*x') + # 2) Death of prey + death_prey=Transition(origin="x", transition_type="D") + event_death_prey=Event(transition_list=[death_prey], rate='beta*x*y') + + # 3) Birth of predator + birth_pred=Transition(destination="y", transition_type="B") + event_birth_pred=Event(transition_list=[birth_pred], rate='delta*x*y') + + # 4) Death of predator + death_pred=Transition(origin="y", transition_type="D") + event_death_pred=Event(transition_list=[death_pred], rate='gamma*y') + + model=SimulateOde(state=state_list, + param=param_list, + event=[event_birth_prey, + event_death_prey, + event_birth_pred, + event_death_pred]) - # set return, depending on whether we have input the parameters if param is None: - return ode_obj + return model else: - ode_obj.parameters = param - return ode_obj + model.parameters = param + return model + +# Doesn't seem like a very useful formulation. + +# def Lotka_Volterra_4State(param=None): +# """ +# The four state Lotka-Volterra model [Lotka1920]_. A common interpretation is that +# a = Grass, x = rabbits, y = foxes and b is the death of foxes. + +# .. math:: +# \\frac{da}{dt} &= k_{0} a x \\\\ +# \\frac{dx}{dt} &= k_{0} a x - k_{1} x y \\\\ +# \\frac{dy}{dt} &= k_{1} x y - k_{2} y \\\\ +# \\frac{db}{dt} &= k_{2} y + +# Examples +# -------- +# >>> import numpy as np +# >>> from pygom import common_models +# >>> x0 = [150.0, 10.0, 10.0, 0.0] +# >>> t = np.linspace(0, 15, 100) +# >>> params = [0.01, 0.1, 1.0] +# >>> ode = common_models.Lotka_Volterra_4State(params) +# >>> ode.initial_values = (x0, t[0]) +# >>> ode.integrate(t[1::]) +# >>> ode.plot() +# """ + +# state_list = ['a', 'x', 'y'] +# param_list = ['k0', 'k1', 'k2'] + +# # 1) Grass turning into rabbits +# trans_grazing=Transition(origin='a', destination='x',transition_type=TransitionType.T) +# event_grazing=Event(rate='k0*a*x', transition_list=[trans_grazing]) + +# # 2) Foxes eating rabbits +# trans_hunting=Transition(origin='x', destination='y',transition_type=TransitionType.T) +# event_hunting=Event(rate='k1*x*y', transition_list=[trans_hunting]) + +# # 3) Foxes natural death rate +# death_pred=Transition(origin="y", transition_type="D") +# event_death_pred=Event(transition_list=[death_pred], rate='k2*y') + +# model=SimulateOde(state=state_list, +# param=param_list, +# event=[event_birth_prey, +# event_death_prey, +# event_birth_pred, +# event_death_pred]) + +# if param is None: +# return model +# else: +# model.parameters = param +# return model + + +def Robertson(param=None): + """ + The so called Robertson problem [Robertson1966]_, which is a standard example used to + test stiff integrator. + + .. math:: + \\frac{dy_{1}}{dt} &= -0.04 y_{1} + 1 \\cdot 10^{4} y_{2} y_{3} \\\\ + \\frac{dy_{2}}{dt} &= 0.04 y_{1} - 1 \\cdot 10^{4} y_{2} y_{3} - 3 \\cdot 10^{7} y_{2}^{2}\\\\ + \\frac{dy_{3}}{dt} &= 3 \\cdot 10^{7} y_{2}^{2} + + Examples + -------- + + >>> from pygom import common_models + >>> import numpy + >>> t = numpy.append(0, 4*numpy.logspace(-6, 6, 1000)) + >>> ode = common_models.Robertson() + >>> ode.initial_values = ([1.0,0.0,0.0], t[0]) + >>> solution = ode.integrate(t[1::]) + >>> ode.plot() # note that this is not being plotted in the log scale + """ + # note how we have short handed the definition + state = ['y1:4'] + # note that we do not have any parameters, or rather, + # we have hard coded in the parameters + param_list = [] + + trans_1_2=Transition(origin='y1', destination='y2',transition_type=TransitionType.T) + event_1_2=Event(rate='0.04*y1', transition_list=[trans_1_2]) + + trans_2_1=Transition(origin='y2', destination='y1',transition_type=TransitionType.T) + event_2_1=Event(rate='1e4*y2*y3', transition_list=[trans_2_1]) + trans_2_3=Transition(origin='y2', destination='y3',transition_type=TransitionType.T) + event_2_3=Event(rate='3e7*y2*y2', transition_list=[trans_2_3]) -def Lotka_Volterra_4State(param=None): + # initialize the model + model = SimulateOde(state, param_list, event=[event_1_2, + event_2_1, + event_2_3]) + + if param is None: + return model + else: + raise Warning("Input parameters not used") + +############################################# +# ODEs +############################################# + + +def SIR_norm(param=None): """ - The four state Lotka-Volterra model [Lotka1920]_. A common interpretation is that - a = Grass, x = rabbits, y = foxes and b is the death of foxes. + A normalized SIR model: .. math:: - \\frac{da}{dt} &= k_{0} a x \\\\ - \\frac{dx}{dt} &= k_{0} a x - k_{1} x y \\\\ - \\frac{dy}{dt} &= k_{1} x y - k_{2} y \\\\ - \\frac{db}{dt} &= k_{2} y + \\frac{dS}{dt} &= -\\beta SI \\\\ + \\frac{dI}{dt} &= \\beta SI - \\gamma I \\\\ + \\frac{dR}{dt} &= \\gamma I + Examples -------- + The model that produced top two graph in Figure 1.3 of the reference above. + First, when everyone is susceptible and only one individual was infected. + >>> import numpy as np >>> from pygom import common_models - >>> x0 = [150.0, 10.0, 10.0, 0.0] - >>> t = np.linspace(0, 15, 100) - >>> params = [0.01, 0.1, 1.0] - >>> ode = common_models.Lotka_Volterra_4State(params) + >>> ode = common_models.SIR({'beta':3.6, 'gamma':0.2}) + >>> t = np.linspace(0, 730, 1001) + >>> N = 7781984.0 + >>> x0 = [1.0, 10/N, 0.0] >>> ode.initial_values = (x0, t[0]) - >>> ode.integrate(t[1::]) + >>> solution = ode.integrate(t[1::]) >>> ode.plot() - """ - # four states - state = ['a', 'x', 'y', 'b'] - # three parameters - param_list = ['k0', 'k1', 'k2'] + Second model with a more *realistic* scenario - # then define the set of ode - transition = [ - Transition(origin='a', destination='x', - equation='k0*a*x', - transition_type=TransitionType.T), - Transition(origin='x', destination='y', - equation='k1*x*y', - transition_type=TransitionType.T), - Transition(origin='y', destination='b', - equation='k2*y', - transition_type=TransitionType.T) - ] + >>> import numpy as np + >>> from pygom import common_models + >>> ode = common_models.SIR({'beta':3.6, 'gamma':0.2}) + >>> t = np.linspace(0, 730, 1001) + >>> N = 7781984.0 + >>> x0 = [0.065, 123*(5.0/30.0)/N, 0.0] + >>> ode.initial_values = (x0, t[0]) + >>> solution = ode.integrate(t[1::]) + >>> ode.plot() + + """ + state = ['S', 'I', 'R'] + param_list = ['beta', 'gamma'] + + dSdt=Transition(origin='S', equation='-beta*S*I', transition_type=TransitionType.ODE) + dIdt=Transition(origin='I', equation='beta*S*I-gamma*I', transition_type=TransitionType.ODE) + dRdt=Transition(origin='R', equation='gamma*I', transition_type=TransitionType.ODE) - ode_obj = SimulateOde(state, param_list, transition=transition) + # initialize the model + ode_obj = SimulateOde(state=state, param=param_list, ode=[dSdt, dIdt, dRdt]) # set return, depending on whether we have input the parameters if param is None: @@ -1103,49 +1151,3 @@ def vanDerPol(param=None): else: ode_obj.parameters = param return ode_obj - - -def Robertson(param=None): - """ - The so called Robertson problem [Robertson1966]_, which is a standard example used to - test stiff integrator. - - .. math:: - \\frac{dy_{1}}{dt} &= -0.04 y_{1} + 1 \\cdot 10^{4} y_{2} y_{3} \\\\ - \\frac{dy_{2}}{dt} &= 0.04 y_{1} - 1 \\cdot 10^{4} y_{2} y_{3} - 3 \\cdot 10^{7} y_{2}^{2}\\\\ - \\frac{dy_{3}}{dt} &= 3 \\cdot 10^{7} y_{2}^{2} - - Examples - -------- - - >>> from pygom import common_models - >>> import numpy - >>> t = numpy.append(0, 4*numpy.logspace(-6, 6, 1000)) - >>> ode = common_models.Robertson() - >>> ode.initial_values = ([1.0,0.0,0.0], t[0]) - >>> solution = ode.integrate(t[1::]) - >>> ode.plot() # note that this is not being plotted in the log scale - """ - # note how we have short handed the definition - state = ['y1:4'] - # note that we do not have any parameters, or rather, - # we have hard coded in the parameters - param_list = [] - transition = [ - Transition(origin='y1', destination='y2', - equation='0.04*y1', - transition_type=TransitionType.T), - Transition(origin='y2', destination='y1', - equation='1e4*y2*y3', - transition_type=TransitionType.T), - Transition(origin='y2', destination='y3', - equation='3e7*y2*y2', - transition_type=TransitionType.T) - ] - # initialize the model - ode_obj = SimulateOde(state, param_list, transition=transition) - - if param is None: - return ode_obj - else: - raise Warning("Input parameters not used") diff --git a/src/pygom/model/deterministic.py b/src/pygom/model/deterministic.py index 3fafc59c..84e1c3fe 100644 --- a/src/pygom/model/deterministic.py +++ b/src/pygom/model/deterministic.py @@ -8,6 +8,8 @@ __all__ = ['DeterministicOde'] +# TODO: check through these dependencies + import copy import io from numbers import Number @@ -19,17 +21,17 @@ from sympy.core.function import diff +from .transition import TransitionType + from .base_ode_model import BaseOdeModel from ._model_errors import ArrayError, InputError, \ IntegrationError, InitializeError -from ._model_verification import simplifyEquation +from ._model_verification import simplifyEquation, checkEquation from . import ode_utils -# from . import _ode_composition + from . import _transition_graph -class HasNewTransition(ode_utils.CompileCanary): - states = ['ode', 'Jacobian', 'diffJacobian', 'grad', 'GradJacobian'] class DeterministicOde(BaseOdeModel): ''' @@ -58,82 +60,58 @@ def __init__(self, param=None, derived_param=None, transition=None, + event=None, birth_death=None, ode=None): ''' Constructor that is built on top of a BaseOdeModel ''' - super(DeterministicOde, self).__init__(state, param, derived_param, transition, + event, birth_death, ode) - self._hasNewTransition = HasNewTransition() - self._ode = None - self._odeCompile = None - # and we assume initially that we don't want the Jacobian - self._Jacobian = None - self._JacobianCompile = None - # wtf... why! - self._diffJacobian = None - self._diffJacobianCompile = None - - # Information... yea, what else would you expect - self._Grad = None - self._GradCompile = None - # more information.... - self._GradJacobian = None - self._GradJacobianCompile = None - # More information!! ROAR! I think this is useless though - # because this is the hessian of the ode which most of the - # time we don't really care - self._Hessian = None - self._HessianWithParam = None + # # First, set up system of odes upon instance being initialised + # self.get_ode_eqn() + + # Tell pygom what it needs if it wants to compile + self.add_func("ode", self.get_ode_eqn, oT="vec", is_master_canary=True) + self.add_func("jacobian", self.get_jacobian_eqn) + self.add_func("diff_jacobian", self.get_diff_jacobian_eqn) + self.add_func("grad", self.get_grad_eqn, oT="mat") + self.add_func("grad_jacobian", self.get_grad_jacobian_eqn) + # TODO: update _Hessian and _HessianWithParam to this framework. + self._Hessian=None + self._HessianWithParam=None # all the symbols that we need in order to compile # s = state + t # sp = state + t + param # the latter is required to compile the symbolic code # to the numeric setting - self._s = self._stateList + [self._t] - self._sp = self._s + self._paramList - - # Calls to the autowrap method can't take ODEVariable class objects - # Better to convert the objects in self._sp back to sympy objects - # This code will convert any ODEVariable object in either the stateDict - # or paramDict dictonary - for i, item in enumerate(self._sp): - try: - self._sp[i] = self._stateDict[item.ID] - except Exception: - pass - try: - self._sp[i] = self._paramDict[item.ID] - except Exception: - pass + self.set_sp() + + self.verbose=False # information regarding the integration. We want an internal # storage so we can invoke the plot method within the same class + # TODO: unsure if this is necessary self._t0 = None self._x0 = None self._odeOutput = None self._odeSolution = None self._odeTime = None - self._intName = None - self._paramValue = [0]*len(self._paramList) + # the class for shape re-adjustment. We would always like to # operate in the matrix form if possible as it takes up less # memory when operating, but the output is required to be of # the vector form self._SAUtil = ode_utils.shapeAdjust(self.num_state, self.num_param) - # compile the code. Note that we need the class because we - # compile both the formatted and unformatted version. - self._SC = ode_utils.compileCode() def __eq__(self, other): if isinstance(other, DeterministicOde): @@ -147,7 +125,7 @@ def __eq__(self, other): def __repr__(self): return "DeterministicOde" + self._get_model_str() - ## Funcitons to allow pickling and unpickling + ## Funcitons to allow pickling and unpickling TODO: are these being utilised? def __getstate__(self): ''' Grab the class's dict and remove the compiled objects @@ -170,10 +148,131 @@ def __setstate__(self, state): ######################################################################## # - # Information about the ode + # Methods to add compiled functions + # + ######################################################################## + + def add_func(self, method_name, sympy_obj_generator_func, oT=None, is_master_canary=False): + ''' + Template to add a method, called with method_name, which gives the numerical output of + compiled_fn_name, which is the compiled version of the sympy object + generated by sympy_obj_generator_func. + This carries out the essential check to see if recompilation is necessary + and acts accordingly. + ''' + compiled_obj_name=method_name+"Compiled" + + def func(self, state, t): + # Check if compiled function is being created for the first time or + # corresponding canary is dead (True) indicating underlying ODE's have changed and + # we need to update both the sympy and compiled objects. + if not hasattr(self, compiled_obj_name) or getattr(self._hasNewTransition, method_name): + # Make new sympy object and compiled it + self.add_compiled_sympy_object(method_name, compiled_obj_name, sympy_obj_generator_func, oT, is_master_canary) + return getattr(self, compiled_obj_name)(time=t, state=state) + setattr(self, method_name, func.__get__(self)) + + def add_compiled_sympy_object(self, method_name, compiled_obj_name, sympy_obj_generator_func, oT, is_master_canary): + ''' + Take sympy_obj_generator_func + ''' + # Make the sympy object + sympy_obj=sympy_obj_generator_func() + + # Compile the sympy object + if self.verbose: + print("... Compiling sympy object with name:", method_name, "...", end="") + f = self._SC.compileExprAndFormat + if self._isDifficult: + compiled_obj=f(self._sp, + sympy_obj, + modules='mpmath', + outType=oT) + else: + compiled_obj=f(self._sp, + sympy_obj, + outType=oT) + if self.verbose: + print("done") + + # Wrap the compiled object + def comp_obj(state, time): + return compiled_obj(self._getEvalParam(state, time, None)) + + # Add this as an attribute in the right place + setattr(self, compiled_obj_name, comp_obj) + + # If all other objects depend on this one, kill all their canaries + # (set to True) to indicate something needs to be done. + if is_master_canary: + self._hasNewTransition.trip() + + # Replace the corresponding dead canary with a live one (True to False) + self._hasNewTransition.reset(method_name) + + ######################################################################## + # + # ODE functions (define/visualise etc...) # ######################################################################## + def get_ode_eqn(self): + ''' + Build the algebraic system of ODE's given the transitions and events. + ''' + # Containers for different contributions to ODE + between_state_ode = sympy.zeros(self.num_state, 1) + birth_death_ode = sympy.zeros(self.num_state, 1) + pure_ode = sympy.zeros(self.num_state, 1) + + # Extract all info from events + for event in self.event_list: + rate=checkEquation(event.rate, *self._getListOfVariablesDict()) + for transition in event.transition_list: + magnitude=checkEquation(transition._magnitude, *self._getListOfVariablesDict()) + rate_of_change=magnitude*rate + if transition.transition_type==TransitionType.B: + destination_index=self.state_list.index(transition.destination) + birth_death_ode[destination_index] += rate_of_change + elif transition.transition_type==TransitionType.D: + origin_index=self.state_list.index(transition.origin) + birth_death_ode[origin_index] -= rate_of_change + elif transition.transition_type==TransitionType.T: + origin_index=self.state_list.index(transition.origin) + destination_index=self.state_list.index(transition.destination) + between_state_ode[origin_index] -= rate_of_change + between_state_ode[destination_index] += rate_of_change + + # Now extract any ODE contributions from ODE type transitions + for ode in self.ode_list: + origin_index=self.state_list.index(ode.origin) + pure_ode[origin_index] += checkEquation(ode.equation, *self._getListOfVariablesDict()) + + # Collect together contributions and make attributes + self._ode = between_state_ode + birth_death_ode + pure_ode + self._birthDeathVector = birth_death_ode + + # # Set list of states and params + # # TODO: should this be handled externally? i.e. how does it know here if params change? + # # TODO: why iter lists here? + # self._s = [s for s in self._iterStateList()] + [self._t] + # self._sp = self._s + [p for p in self._iterParamList()] + + # tests to see whether we have an autonomous system. Need to + # convert a non-autonmous system into an autonomous. Note that + # we will not do the conversion internally and require the + # user to do this. May consider this a feature in the future. + # TODO: I think autonomous systems are allowed? Maybe not deterministically? + for i, eqn in enumerate(self._ode): + if self._t in eqn.atoms(): # TODO: maybe this check doesn't work anyway, for namespace reasons? + raise Exception("Input is a non-autonomous system. " + + "We can only deal with an autonomous " + + "system at this moment in time") + self._ode[i], isDifficult = simplifyEquation(eqn) + self._isDifficult = self._isDifficult or isDifficult + + return self._ode + # TODO: check and see whether it is linear correctly! def linear_ode(self): ''' @@ -189,12 +288,11 @@ def linear_ode(self): # scheme is a waste of time is_linear = True # if we do not current possess the jacobian, we find it! ROAR! - if self._Jacobian is None: - self.get_jacobian_eqn() + J=self.get_jacobian_eqn() # a really stupid way to determining whether it is linear. # have not figured out a better way yet... - a = self._Jacobian.atoms() + a = J.atoms() for s in self._stateDict.values(): if s in a: is_linear = False @@ -214,34 +312,11 @@ def linear_ode(self): # jacobian is actually singular, i.e. if it can be a DAE # def canDAE(self,x0,t0): - ######################################################################## - # - # Information about the ode - # - ######################################################################## - - def get_ode_eqn(self, param_sub=False): + def ode_T(self, t, state): ''' - Find the algebraic equations of the ode system. - - Returns - ------- - :class:`sympy.matrices.matrices` - ode in matrix form - + Same as :meth:`ode` but with t as the first parameter ''' - - if self._ode is None: - self._findOde() - elif self._hasNewTransition.ode: - self._findOde() - else: - pass - - if param_sub: - return self._ode.subs(self._parameters) - else: - return self._ode + return self.ode(state, t) def print_ode(self, latex_output=False): ''' @@ -267,68 +342,6 @@ def print_ode(self, latex_output=False): else: sympy.pretty_print(B) - def _findOde(self): - # lets see how we have defined our ode - # if it is explicit, then we go straight to the easy case - if self._explicitOde: - # we have explicit ode and we should obtain them directly - super(DeterministicOde, self)._computeOdeVector() - else: - # super(DeterministicOde, self)._computeTransitionMatrix() - # super(DeterministicOde, self)._computeTransitionVector() - # convert the transition matrix into the set of ode - self._ode = sympy.zeros(self.num_state, 1) - pureTransitionList = self._getAllTransition(pureTransitions=True) - fromList, \ - to, \ - eqn = self._unrollTransitionList(pureTransitionList) - for i, eqn in enumerate(eqn): - for k in fromList[i]: - self._ode[k] -= eqn - for k in to[i]: - self._ode[k] += eqn - - # now we just need to add in the birth death processes - super(DeterministicOde, self)._computeBirthDeathVector() - self._ode += self._birthDeathVector - - self._s = [s for s in self._iterStateList()] + [self._t] - self._sp = self._s + [p for p in self._iterParamList()] - - # tests to see whether we have an autonomous system. Need to - # convert a non-autonmous system into an autonomous. Note that - # we will not do the conversion internally and require the - # user to do this. May consider this a feature in the future. - for i, eqn in enumerate(self._ode): - if self._t in eqn.atoms(): - raise Exception("Input is a non-autonomous system. " + - "We can only deal with an autonomous " + - "system at this moment in time") - - self. _ode[i], isDifficult = simplifyEquation(eqn) - self._isDifficult = self._isDifficult or isDifficult - - if self._isDifficult: - self._odeCompile = self._SC.compileExprAndFormat(self._sp, - self._ode, - modules='mpmath', - outType="vec") - else: - self._odeCompile = self._SC.compileExprAndFormat(self._sp, - self._ode, - outType="vec") - # assign None to all others because we have reset the set of equations. - self._hasNewTransition.trip() - self._Grad = None - self._Hessian = None - self._Jacobian = None - self._diffJacobian = None - - # happy! - self._hasNewTransition.reset('ode') - - return self._ode - def get_transition_graph(self, file_name=None, show=True): ''' Returns the transition graph using graphviz @@ -356,76 +369,10 @@ def get_transition_graph(self, file_name=None, show=True): else: return dot - # - # this is the main ode solver - # - def ode(self, state, t): - ''' - Evaluate the ode given state and time - - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time - - Returns - ------- - :class:`numpy.ndarray` - output of the same length as the ode - - ''' - return self.eval_ode(time=t, state=state) - - def ode_T(self, t, state): - ''' - Same as :meth:`ode` but with t as the first parameter - ''' - return self.ode(state, t) - - def eval_ode(self, parameters=None, time=None, state=None): - """ - Evaluate the ode given time, state and parameters. An extension - of :meth:`ode` but now also include the parameters. - - Parameters - ---------- - parameters: list - see :meth:`.parameters` - time: numeric - The current time - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - output of the same length as the ode. - - Notes - ----- - There are differences between the output of this function and - :meth:`.ode`. Name and order of state and time are also - different. - - See Also - -------- - :meth:`.ode` - - """ - if self._ode is None or self._hasNewTransition.ode: - self.get_ode_eqn() - - eval_param = self._getEvalParam(state, time, parameters) - return self._odeCompile(eval_param) - ######################################################################## # - # jacobian related operations + # Jacobian related operations # ######################################################################## @@ -479,38 +426,6 @@ def jacobian_eigenvalue(self, state=None, t=None): return scipy.linalg.eig(J)[0] - def jacobian(self, state, t): - ''' - Evaluate the jacobian given state and time - - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time - - Returns - ------- - :class:`numpy.ndarray` - Matrix of dimension [number of state x number of state] - - ''' - return self.eval_jacobian(time=t, state=state) - - def jacobian_T(self, t, state): - ''' - Same as :meth:`jacobian` but with t as first parameter - ''' - return self.jacobian(state, t) - - def _Jacobian_NoCheck(self, state, t): - return self._evalJacobian_NoCheck(time=t, state=state) - - def _JacobianT_NoCheck(self, t, state): - return self._Jacobian_NoCheck(state, t) - def get_jacobian_eqn(self): ''' Returns the jacobian in algebraic form @@ -521,73 +436,21 @@ def get_jacobian_eqn(self): A matrix of dimension [number of state x number of state] ''' - if self._Jacobian is None: - self.get_ode_eqn() - states = [s for s in self._iterStateList()] - self._Jacobian = self._ode.jacobian(states) - for i in range(self.num_state): - for j in range(self.num_state): - eqn = self._Jacobian[i,j] - if eqn != 0: - self._Jacobian[i,j], isDifficult = simplifyEquation(eqn) - self._isDifficult = self._isDifficult or isDifficult - - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._JacobianCompile = f(self._sp, - self._Jacobian, - modules='mpmath') - else: - self._JacobianCompile = f(self._sp, - self._Jacobian) - - self._hasNewTransition.reset('Jacobian') + + self.get_ode_eqn() + states = [s for s in self._iterStateList()] + self._Jacobian = self._ode.jacobian(states) + + # Process output: (1) check if "difficult" and (2) simplify + for i in range(self.num_state): + for j in range(self.num_state): + eqn = self._Jacobian[i,j] + if eqn != 0: + self._Jacobian[i,j], isDifficult = simplifyEquation(eqn) + self._isDifficult = self._isDifficult or isDifficult return self._Jacobian - def eval_jacobian(self, parameters=None, time=None, state=None): - ''' - Evaluate the jacobian given parameters, state and time. An extension - of :meth:`.jacobian` but now also include the parameters. - - Parameters - ---------- - parameters: list - see :meth:`.parameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] - - Notes - ----- - Name and order of state and time are also different. - - See Also - -------- - :meth:`.jacobian` - - ''' - if self._Jacobian is None or self._hasNewTransition.Jacobian: - #self.get_ode_eqn() - self.get_jacobian_eqn() - - eval_param = self._getEvalParam(state, time, parameters) - return self._JacobianCompile(eval_param) - - def _evalJacobian_NoCheck(self, time, state): - ''' - Same as :meth:`eval_jacobian` but without the checks - ''' - eval_param = list(state) + [time] + self._paramValue - return self._JacobianCompile(eval_param) - ###### the sum of jacobian, i.e a_{i} = \sum_{j=1}^{d} J_{i,j} def sens_jacobian_state(self, state_param, t): @@ -617,12 +480,6 @@ def sens_jacobian_state(self, state_param, t): return self.eval_sens_jacobian_state(time=t, state=state, sens=sens) - def sens_jacobian_state_T(self, t, state): - ''' - Same as :meth:`sens_jacobian_state_T` but with t as first parameter - ''' - return self.sens_jacobian_state(state, t) - def eval_sens_jacobian_state(self, time=None, state=None, sens=None): ''' Evaluate the jacobian of the sensitivities w.r.t the states given @@ -666,32 +523,6 @@ def eval_sens_jacobian_state(self, time=None, state=None, sens=None): ############################## derivative of jacobian - def diff_jacobian(self, state, t): - ''' - Evaluate the differential of jacobian given state and time - - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time - - Returns - ------- - :class:`numpy.ndarray` - Matrix of dimension [number of state x number of state] - - ''' - return self.eval_diff_jacobian(time=t, state=state) - - def diff_jacobian_T(self, t, state): - ''' - Same as :meth:`diff_jacobian` but with t as first parameter - ''' - return self.diff_jacobian(state, t) - def get_diff_jacobian_eqn(self): ''' Returns the jacobian differentiate w.r.t. states in algebraic form @@ -704,78 +535,57 @@ def get_diff_jacobian_eqn(self): [number of state x number of state] ''' - if self._diffJacobian is None: - self.get_ode_eqn() - diffJac = list() - - for eqn in self._ode: - J = sympy.zeros(self.num_state, self.num_state) - for i, si in enumerate(self._iterStateList()): - diffEqn, D1 = simplifyEquation(diff(eqn, si, 1)) - for j, sj in enumerate(self._iterStateList()): - J[i,j], D2 = simplifyEquation(diff(diffEqn, sj, 1)) - self._isDifficult = self._isDifficult or D1 or D2 - #binding. - diffJac.append(J) - - # extract first matrix as base. we have to get the first element - # as base if we want to use the class method of the object - diffJacMatrix = diffJac[0] - for i in range(1, len(diffJac)): - # sympy internal matrix joining - diffJacMatrix = diffJacMatrix.col_join(diffJac[i]) - - self._diffJacobian = copy.deepcopy(diffJacMatrix) - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._diffJacobianCompile = f(self._sp, - self._diffJacobian, - modules='mpmath') - else: - self._diffJacobianCompile = f(self._sp, - self._diffJacobian) + self.get_ode_eqn() + diffJac = list() + + for eqn in self._ode: + J = sympy.zeros(self.num_state, self.num_state) + for i, si in enumerate(self._iterStateList()): + diffEqn, D1 = simplifyEquation(diff(eqn, si, 1)) + for j, sj in enumerate(self._iterStateList()): + J[i,j], D2 = simplifyEquation(diff(diffEqn, sj, 1)) + self._isDifficult = self._isDifficult or D1 or D2 + #binding. + diffJac.append(J) - self._hasNewTransition.reset('diffJacobian') + # extract first matrix as base. we have to get the first element + # as base if we want to use the class method of the object + diffJacMatrix = diffJac[0] + for i in range(1, len(diffJac)): + # sympy internal matrix joining + diffJacMatrix = diffJacMatrix.col_join(diffJac[i]) + + self._diffJacobian = copy.deepcopy(diffJacMatrix) return self._diffJacobian + + # Some additional maybe not necessary functions.... - def eval_diff_jacobian(self, parameters=None, time=None, state=None): + def jacobian_T(self, t, state): + ''' + Same as :meth:`jacobian` but with t as first parameter ''' - Evaluate the differential of the jacobian given parameters, - state and time. An extension of :meth:`.diff_jacobian` but now - also include the parameters. + return self.jacobian(state, t) - Parameters - ---------- - parameters: list - see :meth:`.parameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` + def _Jacobian_NoCheck(self, state, t): + return self._evalJacobian_NoCheck(time=t, state=state) - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] + def _JacobianT_NoCheck(self, t, state): + return self._Jacobian_NoCheck(state, t) - Notes - ----- - Name and order of state and time are also different. - - See Also - -------- - :meth:`.jacobian` + def sens_jacobian_state_T(self, t, state): + ''' + Same as :meth:`sens_jacobian_state_T` but with t as first parameter + ''' + return self.sens_jacobian_state(state, t) + def diff_jacobian_T(self, t, state): + ''' + Same as :meth:`diff_jacobian` but with t as first parameter ''' - if self._diffJacobian is None or self._hasNewTransition.diffJacobian: - #self.get_ode_eqn() - self.get_diff_jacobian_eqn() + return self.diff_jacobian(state, t) - eval_param = self._getEvalParam(state, time, parameters) - return self._diffJacobianCompile(eval_param) ######################################################################## # @@ -793,95 +603,26 @@ def get_grad_eqn(self): A matrix of dimension [number of state x number of parameters] ''' - # finds - if self._Grad is None: - ode = self.get_ode_eqn() - self._Grad = sympy.zeros(self.num_state, self.num_param) - - for i in range(self.num_state): - # need to adjust such that the first index is not - # included because it correspond to time - for j, p in enumerate(self._iterParamList()): - eqn, isDifficult = simplifyEquation(diff(ode[i], p, 1)) - self._Grad[i,j] = eqn - self._isDifficult = self._isDifficult or isDifficult + ode = self.get_ode_eqn() + self._Grad = sympy.zeros(self.num_state, self.num_param) - if self._isDifficult: - self._GradCompile = self._SC.compileExprAndFormat(self._sp, - self._Grad, - modules='mpmath', - outType="mat") - else: - self._GradCompile = self._SC.compileExprAndFormat(self._sp, - self._Grad, - outType="mat") - self._hasNewTransition.reset('grad') + for i in range(self.num_state): + # need to adjust such that the first index is not + # included because it correspond to time + for j, p in enumerate(self._iterParamList()): + eqn, isDifficult = simplifyEquation(diff(ode[i], p, 1)) + self._Grad[i,j] = eqn + self._isDifficult = self._isDifficult or isDifficult return self._Grad - def grad(self, state, time): - """ - Evaluate the gradient given state and time - - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: numeric - The current time - - Returns - ------- - :class:`numpy.ndarray` - Matrix of dimension [number of state x number of parameters] - - """ - return self.eval_grad(state=state, time=time) - def grad_T(self, t, state): ''' Same as :meth:`grad_T` but with t as first parameter ''' return self.grad(state, t) - def eval_grad(self, parameters=None, time=None, state=None): - ''' - Evaluate the gradient given parameters, state and time. An extension - of :meth:`grad` but now also include the parameters. - - Parameters - ---------- - parameters: list - see :meth:`.parameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] - - Notes - ----- - Name and order of state and time are also different. - - See Also - -------- - :meth:`.grad` - - ''' - if self._Grad is None or self._hasNewTransition.grad: - #self.get_ode_eqn() - self.get_grad_eqn() - - eval_param = self._getEvalParam(state, time, parameters) - return self._GradCompile(eval_param) - # # jacobian of the Gradiant # @@ -901,99 +642,26 @@ def get_grad_jacobian_eqn(self): :meth:`.get_grad_eqn` ''' - if self._GradJacobian is None: - self._GradJacobian = sympy.zeros(self.num_state*self.num_param, - self.num_state) - G = self.get_grad_eqn() - for k in range(0, self.num_param): - for i in range(0, self.num_state): - for j, s in enumerate(self._iterStateList()): - z = k*self.num_state + i - eqn, isDifficult = simplifyEquation(diff(G[i,k], s, 1)) - self._GradJacobian[z,j] = eqn - self._isDifficult = self._isDifficult or isDifficult - # end of the triple loop. All elements are now filled - - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._GradJacobianCompile = f(self._sp, - self._GradJacobian, - modules='mpmath') - else: - self._GradJacobianCompile = f(self._sp, - self._GradJacobian) - - self._hasNewTransition.reset('GradJacobian') + self._GradJacobian = sympy.zeros(self.num_state*self.num_param, + self.num_state) + G = self.get_grad_eqn() + for k in range(0, self.num_param): + for i in range(0, self.num_state): + for j, s in enumerate(self._iterStateList()): + z = k*self.num_state + i + eqn, isDifficult = simplifyEquation(diff(G[i,k], s, 1)) + self._GradJacobian[z,j] = eqn + self._isDifficult = self._isDifficult or isDifficult + # end of the triple loop. All elements are now filled return self._GradJacobian - def grad_jacobian(self, state, time): - """ - Evaluate the Jacobian of the gradient given state and time - - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: numeric - The current time - - Returns - ------- - :class:`numpy.ndarray` - Matrix of dimension [number of state x number of parameters] - - See also - -------- - :meth:`.grad` - - """ - return self.eval_grad_jacobian(state=state, time=time) - def grad_jacobianT(self, t, state): ''' Same as :meth:`grad_jacobian` but with t as first parameter ''' return self.grad_jacobian(state, t) - def eval_grad_jacobian(self, parameters=None, time=None, state=None): - ''' - Evaluate the jacobian of the gradient given parameters, - state and time. An extension of :meth:`.grad_jacobian` - but now also include the parameters. - - Parameters - ---------- - parameters: list - see :meth:`.parameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] - - Notes - ----- - Name and order of state and time are also different. - - See Also - -------- - :meth:`.grad_jacobian`, :meth:`.get_grad_jacobian_eqn` - - ''' - if self._GradJacobian is None or self._hasNewTransition.GradJacobian: - #self.get_ode_eqn() - self.get_grad_jacobian_eqn() - - eval_param = self._getEvalParam(state, time, parameters) - return self._GradJacobianCompile(eval_param) - ######################################################################## # # hessian related operations @@ -1123,288 +791,338 @@ def _computeHessianParam(self): ######################################################################## # - # Sensitivity related operations (1st forward) + # Initial conditions, integrations and result plots # ######################################################################## - def sensitivity(self, sens, t, state, by_state=False): - """ - Evaluate the sensitivity given state and time. The default is to - output the values by parameters, i.e. :math:`s_{i},\\ldots,s_{i+n}` are - partial derivatives w.r.t. the states for - :math:`i \\in {1,1+p,1+2p,1+3p, \\ldots, 1+(n-1)p}`. This is - to take advantage of the fact that we have a block diagonal - jacobian that was already evaluated + @property + def initial_state(self): + ''' + Return the initial state values + ''' + return self._x0 + + @initial_state.setter + def initial_state(self, x0): + ''' + Set the initial state values Parameters ---------- - sens: array like - The starting sensitivity of size [number of state x number of - parameters]. Which are normally zero or one, - depending on whether the initial conditions are also variables. - t: double - The current time - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - by_state: bool - how we want the output to be arranged. Default is True so - that we have a block diagonal structure + x0: array like + initial condition of x at time 0 - Returns - ------- - :class:`numpy.ndarray` - """ - # TODO: allows the functionality to not evaluate all sensitivity + ''' + err_str = "More than one state in the defined system" - # S = \nabla_{time} \frac{\partial State}{\partial Parameters} - # rearrange the input if required - if by_state: - S = np.reshape(sens, (self.num_state, self.num_param)) + if isinstance(x0, np.ndarray): + self._x0 = x0 + elif isinstance(x0, (list, tuple)): + self._x0 = np.array(x0) + elif isinstance(x0, (int, float)): + if self.num_state == 1: + self._x0 = np.array([x0]) + else: + raise InitializeError(err_str) else: - S = self._SAUtil.vecToMatSens(sens) + raise InitializeError("err_str") - return self.eval_sensitivity(S=S, t=t, state=state, by_state=by_state) + if len(self._x0) != self.num_state: + raise Exception("Number of state is " + + str(self.num_state)+ " but " + + str(len(self._x0))+ " detected") - def sensitivity_T(self, t, sens, state, by_state=False): + @property + def initial_time(self): ''' - Same as :meth:`sensitivity` but with t as first parameter + Return the initial time ''' - return self.sensitivity(sens, t, state, by_state) + return self._t0 - def eval_sensitivity(self, S, t, state, by_state=False): - """ - Evaluate the sensitivity given state and time + @initial_time.setter + def initial_time(self, t0): + ''' + Set the initial time Parameters ---------- - S: array like - Which should be :class:`numpy.ndarray`. - The starting sensitivity of size [number of state x number of - parameters]. Which are normally zero or one, - depending on whether the initial conditions are also variables. - t: double - The current time - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - by_state: bool - how we want the output to be arranged. Default is True so - that we have a block diagonal structure - - Returns - ------- - :class:`numpy.ndarray` - - Notes - ----- - It is different to :meth:`.eval_ode` and :meth:`.eval_jacobian` in - that the extra input argument is not a parameter - - See Also - -------- - :meth:`.sensitivity` - - """ + t0: numeric + initial time where x0 is observed - # jacobian * sensitivities + G - # where G is the gradient - J = self.jacobian(state, t) - G = self.grad(state, t) - A = np.dot(J, S) + G + ''' - if by_state: - return np.reshape(A, self.num_state*self.num_param) + err_str = "Initial time should be a " + if isinstance(t0, Number): + self._t0 = t0 + elif ode_utils.is_list_like(t0): + if len(t0) == 1: + if isinstance(t0[0], Number): + self._t0 = t0[0] + else: + raise InitializeError(err_str + "numeric value") + else: + raise InitializeError(err_str + "single value") + elif isinstance(t0, (list, tuple)): + if len(t0) == 1: + self._t0 = np.array(t0[0]) + else: + raise InitializeError(err_str + "single value") else: - return self._SAUtil.matToVecSens(A) + raise InitializeError(err_str + "numeric value") - def ode_and_sensitivity(self, state_param, t, by_state=False): + @property + def initial_values(self): ''' - Evaluate the sensitivity given state and time + Returns the initial values, both time and state as a tuple (x0, t0) + ''' + return (self.initial_state, self.initial_time) + + @initial_values.setter + def initial_values(self, x0t0): + ''' + Set the initial values, both time and state Parameters ---------- - state_param: array like - The current numerical value for the states as well as the - sensitivities values all in one. We assume that the state - values comes first. - t: double - The current time - by_state: bool - Whether the output vector should be arranged by state or by - parameters. If False, then it means that the vector of output is - arranged according to looping i,j from Sensitivity_{i,j} with i - being the state and j the param. This is the preferred way because - it leds to a block diagonal Jacobian + x0t0: array like + initial condition of x at time t and the initial time t where x + is observed + ''' + assert len(x0t0) == 2, "Initial values require (x0, t0)" + self.initial_state = x0t0[0] + self.initial_time = x0t0[1] - Returns - ------- - :class:`list` - concatenation of 2 element. First contains the ode, second the - sensitivity. Both are of type :class:`numpy.ndarray` + def integrate(self, t, full_output=False): + ''' + Integrate over a range of t when t is an array and a output at time t - See Also - -------- - :meth:`.sensitivity`, :meth:`.ode` + Parameters + ---------- + t: array like + the range of time points which we want to see the result of + full_output: bool + if we want additional information + ''' + # type checking + self._setIntegrateTime(t) + # if our parameters are stochastic, then we are going to generate + # another set of parameters to run + if self._stochasticParam is not None: + # this should always be true. If not, then we have screwed up + # somewhere within this class. + if isinstance(self._stochasticParam, dict): + self.parameters = self._stochasticParam + return self._integrate(self._odeTime, full_output) + + def integrate2(self, t, full_output=False, method=None): ''' + Integrate over a range of t when t is an array and a output + at time t. Select a suitable method to integrate when + method is None. - if len(state_param) == self.num_state: - raise InputError("You have only inputed the initial condition " + - "for the states and not the sensitivity") + Parameters + ---------- + t: array like + the range of time points which we want to see the result of + full_output: bool + if we want additional information + method: str, optional + the integration method. All those available in + :class:`ode ` are allowed with 'vode' + and 'ivode' representing the non-stiff and stiff version + respectively. Defaults to None, which tries to choose the + integration method via eigenvalue analysis (only one) using + the initial conditions + ''' - # unrolling, assuming that we would always put the state first - # there is no safety checks on this because it is impossible to - # distinguish what is state and what is sensitivity as they are - # all numeric value that can take the full range (-\infty,\infty) - state = state_param[0:self.num_state] - sens = state_param[self.num_state::] + self._setIntegrateTime(t) + # if our parameters are stochastic, then we are going to generate + # another set of parameters to run + if self._stochasticParam is not None: + # this should always be true + if isinstance(self._stochasticParam, dict): + self.parameters = self._stochasticParam - out1 = self.ode(state, t) - out2 = self.sensitivity(sens, t, state, by_state) - return np.append(out1, out2) + return self._integrate2(self._odeTime, full_output, method) - def ode_and_sensitivity_T(self, t, state_param, by_state=False): + def _setIntegrateTime(self, t): ''' - Same as :meth:`ode_and_sensitivity` but with t as first parameter + Set the full set of integration time including the origin ''' - return self.ode_and_sensitivity(state_param, t, by_state) - def ode_and_sensitivity_jacobian(self, state_param, t, by_state=False): + assert self._t0 is not None, "Initial time not set" + + if ode_utils.is_list_like(t): + if isinstance(t[0], Number): + t = np.append(self._t0, t) + else: + raise ArrayError("Expecting a list of numeric value") + elif isinstance(t, Number): + t = np.append(self._t0, np.array(t)) + else: + raise ArrayError("Expecting an array like input or a single " + + "numeric value") + + self._odeTime = t + + def _integrate(self, t, full_output=True): ''' - Evaluate the sensitivity given state and time. Output a block - diagonal sparse matrix as default. + Integrate using :class:`scipy.integrate.odeint` underneath + ''' + assert self._t0 is not None, "Initial time not set" - Parameters - ---------- - state_param: array like - The current numerical value for the states as well as the - sensitivities values all in one. We assume that the state - values comes first. - t: double - The current time - by_state: bool - How the output is arranged, according to the vector of output. - It can be in terms of state or parameters, where by state means - that the jacobian is a block diagonal matrix. + f = ode_utils.integrate + self._odeSolution, self._odeOutput = f(self, + self._x0, + t, + full_output=True) + if full_output: + return self._odeSolution, self._odeOutput + else: + return self._odeSolution - Returns - ------- - :class:`numpy.ndarray` - output of a square matrix of size: number of ode + 1 times number - of parameters + def _integrate2(self, t, full_output=True, method=None): + ''' + Integrate using :class:`scipy.integrate.ode` underneath + ''' + assert self._x0 is not None, "Initial state not set" - See Also - -------- - :meth:`.ode_and_sensitivity` + f = ode_utils.integrateFuncJac + self._odeSolution, self._odeOutput = f(self.ode_T, + self.jacobian_T, + self._x0, + t[0], t[1::], + includeOrigin=True, + full_output=True, + method=method) + if full_output: + return self._odeSolution, self._odeOutput + else: + return self._odeSolution + + def plot(self): ''' + Plot the results of the integration - if len(state_param) == self.num_state: - raise InputError("Expecting both the state and the sensitivities") + Notes + ----- + If we have 3 states or more, it will always be arrange such + that it has 3 columns. Uses the operation from + :mod:`odeutils` + ''' + + # just need to make sure that we have + # already gotten the solution to the integration + if self._odeSolution is None: + try: + self._integrate(self._odeTime) + ode_utils.plot_det(self._odeSolution, self._odeTime, self._stateList) + except: + raise IntegrationError("Have not performed the integration yet") else: - state = state_param[0:self.num_state] + ode_utils.plot_det(self._odeSolution, self._odeTime, self._stateList) - # now we start the computation - J = self.jacobian(state, t) - # create the block diagonal Jacobian, assuming that whoever is - # calling this function wants it arranges by state-parameters + ######################################################################## + # Unrolling of the information from vector to sympy + # t + # state + ######################################################################## - # Note that none of the ode integrator in scipy allow a sparse Jacobian - # matrix. All of them accept a banded matrix in packed format but not - # an actual sparse, or specifying the number of bands. - outJ = np.kron(np.eye(self.num_param), J) - # Jacobian of the gradient - GJ = self.grad_jacobian(state, t) - # and now we add the gradient - sensJacobianOfState = GJ + self.sens_jacobian_state(state_param, t) + def _addTimeEvalParam(self, eval_param, t): + eval_param.append((self._t, t)) + return eval_param - if by_state: - arrangeVector = np.zeros(self.num_state * self.num_param) - k = 0 - for j in range(0, self.num_param): - for i in range(0, self.num_state): - if i == 0: - arrangeVector[k] = (i*self.num_state) + j - else: - arrangeVector[k] = (i*(self.num_state - 1)) + j - k += 1 + def _addStateEvalParam(self, eval_param, state): + super(DeterministicOde, self).state = state + if self._state is not None: + eval_param += self._state - outJ = outJ[np.array(arrangeVector,int),:] - idx = np.array(arrangeVector, int) - sensJacobianOfState = sensJacobianOfState[idx,:] - # The Jacobian of the ode, then the sensitivities w.r.t state and - # the sensitivities. In block form. Theoretically, only the diagonal - # blocks are important but we output the full matrix for completeness - return np.asarray(np.bmat([ - [J, np.zeros((self.num_state, self.num_state*self.num_param))], - [sensJacobianOfState, outJ] - ])) + return eval_param - def ode_and_sensitivity_jacobian_T(self, t, state_param, by_state=False): - ''' - Same as :meth:`ode_and_sensitivity_jacobian` but with t as - first parameter - ''' - return self.ode_and_sensitivity_jacobian(state_param, t, by_state) + def _getEvalParam(self, state, time, parameters): + if state is None or time is None: + raise InputError("Have to input both state and time") + + if parameters is not None: + self.parameters = parameters + elif not hasattr(self, "_parameters") or self._parameters is None: + #elif self._parameters is None: + if self.num_param == 0: + pass + else: + raise InputError("Have not set the parameters yet") + + if isinstance(state, list): + eval_param = state + [time] + elif hasattr(state, '__iter__'): + eval_param = list(state) + [time] + else: + eval_param = [state] + [time] + + return eval_param + self._paramValue + + + + # TODO: half of this class is sensitivity related functions + # we are probably better off defininig these elsewhere + # bu that's a task for another day. ######################################################################## # - # Include initial value as parameters. Sensitivity related operations - # (1st forward) + # Sensitivity related operations (1st forward) # ######################################################################## - def sensitivityIV(self, sensIV, t, state): + def sensitivity(self, sens, t, state, by_state=False): """ - Evaluate the sensitivity which include the initial values as - our parameters given state and time. The default is to + Evaluate the sensitivity given state and time. The default is to output the values by parameters, i.e. :math:`s_{i},\\ldots,s_{i+n}` are partial derivatives w.r.t. the states for - :math:`i \\in {1,1+p,1+2p,1+3p, \\ldots, 1+(n-1)p}`. This is to take - advantage of the fact that we have a block diagonal Jacobian that was - already evaluated. + :math:`i \\in {1,1+p,1+2p,1+3p, \\ldots, 1+(n-1)p}`. This is + to take advantage of the fact that we have a block diagonal + jacobian that was already evaluated Parameters ---------- - sensIV: array like + sens: array like The starting sensitivity of size [number of state x number of - parameters] + [number of state x number of state] for the - initial condition. The latter is an identity matrix at time zero. + parameters]. Which are normally zero or one, + depending on whether the initial conditions are also variables. t: double The current time state: array like The current numerical value for the states which can be :class:`numpy.ndarray` or :class:`list` + by_state: bool + how we want the output to be arranged. Default is True so + that we have a block diagonal structure Returns ------- :class:`numpy.ndarray` - output of the same length as the ode - """ + # TODO: allows the functionality to not evaluate all sensitivity - nS = self.num_state - nP = self.num_param - # separate information out. Again, we do have not have checks here - # as it will be impossible to distinguish what is correct - sens = sensIV[:(nS*nP)] - S = self._SAUtil.vecToMatSens(sens) - - IV = np.reshape(sensIV[-(nS*nS):], (nS, nS), 'F') + # S = \nabla_{time} \frac{\partial State}{\partial Parameters} + # rearrange the input if required + if by_state: + S = np.reshape(sens, (self.num_state, self.num_param)) + else: + S = self._SAUtil.vecToMatSens(sens) - return self.eval_sensitivityIV(S=S, IV=IV, t=t, state=state) + return self.eval_sensitivity(S=S, t=t, state=state, by_state=by_state) - def sensitivityIV_T(self, t, sensIV, state): + def sensitivity_T(self, t, sens, state, by_state=False): ''' - Same as :meth:`sensitivityIV` but with t as first parameter + Same as :meth:`sensitivity` but with t as first parameter ''' - return self.sensitivityIV(sensIV, t, state) + return self.sensitivity(sens, t, state, by_state) - def eval_sensitivityIV(self, S, IV, t, state): + def eval_sensitivity(self, S, t, state, by_state=False): """ - Evaluate the sensitivity with initial values given - state and time + Evaluate the sensitivity given state and time Parameters ---------- @@ -1413,47 +1131,42 @@ def eval_sensitivityIV(self, S, IV, t, state): The starting sensitivity of size [number of state x number of parameters]. Which are normally zero or one, depending on whether the initial conditions are also variables. - IV: array like - sensitivities for the initial values t: double The current time state: array like The current numerical value for the states which can be :class:`numpy.ndarray` or :class:`list` + by_state: bool + how we want the output to be arranged. Default is True so + that we have a block diagonal structure Returns ------- :class:`numpy.ndarray` - :math:`f(s(x,\\theta))` and :math:`f(s(x_{0}))` Notes ----- It is different to :meth:`.eval_ode` and :meth:`.eval_jacobian` in - that the extra input argument is not a parameter. + that the extra input argument is not a parameter See Also -------- - :meth:`.sensitivityIV` + :meth:`.sensitivity` """ + # jacobian * sensitivities + G # where G is the gradient - # Evidently, A below uses the same operations as - # A = self.eval_sensitivity(S,t,state) - # but we are evaluating them explicitly here because - # we will be using J as well when computing B - J = self.jacobian(state, t) G = self.grad(state, t) A = np.dot(J, S) + G - # and jacobian * sensitivities of the initial condition - B = np.dot(J, IV) - - # we want to output by parameters - return self._SAUtil.matToVecSens(A), B.flatten('F') + if by_state: + return np.reshape(A, self.num_state*self.num_param) + else: + return self._SAUtil.matToVecSens(A) - def ode_and_sensitivityIV(self, state_param, t): + def ode_and_sensitivity(self, state_param, t, by_state=False): ''' Evaluate the sensitivity given state and time @@ -1465,14 +1178,18 @@ def ode_and_sensitivityIV(self, state_param, t): values comes first. t: double The current time + by_state: bool + Whether the output vector should be arranged by state or by + parameters. If False, then it means that the vector of output is + arranged according to looping i,j from Sensitivity_{i,j} with i + being the state and j the param. This is the preferred way because + it leds to a block diagonal Jacobian Returns ------- :class:`list` - concatenation of 3 element. First contains the ode, second the - sensitivity, then the sensitivity of the initial value. All - of them are of type - :class:`numpy.ndarray` + concatenation of 2 element. First contains the ode, second the + sensitivity. Both are of type :class:`numpy.ndarray` See Also -------- @@ -1485,21 +1202,23 @@ def ode_and_sensitivityIV(self, state_param, t): "for the states and not the sensitivity") # unrolling, assuming that we would always put the state first - state = state_param[0:self.num_state] - # the remainings - sens_iv = state_param[self.num_state::] - # separate evaluation - out1 = self.ode(state,t) - out2,out3 = self.sensitivityIV(sens_iv, t, state) - return np.append(np.append(out1, out2), out3) + # there is no safety checks on this because it is impossible to + # distinguish what is state and what is sensitivity as they are + # all numeric value that can take the full range (-\infty,\infty) + state = state_param[0:self.num_state] + sens = state_param[self.num_state::] - def ode_and_sensitivityIV_T(self, t, state_param): + out1 = self.ode(state, t) + out2 = self.sensitivity(sens, t, state, by_state) + return np.append(out1, out2) + + def ode_and_sensitivity_T(self, t, state_param, by_state=False): ''' - Same as :meth:`ode_and_sensitivityIV` but with t as first parameter + Same as :meth:`ode_and_sensitivity` but with t as first parameter ''' - return self.ode_and_sensitivityIV(state_param, t) + return self.ode_and_sensitivity(state_param, t, by_state) - def ode_and_sensitivityIV_jacobian(self, state_param, t): + def ode_and_sensitivity_jacobian(self, state_param, t, by_state=False): ''' Evaluate the sensitivity given state and time. Output a block diagonal sparse matrix as default. @@ -1512,7 +1231,7 @@ def ode_and_sensitivityIV_jacobian(self, state_param, t): values comes first. t: double The current time - byState: bool + by_state: bool How the output is arranged, according to the vector of output. It can be in terms of state or parameters, where by state means that the jacobian is a block diagonal matrix. @@ -1534,688 +1253,644 @@ def ode_and_sensitivityIV_jacobian(self, state_param, t): else: state = state_param[0:self.num_state] - nS = self.num_state - nP = self.num_param - # now we start the computation, the simply one :) + # now we start the computation J = self.jacobian(state, t) + # create the block diagonal Jacobian, assuming that whoever is + # calling this function wants it arranges by state-parameters - # now the jacobian of the state vs initial value - DJ = self.diff_jacobian(state, t) - A = DJ.dot(np.reshape(state_param[(nS*(nP+1))::], (nS, nS), 'F')) - A = np.reshape(A.transpose(), (nS*nS, nS)) - - if nP == 0: - return np.asarray(np.bmat([ - [J, np.zeros((nS, nS*nS))], - [A, np.kron(np.eye(nS), J)] - ])) - else: - # create the block diagonal jacobian, assuming that whoever is - # calling this function wants it arranges by state-parameters - outJ = np.kron(np.eye(nP), J) + # Note that none of the ode integrator in scipy allow a sparse Jacobian + # matrix. All of them accept a banded matrix in packed format but not + # an actual sparse, or specifying the number of bands. + outJ = np.kron(np.eye(self.num_param), J) + # Jacobian of the gradient + GJ = self.grad_jacobian(state, t) + # and now we add the gradient + sensJacobianOfState = GJ + self.sens_jacobian_state(state_param, t) - # jacobian of the gradient - GJ = self.grad_jacobian(state, t) - GS = self.sens_jacobian_state(state_param[:(nS*(nP + 1))], t) - sensJacobianOfState = GJ + GS + if by_state: + arrangeVector = np.zeros(self.num_state * self.num_param) + k = 0 + for j in range(0, self.num_param): + for i in range(0, self.num_state): + if i == 0: + arrangeVector[k] = (i*self.num_state) + j + else: + arrangeVector[k] = (i*(self.num_state - 1)) + j + k += 1 - # The jacobian of the ode, then the sensitivities w.r.t state - # and the sensitivities. In block form - return np.asarray(np.bmat([ - [J, np.zeros((nS, nS*nP)), np.zeros((nS, nS*nS))], - [sensJacobianOfState, outJ, np.zeros((nS*nP, nS*nS))], - [A, np.zeros((nS*nS, nS*nP)), np.kron(np.eye(nS), J)] - ])) + outJ = outJ[np.array(arrangeVector,int),:] + idx = np.array(arrangeVector, int) + sensJacobianOfState = sensJacobianOfState[idx,:] + # The Jacobian of the ode, then the sensitivities w.r.t state and + # the sensitivities. In block form. Theoretically, only the diagonal + # blocks are important but we output the full matrix for completeness + return np.asarray(np.bmat([ + [J, np.zeros((self.num_state, self.num_state*self.num_param))], + [sensJacobianOfState, outJ] + ])) - def ode_and_sensitivityIV_jacobian_T(self, t, state_param): + def ode_and_sensitivity_jacobian_T(self, t, state_param, by_state=False): ''' - Same as :meth:`ode_and_sensitivityIV_jacobian` but with t as + Same as :meth:`ode_and_sensitivity_jacobian` but with t as first parameter ''' - return self.ode_and_sensitivityIV_jacobian(state_param, t) + return self.ode_and_sensitivity_jacobian(state_param, t, by_state) - ############################################################################ + ######################################################################## # - # Adjoint + # Include initial value as parameters. Sensitivity related operations + # (1st forward) # - ############################################################################ + ######################################################################## - def adjoint_interpolate(self, state, t, interpolant, func=None): - ''' - Compute the adjoint given the adjoint vector, time, the functions - which was used to interpolate the state variable + def sensitivityIV(self, sensIV, t, state): + """ + Evaluate the sensitivity which include the initial values as + our parameters given state and time. The default is to + output the values by parameters, i.e. :math:`s_{i},\\ldots,s_{i+n}` are + partial derivatives w.r.t. the states for + :math:`i \\in {1,1+p,1+2p,1+3p, \\ldots, 1+(n-1)p}`. This is to take + advantage of the fact that we have a block diagonal Jacobian that was + already evaluated. Parameters ---------- - state: array like - The current value of lambda, where lambda's are the Lagrangian - multipliers of the differential equation. + sensIV: array like + The starting sensitivity of size [number of state x number of + parameters] + [number of state x number of state] for the + initial condition. The latter is an identity matrix at time zero. t: double - The current time. - interpolant: list - list of interpolating functions of the state - func: callable - This should take inputs similar to an ode, i.e. of the form - func(y,t). If j(y,t) is the cost function, then func - is a function that calculates - :math:`\\partial j \\over \\partial x`. - - Returns - ------- - :class:`numpy.ndarray` - output of the same length as the ode - ''' - state_param = [o(t) for o in interpolant] - return self.adjoint(state, t, state_param, func) - - def adjoint_interpolate_T(self, t, state, interpolant, objInput=None): - ''' - Same as :meth:`adjoint_interpolate` but with t as first parameter - ''' - return self.adjoint_interpolate(state, t, interpolant, objInput) - - def _adjointInterpolate_NoCheck(self, state, t, - interpolant, func=None): - state_param = [o(t) for o in interpolant] - return self._adjoint_NoCheck(state, t, state_param, func) - - def _adjointInterpolateT_NoCheck(self, t, state, - interpolant, func=None): - return self._adjoint_NoCheck(state, t, interpolant, func) - - def adjoint(self, state, t, state_param, func=None): - ''' - Compute the adjoint given the adjoint vector, time, state variable - and the objective function. Note that this function is very - restrictive in the sense that the (original) state variable changes - through time but this assumes it is a constant, i.e. we assume that - the original system is linear. - - Parameters - ---------- + The current time state: array like - The current value of lambda, where lambda's are the Lagrangian - multipliers of the differential equation. - t: double - The current time. - state_param: array like - The state vector that is (or maybe) required to evaluate the - jacobian of the original system - func: callable - This should take inputs similar to an ode, i.e. of the form - func(y,t). If j(y,t) is the cost function, then func - is a function that calculates - :math:`\\partial j \\over \\partial x`. + The current numerical value for the states which can be + :class:`numpy.ndarray` or :class:`list` Returns ------- :class:`numpy.ndarray` output of the same length as the ode - Notes - ----- - The size of lambda should be the same as the state. The integral - should be starting from T, the final time of the original system - and is integrated backwards (for stability). - - ''' - J = self.jacobian(state_param, t) - - if func is None: - return np.dot(state, -J) - else: - return func(state_param, t) - J.transpose().dot(state) - - def _adjoint_NoCheck(self, state, t, state_param, func=None): - J = self._Jacobian_NoCheck(state_param, t) - if func is None: - return np.dot(state, -J) - else: - return func(state_param, t) - J.transpose().dot(state) - - def _adjoinT_NoCheck(self, t, state, state_param, func=None): - return self._adjoint_NoCheck(state, t, state_param, func) - - def adjoint_T(self, t, state, state_param, func=None): - ''' - Same as :meth:`adjoint` but with t as first parameter - ''' - return self.adjoint(state, t, state_param, func) - - def adjoint_jacobian(self, state, t, state_param, func=None): - ''' - Compute the jacobian of the adjoint given the adjoint vector, time, - state variable and the objective function. This is simply the same - as the negative jacobian of the ode transposed. - - Parameters - ---------- - state: array like - The current value of lambda, where lambda's are the Lagrangian - multipliers of the differential equation. - t: double - The current time. - state_param: array like - The state vector that is (or maybe) required to evaluate the - jacobian of the original system - func: callable - This should take inputs similar to an ode, i.e. of the form - func(y,t). If j(y,t) is the cost function, then func - is a function that calculates - :math:`\\partial j \\over \\partial x`. - - Returns - ------- - :class:`numpy.ndarray` - output of is a two dimensional array of size - [number of state x number of state] + """ - Notes - ----- - It takes the same number of argument as the adjoint for simplicity - when integrating. + nS = self.num_state + nP = self.num_param + # separate information out. Again, we do have not have checks here + # as it will be impossible to distinguish what is correct + sens = sensIV[:(nS*nP)] + S = self._SAUtil.vecToMatSens(sens) - See Also - -------- - :meth:`.adjoint` + IV = np.reshape(sensIV[-(nS*nS):], (nS, nS), 'F') - ''' - return -self.jacobian(state_param, t).transpose() + return self.eval_sensitivityIV(S=S, IV=IV, t=t, state=state) - def adjoint_jacobian_T(self, t, state, state_param, func=None): + def sensitivityIV_T(self, t, sensIV, state): ''' - Same as :meth:`adjoint_jacobian_T` but with t being the - first parameter + Same as :meth:`sensitivityIV` but with t as first parameter ''' - return self.adjoint_jacobian(state, t, state_param, func) + return self.sensitivityIV(sensIV, t, state) - def adjoint_interpolate_jacobian(self, state, t, - interpolant, func=None): - ''' - Compute the Jacobian of the adjoint given the adjoint vector, time, - function of the interpolation on the state variables and the - objective function. This is simply the same as the negative - Jacobian of the ode transposed. + def eval_sensitivityIV(self, S, IV, t, state): + """ + Evaluate the sensitivity with initial values given + state and time Parameters ---------- - state: array like - The current value of lambda, where lambda's are the Lagrangian - multipliers of the differential equation. + S: array like + Which should be :class:`numpy.ndarray`. + The starting sensitivity of size [number of state x number of + parameters]. Which are normally zero or one, + depending on whether the initial conditions are also variables. + IV: array like + sensitivities for the initial values t: double - The current time. - interpolant: list - list of interpolating functions of the state - func: callable - This should take inputs similar to an ode, i.e. of the form - func(y,t). If j(y,t) is the cost function, then func is - a function that calculates :math:`\\partial j \\over \\partial x`. + The current time + state: array like + The current numerical value for the states which can be + :class:`numpy.ndarray` or :class:`list` Returns ------- :class:`numpy.ndarray` - output of is a two dimensional array of size - [number of state x number of state] + :math:`f(s(x,\\theta))` and :math:`f(s(x_{0}))` Notes ----- - Same as :meth:`.adjoint_jacobian` but takes a list of interpolating - function instead of a single (vector) value + It is different to :meth:`.eval_ode` and :meth:`.eval_jacobian` in + that the extra input argument is not a parameter. See Also -------- - :meth:`.adjoint_jacobian` + :meth:`.sensitivityIV` - ''' - state_param = [o(t) for o in interpolant] - return self.adjoint_jacobian(state, t, state_param, func) + """ + # jacobian * sensitivities + G + # where G is the gradient + # Evidently, A below uses the same operations as + # A = self.eval_sensitivity(S,t,state) + # but we are evaluating them explicitly here because + # we will be using J as well when computing B - def adjoint_interpolate_jacobian_T(self, t, state, interpolant, func=None): - ''' - Same as :meth:`adjoint_interpolate_jacobian` but with t as - first parameter - ''' - return self.adjoint_interpolate_jacobian(state, t, - interpolant, func) + J = self.jacobian(state, t) + G = self.grad(state, t) + A = np.dot(J, S) + G - ######################################################################## - # - # Sensitivity, forward-forward operations - # - ######################################################################## + # and jacobian * sensitivities of the initial condition + B = np.dot(J, IV) - def forwardforward(self, ff, t, state, s): + # we want to output by parameters + return self._SAUtil.matToVecSens(A), B.flatten('F') + + def ode_and_sensitivityIV(self, state_param, t): ''' - Evaluate a single :math:`f(x)` of the forward-forward sensitivities + Evaluate the sensitivity given state and time Parameters ---------- - ff: array like - the forward-forward sensitivities in vector form - t: numeric - time - state: array like - the current state - s: array like - forward sensitivities in vector form + state_param: array like + The current numerical value for the states as well as the + sensitivities values all in one. We assume that the state + values comes first. + t: double + The current time Returns ------- - :class:`numpy.ndarray` - :math:`f(x)` of size [number of state * - (number of parameters * number of parameters)] + :class:`list` + concatenation of 3 element. First contains the ode, second the + sensitivity, then the sensitivity of the initial value. All + of them are of type + :class:`numpy.ndarray` + + See Also + -------- + :meth:`.sensitivity`, :meth:`.ode` ''' - # byState is simply stupid in the forward forward case because the - # second derivative makes things only rational if we look at it from - # the state point of view - S = self._SAUtil.vecToMatSens(s) - FF = self._SAUtil.vecToMatFF(ff) - return self.eval_forwardforward(FF=FF, S=S, state=state, t=t) - def forwardforward_T(self, t, ff, s, state): + if len(state_param) == self.num_state: + raise InputError("You have only inputed the initial condition " + + "for the states and not the sensitivity") + + # unrolling, assuming that we would always put the state first + state = state_param[0:self.num_state] + # the remainings + sens_iv = state_param[self.num_state::] + # separate evaluation + out1 = self.ode(state,t) + out2,out3 = self.sensitivityIV(sens_iv, t, state) + return np.append(np.append(out1, out2), out3) + + def ode_and_sensitivityIV_T(self, t, state_param): ''' - Same as :meth:`forwardforward` but with t as the first - parameter + Same as :meth:`ode_and_sensitivityIV` but with t as first parameter ''' - return self.forwardforward(ff, t, state, s) + return self.ode_and_sensitivityIV(state_param, t) - def eval_forwardforward(self, FF, S, state, t): + def ode_and_sensitivityIV_jacobian(self, state_param, t): ''' - Evaluate a single f(x) of the forward-forward sensitivities + Evaluate the sensitivity given state and time. Output a block + diagonal sparse matrix as default. Parameters ---------- - FF: array like - this is in fact a 3rd order Tensor, aka 3d array - S: array like - sensitivities in matrix form - state: array like - the current state - t: numeric - time + state_param: array like + The current numerical value for the states as well as the + sensitivities values all in one. We assume that the state + values comes first. + t: double + The current time + byState: bool + How the output is arranged, according to the vector of output. + It can be in terms of state or parameters, where by state means + that the jacobian is a block diagonal matrix. Returns ------- :class:`numpy.ndarray` - f(x) of size [number of state * - (number of parameters * number of parameters)] + output of a square matrix of size: number of ode + 1 times number + of parameters + + See Also + -------- + :meth:`.ode_and_sensitivity` ''' + if len(state_param) == self.num_state: + raise InputError("Expecting both the state and the sensitivities") + else: + state = state_param[0:self.num_state] + + nS = self.num_state + nP = self.num_param + # now we start the computation, the simply one :) J = self.jacobian(state, t) - diffJ = self.diff_jacobian(state, t) - # evaluating by state/ode, the matrix of second derivative - # we have kron products into all these evaluations and the class - # here use a sparse matrix operation - outFF = self._SAUtil.kronParam(J).dot(FF) - outFF += self._SAUtil.kronState(A=S.T, pre=True).dot(diffJ).dot(S) + # now the jacobian of the state vs initial value + DJ = self.diff_jacobian(state, t) + A = DJ.dot(np.reshape(state_param[(nS*(nP+1))::], (nS, nS), 'F')) + A = np.reshape(A.transpose(), (nS*nS, nS)) - # now we need to magic our list / matrix into a vector, aka append - # each of the vectorized matrix one after another - return self._SAUtil.matToVecFF(outFF) + if nP == 0: + return np.asarray(np.bmat([ + [J, np.zeros((nS, nS*nS))], + [A, np.kron(np.eye(nS), J)] + ])) + else: + # create the block diagonal jacobian, assuming that whoever is + # calling this function wants it arranges by state-parameters + outJ = np.kron(np.eye(nP), J) - def ode_and_forwardforward(self, state_param, t): - ''' - Evaluate a single f(x) of the ode and the - forward-forward sensitivities + # jacobian of the gradient + GJ = self.grad_jacobian(state, t) + GS = self.sens_jacobian_state(state_param[:(nS*(nP + 1))], t) + sensJacobianOfState = GJ + GS - Parameters - ---------- - state_param: array like - state and forward-forward sensitivities in vector form - t: numeric - time + # The jacobian of the ode, then the sensitivities w.r.t state + # and the sensitivities. In block form + return np.asarray(np.bmat([ + [J, np.zeros((nS, nS*nP)), np.zeros((nS, nS*nS))], + [sensJacobianOfState, outJ, np.zeros((nS*nP, nS*nS))], + [A, np.zeros((nS*nS, nS*nP)), np.kron(np.eye(nS), J)] + ])) - Returns - ------- - :class:`numpy.ndarray` - same size as the state_param input + def ode_and_sensitivityIV_jacobian_T(self, t, state_param): ''' + Same as :meth:`ode_and_sensitivityIV_jacobian` but with t as + first parameter + ''' + return self.ode_and_sensitivityIV_jacobian(state_param, t) - if len(state_param) == self.num_state: - raise InputError("You have only inputed the initial condition " + - "for the states and not the sensitivity") - elif len(state_param) == ((self.num_state + 1)*self.num_param): - raise InputError("You have only inputed the initial condition " + - "for the states and the sensitivity but not " + - "the forward forward condition") - - # unrolling of parameters - state = state_param[0:self.num_state] - # we want the index up to numState * (numParam + 1) - # as in, (numState * numParam + numState, - # number of sensitivities + number of ode) - sens = state_param[self.num_state:(self.num_state*(self.num_param + 1))] - # the rest are then the forward forward sensitivities - ff = state_param[(self.num_state*(self.num_param + 1))::] + ############################################################################ + # + # Adjoint + # + ############################################################################ - out1 = self.ode(state, t) - out2 = self.sensitivity(sens, t, state) - out3 = self.forwardforward(ff, t, state, sens) + def adjoint_interpolate(self, state, t, interpolant, func=None): + ''' + Compute the adjoint given the adjoint vector, time, the functions + which was used to interpolate the state variable - return np.append(np.append(out1, out2), out3) + Parameters + ---------- + state: array like + The current value of lambda, where lambda's are the Lagrangian + multipliers of the differential equation. + t: double + The current time. + interpolant: list + list of interpolating functions of the state + func: callable + This should take inputs similar to an ode, i.e. of the form + func(y,t). If j(y,t) is the cost function, then func + is a function that calculates + :math:`\\partial j \\over \\partial x`. - def ode_and_forwardforward_T(self, t, state_param): + Returns + ------- + :class:`numpy.ndarray` + output of the same length as the ode ''' - Same as :meth:`odeAndForwardForward` but with time - as the first input + state_param = [o(t) for o in interpolant] + return self.adjoint(state, t, state_param, func) + def adjoint_interpolate_T(self, t, state, interpolant, objInput=None): ''' - return self.ode_and_forwardforward(state_param, t) + Same as :meth:`adjoint_interpolate` but with t as first parameter + ''' + return self.adjoint_interpolate(state, t, interpolant, objInput) - def ode_and_forwardforward_jacobian(self, state_param, t): + def _adjointInterpolate_NoCheck(self, state, t, + interpolant, func=None): + state_param = [o(t) for o in interpolant] + return self._adjoint_NoCheck(state, t, state_param, func) + + def _adjointInterpolateT_NoCheck(self, t, state, + interpolant, func=None): + return self._adjoint_NoCheck(state, t, interpolant, func) + + def adjoint(self, state, t, state_param, func=None): ''' - Return the jacobian after evaluation given the input - of the state and the forward forward sensitivities + Compute the adjoint given the adjoint vector, time, state variable + and the objective function. Note that this function is very + restrictive in the sense that the (original) state variable changes + through time but this assumes it is a constant, i.e. we assume that + the original system is linear. Parameters ---------- + state: array like + The current value of lambda, where lambda's are the Lagrangian + multipliers of the differential equation. + t: double + The current time. state_param: array like - state and forward-forward sensitivities in vector form - t: numeric - time + The state vector that is (or maybe) required to evaluate the + jacobian of the original system + func: callable + This should take inputs similar to an ode, i.e. of the form + func(y,t). If j(y,t) is the cost function, then func + is a function that calculates + :math:`\\partial j \\over \\partial x`. Returns ------- :class:`numpy.ndarray` - size of (a,a) where a is the length of the - state_param input - ''' - if len(state_param) == self.num_state: - state = state_param - else: - state = state_param[0:self.num_state] + output of the same length as the ode - J = self.jacobian(state, t) - # create the block diagonal jacobian, assuming that whoever is - # calling this function wants it arranges by state-parameters - # We are only construct the block diagonal jacobian here - # instead of the full one unlike some of the other methods within - # this class - outJS = np.kron(np.eye(self.num_param), J) - outJFF = np.kron(np.eye(self.num_param*self.num_param), J) - # The jacobian of the ode, then the sensitivities, then the - # forward forward sensitivities - return scipy.linalg.block_diag(J, outJS, outJFF) + Notes + ----- + The size of lambda should be the same as the state. The integral + should be starting from T, the final time of the original system + and is integrated backwards (for stability). - def ode_and_forwardforward_jacobian_T(self, t, state_param): - ''' - Same as :meth:`ode_and_forwardforward_jacobian` but - with t being the first parameters ''' - return self.ode_and_forwardforward_jacobian(state_param, t) + J = self.jacobian(state_param, t) - ######################################################################## - # - # Initial conditions, integrations and result plots - # - ######################################################################## + if func is None: + return np.dot(state, -J) + else: + return func(state_param, t) - J.transpose().dot(state) - @property - def initial_state(self): + def _adjoint_NoCheck(self, state, t, state_param, func=None): + J = self._Jacobian_NoCheck(state_param, t) + if func is None: + return np.dot(state, -J) + else: + return func(state_param, t) - J.transpose().dot(state) + + def _adjoinT_NoCheck(self, t, state, state_param, func=None): + return self._adjoint_NoCheck(state, t, state_param, func) + + def adjoint_T(self, t, state, state_param, func=None): ''' - Return the initial state values + Same as :meth:`adjoint` but with t as first parameter ''' - return self._x0 + return self.adjoint(state, t, state_param, func) - @initial_state.setter - def initial_state(self, x0): + def adjoint_jacobian(self, state, t, state_param, func=None): ''' - Set the initial state values + Compute the jacobian of the adjoint given the adjoint vector, time, + state variable and the objective function. This is simply the same + as the negative jacobian of the ode transposed. Parameters ---------- - x0: array like - initial condition of x at time 0 + state: array like + The current value of lambda, where lambda's are the Lagrangian + multipliers of the differential equation. + t: double + The current time. + state_param: array like + The state vector that is (or maybe) required to evaluate the + jacobian of the original system + func: callable + This should take inputs similar to an ode, i.e. of the form + func(y,t). If j(y,t) is the cost function, then func + is a function that calculates + :math:`\\partial j \\over \\partial x`. - ''' - err_str = "More than one state in the defined system" + Returns + ------- + :class:`numpy.ndarray` + output of is a two dimensional array of size + [number of state x number of state] - if isinstance(x0, np.ndarray): - self._x0 = x0 - elif isinstance(x0, (list, tuple)): - self._x0 = np.array(x0) - elif isinstance(x0, (int, float)): - if self.num_state == 1: - self._x0 = np.array([x0]) - else: - raise InitializeError(err_str) - else: - raise InitializeError("err_str") + Notes + ----- + It takes the same number of argument as the adjoint for simplicity + when integrating. - if len(self._x0) != self.num_state: - raise Exception("Number of state is " + - str(self.num_state)+ " but " + - str(len(self._x0))+ " detected") + See Also + -------- + :meth:`.adjoint` - @property - def initial_time(self): ''' - Return the initial time + return -self.jacobian(state_param, t).transpose() + + def adjoint_jacobian_T(self, t, state, state_param, func=None): ''' - return self._t0 + Same as :meth:`adjoint_jacobian_T` but with t being the + first parameter + ''' + return self.adjoint_jacobian(state, t, state_param, func) - @initial_time.setter - def initial_time(self, t0): + def adjoint_interpolate_jacobian(self, state, t, + interpolant, func=None): ''' - Set the initial time + Compute the Jacobian of the adjoint given the adjoint vector, time, + function of the interpolation on the state variables and the + objective function. This is simply the same as the negative + Jacobian of the ode transposed. Parameters ---------- - t0: numeric - initial time where x0 is observed - - ''' - - err_str = "Initial time should be a " - if isinstance(t0, Number): - self._t0 = t0 - elif ode_utils.is_list_like(t0): - if len(t0) == 1: - if isinstance(t0[0], Number): - self._t0 = t0[0] - else: - raise InitializeError(err_str + "numeric value") - else: - raise InitializeError(err_str + "single value") - elif isinstance(t0, (list, tuple)): - if len(t0) == 1: - self._t0 = np.array(t0[0]) - else: - raise InitializeError(err_str + "single value") - else: - raise InitializeError(err_str + "numeric value") + state: array like + The current value of lambda, where lambda's are the Lagrangian + multipliers of the differential equation. + t: double + The current time. + interpolant: list + list of interpolating functions of the state + func: callable + This should take inputs similar to an ode, i.e. of the form + func(y,t). If j(y,t) is the cost function, then func is + a function that calculates :math:`\\partial j \\over \\partial x`. - @property - def initial_values(self): - ''' - Returns the initial values, both time and state as a tuple (x0, t0) - ''' - return (self.initial_state, self.initial_time) + Returns + ------- + :class:`numpy.ndarray` + output of is a two dimensional array of size + [number of state x number of state] - @initial_values.setter - def initial_values(self, x0t0): - ''' - Set the initial values, both time and state + Notes + ----- + Same as :meth:`.adjoint_jacobian` but takes a list of interpolating + function instead of a single (vector) value - Parameters - ---------- - x0t0: array like - initial condition of x at time t and the initial time t where x - is observed - ''' - assert len(x0t0) == 2, "Initial values require (x0, t0)" - self.initial_state = x0t0[0] - self.initial_time = x0t0[1] + See Also + -------- + :meth:`.adjoint_jacobian` - def integrate(self, t, full_output=False): ''' - Integrate over a range of t when t is an array and a output at time t + state_param = [o(t) for o in interpolant] + return self.adjoint_jacobian(state, t, state_param, func) - Parameters - ---------- - t: array like - the range of time points which we want to see the result of - full_output: bool - if we want additional information + def adjoint_interpolate_jacobian_T(self, t, state, interpolant, func=None): ''' - # type checking - self._setIntegrateTime(t) - # if our parameters are stochastic, then we are going to generate - # another set of parameters to run - if self._stochasticParam is not None: - # this should always be true. If not, then we have screwed up - # somewhere within this class. - if isinstance(self._stochasticParam, dict): - self.parameters = self._stochasticParam + Same as :meth:`adjoint_interpolate_jacobian` but with t as + first parameter + ''' + return self.adjoint_interpolate_jacobian(state, t, + interpolant, func) - return self._integrate(self._odeTime, full_output) + ######################################################################## + # + # Sensitivity, forward-forward operations + # + ######################################################################## - def integrate2(self, t, full_output=False, method=None): + def forwardforward(self, ff, t, state, s): ''' - Integrate over a range of t when t is an array and a output - at time t. Select a suitable method to integrate when - method is None. + Evaluate a single :math:`f(x)` of the forward-forward sensitivities Parameters ---------- - t: array like - the range of time points which we want to see the result of - full_output: bool - if we want additional information - method: str, optional - the integration method. All those available in - :class:`ode ` are allowed with 'vode' - and 'ivode' representing the non-stiff and stiff version - respectively. Defaults to None, which tries to choose the - integration method via eigenvalue analysis (only one) using - the initial conditions - ''' + ff: array like + the forward-forward sensitivities in vector form + t: numeric + time + state: array like + the current state + s: array like + forward sensitivities in vector form - self._setIntegrateTime(t) - # if our parameters are stochastic, then we are going to generate - # another set of parameters to run - if self._stochasticParam is not None: - # this should always be true - if isinstance(self._stochasticParam, dict): - self.parameters = self._stochasticParam + Returns + ------- + :class:`numpy.ndarray` + :math:`f(x)` of size [number of state * + (number of parameters * number of parameters)] - return self._integrate2(self._odeTime, full_output, method) + ''' + # byState is simply stupid in the forward forward case because the + # second derivative makes things only rational if we look at it from + # the state point of view + S = self._SAUtil.vecToMatSens(s) + FF = self._SAUtil.vecToMatFF(ff) + return self.eval_forwardforward(FF=FF, S=S, state=state, t=t) - def _setIntegrateTime(self, t): + def forwardforward_T(self, t, ff, s, state): ''' - Set the full set of integration time including the origin + Same as :meth:`forwardforward` but with t as the first + parameter ''' + return self.forwardforward(ff, t, state, s) - assert self._t0 is not None, "Initial time not set" + def eval_forwardforward(self, FF, S, state, t): + ''' + Evaluate a single f(x) of the forward-forward sensitivities - if ode_utils.is_list_like(t): - if isinstance(t[0], Number): - t = np.append(self._t0, t) - else: - raise ArrayError("Expecting a list of numeric value") - elif isinstance(t, Number): - t = np.append(self._t0, np.array(t)) - else: - raise ArrayError("Expecting an array like input or a single " + - "numeric value") + Parameters + ---------- + FF: array like + this is in fact a 3rd order Tensor, aka 3d array + S: array like + sensitivities in matrix form + state: array like + the current state + t: numeric + time - self._odeTime = t + Returns + ------- + :class:`numpy.ndarray` + f(x) of size [number of state * + (number of parameters * number of parameters)] - def _integrate(self, t, full_output=True): - ''' - Integrate using :class:`scipy.integrate.odeint` underneath ''' - assert self._t0 is not None, "Initial time not set" - - f = ode_utils.integrate - self._odeSolution, self._odeOutput = f(self, - self._x0, - t, - full_output=True) - if full_output: - return self._odeSolution, self._odeOutput - else: - return self._odeSolution - def _integrate2(self, t, full_output=True, method=None): - ''' - Integrate using :class:`scipy.integrate.ode` underneath - ''' - assert self._x0 is not None, "Initial state not set" + J = self.jacobian(state, t) + diffJ = self.diff_jacobian(state, t) - f = ode_utils.integrateFuncJac - self._odeSolution, self._odeOutput = f(self.ode_T, - self.jacobian_T, - self._x0, - t[0], t[1::], - includeOrigin=True, - full_output=True, - method=method) + # evaluating by state/ode, the matrix of second derivative + # we have kron products into all these evaluations and the class + # here use a sparse matrix operation + outFF = self._SAUtil.kronParam(J).dot(FF) + outFF += self._SAUtil.kronState(A=S.T, pre=True).dot(diffJ).dot(S) - if full_output: - return self._odeSolution, self._odeOutput - else: - return self._odeSolution + # now we need to magic our list / matrix into a vector, aka append + # each of the vectorized matrix one after another + return self._SAUtil.matToVecFF(outFF) - def plot(self): + def ode_and_forwardforward(self, state_param, t): ''' - Plot the results of the integration + Evaluate a single f(x) of the ode and the + forward-forward sensitivities - Notes - ----- - If we have 3 states or more, it will always be arrange such - that it has 3 columns. Uses the operation from - :mod:`odeutils` + Parameters + ---------- + state_param: array like + state and forward-forward sensitivities in vector form + t: numeric + time + + Returns + ------- + :class:`numpy.ndarray` + same size as the state_param input ''' - # just need to make sure that we have - # already gotten the solution to the integration - if self._odeSolution is None: - try: - self._integrate(self._odeTime) - ode_utils.plot_det(self._odeSolution, self._odeTime, self._stateList) - except: - raise IntegrationError("Have not performed the integration yet") - else: - ode_utils.plot_det(self._odeSolution, self._odeTime, self._stateList) + if len(state_param) == self.num_state: + raise InputError("You have only inputed the initial condition " + + "for the states and not the sensitivity") + elif len(state_param) == ((self.num_state + 1)*self.num_param): + raise InputError("You have only inputed the initial condition " + + "for the states and the sensitivity but not " + + "the forward forward condition") - ######################################################################## - # Unrolling of the information from vector to sympy - # t - # state - ######################################################################## + # unrolling of parameters + state = state_param[0:self.num_state] + # we want the index up to numState * (numParam + 1) + # as in, (numState * numParam + numState, + # number of sensitivities + number of ode) + sens = state_param[self.num_state:(self.num_state*(self.num_param + 1))] + # the rest are then the forward forward sensitivities + ff = state_param[(self.num_state*(self.num_param + 1))::] - def _addTimeEvalParam(self, eval_param, t): - eval_param.append((self._t, t)) - return eval_param + out1 = self.ode(state, t) + out2 = self.sensitivity(sens, t, state) + out3 = self.forwardforward(ff, t, state, sens) - def _addStateEvalParam(self, eval_param, state): - super(DeterministicOde, self).state = state - if self._state is not None: - eval_param += self._state + return np.append(np.append(out1, out2), out3) - return eval_param + def ode_and_forwardforward_T(self, t, state_param): + ''' + Same as :meth:`odeAndForwardForward` but with time + as the first input - def _getEvalParam(self, state, time, parameters): - if state is None or time is None: - raise InputError("Have to input both state and time") + ''' + return self.ode_and_forwardforward(state_param, t) - if parameters is not None: - self.parameters = parameters - elif self._parameters is None: - if self.num_param == 0: - pass - else: - raise InputError("Have not set the parameters yet") + def ode_and_forwardforward_jacobian(self, state_param, t): + ''' + Return the jacobian after evaluation given the input + of the state and the forward forward sensitivities - if isinstance(state, list): - eval_param = state + [time] - elif hasattr(state, '__iter__'): - eval_param = list(state) + [time] + Parameters + ---------- + state_param: array like + state and forward-forward sensitivities in vector form + t: numeric + time + + Returns + ------- + :class:`numpy.ndarray` + size of (a,a) where a is the length of the + state_param input + ''' + if len(state_param) == self.num_state: + state = state_param else: - eval_param = [state] + [time] + state = state_param[0:self.num_state] - return eval_param + self._paramValue + J = self.jacobian(state, t) + # create the block diagonal jacobian, assuming that whoever is + # calling this function wants it arranges by state-parameters + # We are only construct the block diagonal jacobian here + # instead of the full one unlike some of the other methods within + # this class + outJS = np.kron(np.eye(self.num_param), J) + outJFF = np.kron(np.eye(self.num_param*self.num_param), J) + # The jacobian of the ode, then the sensitivities, then the + # forward forward sensitivities + return scipy.linalg.block_diag(J, outJS, outJFF) + + def ode_and_forwardforward_jacobian_T(self, t, state_param): + ''' + Same as :meth:`ode_and_forwardforward_jacobian` but + with t being the first parameters + ''' + return self.ode_and_forwardforward_jacobian(state_param, t) diff --git a/src/pygom/model/epi_analysis.py b/src/pygom/model/epi_analysis.py index 0a89462e..432509bd 100644 --- a/src/pygom/model/epi_analysis.py +++ b/src/pygom/model/epi_analysis.py @@ -8,7 +8,7 @@ import sympy -from .simulate import SimulateOde +from .simulate import SimulateOde, TransitionType __all__ = [ 'DFE', @@ -149,12 +149,16 @@ def disease_progression_matrices(ode, disease_state, diff=True): state_list.append(s) FList = list() - for t in ode.transition_list: - orig = _get_single_state_name(t.origin) - dest = _get_single_state_name(t.destination) - if isinstance(orig, str) and isinstance(dest, str): - if orig not in disease_state and dest in disease_state: - FList.append(t) + + for event in ode.event_list: + for trans in event.transition_list: + if trans.transition_type==TransitionType.T: + orig = _get_single_state_name(trans.origin) + dest = _get_single_state_name(trans.destination) + if isinstance(orig, str) and isinstance(dest, str): + if orig not in disease_state and dest in disease_state: + trans._equation=event.rate + FList.append(trans) ode2 = SimulateOde(ode.state_list, ode.param_list, transition=FList) diff --git a/src/pygom/model/ode_utils/__init__.py b/src/pygom/model/ode_utils/__init__.py index 02f4ecd1..8f0cfe19 100644 --- a/src/pygom/model/ode_utils/__init__.py +++ b/src/pygom/model/ode_utils/__init__.py @@ -480,6 +480,7 @@ def __init__(self, backend=None): those linked with Theano are not. ''' if backend is None: + print("...Finding available backend...", end="") self._backend = None x = sympy.Symbol('x') expr = sympy.sin(x)/x @@ -517,6 +518,7 @@ def __init__(self, backend=None): # stuff in a parallel setting where we create objects in # pure computation nodes with no compile mechanism self._backend = 'lambda' + print("done: ", self._backend) else: self._backend = backend diff --git a/src/pygom/model/simulate.py b/src/pygom/model/simulate.py index 571b960d..9c93a5c3 100644 --- a/src/pygom/model/simulate.py +++ b/src/pygom/model/simulate.py @@ -28,15 +28,16 @@ class HasNewTransition(ode_utils.CompileCanary): states = ['ode', - 'Jacobian', - 'diffJacobian', + 'jacobian', + 'diff_jacobian', 'grad', - 'GradJacobian', - 'transitionMatrixCompile', - 'transitionVector', - 'birthDeathRateCompile', - 'computeTransitionMeanVar', - 'transitionJacobian'] + 'grad_jacobian', + 'transitionJacobian', + "pureOdeVector", + "vMat", + "eventRateVector", + "transitionMean", + "transitionVar"] class SimulateOde(DeterministicOde): ''' @@ -46,14 +47,16 @@ class SimulateOde(DeterministicOde): Parameters ---------- state: list - A list of states (string) + A list of states (string) or (string, (numeric, numeric)) if specifying limits param: list A list of the parameters (string) derived_param: list A list of the derived parameters (tuple of (string,string)) transition: list - A list of transition (:class:`Transition`) - birth_death: list + A list of transition (:class:`Transition`) #TODO Now this might actually only be deterministic ODE objects. Check. + transition: list + A list of events (:class:`Event`) + birth_death: list #TODO Now these are wrapped in events. Should try to make work for back compat. A list of birth or death process (:class:`Transition`) ode: list A list of ode (:class:`Transition`) @@ -65,6 +68,7 @@ def __init__(self, param=None, derived_param=None, transition=None, + event=None, birth_death=None, ode=None): ''' @@ -75,34 +79,41 @@ def __init__(self, param, derived_param, transition, + event, birth_death, ode) + # Ledger keeping record of whether each important function is up to date with + # underlying model, or needs to be recompiled. Colloquially, each function has + # an associated canary and if True (dead) it means something needs to be done. self._hasNewTransition = HasNewTransition() - # need a manual override because it is possible that we - # want to perform simulation in a parallel/distributed manner - # and there are issues with pickling fortran objects - self._SC = ode_utils.compileCode(backend='cython') - - self._birthDeathRate = None - self._birthDeathRateCompile = None + self.pre_tau=None # If tau is set, then this overrides the adaptive tau leap. + self._epsilon=0.03 # Default parameter recommended by Cao et al. - # information required for the tau leap - self._transitionJacobian = None + self._stochasticParam=None - self._transitionMean = None - self._transitionMeanCompile = None + # TODO: I think the changes I've made might result in compilation for every iteration + # if working in parallel. Must check this. - self._transitionVar = None - self._transitionVarCompile = None - - self._transitionVectorCompile = None - self._transitionMatrixCompile = None + # Compile the code. Note that we need the class because we + # compile both the formatted and unformatted version. + # Need a manual override of backend because it is possible that we + # want to perform simulation in a parallel/distributed manner + # and there are issues with pickling fortran objects + self._SC = ode_utils.compileCode(backend='cython') - # micro times for jumps - self._tau = None - self._tauDict = None + # Add templates of compiled sympy functions with: + # 1) Name of the compiled version of the sympy object + # 2) The function used to generate the underlying sympy object + # (convention: starts with "get_", in previous versions have + # started with get_ or _compute) + self.add_func("vMat", self.get_StateChangeMatrix) + self.add_func("eventRateVector", self.get_EventRateVector) + self.add_func("transitionMean", self.get_TransitionMean) + self.add_func("transitionVar", self.get_TransitionVar) + self.add_func("pureOdeVector", self.get_pureOdeVector) + self.add_func("transitionJacobian", self.get_TransitionJacobian) def __repr__(self): return "SimulateOde" + self._get_model_str() @@ -121,9 +132,15 @@ def exact(self, x0, t0, t1, output_time=False): t1: double final time ''' - return(exact(x0, t0, t1, self._vMat, self.transition_vector, + return(exact(x0, t0, t1, self.vMat, self.eventRateVector, output_time=output_time)) + ########################################################################### + # + # Solver functions + # + ########################################################################### + def cle(self, x0, t0, t1, output_time=False): ''' Stochastic simulation using the CLE approximation starting from time @@ -143,7 +160,7 @@ def cle(self, x0, t0, t1, output_time=False): t1: double final time ''' - return(cle(x0, t0, t1, self._vMat, self.transition_vector, + return(cle(x0, t0, t1, self.vMat, self.eventRateVector, output_time=output_time)) def hybrid(self, x0, t0, t1, output_time=False): @@ -162,10 +179,10 @@ def hybrid(self, x0, t0, t1, output_time=False): t1: double final time ''' - return(hybrid(x0, t0, t1, self._vMat, self._lambdaMat, - self.transition_vector, - self.transition_mean, - self.transition_var, + return(hybrid(x0, t0, t1, self.vMat, + self.eventRateVector, + self.transitionMean, + self.transitionVar, output_time=output_time)) def simulate_param(self, t, iteration, parallel=False, full_output=False): @@ -194,8 +211,9 @@ def simulate_param(self, t, iteration, parallel=False, full_output=False): ''' # if our parameters not stochastic, then we are going to - # throw a warning because simulating a deterministic system is - # just plain stupid + # throw a warning because trying to randomly draw parameters + # when they are set to be constant is just plain stupid + if self._stochasticParam is None: raise InputError("Deterministic parameters.") if iteration is None: @@ -329,7 +347,7 @@ def sim(x): # Same as function below, just trying out new naming convention def solve_stochast(self, t, iteration, parallel=False, - exact=False, full_output=False): + exact=False, full_output=False): ''' Simulate the ode using stochastic simulation. It switches between a first reaction method and a :math:`\\tau`-leap @@ -356,6 +374,8 @@ def solve_stochast(self, t, iteration, parallel=False, sim_X: list of length iteration each with (len(t),len(state)) if t is a vector, else it outputs unequal shape that was record of all the jumps + sim_Jump: list of :class:`numpy.ndarray` + Number times each transition happens per timestep sim_T: list or :class:`numpy.ndarray` if t is a single value, it outputs unequal shape that was record of all the jumps. if t is a vector, it outputs t so that @@ -363,14 +383,14 @@ def solve_stochast(self, t, iteration, parallel=False, ''' - assert len(self._odeList) == 0, \ - "Currently only able to simulate when only transitions are present" + # assert len(self._odeList) == 0, \ + # "Currently only able to simulate when only transitions are present" assert np.all(np.mod(self._x0, 1) == 0), \ "Can only simulate a jump process with integer initial values" - # this determines what type of output we want + # Determine if results are output to predefined timepoints or the timepoints + # as determined by the numerical solver timePoint = False - if isinstance(t, Number):#, (int, float, np.int64, np.float64)): finalT = t elif isinstance(t, (list, tuple)): @@ -386,9 +406,6 @@ def solve_stochast(self, t, iteration, parallel=False, else: raise InputError("Unknown data type for time") - if self._transitionVectorCompile is None: - self._compileTransitionVector() - if parallel: try: import dask.bag @@ -408,144 +425,52 @@ def jump_partial(final_t): return(self._jump(final_t, logging.debug("Performing serial simulation") xtmp = [self._jump(finalT, exact=exact, full_output=True) for _i in range(iteration)] + # Unpack output xmat = list(zip(*xtmp)) - simXList, simTList = list(xmat[0]), list(xmat[1]) - ## print("Finish computation") - # now we want to fix our simulation, if they need fixing that is - # print timePoint + simXList, simJumpList, simTList, simdTList = list(xmat[0]), list(xmat[1]), list(xmat[2]), list(xmat[3]) + + # Process simulation output if user has specified target time steps if timePoint: for _i in range(len(simXList)): + # TODO: this seems like an overcomplicated way to do things + # unroll, always the first element # it is easy to remember that we are accessing the first # element because pop is spelt similar to poop and we # all know that your execute first in first out when you # poop! - simX = simXList.pop(0) - simT = simTList.pop(0) - - x = self._extractObservationAtTime(simX, simT, t) - simTList.append(t) - simXList.append(x) - # note that we have to remain in list form because the number of - # simulation will be different if we are not dealing with - # a specific set of time points - - if full_output: - if timePoint: - return simXList, t - else: - return simXList, simTList - else: - return simXList + # Get time points of run _i + simT = simTList.pop(0) # get timepoints and remove (temporarily) - def simulate_jump(self, t, iteration, parallel=False, - exact=False, full_output=False): - ''' - Simulate the ode using stochastic simulation. It switches - between a first reaction method and a :math:`\\tau`-leap - algorithm internally. When a parallel backend exists, then a new random - state (seed) will be used for each processor. This is due to a lack - of appropriate parallel seed random number generator in python. - - Parameters - ---------- - t: array like - the range of time points which we want to see the result of - or the final time point - iteration: int - number of iterations you wish to simulate - parallel: bool, optional - Defaults to True - exact: bool, optional - True if exact simulation is desired, defaults to False - full_output: bool, optional - if we want additional information, sim_T - - Returns - ------- - sim_X: list - of length iteration each with (len(t),len(state)) if t is a vector, - else it outputs unequal shape that was record of all the jumps - sim_T: list or :class:`numpy.ndarray` - if t is a single value, it outputs unequal shape that was - record of all the jumps. if t is a vector, it outputs t so that - it is a :class:`numpy.ndarray` instead - - ''' - - assert len(self._odeList) == 0, \ - "Currently only able to simulate when only transitions are present" - assert np.all(np.mod(self._x0, 1) == 0), \ - "Can only simulate a jump process with integer initial values" - - # this determines what type of output we want - timePoint = False - - if isinstance(t, Number):#, (int, float, np.int64, np.float64)): - finalT = t - elif isinstance(t, (list, tuple)): - t = np.array(t) - if len(t) == 1: - finalT = t - else: - finalT = t[-1:] - timePoint = True - elif isinstance(t, np.ndarray): - finalT = t[-1:] - timePoint = True - else: - raise InputError("Unknown data type for time") - - if self._transitionVectorCompile is None: - self._compileTransitionVector() - - if parallel: - try: - import dask.bag - logging.debug("Using Dask for parallel simulation") - def jump_partial(final_t): return(self._jump(final_t, - exact=exact, - full_output=True, - seed=True)) + # 1. Process states + simX = simXList.pop(0) # get states and remove (will be appended after processing) + if exact: + x = self._extractObservationAtTime(simX, simT, t) + else: + x = self._interpolateObservationAtTime(simX, simT, t) + simXList.append(x) # processed results now go at the end of the list - xtmp = dask.bag.from_sequence(np.ones(iteration)*finalT) - xtmp = xtmp.map(jump_partial).compute() - except Exception as e: - raise e - logging.warning("Parallel simulation failed reverting to serial") - xtmp = [self._jump(finalT, exact=exact, full_output=True) for _i in range(iteration)] - else: - logging.debug("Performing serial simulation") - xtmp = [self._jump(finalT, exact=exact, full_output=True) for _i in range(iteration)] + # 2. Process jumps + simJump = simJumpList.pop(0) + jump=self._addJumpsBetweenTime(simJump, simT, t, exact) + simJumpList.append(jump) # processed results go at end of list - xmat = list(zip(*xtmp)) - simXList, simTList = list(xmat[0]), list(xmat[1]) - ## print("Finish computation") - # now we want to fix our simulation, if they need fixing that is - # print timePoint - if timePoint: - for _i in range(len(simXList)): - # unroll, always the first element - # it is easy to remember that we are accessing the first - # element because pop is spelt similar to poop and we - # all know that your execute first in first out when you - # poop! - simX = simXList.pop(0) - simT = simTList.pop(0) + # If user has specified timesteps then this is not a useful step, will probably delete + # # 3. Process timesteps (essentially send to back of list to match new X and jump positions) + # dt=simdTList.pop(0) # send dt to back too + # simdTList.append(dt) + # simTList.append(t) # do same with timepoints - x = self._extractObservationAtTime(simX, simT, t) - simTList.append(t) - simXList.append(x) # note that we have to remain in list form because the number of # simulation will be different if we are not dealing with # a specific set of time points if full_output: if timePoint: - return simXList, t + return simXList, simJumpList, t else: - return simXList, simTList + return simXList, simJumpList, simTList else: return simXList @@ -553,6 +478,7 @@ def _jump(self, finalT, exact=False, full_output=True, seed=None): ''' Jumps from the initial time self._t0 to the input time finalT ''' + if isinstance(self._stochasticParam, dict): self.parameters = self._stochasticParam @@ -564,426 +490,279 @@ def _jump(self, finalT, exact=False, full_output=True, seed=None): x = copy.deepcopy(self._x0) # holders and record information - xList = [x.copy()] - tList = [t] + xList = [x.copy()] # states + tList = [t] # timepoints + dtList=[] # timesteps (can be inferred from timepoints, but useful for now to debug tau leap) + jumpList=[] # transitions - # we want to construct some jump times (TODO: doesn't seem like _GMat is used anywhere) - if self._GMat is None: - self._computeDependencyMatrix() + # We explicitly update self._lambdaMat since it doesn't have a canary + # TODO: (1) Should non compiled objects also have canaries? + # (2) self._lambdaMat might not be useful anyway though... + self.get_ReactantMatrix() - # keep jumping, Whoop Whoop (put your hands up!). - f = firstReaction + # keep jumping, Whoop Whoop (put your hands up!) while t < finalT: - # print(t) + # Take a timetep try: if exact: - x, t, success = f(x, t, self._vMat, - self.transition_vector, seed=seed) + # Use Gillespie algorithm for entire simulation + t, jump_time, x, jumps, success = firstReaction(x, + self._state_lims, + t, + self.vMat, + self.eventRateVector, + seed=seed) + if success==False: + break else: - if np.min(x) > 10: - x_tmp, t_tmp, success = tauLeap(x, t, - # self._vMat, self._lambdaMat, - self._vMat, self._lambdaMatOD, # I think that the wrong matrix has been used, trying this one instead - self.transition_vector, - self.transition_mean, - self.transition_var, - seed=seed) - if success: - x, t = x_tmp, t_tmp - else: - x, t, success = f(x, t, self._vMat, - self.transition_vector, seed=seed) + #if np.min(x) < 10: + #Use tau leap when population of any state is small. + # TODO: Why? If e.g. one state always has a population zero then we force ourselves + # to use Gillespie. We also have a safety procedure to stop variables going + # outside their bounds anyway, so not sure what this achieves. + t_new, jump_time, x_new, jumps, success = tauLeap(x, + self._state_lims, + t, + self.vMat, + self._lambdaMat, + self.eventRateVector, + self.transitionMean, + self.transitionVar, + self.pureOdeVector, + epsilon=self._epsilon, + seed=seed, + pre_tau=self.pre_tau) + + if success: + # Jump results in all states within their limits, continue. + t, x = t_new, x_new else: - x, t, success = f(x, t, self._vMat, - self.transition_vector, seed=seed) + # Retry with first reaction method. + t, jump_time, x, jumps, success = firstReaction(x, + self._state_lims, + t, + self.vMat, + self.eventRateVector, + seed=seed) + + if success==False: + break + if success: - xList.append(x.copy()) + xList.append(x.copy()) # TODO: why is x a copy and the rest not? tList.append(t) + dtList.append(jump_time) + jumpList.append(jumps) else: break - ## print("x: %s, t: %s" % (x, t)) - ## raise Exception('WTF') except SimulationError: break - return np.array(xList), np.array(tList) + return np.array(xList), np.array(jumpList), np.array(tList), np.array(dtList) + + ########################################################################### + # + # Functions to process simulation output + # + ########################################################################### def _extractObservationAtTime(self, X, t, targetTime): ''' Given simulation and a set of time points which we would like to observe, we extract the observations :math:`x_{t}` with :math:`\\min\\{ \\abs( t - targetTime) \\}` - ''' - y = list() - # maxTime = max(t) - index = 0 - for i in targetTime: - if np.any(t == i): - index = np.where(t == i)[0][0] - else: - index = np.searchsorted(t, i) - 1 - y.append(X[index]) - - return np.array(y) - - ######################################################################## - # - # Operators with regard to the transition matrix - # - ######################################################################## - - def get_transition_matrix(self): - ''' - Returns the transition matrix in algebraic form. - - Returns - ------- - :class:`sympy.matrices.matrices` - A matrix of dimension [number of state x number of state] - - ''' - if self._transitionMatrix is None: - super(SimulateOde, self)._computeTransitionMatrix() - - if self._transitionMatrixCompile is not None \ - or not self._hasNewTransition.transitionMatrixCompile: - return self._transitionMatrix - else: - return super(SimulateOde, self)._computeTransitionMatrix() - - def get_transition_vector(self): - ''' - Returns the set of transitions in a single vector, transitions - between state to state first then the birth and death process - - Returns - ------- - :class:`sympy.matrices.matrices` - A matrix of dimension [total number of transitions x 1] - - ''' - if self._transitionVectorCompile is not None \ - or not self._hasNewTransition.transitionVector: - return self._transitionVector - else: - return super(SimulateOde, self)._computeTransitionVector() - - def transition_matrix(self, state, t): - ''' - Evaluate the transition matrix given state and time Parameters ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time + t (list): Timepoints of simulation + X (list of lists): State values at each timepoint + targetTime (list): Desired timepoints Returns ------- - :class:`numpy.ndarray` - a 2d array of size (M,M) where M is the number - of transitions - + X_out (np.array): Value of states at targetTime ''' - return self.eval_transition_matrix(time=t, state=state) + X_out = [] + + for t_target in targetTime: + if np.any(t == t_target): + index = np.where(t == t_target)[0][0] + else: + index = max(np.searchsorted(t, t_target) - 1, 0) + X_out.append(X[index]) - def eval_transition_matrix(self, parameters=None, time=None, state=None): + return np.array(X_out) + + def _interpolateObservationAtTime(self, X, t, targetTime): ''' - Evaluate the transition matrix given parameters, state and time. Note - that the output is not in sparse format + Given simulation and a set of time points which we would like to + observe, we interpolate the observations onto the desired grid. Parameters ---------- - parameters: list - see :meth:`.setParameters` - time: double - The current time - state: array list - The current numerical value for the states which can - :class:`numpy.ndarray` or :class:`list` + t (list): Timepoints of simulation + X (list of lists): State values at each timepoint + targetTime (list): Desired timepoints Returns ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] - + X_out (np.array): Value of states at targetTime + ''' - if self._transitionMatrixCompile is None \ - or self._hasNewTransition.transitionMatrixCompile: - self._compileTransitionMatrix() - eval_param = self._getEvalParam(state, time, parameters) - return self._transitionMatrixCompile(eval_param) + X=np.array(X) # Convert to numpy array so we can interpolate between timepoints - def _compileTransitionMatrix(self): - ''' - We would also need to compile the function so that - it can be evaluated faster. - ''' - if self._transitionMatrix is None \ - or self._hasNewTransition.transitionMatrixCompile: - super(SimulateOde, self)._computeTransitionMatrix() - - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._transitionMatrixCompile = f(self._sp, - self._transitionMatrix, - modules='mpmath') - else: - self._transitionMatrixCompile = f(self._sp, - self._transitionMatrix) + dims=X.shape # Get dimensions of data (timepoints x vars) + n_state=dims[1] + + X_out=np.zeros((len(targetTime), n_state)) # empty matrix to receive scaled data = (new timepoints x vars) - self._hasNewTransition.reset('transitionMatrixCompile') + # linearly interpolate to new timepoints + for i in range(n_state): + X_out[:,i]=np.interp(targetTime, t, X[:,i]) - return None + return X_out - def transition_vector(self, state, t): + def _addJumpsBetweenTime(self, dX, t, targetTime, exact): ''' - Evaluate the transition vector given state and time + Given number of events occuring at certain times find total + number of occurrances between the desired timepoints. Parameters ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time + t (list): Timepoints that events occurred + dX (list of lists): Number of events at each timepoint + targetTime (list): Desired timepoints + exact (bool): If first reaction method used (otherwise tau assumed) Returns ------- - :class:`numpy.ndarray` - a 1d array of size K where K is the number of between - states transitions and the number of birth death - processes - ''' - return self.eval_transition_vector(time=t, state=state) - - def eval_transition_vector(self, parameters=None, time=None, state=None): + X_out (np.array): Value of states at targetTime + ''' - Evaluate the transition vector given parameters, state and time. Note - that the output is not in sparse format - Parameters - ---------- - parameters: list - see :meth:`.setParameters` - time: double - The current time - state: array list - The current numerical value for the states which can - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - vector of dimension [total number of transitions] + dX=np.array(dX) # convert to numpy array so we can interpolate between timepoints - ''' - if self._transitionVectorCompile is None \ - or self._hasNewTransition.transitionVector: - self._compileTransitionVector() + dims=dX.shape # Get dimensions of data (timepoints x n_trans) + n_trans=dims[1] - eval_param = self._getEvalParam(state, time, parameters) - return self._transitionVectorCompile(eval_param) + # empty matrix to receive scaled data = (new timepoints x n_trans) + # minus one because we are looking at jumps which occur betwen timepoints + # (e.g. 2 timepoints =1 jump, 10 timepoints =9) + X_out=np.zeros((len(targetTime)-1, n_trans)) - def _compileTransitionVector(self): - ''' - We would also need to compile the function so that - it can be evaluated faster. - ''' - if self._transitionVector is None \ - or self._hasNewTransition.transitionVector: - super(SimulateOde, self)._computeTransitionVector() - - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._transitionVectorCompile = f(self._sp, - self._transitionVector, - modules='mpmath') - else: - self._transitionVectorCompile = f(self._sp, - self._transitionVector) + # if exact, each point corresponds to a transitions and has weight 1. + for i in range(n_trans): + if exact: + hist, bin_edges=np.histogram(t, bins=targetTime) + else: + hist, bin_edges=np.histogram(t[1:], bins=targetTime, weights=dX[:,i]) + X_out[:,i]=hist - self._hasNewTransition.reset('transitionVector') + return X_out - return + ########################################################################### + # + # Functions to compute sympy objects and also compile them + # + ########################################################################### - def get_birth_death_rate(self): + def get_TransitionJacobian(self): ''' - Find the algebraic equations of birth and death processes - - Returns - ------- - :class:`sympy.matrices.matrices` - birth death process in matrix form + Evaluate equation (7) from https://people.cs.vt.edu/~ycao/publication/newstepsize.pdf + where F_[i,j] is the change in transition rate a[i], if a transition of type j occurs: + F_[i,j] = sum_k diff(a[i], x_k) v_[k,j] + where k=state and v[k,j] is how much state x_k changes by if transition of type j occurs. ''' - if self._birthDeathRate is None or self._hasNewTransition: - self._computeBirthDeathRate() - return self._birthDeathRate + # Ensure objects, vMat and eventRateVector, are up to date + # TODO: Maybe a better naming convention, where generator function and the object + # it creates have some similarity. + self.get_StateChangeMatrix() + self.get_EventRateVector() - def birth_death_rate(self, state, t): - ''' - Evaluate the birth death rates given state and time + F = sympy.zeros(self.num_events, self.num_events) - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`np.ndarray` or :class:`list` - t: double - The current time + for event_index_i, rate in enumerate(self._eventRateVector): + for event_index_j in range(self.num_events): + for state_index, state in enumerate(self._iterStateList()): + diffEqn, isDifficult = simplifyEquation( sympy.diff(rate, state, 1) ) # diff(a_i, x_k) + F[event_index_i, event_index_j] += diffEqn*self._vMat[state_index, event_index_j] + self._isDifficult = self._isDifficult or isDifficult - Returns - ------- - :class:`numpy.ndarray` - an array of size (M,M) where M is the number - of birth and death actions + self._transitionJacobian = F - ''' - return self.eval_birth_death_rate(time=t, state=state) + return self._transitionJacobian - def eval_birth_death_rate(self, parameters=None, time=None, state=None): + def get_TransitionMean(self): ''' - Evaluate the birth and death rates given parameters, state and time. - - Parameters - ---------- - parameters: list - see :meth:`.setParameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of birth and death rates x 1] - + This is the mean and variance of the changes in the transition rates + (aka propensity funtions) after a potential timestep: + equations (8a) and (8b) from https://people.cs.vt.edu/~ycao/publication/newstepsize.pdf + For n transitions the outputs are 2 vectors, each of length n. + Outputs are added to self as mu and sigma2 ''' - if self._birthDeathRateCompile is None \ - or self._hasNewTransition.birthDeathRateCompile: - self._computeBirthDeathRate() - eval_param = self._getEvalParam(state, time, parameters) - return self._birthDeathRateCompile(eval_param) + # Ensure objects are up to date + self.get_TransitionJacobian() + self.get_EventRateVector() - def _computeBirthDeathRate(self): - ''' - Note that this is different to _birthDeathVector because - this is of length (number of birth and death process) while - _birthDeathVector in baseOdeModel has the same length as - the number of states - ''' - if self.num_birth_deaths == 0: - A = sympy.zeros(1, 1) - else: - A = sympy.zeros(self.num_birth_deaths, 1) - - # go through all the transition objects - for i, bd in enumerate(self.birth_death_list): - A[i] += eval(self._checkEquation(bd.equation())) - - # assign back - self._birthDeathRate = A - # compilation of the symbolic calculation. Note here that we are - # going to recompile the total transitions because it might - # have changed - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._birthDeathRateCompile = f(self._sp, - self._birthDeathRate, - modules='mpmath') - else: - self._birthDeathRateCompile = f(self._sp, - self._birthDeathRate) + F = self._transitionJacobian - self._hasNewTransition.reset('birthDeathRateCompile') + mu = sympy.zeros(self.num_events, 1) + for event_index_i in range(self.num_events): + for event_index_j, rate_j in enumerate(self._eventRateVector): + mu[event_index_i] += F[event_index_i, event_index_j] * rate_j - return None + self._transitionMean = mu - def total_transition(self, state, t): - ''' - Evaluate the total transition rate given state and time + # TODO: Propensity functions also change if there is time dependence + # This will be addressed better in the next version where tau + # leaping will be updated. + # # If time dependence, add in another term to reflect this: + # timelike_symbols=[symb for symb in eqn_i.free_symbols if str(symb)=='t'] + # is_time_dependent=len(timelike_symbols)>0 + # if is_time_dependent and self.tstep: + # time_variable = [timelike_symbols][0] + # mu[i] += sympy.diff(eqn_i, time_variable, 1) # mean changes but sd does not, TODO: check this - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time + return self._transitionMean - Returns - ------- - float - total rate + def get_TransitionVar(self): ''' - return sum(self.transition_vector(time=t, state=state)) - - def transition_mean(self, state, t): + This is the mean and variance of the changes in the transition rates + (aka propensity funtions) after a potential timestep: + equations (8a) and (8b) from https://people.cs.vt.edu/~ycao/publication/newstepsize.pdf + For n transitions the outputs are 2 vectors, each of length n. + Outputs are added to self as mu and sigma2 ''' - Evaluate the mean of the transitions given state and time. For - m transitions and n states, we have - - .. math:: - f_{j,k} &= \\sum_{i=1}^{n} \\frac{\\partial a_{j}(x)}{\\partial x_{i}} v_{i,k} \\\\ - \\mu_{j} &= \\sum_{k=1}^{m} f_{j,k}(x)a_{k}(x) \\\\ - \\sigma^{2}_{j}(x) &= \\sum_{k=1}^{m} f_{j,k}^{2}(x) a_{k}(x) - where :math:`v_{i,k}` is the state change matrix. + # Ensure objects are up to date + self.get_TransitionJacobian() + self.get_EventRateVector() - Parameters - ---------- - state: array like - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - t: double - The current time - - Returns - ------- - :class:`numpy.ndarray` - an array of size m where m is the number of transition - - ''' - return self.eval_transition_mean(time=t, state=state) + F = self._transitionJacobian - def eval_transition_mean(self, parameters=None, time=None, state=None): - ''' - Evaluate the transition mean given parameters, state and time. + sigma2 = sympy.zeros(self.num_events, 1) + for event_index_i in range(self.num_events): + for event_index_j, rate_j in enumerate(self._eventRateVector): + sigma2[event_index_i] += F[event_index_i, event_index_j] * F[event_index_i, event_index_j] * rate_j - Parameters - ---------- - parameters: list - see :meth:`.setParameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` + self._transitionVar = sigma2 - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] + return self._transitionVar - ''' - if self._transitionMeanCompile is None \ - or self._hasNewTransition.computeTransitionMeanVar: - self._computeTransitionMeanVar() - eval_param = self._getEvalParam(state, time, parameters) - return self._transitionMeanCompile(eval_param) + ########################################################################### + # + # Other functions, depending on the compiled sympy objects + # + ########################################################################### - def transition_var(self, state, t): + def total_transition(self, state, t): ''' - Evaluate the variance of the transitions given state and time + Evaluate the total transition rate given state and time Parameters ---------- @@ -995,101 +774,20 @@ def transition_var(self, state, t): Returns ------- - :class:`numpy.ndarray` - an array of size M where M is the number of transition - - ''' - return self.eval_transition_var(time=t, state=state) - - def eval_transition_var(self, parameters=None, time=None, state=None): - ''' - Evaluate the transition variance given parameters, state and time. - - Parameters - ---------- - parameters: list - see :meth:`.setParameters` - time: double - The current time - state: array list - The current numerical value for the states which can be - :class:`numpy.ndarray` or :class:`list` - - Returns - ------- - :class:`numpy.matrix` or :class:`mpmath.matrix` - Matrix of dimension [number of state x number of state] - - ''' - if self._transitionVarCompile is None \ - or self._hasNewTransition.computeTransitionMeanVar: - self._computeTransitionMeanVar() - - eval_param = self._getEvalParam(state, time, parameters) - return self._transitionVarCompile(eval_param) - - def _computeTransitionJacobian(self): - if self._GMat is None: - self._computeDependencyMatrix() - - F = sympy.zeros(self.num_transitions, self.num_transitions) - for i in range(self.num_transitions): - for j, eqn in enumerate(self._transitionVector): - for k, state in enumerate(self._iterStateList()): - diffEqn = sympy.diff(eqn, state, 1) - tempEqn, isDifficult = simplifyEquation(diffEqn) - F[i,j] += tempEqn*self._vMat[k,i] - self._isDifficult = self._isDifficult or isDifficult - - self._transitionJacobian = F - - self._hasNewTransition.reset('transitionJacobian') - return F + float + total rate - def _computeTransitionMeanVar(self): - ''' - This is the mean and variance information that we need - for the :math:`\\tau`-Leap ''' + return sum(self.eventRateVector(time=t, state=state)) - if self._transitionJacobian is None or self._hasNewTransition.transitionJacobian: - self._computeTransitionJacobian() - - F = self._transitionJacobian - # holders - mu = sympy.zeros(self.num_transitions, 1) - sigma2 = sympy.zeros(self.num_transitions, 1) - # we calculate the mean and variance - for i in range(self.num_transitions): - for j, eqn in enumerate(self._transitionVector): - mu[i] += F[i,j] * eqn - sigma2[i] += F[i,j] * F[i,j] * eqn - - self._transitionMean = mu - self._transitionVar = sigma2 - - # now we are going to compile them - f = self._SC.compileExprAndFormat - if self._isDifficult: - self._transitionMeanCompile = f(self._sp, - self._transitionMean, - modules='mpmath') - self._transitionVarCompile = f(self._sp, - self._transitionVar, - modules='mpmath') - else: - self._transitionMeanCompile = f(self._sp, self._transitionMean) - self._transitionVarCompile = f(self._sp, self._transitionVar) - - self._hasNewTransition.reset('computeTransitionMeanVar') - - return None - - ######################################################################## + ########################################################################### # # Unrolling of ode to transitions # - ######################################################################## + # TODO: I doubt any of this works with the event based framework + # but it didn't work perfectly anyway. Will be a challenge + # now we are dealing with more general systems. + ########################################################################### def get_unrolled_obj(self): ''' @@ -1197,7 +895,7 @@ def plot(self, sim_X=None, sim_T=None): ''' Plot the results of a simulation - Takes the output of a function like `simulate_jump` + Takes the output of a function like `solve_stochast` Parameters ---------- diff --git a/src/pygom/model/stochastic_simulation.py b/src/pygom/model/stochastic_simulation.py index 07adab7b..4718688d 100644 --- a/src/pygom/model/stochastic_simulation.py +++ b/src/pygom/model/stochastic_simulation.py @@ -78,7 +78,7 @@ def exact(x0, t0, t1, state_change_mat, transition_func, return x -def hybrid(x0, t0, t1, state_change_mat, reactant_mat, +def hybrid(x0, t0, t1, state_change_mat, transition_func, transition_mean_func, transition_var_func, output_time=False, seed=None): """ @@ -140,7 +140,7 @@ def hybrid(x0, t0, t1, state_change_mat, reactant_mat, while t < t1: if np.min(x) > 10: x_new, t_new, s = tauLeap(x, t, - state_change_mat, reactant_mat, + state_change_mat, transition_func, transition_mean_func, transition_var_func, @@ -380,7 +380,7 @@ def directReaction(x, t, state_change_mat, transition_func, seed=None): # we can't jump raise SimulationError("Cannot perform any more reactions") -def firstReaction(x, t, state_change_mat, transition_func, seed=None): +def firstReaction(x, x_lims, t, state_change_mat, transition_func, seed=None): """ The first reaction method @@ -388,6 +388,9 @@ def firstReaction(x, t, state_change_mat, transition_func, seed=None): ---------- x: array like state vector + x_lims: array like + list of length 2 lists giving [max, min] limits for each state + can be [None, None] if no limits. t: double time state_change_mat: array like @@ -409,25 +412,38 @@ def firstReaction(x, t, state_change_mat, transition_func, seed=None): Returns ------- - x: array like - state vector - t: double - time + t_new: double + New timepoint + jump_times: double + timestep + x_new: array like + new state + jumps: array like + list giving identity of the transition which fired in the timestep success: - if the leap was successful. A change in both x and t if it is - successful, no change otherwise + if the leap was successful (where success is defined as all x[i] falling within x_lims[i]) + Results in a change in both x and t if it is successful, no change otherwise. """ + changes=state_change_mat(x, t) rates = transition_func(x, t) + # For now we assume when all transition rates are zero, further simulation is not necessary. + if all(rates==0): + return 0, 0, 0, 0, False + # find our jump times jump_times = _newJumpTimes(rates, seed=seed) if np.all(jump_times == np.inf): return x, t, False # first jump min_index = np.argmin(jump_times) - new_x = _updateStateWithJump(x, min_index, state_change_mat) - return _checkJump(x, new_x, t, jump_times[min_index]) + new_x = _updateStateWithJump(x, min_index, changes) + + # record which state the jump was in + jumps=[0]*len(rates) + jumps[min_index]=1 + return _checkJump(x, new_x, x_lims, t, jump_times[min_index], jumps) def nextReaction(x, t, state_change_mat, dependency_graph, old_rates, jump_times, transition_func, seed=None): @@ -435,10 +451,11 @@ def nextReaction(x, t, state_change_mat, dependency_graph, The next reaction method """ + changes=state_change_mat(x, t) # smallest time :) index = np.argmin(jump_times) # moving state and time - new_x = _updateStateWithJump(x, index, state_change_mat) + new_x = _updateStateWithJump(x, index, changes) t = jump_times[index] # recalculate the new transition matrix if hasattr(transition_func, '__call__'): @@ -468,11 +485,25 @@ def nextReaction(x, t, state_change_mat, dependency_graph, raise SimulationError("Cannot perform any more reactions") -def tauLeap(x, t, state_change_mat, reactant_mat, - transition_func, transition_mean_func, transition_var_func, - epsilon=0.1, seed=None): +def tauLeap(x, + x_lims, + t, + state_change_mat, + reactant_mat, + transition_func, + transition_mean_func, + transition_var_func, + pureOde, + epsilon=0.03, + seed=None, + pre_tau=None): """ - The Poisson :math:`\\tau`-Leap + The Poisson :math:`\\tau`-Leap. Calculates the appropriate time step + and then moves the system forwards by this amount. The time step + calculation involves two stages: first, a calculation of the step size + according to the timescales of the system and second, a refinement of + this if necessary taking into account the risk of states having negative + populations. Parameters ---------- @@ -499,7 +530,8 @@ def tauLeap(x, t, state_change_mat, reactant_mat, a function that takes the input argument (x,t) and returns the vector of transition variance epsilon: double, optional - tolerance of the size of the jump, defaults to 0.1 + tolerance of the size of the jump, defaults to 0.03 as recommended by + Cao et al. https://doi.org/10.1063/1.2159468 seed: optional represents which type of seed to use. None will defaults to the current global state while False will reinitialize to the initial @@ -511,77 +543,152 @@ def tauLeap(x, t, state_change_mat, reactant_mat, Returns ------- - x: array like - state vector - t: double - time + t_new: double + New timepoint + jump_times: double + timestep + x_new: array like + new state + jumps: array like + transition values success: - if the leap was successful. A change in both x and t if it is - successful, no change otherwise + if the leap was successful (where success is defined as all x[i] falling within x_lims[i]) + Results in a change in both x and t if it is successful, no change otherwise. """ - # go through the list of transitions + determ_changes = pureOde(x, t) + changes = state_change_mat(x, t) rates = transition_func(x, t) + # For now we assume when all transition rates are zero, further simulation is not necessary. + if all(rates==0): + return 0, 0, 0, 0, False + + # Step 1: Calculate step size due to timescales of the system + # TODO: add in minimum stepsize condition from Cao equations (11)-(13) + + # If no timestep specified, do adaptive tau leap. + if pre_tau==None: + tau_scale=_get_adaptive_tau_step(x, + t, + rates, + transition_mean_func, + transition_var_func, + epsilon=epsilon) + else: + tau_scale=pre_tau - mu = transition_mean_func(x, t) - sigma2 = transition_var_func(x, t) - # then we go find out the condition - # \min_{j \in \left[1,M\right]} \{ l,r \} - # where l = \gamma / \abs(\mu_{j}(x)) , - # and r = \gamma^{2} / \sigma_{j}^{2}(x) - top = epsilon*np.sum(rates) - try: - l = top/abs(mu) - except Warning: - print("Warning as an exception") - print(mu) - print(x) - print(t) - print(rates) - r = (top**2)/sigma2 - tau_scale = min(min(l), min(r)) - # note that the above calculation is actually very slow, because - # we can rewrite the conditions into - # \min \{ \min_{j \in \left[1,M\right]} l , \min_{j \in \left[1,M\right]} r \} - # which again can be further simplified into - # \gamma / \max_{j \in \left[1,\M\right]} \{ \abs(\mu_{j}(x),\sigma_{j}^{2} \} + # Step 2: we put in an additional safety mechanism here where we also evaluate + # the probability that a realization exceeds the observations and further + # decrease the time step. + # TODO: consider how Cao implemented this - # we put in an additional safety mechanism here where we also evaluate - # the probability that a realization exceeds the observations and further - # decrease the time step. + loss_mat=reactant_mat.copy() + loss_mat[loss_mat==1]=0 + loss_mat[loss_mat==-1]=1 + tau_scale, safe = _cy_test_tau_leap_safety(x.astype(np.float64, copy=False), - reactant_mat.astype(np.int64, copy=False), + loss_mat.astype(np.int64, copy=False), rates.astype(np.float64, copy=False), float(tau_scale), float(epsilon)) if safe is False: return x, t, False - # make the jumps - new_x = x.copy() + # containers for output + new_x = x.copy() # updated state populations + jumps=[0]*len(rates) # transitions + + # take stochastic step for i, r in enumerate(rates): - # realization - try: - jumpQuantity = rpois(1, tau_scale*r, seed=seed) - except Exception as e: -# print tauScale, r -# print "l = %s " % l -# print "r = %s " % (top**2 / sigma2) -# print "top = %s " % top -# print "min (l, r) = (%s, %s)" % (min(l), min(top**2 / sigma2)) -# print "tauScale = %s" % tauScale -# print "exceed %s " % len(exceedCDFArray) -# print "mu = %s " % mu -# print "sigma2 = %s " % sigma2 - raise e - - # print jumpQuantity - # move the particles! - new_x = _updateStateWithJump(new_x, i, state_change_mat, jumpQuantity) - ## done moving - return _checkJump(x, new_x, t, tau_scale) + n_event_occurances = rpois(1, tau_scale*r, seed=seed) + jumps[i]=n_event_occurances + new_x = _updateStateWithJump(new_x, i, changes, n_event_occurances) + + # deterministic changes + new_x = new_x + determ_changes*tau_scale + + + return _checkJump(x, new_x, x_lims, t, tau_scale, jumps) +# TODO: Check speed performance of this and see if cython version necessary +def _get_adaptive_tau_step(x, + t, + rates, + transition_mean_func, + transition_var_func, + epsilon): + + """ + Adaptive :math:`\\tau`-Leap calculator + + Calculates the time step size such that, given the current state of the + system, (x,t), no propensity function, a[i](x,t), (where i denotes the transition) + changes appreciably over the course of the time step. + Parameters + ---------- + x: array like + state vector + t: double + time + rates: array like + values of rates of each transition, i (i.e. evaluation of the propensity + functions a[i](x,t)) + transition_mean_func: callable + a function that takes the input argument (x,t) and returns the vector + of the mean expected rates of change of the a[i] with time + transition_var_func: callable + a function that takes the input argument (x,t) and returns the vector + of the variance of the expected rates of change of the a[i] with time + epsilon: double, optional + tolerance of the size of the jump, (0.03 is recommended by + Cao et al. https://doi.org/10.1063/1.2159468) + + Returns + ------- + tau_scale: double + time step which is short enough such that system equations don't change + appreciably + """ + + mu = transition_mean_func(x, t) # mu[i]*dt = mean of expected change in a[i] in dt + sigma2 = transition_var_func(x, t) # sqrt(sigma2*dt) = standard deviation of expected change in a[i] in dt + + # Some rates could be 0. Remove them to avoid dividing by 0 later on. + mu=mu[mu!=0] + sigma2=sigma2[sigma2!=0] + + if mu.size==0 and sigma2.size==0: + # These values could be 0 if e.g. the epidemic is over and nothing + # is happening anymore. The function needs to return something, though might be + # better end the simulation (assuming nothing will bring the system + # back to life, e.g. external introductions or immune waning). + # For now default to step size of 1, just to complete the run. + return np.float64(1) + + else: + # Equations (7)-(9) from Cao et al. https://doi.org/10.1063/1.2159468 + # (publicly available copy https://people.cs.vt.edu/~ycao/publication/newstepsize.pdf) + bound = epsilon*np.sum(rates) + if mu.size==0: + tau_scale = min((bound**2)/sigma2) + elif sigma2.size==0: + tau_scale = min(bound/abs(mu)) + else: + tau_scale_mu=min(bound/abs(mu)) + tau_scale_sig=min((bound**2)/sigma2) + tau_scale=min(tau_scale_mu, tau_scale_sig) + + return tau_scale + + # TODO: note that the above calculation is actually very slow, because + # we can rewrite the conditions into + # \min \{ \min_{j \in \left[1,M\right]} l , \min_{j \in \left[1,M\right]} r \} + # which again can be further simplified into + # \gamma / \max_{j \in \left[1,\M\right]} \{ \abs(\mu_{j}(x),\sigma_{j}^{2} \} + # where l= bound/abs(mu) and r=(bound**2)/sigma2 + +# TODO: Check speed performance of this vs cython version def _test_tau_leap_safety(x, reactant_mat, rates, tau_scale, epsilon): """ Additional safety test on :math:`\\tau`-leap, decrease the step size if @@ -643,12 +750,50 @@ def _updateStateWithJump(x, transition_index, state_change_mat, n=1.0): return x + state_change_mat[:, transition_index]*n -def _checkJump(x, new_x, t, jump_time): - failed_jump = np.any(new_x < 0) +# def _checkJump(new_x, x_lims): +# # Check if new values fall outside of limits +# failed_jump=False +# for i, x_lim in enumerate(x_lims): +# if x_lim != [None, None]: +# x_min=x_lim[0] +# x_max=x_lim[1] +# if x_min is None: +# if new_x[i]>x_max: +# failed_jump=True +# elif x_max is None: +# if new_x[i]x_max: +# failed_jump=True + +# return failed_jump + +def _checkJump(x, x_new, x_lims, t, jump_time, jumps): + # Check that new values fall within limits and increment time + + failed_jump=False + for i, x_lim in enumerate(x_lims): + if x_lim != (None, None): + x_min=x_lim[0] + x_max=x_lim[1] + if x_min is None: + if x_new[i]>x_max: + failed_jump=True + elif x_max is None: + if x_new[i]x_max: + failed_jump=True if failed_jump: - # print "Illegal jump, x: %s, new x: %s" % (x, new_x) - return x, t, False + print("Illegal jump, x: %s, new x: %s" % (x, x_new)) + success=False + x_new=x + t_new=t else: - t += jump_time - return new_x, t, True + success=True + t_new = t + jump_time + + return t_new, jump_time, x_new, jumps, success diff --git a/src/pygom/model/transition.py b/src/pygom/model/transition.py index a6f67e0d..b3de94c2 100644 --- a/src/pygom/model/transition.py +++ b/src/pygom/model/transition.py @@ -7,6 +7,7 @@ """ __all__ = [ + 'Event', 'Transition', 'TransitionType' ] @@ -25,7 +26,73 @@ class InputStateError(Exception): ''' pass -class Transition(object): +class Event: + ''' + Class to contain transitions + ''' + + def __init__(self, + transition_list, + rate=None): + + # If one solitary unlisted transition provided, gather it into a list + if not isinstance(transition_list, list): + if isinstance(transition_list, Transition): + transition_list=[transition_list] + else: + raise InputStateError("Transition object provided not of class Transition") + + # Check each transition is of the type, Transition + for transition in transition_list: + if not isinstance(transition, Transition): + raise InputStateError("At least one Transition object provided not of class Transition") + + # Check that ODE's have not been supplied + for transition in transition_list: + if transition.transition_type == TransitionType.ODE: + raise InputStateError("ODEs cannot be wrapped in an Event class. To pass pure ODEs to"+ + "SimulateOde, use the ode argument") + + # Check enough information has been provided and unpack it. + # Sufficient input consists of either: + # 1) One transition with an equation + no rate + # 2) One transition without an equation + rate + # 3) Multiple transitions each without equations + rate + # 4) Multiple transitions where only 1 has equation + no rate + + if len(transition_list)==1: + if transition.equation is not None: + if rate is not None: + raise InputStateError("Event rate dictates the rate at which its"+ + "member Transitions occur. It is superfluous for transitions"+ + "to declare their own rate and would be incorrect if it differed"+ + "from that in the Event anyway.") + else: + self.rate=transition.equation + elif rate is None: + raise InputStateError("Rate cannot be found in Event or Transitions") + else: + self.rate=rate + else: + n_eq=0 + for transition in transition_list: + if transition.equation is not None: + n_eq+=1 + if n_eq>1: + raise InputStateError("Zero or one equations needed, but ", n_eq, " provided") + elif (n_eq==1) and (rate is not None): + raise InputStateError("Rate and equation defined, but only one should be provided") + elif (n_eq==0) and (rate is None): + raise InputStateError("Rate cannot be found in Event or Transitions") + else: + self.rate=rate + + self.transition_list=transition_list + + + + +class Transition: ''' This class carries the information for transitions defined for an ode, which includes the ode itself, a birth death @@ -48,67 +115,84 @@ class Transition(object): it throws an error ''' - def __init__(self, origin, equation, transition_type='ODE', - destination=None, ID=None, name=None): + def __init__(self, + origin=None, + equation=None, # If equation is given + transition_type='ODE', + destination=None, + magnitude='1', + ID=None, + name=None): ''' Constructor for the class. ''' self.ID = ID self.name = name - # we naturally assume that the between state transition - # is false, i.e. everything is either an ode or a birth - # death process type _equation - self._betweenStateTransition = False - self._transition_type = None self._setTransitionType(transition_type) + self._setMagnitude(magnitude) + + # Check origins and destinations are consistent with transition type + + if self.transition_type == TransitionType.ODE: + if destination is not None: + raise InputStateError("Please define ODEs with the dependant variable as the origin") + if origin is None: + raise InputStateError("Please define ODEs with the dependant variable as the origin") + self._setOrigState(origin) + + if self.transition_type == TransitionType.B: + if origin is not None: + # TODO: This warning can be really annoying, I want it to just appear once. + # print("Update: In the latest version, you should define births as having a destination state instead of an origin.") + destination=origin + elif destination is None: + raise InputStateError("Birth process has no origin or destination") + # if destination is None: + # raise InputStateError("Birth process requires destination") + # if origin is not None: + # raise InputStateError("Birth process can only have a destination, please remove origin") + self._setDestState(destination) + + if self.transition_type == TransitionType.D: + if origin is None: + raise InputStateError("Death process requires origin") + if destination is not None: + raise InputStateError("Death process can only have an origin, please remove destination") + self._setOrigState(origin) - # private variables - self._orig_state = None - self._dest_state = None - self._equation = None - - if destination is not None: - if origin == destination: - if self.transition_type != TransitionType.T: - self._setOrigState(origin) - self._setEquation(equation) - else: - raise InputStateError("Input have the same state for " + - "the origin and destination, but " + - "transition type is " + - self._transition_type.name) - else: - if self.transition_type == TransitionType.T: - self._setOrigState(origin) - self._setDestState(destination) - self._setEquation(equation) + if self.transition_type == TransitionType.T: + if origin is None: + if destination is not None: + raise InputStateError("No origin, but transition type is between 2 compartments") else: - raise InputStateError("Input have both origin and " + - "destination state but transition " + - "type is " + self._transition_type.name) - else: # no destination - if self.transition_type != TransitionType.T: - self._setOrigState(origin) - self._setEquation(equation) - else: - raise InputStateError("Input only have origin, but " + - "transition type is " + - self._transition_type.name) + raise InputStateError("No origin or destination, but transition type is between 2 compartments") + if destination is None: + raise InputStateError("No destination, but transition type is between 2 compartments") + if origin == destination: + raise InputStateError("Origin and destination cannot be the same") + self._setOrigState(origin) + self._setDestState(destination) + + # If we get this far, then origin/destination checks have been successful + # Now add equation if it has been provided + + self._setEquation(equation) + # if equation is not None: + # # TODO: We need to create an event class somehow. + # self._setEquation(equation) def __str__(self): if self.transition_type == TransitionType.T: - return 'Transition from %s to %s, %s' % \ - (self._orig_state, self._dest_state, self._equation) + return 'Transition of size %s from %s to %s' % (self._magnitude, self._orig_state, self._dest_state) elif self.transition_type == TransitionType.ODE: return 'ODE for %s, %s' % (self._orig_state, self._equation) elif self.transition_type == TransitionType.B: - return 'Birth process to %s, %s' % (self._orig_state, self._equation) + return 'Birth process of size %s into %s' % (self._magnitude, self._orig_state, self._equation) elif self.transition_type == TransitionType.D: - return 'Death process from %s, %s' % (self._orig_state, self._equation) + return 'Death process of size %s from %s' % (self._magnitude, self._orig_state, self._equation) def __repr__(self): - if self.transition_type == TransitionType.T: repr_str = """Transition('%s', '%s', 'T', '%s'""" % \ (self._orig_state, self._equation, self._dest_state) @@ -175,6 +259,19 @@ def destination(self): ''' return self._dest_state + @property + def stochastic(self): + ''' + Return the secondary effects + + Returns + ------- + string + The destination state + + ''' + return self._stochastic + @property def equation(self): ''' @@ -239,6 +336,22 @@ def _setDestState(self, dest_state): self._dest_state = dest_state return self + def _setMagnitude(self, magnitude): + """ + Set the magnitude + """ + self._magnitude = magnitude + return self + + def _setStochastic(self, stochastic): + """ + Set the destination state + :param destination: Destination State + :type destination: String + """ + self._stochastic = stochastic + return self + def _setEquation(self, equation): ''' Set the transition _equation @@ -249,7 +362,9 @@ def _setEquation(self, equation): return self def _setTransitionType(self, transition_type): - # we also need the transition type + ''' + Set the transition type + ''' if isinstance(transition_type, TransitionType): self._transition_type = transition_type elif isinstance(transition_type, str): diff --git a/tests/simple_jump_process.py b/tests/simple_jump_process.py index 62eafa11..e41b60b5 100644 --- a/tests/simple_jump_process.py +++ b/tests/simple_jump_process.py @@ -22,7 +22,7 @@ import pkg_resources print('PyGOM version %s' %pkg_resources.get_distribution('pygom').version) -from pygom import Transition, TransitionType, SimulateOde +from pygom import Transition, TransitionType, Event, SimulateOde import numpy as np # Setup logging @@ -31,34 +31,39 @@ # construct model -states = ['S', 'I', 'R'] -params = ['beta', 'gamma', 'N'] -transitions = [Transition(origin='S', destination='I', equation='beta*S*I/N', - transition_type=TransitionType.T), - Transition(origin='I', destination='R', equation='gamma*I', - transition_type=TransitionType.T)] +state_list = [('S', (0,None)), ('I', (0, None)), ('R', (0, None))] +param_list = ['beta', 'gamma', 'N'] + +trans_inf=Transition(origin='S', destination='I',transition_type=TransitionType.T) +event_inf=Event(rate='beta*S*I/N', transition_list=[trans_inf]) + +trans_rec=Transition(origin='I', destination='R',transition_type=TransitionType.T) +event_rec=Event(rate='gamma*I', transition_list=[trans_rec]) + +model = SimulateOde(state=state_list, + param=param_list, + event=[event_inf, event_rec]) # initial conditions -N = 7781984.0 -in_inf = round(0.0000001*N) -init_state = [N - in_inf, in_inf, 0.0] -# -# # time +N = 7781984.0 # not sure why this number was chosen initially... +i0 = 10 # try to avoid stochastic extinction +init_state = [N - i0, i0, 0.0] + +# time max_t = 9 # 50 t = np.linspace (0 , max_t , 101) -# -# # deterministic parameter values -param_evals = [('beta', 3.6), ('gamma', 0.2), ('N', N)] -# construct model -model_j = SimulateOde(states, params, transition=transitions) -model_j.parameters = param_evals -model_j.initial_values = (init_state, t[0]) +# deterministic parameter values +param_evals = [('beta', 3.6), ('gamma', 0.2), ('N', N)] # R0=18 +# add params and ICs to model +model.parameters = param_evals +model.initial_values = (init_state, t[0]) # run 10 simulations +N_ITERATION=10 start = time.time() -simX, simT = model_j.simulate_jump(t[1::], iteration=10, full_output=True) +solution, simJump, simT = model.solve_stochast(t, iteration=N_ITERATION, full_output=True) end = time.time() logging.info('Simulation took {} seconds'.format(end - start)) diff --git a/tests/test_abc.py b/tests/test_abc.py index 6827e724..fcf0f908 100644 --- a/tests/test_abc.py +++ b/tests/test_abc.py @@ -13,7 +13,8 @@ def setUp(self): self.ode = common_models.SIR_norm({'beta':0.5, 'gamma':1.0/3.0}) # the initial state, normalized to one - self.x0 = [1, 1.27e-6, 0] + i0=1.27e-6 + self.x0 = [1-i0, i0, 0] # set the time sequence that we would like to observe self.t = np.linspace(0, 150, 100) self.ode.initial_values = (self.x0, self.t[0]) diff --git a/tests/test_epi_analysis.py b/tests/test_epi_analysis.py index b8d63ecf..6f622615 100644 --- a/tests/test_epi_analysis.py +++ b/tests/test_epi_analysis.py @@ -1,12 +1,12 @@ -from unittest import main, TestCase +import unittest import sympy from pygom.model import common_models, epi_analysis -class TestEpiAnalysis(TestCase): - +class TestEpiAnalysis(unittest.TestCase): + @unittest.skip("Skipping R0 calculation. This function needs development.") def test_simple(self): """ This actually only test the internal consistency of the functions @@ -26,4 +26,4 @@ def test_simple(self): if __name__ == '__main__': - main() + unittest.main() diff --git a/tests/test_input_symbols.py b/tests/test_input_symbols.py index bc34cd53..4fceb354 100644 --- a/tests/test_input_symbols.py +++ b/tests/test_input_symbols.py @@ -1,7 +1,7 @@ from unittest import main, TestCase from pygom.model.transition import Transition -from pygom.model.deterministic import DeterministicOde +from pygom import SimulateOde class TestInputSymbols(TestCase): @@ -11,11 +11,11 @@ def test_Signs(self): """ state_list = [['S+'], ['S-'], ['S*'], ['S\\'], ['_S']] param_list = ['beta'] - ode = DeterministicOde(['S'], param_list) + ode = SimulateOde(state=['S'], param=param_list) total_fail = 0 for state in state_list: - self.assertRaises(AssertionError, DeterministicOde, + self.assertRaises(AssertionError, SimulateOde, state, param_list) # Happy! :) @@ -31,7 +31,7 @@ def test_multi_symbol_in_str(self): Transition(origin='D', equation='(1-f) * alpha * I', transition_type='ODE') ] - ode = DeterministicOde(state_list, param_list, ode=odeList) + ode = SimulateOde(state=state_list, param=param_list, ode=odeList) # this should not throw an error if the model is initialized correctly A = ode.get_ode_eqn() diff --git a/tests/test_model_existing.py b/tests/test_model_existing.py index 8e53d24e..7a1e0e7c 100644 --- a/tests/test_model_existing.py +++ b/tests/test_model_existing.py @@ -48,11 +48,30 @@ def test_SEIR_periodic(self): ''' Test the SEIR model from the set of pre-defined models in common_models ''' - ode = common_models.SEIR_Birth_Death_Periodic() + + # Set up PyGOM object + alpha=1/2 + gamma=1/4 + beta0=0.3 + delta=0.2 + period=365 + + ode = common_models.SEIR_Birth_Death_Periodic({'alpha':alpha, + 'gamma':gamma, + 'beta0':beta0, + 'delta':delta, + 'period':period}) + + N=1e4 + E0=10 + I0=0 + R0=0 + S0=N-(E0+I0+R0) + + x0 = [S0, E0, I0, R0, N] + ode.initial_values = (x0, 0) + t = numpy.linspace(0, 100, 1001) - x0 = [0.0658, 0.0007, 0.0002, 0.] - ode.initial_values = (x0,0) - ode.parameters = [0.02, 35.84, 100, 1800, 0.27] # try to integrate to see if there is any problem _solution, _output = ode.integrate(t[1::], True) diff --git a/tests/test_model_multiple_origin.py b/tests/test_model_multiple_origin.py index 6ac286c0..51004804 100644 --- a/tests/test_model_multiple_origin.py +++ b/tests/test_model_multiple_origin.py @@ -1,12 +1,12 @@ -from unittest import main, TestCase +import unittest import numpy as np -from pygom import DeterministicOde, SimulateOde, Transition, TransitionType +from pygom import SimulateOde, Transition, TransitionType -class TestModelMultipleOrigin(TestCase): - +class TestModelMultipleOrigin(unittest.TestCase): + @unittest.skip("Skipping multiple origin. This is better done with Events, new test needed.") def setUp(self): # Tests the following system, solving the deterministic version # A + A -> C @@ -41,8 +41,9 @@ def setUp(self): transition_type=TransitionType.B) ] + @unittest.skip("Skipping multiple origin. This is better done with Events, new test needed.") def test_deterministic(self): - ode = DeterministicOde(self.states, + ode = SimulateOde(self.states, self.params, birth_death=self.birth_deaths, transition=self.transitions) @@ -51,6 +52,7 @@ def test_deterministic(self): ode.initial_values = (self.x0, self.t[0]) _solution = ode.integrate(self.t[1::]) + @unittest.skip("Skipping multiple origin. This is better done with Events, new test needed.") def test_stochastic(self): ode = SimulateOde(self.states, self.params, birth_death=self.birth_deaths, @@ -58,8 +60,9 @@ def test_stochastic(self): ode.parameters = self.param_eval ode.initial_values = (self.x0, self.t[0]) - _simX, _simT = ode.simulate_jump(self.t, 5, parallel=False, full_output=True) + _simX, _simJump, _simT = ode.solve_stochast(self.t, 5, parallel=False, full_output=True) + @unittest.skip("Skipping multiple origin. This is better done with Events, new test needed.") def tearDown(self): self.transitions = None self.birth_deaths = None @@ -68,4 +71,4 @@ def tearDown(self): if __name__ == '__main__': - main() + unittest.main() diff --git a/tests/test_model_vector.py b/tests/test_model_vector.py index 4f868fe1..db287759 100644 --- a/tests/test_model_vector.py +++ b/tests/test_model_vector.py @@ -1,12 +1,11 @@ -from unittest import main, TestCase - +import unittest import numpy -from pygom import Transition, TransitionType, DeterministicOde, ODEVariable - +from pygom import Transition, TransitionType, SimulateOde, ODEVariable -class TestModelVector(TestCase): +class TestModelVector(unittest.TestCase): + @unittest.skip("In adding state limits, this functionality may be lost") def test_Vector_State1(self): # state is a vector state_list = ['y1:4'] @@ -27,7 +26,7 @@ def test_Vector_State1(self): transition_type=TransitionType.T) ] # initialize the model - ode = DeterministicOde(state_list, param_list, + ode = SimulateOde(state_list, param_list, transition=transition_list) ode.get_ode_eqn() @@ -56,7 +55,7 @@ def test_Vector_State2(self): transition_type=TransitionType.T) ] - ode = DeterministicOde(state_list, param_list, + ode = SimulateOde(state_list, param_list, transition=transition_list) ode.get_ode_eqn() @@ -87,7 +86,7 @@ def test_Vector_State3(self): transition_type=TransitionType.T) ] - ode = DeterministicOde(state_list, param_list, + ode = SimulateOde(state_list, param_list, transition=transition_list) ode.get_ode_eqn() @@ -98,4 +97,4 @@ def test_Vector_State3(self): if __name__ == '__main__': - main() + unittest.main() diff --git a/tests/test_ode_decomposition.py b/tests/test_ode_decomposition.py index 97ee81a3..c7f119cd 100644 --- a/tests/test_ode_decomposition.py +++ b/tests/test_ode_decomposition.py @@ -8,11 +8,10 @@ class TestOdeDecomposition(TestCase): - def test_simple(self): - ode1 = Transition('S', '-beta*S*I', 'ode') - ode2 = Transition('I', 'beta*S*I - gamma * I', 'ode') - ode3 = Transition('R', 'gamma*I', 'ode') + ode1 = Transition(origin='S', equation='-beta*S*I', transition_type=TransitionType.ODE) + ode2 = Transition(origin='I', equation='beta*S*I - gamma * I', transition_type=TransitionType.ODE) + ode3 = Transition(origin='R', equation='gamma*I', transition_type=TransitionType.ODE) state_list = ['S', 'I', 'R'] param_list = ['beta', 'gamma'] ode = SimulateOde(state_list, param_list, ode=[ode1, ode2, ode3]) @@ -31,12 +30,12 @@ def test_hard(self): state_list = ['S', 'L', 'I', 'A', 'R', 'D'] param_list = ['beta', 'p', 'kappa', 'alpha', 'f', 'delta', 'epsilon', 'N'] ode_list = [ - Transition('S', '- beta * S/N * ( I + delta * A)', 'ODE'), - Transition('L', 'beta * S/N * (I + delta * A) - kappa * L', 'ODE'), - Transition('I', 'p * kappa * L - alpha * I', 'ODE'), - Transition('A', '(1-p) * kappa * L - epsilon * A', 'ODE'), - Transition('R', 'f * alpha * I + epsilon * A', 'ODE'), - Transition('D', '(1-f) * alpha * I', 'ODE') + Transition(origin='S', equation='- beta * S/N * ( I + delta * A)', transition_type=TransitionType.ODE), + Transition(origin='L', equation='beta * S/N * (I + delta * A) - kappa * L', transition_type=TransitionType.ODE), + Transition(origin='I', equation='p * kappa * L - alpha * I', transition_type=TransitionType.ODE), + Transition(origin='A', equation='(1-p) * kappa * L - epsilon * A', transition_type=TransitionType.ODE), + Transition(origin='R', equation='f * alpha * I + epsilon * A', transition_type=TransitionType.ODE), + Transition(origin='D', equation='(1-f) * alpha * I', transition_type=TransitionType.ODE) ] ode = SimulateOde(state_list, param_list, ode=ode_list) @@ -57,7 +56,6 @@ def test_bd(self): equation='beta * S * I - gamma * I - mu * I', transition_type=TransitionType.ODE), Transition(origin='R', - destination='R', equation='gamma * I', transition_type=TransitionType.ODE) ] @@ -75,13 +73,13 @@ def test_derived_param(self): ode = common_models.Legrand_Ebola_SEIHFR() ode_list = [ - Transition('S', '-(beta_I*S*I + beta_H_Time*S*H + beta_F_Time*S*F)'), - Transition('E', '(beta_I*S*I + beta_H_Time*S*H + beta_F_Time*S*F) - alpha*E'), - Transition('I', '-gamma_I*(1 - theta_1)*(1 - delta_1)*I - gamma_D*(1 - theta_1)*delta_1*I - gamma_H*theta_1*I + alpha*E'), - Transition('H', 'gamma_H*theta_1*I - gamma_DH*delta_2*H - gamma_IH*(1 - delta_2)*H'), - Transition('F', '- gamma_F*F + gamma_DH*delta_2*H + gamma_D*(1 - theta_1)*delta_1*I'), - Transition('R', 'gamma_I*(1 - theta_1)*(1 - delta_1)*I + gamma_F*F + gamma_IH*(1 - delta_2)*H'), - Transition('tau', '1') + Transition(origin='S', equation='-(beta_I*S*I + beta_H_Time*S*H + beta_F_Time*S*F)'), + Transition(origin='E', equation= '(beta_I*S*I + beta_H_Time*S*H + beta_F_Time*S*F) - alpha*E'), + Transition(origin='I', equation= '-gamma_I*(1 - theta_1)*(1 - delta_1)*I - gamma_D*(1 - theta_1)*delta_1*I - gamma_H*theta_1*I + alpha*E'), + Transition(origin='H', equation= 'gamma_H*theta_1*I - gamma_DH*delta_2*H - gamma_IH*(1 - delta_2)*H'), + Transition(origin='F', equation= '- gamma_F*F + gamma_DH*delta_2*H + gamma_D*(1 - theta_1)*delta_1*I'), + Transition(origin='R', equation= 'gamma_I*(1 - theta_1)*(1 - delta_1)*I + gamma_F*F + gamma_IH*(1 - delta_2)*H'), + Transition(origin='tau', equation= '1') ] ode1 = SimulateOde(ode.state_list, ode.param_list, ode._derivedParamEqn, ode=ode_list) diff --git a/tests/test_ode_simulate_jump.py b/tests/test_ode_simulate_jump.py index e49761e8..80cd87cf 100644 --- a/tests/test_ode_simulate_jump.py +++ b/tests/test_ode_simulate_jump.py @@ -46,13 +46,13 @@ def test_simulate_jump_serial(self): solution = self.odeS.integrate(self.t[1::]) # random evaluation to see if the functions break down - self.odeS.transition_mean(self.x0, self.t[0]) - self.odeS.transition_var(self.x0, self.t[0]) + self.odeS.transitionMean(self.x0, self.t[0]) + self.odeS.transitionVar(self.x0, self.t[0]) - self.odeS.transition_mean(solution[self.index,:], self.t[self.index]) - self.odeS.transition_var(solution[self.index,:], self.t[self.index]) + self.odeS.transitionMean(solution[self.index,:], self.t[self.index]) + self.odeS.transitionVar(solution[self.index,:], self.t[self.index]) - _simX, _simT = self.odeS.simulate_jump(250, self.n_sim, parallel=False, full_output=True) + _simX, _simJump, _simT = self.odeS.solve_stochast(250, self.n_sim, parallel=False, full_output=True) def test_simulate_jump_same_seed(self): """ @@ -68,11 +68,11 @@ def test_simulate_jump_same_seed(self): # But if we run it in serial then the seed will be used # and the output will be identical np.random.seed(seed) - simX1, simT1 = self.odeS.simulate_jump(self.t_seed[1::], self.n_sim, - parallel=False, full_output=True) + simX1, simJump1, simT1 = self.odeS.solve_stochast(self.t_seed[1::], self.n_sim, + parallel=False, full_output=True) np.random.seed(seed) - simX2, simT2 = self.odeS.simulate_jump(self.t_seed[1::], self.n_sim, - parallel=False, full_output=True) + simX2, simJump2, simT2 = self.odeS.solve_stochast(self.t_seed[1::], self.n_sim, + parallel=False, full_output=True) for i, xi in enumerate(simX1): self.assertTrue(np.allclose(simX2[i], xi)) @@ -83,11 +83,11 @@ def test_simulate_jump_different_seed(self): under a CTMC interpretation regardless of the backend. """ np.random.seed(1) - simX1, simT1 = self.odeS.simulate_jump(self.t_seed[1::], self.n_sim, - parallel=False, full_output=True) + simX1, simJump1, simT1 = self.odeS.solve_stochast(self.t_seed[1::], self.n_sim, + parallel=False, full_output=True) np.random.seed(2) - simX2, simT2 = self.odeS.simulate_jump(self.t_seed[1::], self.n_sim, - parallel=False, full_output=True) + simX2, simJump2, simT2 = self.odeS.solve_stochast(self.t_seed[1::], self.n_sim, + parallel=False, full_output=True) for i, xi in enumerate(simX1): self.assertFalse(np.allclose(simX2[i], xi)) diff --git a/tests/test_pickle.py b/tests/test_pickle.py index 938c3776..91a8dcec 100644 --- a/tests/test_pickle.py +++ b/tests/test_pickle.py @@ -2,11 +2,11 @@ import io import numpy -from unittest import TestCase +import unittest from pygom.model import Transition, TransitionType, SimulateOde -class TestPickling(TestCase): - +class TestPickling(unittest.TestCase): + @unittest.skip("Skipping pickling tests. Need a new set of tests for the new way compilation is done.") def setUp(self): stateList = ['a', 'x', 'y', 'b'] paramList = ['k0', 'k1', 'k2'] @@ -26,11 +26,12 @@ def setUp(self): ] self.ode = SimulateOde(stateList, paramList, transition=transitionList) + @unittest.skip("Skipping pickling tests. Need a new set of tests for the new way compilation is done.") def test_pickle(self): ''' Can we pickle and unpickle an ode object? ''' - #cause some compilation to happen + # cause some compilation to happen x0 = [150.0, 10.0, 10.0, 0.0] t = numpy.linspace(0, 15, 100) self.ode.initial_values = (x0, t[0]) diff --git a/tests/test_sir_discrete_estimate.py b/tests/test_sir_discrete_estimate.py index ed904f49..10435f41 100644 --- a/tests/test_sir_discrete_estimate.py +++ b/tests/test_sir_discrete_estimate.py @@ -4,7 +4,7 @@ import scipy.optimize from pygom import PoissonLoss -from pygom import Transition, TransitionType, DeterministicOde +from pygom import Transition, TransitionType, SimulateOde class TestSIRDiscreteEstimate(TestCase): @@ -28,7 +28,7 @@ def setUp(self): transition_type=TransitionType.T) ] # initialize the model - self.ode = DeterministicOde(state_list, param_list, transition=transition_list) + self.ode = SimulateOde(state_list, param_list, transition=transition_list) self.ode.parameters = param_eval self.ode.initial_values = (self.x0, self.t[0])