3-Ecosystem.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Julia ecosystems of scientific computing\n",
    "\n",
    "There are many Julia organizations about seemingly every scientific area. Some examples:\n",
    "\n",
    "- Astrophysics: [JuliaAstro](https://juliaastro.github.io/), [JuliaSpace](https://github.com/JuliaSpace)\n",
    "- Bio/Chemistry: [JuliaBio](https://biojulia.net/), [Molecular simulations](https://github.com/JuliaMolSim)\n",
    "- Complex systems, nonlinear dynamics: [JuliaDynamics](https://juliadynamics.github.io/JuliaDynamics/)\n",
    "- Differential equations: [JuliaDiffEq](https://juliadiffeq.org/)\n",
    "- Solid state: [QuantumOptics](https://qojulia.org/), [JuliaPhysics](https://github.com/JuliaPhysics)\n",
    "- Economics: [QuantEcon](https://julia.quantecon.org/), [JuliaQuant](https://github.com/JuliaQuant)\n",
    "- Geosciences/Climate: [JuliaGeo](https://github.com/JuliaGeo), [JuliaEarth](https://github.com/JuliaEarth), [JuliaClimate](https://github.com/JuliaClimate).\n",
    "\n",
    "among many many others, not even mentioning mathematics-focused organizations like nonlinear optimazation, etc....\n",
    "\n",
    "\n",
    "In this last session I will (**very briefly**) overview some powerful Julia packages I found useful for *my own work* and hopefully you will too. Even if the packages relevant for me are not useful in your field, it is still good practice to solve the exercises, to \"learn how to learn Julia packages\". \n",
    "\n",
    "*Quick note: I use `PyPlot` (the matplotlib package of Python) to plot, because it is super-duper powerful. All Python packages are immediatelly and directly usable in Julia with exactly same syntax as Python (besides the indexing thingy: Julia indices start from 1.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot\n",
    "# set default figure size:\n",
    "PyPlot.rc(\"figure\", figsize = (5, 3))\n",
    "# enable 3D plotting\n",
    "using3D()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# 1. DifferentialEquations.jl\n",
    "\n",
    "[DifferentialEquations.jl](https://docs.juliadiffeq.org/latest/) is by far [the best](https://www.stochasticlifestyle.com/comparison-differential-equation-solver-suites-matlab-r-julia-python-c-fortran/) free and open source differential equations solver (not for Julia, for any language). It can solve standard ODEs, Delay-DEs, stochastic DEs, has tools for PDEs, event handling, other multiple features, 100s of solvers, and *even more*.\n",
    "\n",
    "Here we will focus on ODEs and use the module `OrdinaryDiffEq` only.\n",
    "\n",
    "## Defining and solving some ODEs\n",
    "\n",
    "The way DifferentialEquations.jl works is quite straightforward:\n",
    "\n",
    "1. Make your set of ODEs a Julia function `f`\n",
    "2. Put `f`, an initial state and a parameter container into an `ODEProblem`.\n",
    "2. Choose the solvers and the arguments of the solvers you will use (e.g. tolerances, etc.)\n",
    "3. Give `f` as well as the auxilary arguments to the function `solve`!\n",
    "\n",
    "Let's see it in practice by solving the Lorenz system\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= \\sigma (y - x) \\\\\n",
    "\\dot{y} &= x (\\rho - z) - y \\\\\n",
    "\\dot{z} &= xy -\\beta z\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "First step is to make this a Julia function. There is some strictness when writing this function in Julia (to play well with another software, see below). \n",
    "Specifically, it can only be one of two forms: out-of-place (oop) or in-place (iip). Here is how to define it (`p` is the parameter container, `t` is time):\n",
    "\n",
    "* **oop** : The `eom` function must be in the form `eom(x, p, t) -> SVector`\n",
    "  which means that given a state `x::SVector` it returns an [`SVector`](http://juliaarrays.github.io/StaticArrays.jl/stable/pages/api.html#SVector-1)\n",
    "  (from the [StaticArrays](https://github.com/JuliaArrays/StaticArrays.jl) module)\n",
    "  containing the derivatives.\n",
    "* **iip** : The `eom` function must be in the form `eom!(dx, x, p, t)`\n",
    "  which means that given a state `x::Vector` it writes in-place the derivatives in `dx`.\n",
    "\n",
    "We advise to use **oop** for systems with dimension ≤ 10, and use **iip** otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lorenz_rule (generic function with 1 method)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using OrdinaryDiffEq, StaticArrays\n",
    "\n",
    "function lorenz_rule(u, p, t)\n",
    "    σ, ρ, β = p\n",
    "    x, y, z = u\n",
    "    dx = σ*(y - x)\n",
    "    dy = x*(ρ-z) - y\n",
    "    dz = x*y - β*z\n",
    "    return SVector(dx, dy, dz)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then set the initial state and parameter container"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 10.0               \n",
       " 28.0               \n",
       "  2.6666666666666665"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u₀ = SVector(10.0, 10.0, 10.0)\n",
    "p₀ = [10, 28, 8/3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "then put everything into the `ODEProblem` structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mSArray{Tuple{3},Float64,1,3}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mfalse\u001b[0m\n",
       "timespan: (0.0, 100.0)\n",
       "u0: [10.0, 10.0, 10.0]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# third argument is the timespan to solve in\n",
    "prob = ODEProblem(lorenz_rule, u₀, (0.0, 100.0), p₀)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, so now we choose the solver to use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Vern9(true)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alg = Vern9() # 9-th order adaptive solver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's solve the Lorenz system using the default settings of DifferentialEquations.jl (without specifying anything else)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: specialized 9th order lazy interpolation\n",
       "t: 902-element Array{Float64,1}:\n",
       "   0.0                \n",
       "   0.09355226310426   \n",
       "   0.17283944628206213\n",
       "   0.24997046635545134\n",
       "   0.33111610744803827\n",
       "   0.42743131783646965\n",
       "   0.5201140913658462 \n",
       "   0.6242605175854586 \n",
       "   0.7340052492650533 \n",
       "   0.8380149776590866 \n",
       "   0.9438866257985115 \n",
       "   1.0545811111840224 \n",
       "   1.1789855148275294 \n",
       "   ⋮                  \n",
       "  98.86131214292969   \n",
       "  98.966663437393     \n",
       "  99.07194022267977   \n",
       "  99.19597178668509   \n",
       "  99.33755089044504   \n",
       "  99.44051282392593   \n",
       "  99.54192389117195   \n",
       "  99.62958862392502   \n",
       "  99.74154878708663   \n",
       "  99.84341219700966   \n",
       "  99.96495889802289   \n",
       " 100.0                \n",
       "u: 902-element Array{SArray{Tuple{3},Float64,1,3},1}:\n",
       " [10.0, 10.0, 10.0]                                             \n",
       " [14.527288897352587, 21.12071452189923, 24.655401013820843]    \n",
       " [16.260683509932253, 11.98774098852595, 40.866652625646566]    \n",
       " [9.410451093456127, -1.345343845837725, 37.613015846596966]    \n",
       " [2.332877467383761, -3.820315512793081, 29.11993614068686]     \n",
       " [-1.363730916283803, -3.6200129433647934, 22.48755819939663]   \n",
       " [-3.0793598140458336, -4.909411322273567, 18.353583156361175]  \n",
       " [-5.653731471389623, -9.030464568182996, 16.635620614877244]   \n",
       " [-10.553562838684254, -15.643232097626619, 22.306048833633962] \n",
       " [-13.629404308689935, -12.731847509904549, 34.7327079238001]   \n",
       " [-8.73112638842306, -2.4374548338614304, 33.84398423590063]    \n",
       " [-3.5216050466064086, -0.7920643598010602, 25.81488840056454]  \n",
       " [-2.188364539893828, -2.374221013785329, 18.917963481888982]   \n",
       " ⋮                                                              \n",
       " [-0.18953595819341174, -0.1899008697655977, 13.894665368203388]\n",
       " [-0.3106761892366233, -0.5425837290776738, 10.499435002896558] \n",
       " [-0.7525562478063783, -1.4333691104014283, 7.975558874786937]  \n",
       " [-2.439921484684283, -4.83457134291546, 6.225996314352647]     \n",
       " [-9.617219146231147, -18.150671859800376, 12.23696710495414]   \n",
       " [-17.72048745515594, -19.932931457547983, 38.048396441243426]  \n",
       " [-9.847439370037272, 3.0461861243951347, 39.62042332391549]    \n",
       " [-0.9147669616271994, 5.897292617677333, 29.53508004846403]    \n",
       " [3.5709736798692733, 5.943766108819459, 22.935183751393748]    \n",
       " [5.888075610666564, 8.431076511543743, 20.51414073869932]      \n",
       " [9.692841037030911, 13.083702462668564, 23.857567507088994]    \n",
       " [10.805337687945048, 13.661084947480466, 26.3515033643232]     "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = solve(prob; alg = alg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, so what is the returned result? We didn't specify when to save or anything...\n",
    "\n",
    "The solver we chose, `Vern9` (also true for the default solver) is an adaptive step solver. The system is evolved with adaptive step, until we reach the end of the time span. A state is recorded at every step. E.g. the solution at the third step is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.17283944628206213, [16.260683509932253, 11.98774098852595, 40.866652625646566])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(sol.t[3], sol.u[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And using the syntax `sol[i, j]` we can access the `i` variable at the `j`-th time point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.260683509932253"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol[1, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot3D(sol[1, :], sol[2, :], sol[3, :]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the mechanics of the solver, `sol` object allows arbitrary interpolation in time by saving some extra derivative-related numbers. This means that we can use `sol` as a function of time, `sol(t)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element SArray{Tuple{3},Float64,1,3} with indices SOneTo(3):\n",
       "  0.815736398746072 \n",
       " -2.6297520921486752\n",
       " 25.431305588918814 "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol(5.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = 0:0.01:10\n",
    "X, Y, Z = zero(t), zero(t), zero(t)\n",
    "for (i, τ) in enumerate(t)\n",
    "    X[i], Y[i], Z[i] = sol(τ)\n",
    "end\n",
    "plot3D(X, Y, Z);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that it is possible to skip this advanced feature of interpolation (and thus also skip collecting the extra interpolation-related numbers) and only save at some pre-defined time points by passing the extra argument `saveat = [points I want]`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numbers with uncertainty\n",
    "\n",
    "The module `Measurements` provide numeric types that have error bars; so that your numeric operations propagate the errors as is done in experimental physics.\n",
    "\n",
    "Without any effort, you can solve a differential equation of numbers with error bars! And your solution will itself be a sequence of numbers with properly calculated errorbars.\n",
    "\n",
    "* How does this happen? Because `OrdinaryDiffEq` uses internally standard mathematical operations on numbers to solve an ODE. \n",
    "* `Measurements` defines a number type (`Measurement`, not that different from the `RationalNumber` you defined in a previous exercise). This number naturally supports arithmetics on `+, -, *,...` etc. on numbers with errors.\n",
    "\n",
    "Let's see how `Measurements` works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.5 \\pm 0.1$"
      ],
      "text/plain": [
       "0.5 ± 0.1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 0.5 ± 0.1 # \\pm<TAB> = ±"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Measurement{Float64}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-9.2 \\pm 2.3$"
      ],
      "text/plain": [
       "-9.2 ± 2.3"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(sqrt(x) - 3) * (4 ± 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay let's rivisit now the Lorenz problem, but initialize it with a state that has `Measurement` as its number type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element SArray{Tuple{3},Measurement{Float64},1,3} with indices SOneTo(3):\n",
       " 10.0 ± 0.1\n",
       " 10.0 ± 0.1\n",
       " 10.0 ± 0.1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uunc = SVector(10.0 ± 0.1, 10.0 ± 0.1, 10.0 ± 0.1)\n",
    "# notice we could also add errors to parameters p₀"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mSArray{Tuple{3},Measurement{Float64},1,3}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mfalse\u001b[0m\n",
       "timespan: (0.0, 10.0)\n",
       "u0: Measurement{Float64}[10.0 ± 0.1, 10.0 ± 0.1, 10.0 ± 0.1]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probunc = ODEProblem(lorenz_rule, uunc, (0.0, 10.0), p₀)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: specialized 9th order lazy interpolation\n",
       "t: 122-element Array{Float64,1}:\n",
       "  0.0                \n",
       "  0.13234363885533806\n",
       "  0.21267992404209823\n",
       "  0.29337792152226183\n",
       "  0.377346397107085  \n",
       "  0.4634969826202153 \n",
       "  0.5466201560209227 \n",
       "  0.6341784834884603 \n",
       "  0.7219957607908694 \n",
       "  0.80704728617099   \n",
       "  0.8926799958261173 \n",
       "  0.9727071726523201 \n",
       "  1.0567175506211872 \n",
       "  ⋮                  \n",
       "  9.123000369387853  \n",
       "  9.205257719137007  \n",
       "  9.28304739339006   \n",
       "  9.362874619555148  \n",
       "  9.44713675740573   \n",
       "  9.524040468207755  \n",
       "  9.603166507716589  \n",
       "  9.683639775594193  \n",
       "  9.768834133488447  \n",
       "  9.856926418552634  \n",
       "  9.93911524402789   \n",
       " 10.0                \n",
       "u: 122-element Array{SArray{Tuple{3},Measurement{Float64},1,3},1}:\n",
       " [10.0 ± 0.1, 10.0 ± 0.1, 10.0 ± 0.1]            \n",
       " [16.506 ± 0.063, 19.38 ± 0.11, 34.17 ± 0.22]    \n",
       " [13.346 ± 0.079, 3.63 ± 0.19, 41.119 ± 0.075]   \n",
       " [5.124 ± 0.098, -3.537 ± 0.091, 32.742 ± 0.093] \n",
       " [0.086 ± 0.078, -3.643 ± 0.073, 25.565 ± 0.06]  \n",
       " [-2.086 ± 0.081, -3.897 ± 0.098, 20.652 ± 0.044]\n",
       " [-3.6 ± 0.11, -5.66 ± 0.15, 17.555 ± 0.076]     \n",
       " [-6.0 ± 0.15, -9.6 ± 0.2, 16.74 ± 0.2]          \n",
       " [-9.94 ± 0.17, -15.05 ± 0.11, 21.12 ± 0.43]     \n",
       " [-13.46 ± 0.017, -15.37 ± 0.31, 31.51 ± 0.36]   \n",
       " [-11.83 ± 0.21, -6.55 ± 0.3, 36.35 ± 0.18]      \n",
       " [-6.99 ± 0.16, -1.292 ± 0.032, 31.73 ± 0.29]    \n",
       " [-3.465 ± 0.025, -0.81 ± 0.13, 25.67 ± 0.21]    \n",
       " ⋮                                               \n",
       " [-13.0 ± 99.0, -20.0 ± 250.0, 26.0 ± 56.0]      \n",
       " [-10.0 ± 140.0, -12.0 ± 20.0, 40.0 ± 290.0]     \n",
       " [-10.0 ± 27.0, -0.0 ± 250.0, 40.0 ± 150.0]      \n",
       " [-0.0 ± 150.0, 0.0 ± 240.0, 29.0 ± 10.0]        \n",
       " [-0.0 ± 200.0, -0.0 ± 240.0, 23.0 ± 59.0]       \n",
       " [-0.0 ± 240.0, -0.0 ± 330.0, 19.0 ± 84.0]       \n",
       " [-0.0 ± 350.0, -0.0 ± 540.0, 20.0 ± 130.0]      \n",
       " [-0.0 ± 570.0, -0.0 ± 960.0, 10.0 ± 270.0]      \n",
       " [-0.0 ± 1000.0, -0.0 ± 1800.0, 10.0 ± 810.0]    \n",
       " [-0.0 ± 1900.0, -0.0 ± 2800.0, 0.0 ± 2800.0]    \n",
       " [-0.0 ± 1900.0, -20.0 ± 320.0, 0.0 ± 6500.0]    \n",
       " [-20.0 ± 180.0, -0.0 ± 5100.0, 0.0 ± 4500.0]    "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solunc = solve(probunc; alg = alg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that *obviously* trying to solve a chaotic system with such huge errors will diverge... No matter though, let's see the solution anyway."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101-element Array{Measurement{Float64},1}:\n",
       "   10.0 ± 0.1  \n",
       " 11.658 ± 0.083\n",
       " 14.942 ± 0.082\n",
       " 16.761 ± 0.048\n",
       " 14.501 ± 0.066\n",
       "   9.41 ± 0.1  \n",
       "  4.565 ± 0.096\n",
       "  1.277 ± 0.083\n",
       " -0.663 ± 0.076\n",
       " -1.835 ± 0.079\n",
       " -2.724 ± 0.089\n",
       "  -3.67 ± 0.11 \n",
       "   -4.9 ± 0.13 \n",
       "        ⋮      \n",
       "    9.9 ± 3.4  \n",
       "   12.7 ± 2.1  \n",
       "   14.3 ± 1.1  \n",
       "   13.4 ± 4.1  \n",
       "   10.3 ± 4.6  \n",
       "    6.7 ± 3.0  \n",
       "    4.0 ± 1.0  \n",
       "    2.3 ± 0.55 \n",
       "    1.4 ± 1.7  \n",
       "    1.1 ± 2.6  \n",
       "    1.0 ± 3.6  \n",
       "    1.2 ± 4.9  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 0:0.05:5\n",
    "Xunc = [solunc(τ)[1] for τ in t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101-element Array{Float64,1}:\n",
       " 0.1                \n",
       " 0.08342714456816318\n",
       " 0.08243145121464032\n",
       " 0.04765367655591914\n",
       " 0.0663485293647113 \n",
       " 0.1003943815025594 \n",
       " 0.09643886077929786\n",
       " 0.08309413890388685\n",
       " 0.07640955696024836\n",
       " 0.07864193098067553\n",
       " 0.08891403394179949\n",
       " 0.1068415764868824 \n",
       " 0.13156908343006712\n",
       " ⋮                  \n",
       " 3.437099774976129  \n",
       " 2.0540397206706342 \n",
       " 1.0879109371031364 \n",
       " 4.094594616200674  \n",
       " 4.576490135852936  \n",
       " 2.9816543947907004 \n",
       " 1.00086937886618   \n",
       " 0.5510702440924684 \n",
       " 1.6544674631819647 \n",
       " 2.56281860734045   \n",
       " 3.5545242140327025 \n",
       " 4.900933699218517  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xv = Measurements.value.(Xunc) # get values (broadcasting)\n",
    "Xe = Measurements.uncertainty.(Xunc) # get errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot errors nicely\n",
    "plot(t, Xv)\n",
    "fill_between(t, Xv .- Xe, Xv .+ Xe, color = \"C3\", alpha = 0.25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My guess is that you could probably/maybe get something like this in Python with a lot of effort. The case of Julia here is unbelievably cool because:\n",
    "\n",
    "1. `Measurements` has never written any code that solves a differential equation.\n",
    "2. `OrdinaryDiffEq` has never written any code that controls how an error is propagated.\n",
    "3. There isn't any boilerplate code \"connecting\" the two packages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Event handling\n",
    "\n",
    "DifferentialEquations.jl implements a simple API so that \"events\" (arbitrary things) happen to your solution as it is progressing in time. This is done with the [`Callback` interface](https://docs.juliadiffeq.org/latest/features/callback_functions/#callbacks-1). For example, a `ContinuousCallback` represents an event that \"triggers\" when a continuous univariate function reaches the value `0`. Similarly, a `DiscreteCallback` triggers when a boolean function evaluates to `true`.\n",
    "\n",
    "Let's modify the Lorenz problem with a callback. For the callback we need to define a `condition` function, and also an `affect!` function, that says what happens once the callback is triggered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "condition (generic function with 1 method)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition(u, t, integrator) = u[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "affect! (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function affect!(integrator)\n",
    "    u = integrator.u\n",
    "    integrator.u = (u[1], u[2], 0.9u[3])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "cb = ContinuousCallback(condition, affect!);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall the `prob` definition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mSArray{Tuple{3},Float64,1,3}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mfalse\u001b[0m\n",
       "timespan: (0.0, 10.0)\n",
       "u0: [10.0, 10.0, 10.0]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob = ODEProblem(lorenz_rule, u₀, (0.0, 10.0), p₀)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "sol = solve(prob; alg = Vern9(), callback = cb);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = 0:0.01:10\n",
    "X, Y, Z = zero(t), zero(t), zero(t)\n",
    "for (i, τ) in enumerate(t)\n",
    "    X[i], Y[i], Z[i] = sol(τ)\n",
    "end\n",
    "plot3D(X, Y, Z);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. DynamicalSystems.jl\n",
    "[DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/dev/) is an award-winning library for nonlinear dynamics and chaos. \n",
    "\n",
    "*Disclaimer: I am one of the developers of this library.*\n",
    "\n",
    "Around 1/3 of the functionality of DynamicalSystems.jl treats systems with known rule $f$, and directly uses this rule to evolve the state space and the tangent space (the linearized dynamics). DynamicalSystems.jl builds on top of DifferentialEquations.jl to evolve systems in time. The rest of the functionality treats timeseries directly, doesn't matter where you got em from."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using known rule $f$\n",
    "\n",
    "If you have a dynamical system where you know its rule $f$, there are a lot of things you can do with in DynamicalSystems.jl. But for all of them, step 1 is to make this rule $f$ into a `DynamicalSystem` instance. The process here is almost identical to DifferentialEquations.jl:\n",
    "\n",
    "1. Make $f$ a Julia function (using the same syntax as in DifferentialEquations.jl).\n",
    "2. Choose initial state and parameter container (again same as DiffEq).\n",
    "3. Pass these arguments to the `ContinuousDynamicalSystem` constructor (or `DiscreteDynamicalSystem`, for discrete systems).\n",
    "\n",
    "Here we already have `lorenz_rule, u₀, p₀` defined, so the process  is kind of trivial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-dimensional continuous dynamical system\n",
       " state:       [10.0, 10.0, 10.0]\n",
       " e.o.m.:      lorenz_rule\n",
       " in-place?    false\n",
       " jacobian:    ForwardDiff\n",
       " parameters:  [10.0, 28.0, 2.6666666666666665]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DynamicalSystems\n",
    "lorenz = ContinuousDynamicalSystem(lorenz_rule, u₀, p₀)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then you can use this `lorenz` object in various functions of the library. For example, to obtain the Lyapunov spectrum you use `lyapunovs`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       "   0.9040593406250697    \n",
       "  -0.00020020892167364334\n",
       " -14.570501871732901     "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lyapunovs(lorenz, 10000) # 2nd argument is for how much time to evolve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same story happens if you want to get only the maximum Lyapunov exponent. You use the function `lyapunov` (which uses a different algorithm):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9056913975220796"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lyapunov(lorenz, 10000.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, obtain a Poincare surface of section with the plane that e.g. the $y$ variable crosses zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-dimensional Dataset{Float64} with 476 points\n",
       "  -7.10792   -3.66265e-7   33.0688\n",
       " -11.5291    -3.14584e-9   40.5135\n",
       "   2.24303   -6.15224e-12  24.2377\n",
       "  -7.09758   -2.29198e-7   33.0521\n",
       " -11.5026    -1.91843e-9   40.4678\n",
       "   1.97185    2.285e-9     23.6029\n",
       "  -6.36179   -1.0439e-6    31.8233\n",
       " -10.1942    -2.49149e-9   38.2322\n",
       "   3.34247    2.59029e-6   26.5141\n",
       "  -8.63591   -1.86515e-7   35.614 \n",
       "  -7.42905   -3.67076e-7   33.604 \n",
       " -12.9019    -4.30439e-10  42.9089\n",
       "   0.36134   -1.21471e-10  17.5907\n",
       "   ⋮                              \n",
       "  -8.64694   -2.2795e-7    35.6321\n",
       "  -7.49088   -4.44474e-7   33.7069\n",
       " -13.8631    -1.37158e-8   44.6206\n",
       "  -9.88093   -1.15107e-7   37.7025\n",
       "   1.48638   -9.72846e-10  22.338 \n",
       "  -8.1977    -1.90012e-7   34.883 \n",
       "  -7.58548   -3.62746e-8   33.8638\n",
       "  -5.36086   -4.32412e-7   30.1306\n",
       "  -9.28587   -6.20987e-8   36.7013\n",
       " -10.6931     1.32382e-8   39.0799\n",
       "   0.763925  -2.1828e-10   19.8526\n",
       "  -6.70268   -3.30653e-7   32.3929"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plane = (2, 0.0) # plane[1]: which variable, plane[2]: which value\n",
    "psos = poincaresos(lorenz, (2, 0.0), 1000.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter(psos[:, 1], psos[:, 3], s = 1);\n",
    "xlabel(\"X\"); ylabel(\"Z\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear timeseries analysis\n",
    "\n",
    "Both basic as well as advanced tools for nonlinear timeseries analysis are included in DynamicalSystems.jl. To spare you the boredom I won't talk about them though! I'll only mention entropy, because it is relevant to one of the exercises. Let's say that you have a nice trajectory sampled at discrete times (which is what the function `trajectory` does)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-dimensional Dataset{Float64} with 20001 points\n",
       "  10.0         10.0       10.0   \n",
       "  11.6604      17.4659    15.75  \n",
       "  14.9431      21.227     26.2311\n",
       "  16.7587      16.6772    37.8091\n",
       "  14.4989       6.06744   41.6612\n",
       "   9.40731     -1.34788   37.6097\n",
       "   4.5647      -3.65188   32.0526\n",
       "   1.27841     -3.76227   27.5651\n",
       "  -0.660687    -3.58262   24.0887\n",
       "  -1.83235     -3.75926   21.3038\n",
       "  -2.72165     -4.46127   19.0841\n",
       "  -3.66336     -5.7684    17.464 \n",
       "  -4.89541     -7.77907   16.6366\n",
       "   ⋮                             \n",
       "  -8.7667     -14.7776    16.5172\n",
       " -11.9634     -18.3725    22.6565\n",
       " -14.5968     -17.9932    31.5653\n",
       " -14.751      -11.7214    38.2464\n",
       " -11.8535      -4.01615   38.369 \n",
       "  -7.72111      0.296008  34.3243\n",
       "  -4.24419      1.48778   29.7596\n",
       "  -1.98705      1.41035   25.8345\n",
       "  -0.714311     1.11662   22.5334\n",
       "  -0.0343316    0.956168  19.7044\n",
       "   0.357267     0.996214  17.2529\n",
       "   0.654459     1.24426   15.126 "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tr = trajectory(lorenz, 1000.0; dt = 0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above result is not a `Matrix`, but a vector-of-vectors (for performance purposes). This `tr` represents in fact the attractor of the Lorenz system, since this is what we just evolved in time. Typically one is interested in the entropy of this attractor, by partitioning the state space in boxes of size `ε` (it will become apparent in a bit why).\n",
    "\n",
    "You can get this entropy (of order α) using the function `genentropy(α, ε, tr)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.837529474680585"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = genentropy(1, 0.1, tr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.90353755128635"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = genentropy(1, 0.01, tr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This quantity is interesting because it can be used to calculate the fractal dimension of the `tr` object. The way it works is simple: You look at how `H` changes for varying `ε`. If `D` is the fractal dimension of `tr`, then it typically holds that `H ~ ε^(-D)`. \n",
    "\n",
    "In reality what one does is calculate `H` for many different `ε` and plot the result, and then _manually_ identify the slope of the curve `H` vs. `-log(ε)`. e.g.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33-element Array{Float64,1}:\n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90353755128635  \n",
       "  9.90312168377139  \n",
       "  9.900557167429135 \n",
       "  9.891269459595035 \n",
       "  9.860042707793426 \n",
       "  9.78074383756112  \n",
       "  ⋮                 \n",
       "  2.702396852726326 \n",
       "  1.9641564466046155\n",
       "  0.821385539477985 \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               \n",
       " -0.0               "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "εs = ℯ .^ (-8:0.5:8) # \\euler<TAB} = ℯ\n",
    "Hs = genentropy.(1, εs, Ref(tr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we did above is use broadcasting (the `.` syntax), to calculate the entropy for every `ε` value. What's with the `Ref()`? This `Ref()` specifies that its argument `tr` shoud **not** be broadcasted over. Since both `ε` as well as `tr` are iterable, Julia would normally try to broadcast across both arguments, which we don't want in this case.\n",
    "\n",
    "Anyway, this is the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcYAAAEmCAYAAAD4JjCrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3deVxU5eIG8GcYYAAdUEBEcEBwAzETcc0tFTE1tbxtZss162aZS16vy9XbYipXK7OyXLJrmkr+bqVlWYrexP0KuC+AKAjigivDOjAz7+8PdC4kICTDe2Z4vp/PfGDOnDPzwMfh8Z1zzntUQggBIiIiAgA4yA5ARESkJCxGIiKiMliMREREZbAYiYiIymAxEhERlcFiJCIiKoPFSEREVAaLkYiIqAxH2QGszWw24+LFi9BqtVCpVLLjEBGRBEII5Obmws/PDw4OVY8J7b4YL168CJ1OJzsGEREpQGZmJpo3b17lOnZfjFqtFkDpL8Pd3V1yGiIikkGv10On01k6oSp2X4x3Pj51d3dnMRIR1XPV2aXGg2+IiIjKkFqMu3btwrBhw+Dn5weVSoVNmzaVe1wIgXfeeQd+fn5wdXXFww8/jJMnT0pKS0RE9YHUYszPz8eDDz6IJUuWVPj4woULsWjRIixZsgTx8fHw9fXFwIEDkZubW8dJiYiovpC6j3Hw4MEYPHhwhY8JIbB48WLMmjULI0eOBACsXr0aTZs2xfr16/Hqq6/WZVQiIqonFLuPMS0tDZcvX0ZUVJRlmUajQd++fbFv375KtzMYDNDr9eVuRERE1aXYYrx8+TIAoGnTpuWWN23a1PJYRaKjo+Hh4WG58RxGIiKqCcWfrvH7Q2uFEFUebjtz5kxMmTLFcv/OuStEZN+MJjPyDEbkFhmRU1iC3CIj9EWlX3OLSqAvLP1abDLDaBYwmswwmkTp9+b/fV9iMsNkFjCaBMxCQKD0745ZAAIALN8LCAEIAZiFkPzT278ATzeseKFznbyWYovR19cXQOnIsVmzZpbl2dnZd40iy9JoNNBoNFbPR0R1y2wWuJhTiHNX83Huah7OXcvHuav5SLuWj1sFxcgvNsmOSFZkMtfdfz4UW4xBQUHw9fVFbGwswsPDAQDFxcWIi4vDggULJKcjImsRQiDpci6SL+fi3NU8nLUUYB6KSsz33N7VSQ2tiyPcXZ2gdXGE1sUJ7mW+ahwdoHZwgKNaBUcHFRzVDre/quDk4AD17e8dHRzgoAJUqtJPrlT431cHB0AFFaACHCyPVZyn9FG6X67O6jp7LanFmJeXh9TUVMv9tLQ0HDlyBJ6enggICMDkyZMxf/58tG7dGq1bt8b8+fPh5uaGZ599VmJqIrKGfIMRm45k4ev955F0ueJTspzUKgR6NUCwdwMEN2mI4Cal3zfRaqB1KS1CJ7ViD50gGyG1GBMSEtCvXz/L/Tv7Bl988UV89dVXmDZtGgoLC/H666/j5s2b6NatG7Zt21atue6IyDakXMnF2gPn8f2hLOQZjAAAjaMDHtQ1QssmDRDsfbsAmzSErrErHFl8ZGUqIex7r7Fer4eHhwdycnI4VyqRQhQbzdh68jLWHjiP/6bdsCwP8m6A0d0C8EREczRyc5aYkOxNTbpAsfsYicj+XLxViJiDGYg5mIlreQYAgNpBhYGhTfFc90A81NILDg7cJ0dysRiJyOou5RTinR9PIvbUFdw5uLCJVoNRXQMwqqsOzTxc5QYkKoPFSERWdSIrB2NXx+OKvnSE2CPYC8/3CMTAdk15oAwpEouRiKxm28nLmPTNERSWmNDapyGWPNsJbX158BwpG4uRiGqdEAJf7knDvC2nIQTQu7U3PhvdCe4uTrKjEd0Ti5GIalWJyYy3fzyJ9f/NAACM7haAd4eH8TQLshksRiKqNfqiEoxfdwi7z1yDSgXMGhKKsb2CqpzfmEhpWIxEVCsybxTgpa/icSY7D27Oanz8TDgGtqt8XmMipWIxEtF9O5RxE39Zk4BrecVo6q7Bly92QXt/D9mxiP4QFiMR3ZfNRy/ir/8+imKjGWF+7vjyxS7w9XCRHYvoD2MxEtEfIoTAZ7+l4oNtKQCAyNCm+PiZjmig4Z8Vsm38F0xEf8iXe9IspfhyryDMHBIKNadzIzvAYiSiGjt+IQcLfk0CAPx9SAj+0qel5EREtYcnFhFRjeQZjJgQcwglJoFHwnzxSu9g2ZGIahWLkYhq5K0fTiD9egH8PFzwzz89wHMUye6wGImo2jYevoDvD2XBQQV8PCqc10wku8RiJKJqSbuWj9kbTwAAJke2QZcWnpITEVkHi5GI7qnYaMbEmMPILzahW5AnxvdrJTsSkdWwGInont7fmoTjWTlo5OaExc905GkZZNdYjERUpd+Ss/HF7jQAwMI/dUAzD1fJiYisi8VIRJXKzi3C1P87CgB4sUcgosJ8JScisj4WIxFVyGwWmLLhKK7nFyPEV4uZQ0JlRyKqEyxGIqrQ8l3nsCf1Glyd1FjybDhcnNSyIxHVCRYjEd3lcMZNfLgtGQDwzvB2aOWjlZyIqO6wGImoHH1RCSZ+cxhGs8DQDs3wVGed7EhEdYrFSEQWQgjM2ngCmTcK0byxK6JHcso3qn9YjERk8dOxS9h89CLUDip8Mioc7i5OsiMR1TkWIxEBAAqKjZi/5TQA4I1+rdApoLHkRERysBiJCACwLO4cLuUUwb+RK157mNdXpPqLxUhEuHCzAMvjzgIAZg0N5akZVK+xGIkI0b8kwWA0o3uwJwa35+w2VL8puhiNRiNmz56NoKAguLq6Ijg4GHPmzIHZbJYdjchu/Pfcdfx87BIcVMBbj4bxKFSq9xxlB6jKggULsGzZMqxevRphYWFISEjAmDFj4OHhgUmTJsmOR2TzTGaBdzefAgCM6hqAdn7ukhMRyafoYty/fz9GjBiBoUOHAgBatGiBmJgYJCQkSE5GZB82xGfi1CU93F0cMWVgG9lxiBRB0R+l9urVCzt27EBKSgoA4OjRo9izZw+GDBkiORmR7cspLMEHt6d9mxzZBl4NNZITESmDokeM06dPR05ODkJCQqBWq2EymTBv3jyMGjWq0m0MBgMMBoPlvl6vr4uoRDbnkx1ncCO/GC2bNMDzPQJlxyFSDEWPGDds2IC1a9di/fr1OHToEFavXo0PPvgAq1evrnSb6OhoeHh4WG46Hed5JPq91Ow8rN6XDgB4a1gYnNSK/lNAVKdUQgghO0RldDodZsyYgfHjx1uWzZ07F2vXrkVSUlKF21Q0YtTpdMjJyYG7Ow8sIAKAP686iJ3JVxEZ6oOVL3aRHYfI6vR6PTw8PKrVBYr+KLWgoAAODuX/J6tWq6s8XUOj0UCj4b4Sosr8lpSNnclX4aRWYdbQdrLjECmOootx2LBhmDdvHgICAhAWFobDhw9j0aJFeOmll2RHI7JJxUYz3vup9PSMl3oGIci7geRERMqj6GL89NNP8Y9//AOvv/46srOz4efnh1dffRVvvfWW7GhENmn1vnScu5YP74bOeKN/K9lxiBRJ0fsYa0NNPlcmsmdXcw3o/8FO5BqMWPinDniqCw9Mo/qjJl3AQ9GI6okPtyUj12DEA/4eeCKiuew4RIrFYiSqB05k5WBDQiYA4J3h7eDgwPlQiSrDYiSyc0IIvLv5JIQARnT0Q0Sgp+xIRIrGYiSyc1uOX0Z8+k24OqkxY3CI7DhEisdiJLJjJSYz3t9aOhnGX/oEo5mHq+RERMrHYiSyYxviM5F+vQBeDZzxSp9g2XGIbAKLkchOFRQb8fGOMwCACf1boaFG0actEykGi5HITv1rTxqu5hqg83TFs9149Qyi6mIxEtmhm/nFWB53DgAwNaotnB35VieqLr5biOzQZ7+lItdgRLtm7hjWwU92HCKbwmIksjNZtwqxZv95AMC0R9ryZH6iGmIxEtmZj2JTUGwyo3uwJ/q2aSI7DpHNYTES2ZGUK7n4/tAFAMD0R0KgUnG0SFRTLEYiO7Lw12SYBfBImC/CAxrLjkNkk1iMRHYiIf0Gtp++AgcVMHVQW9lxiGwWi5HIDggh8M9fSqd+e6qzDq18GkpORGS7WIxEdmDH6WwknL8JjaMDJke2kR2HyKaxGIlsnMkssPD2ROF/7tkCvh4ukhMR2TYWI5GN23g4CylX8uDu4ojX+7aSHYfI5rEYiWxYUYkJH8WmAABee7gVPNycJCcisn0sRiIbtvbAeWTdKkRTdw3+/FAL2XGI7AKLkchG6YtK8NlvqQCANyPbwNVZLTkRkX1gMRLZqC92ncPNghK0bNIAT0Q0lx2HyG6wGIlsUHZuEVbuTgMA/G1QWziq+VYmqi18NxHZoCX/SUVhiQkP6hphUJiv7DhEdoXFSGRjMm8UIOZgBgBg+iNtOVE4US1jMRLZmI+2p6DEJNCrlTceauktOw6R3WExEtmQlCu52Hg4C0DpvkUiqn0sRiIb8uG2ZAgBDAprigd1jWTHIbJLLEYiG3E08xa2nrwClQqYGsXRIpG1sBiJbMT7W5MBAI+H+6N1U63kNET2i8VIZAP2pV7DntRrcFKr8CYvK0VkVYovxqysLDz33HPw8vKCm5sbOnbsiMTERNmxiOqMEAILb48WR3UNgM7TTXIiIvvmKDtAVW7evImePXuiX79++OWXX+Dj44OzZ8+iUSMedED1x/bT2TiSeQsuTg54oz8vK0VkbYouxgULFkCn02HVqlWWZS1atJAXiKiOmcwCH9weLY7pGQQfLS9CTGRtiv4o9ccff0Tnzp3x5JNPwsfHB+Hh4fjiiy+q3MZgMECv15e7EdmqzUcvIvlKLtxdHDGuT0vZcYjqBUUX47lz57B06VK0bt0aW7duxbhx4zBx4kSsWbOm0m2io6Ph4eFhuel0ujpMTFR7io1mLLp9EeJX+7bkRYiJ6ohKCCFkh6iMs7MzOnfujH379lmWTZw4EfHx8di/f3+F2xgMBhgMBst9vV4PnU6HnJwcuLu7Wz0zUW1Ze+A8Zm86Ae+GGuya9jDcnBW954NI0fR6PTw8PKrVBYoeMTZr1gzt2rUrtyw0NBQZGRmVbqPRaODu7l7uRmRrCotN+GTHGQDAhP6tWIpEdUjRxdizZ08kJyeXW5aSkoLAwEBJiYjqxpr96cjONcC/kSue6crdAUR1SdHF+Oabb+LAgQOYP38+UlNTsX79eqxYsQLjx4+XHY3IavRFJVgadxYA8ObANtA4qiUnIqpfFF2MXbp0wcaNGxETE4P27dvjvffew+LFizF69GjZ0YisZuWuc7hVUIJWPg3xeLi/7DhE9Y7id1w8+uijePTRR2XHIKoT1/IMWLknDQAwNaoN1A68CDFRXVP0iJGovvn8t7MoKDahQ3MPDArzlR2HqF5iMRIpRNatQqw9cB5A6UWIVSqOFolkYDESKcTH21NQbDKje7AnerXylh2HqN5iMRIpQGp2Hr5NvAAAmPZICEeLRBKxGIkUYFFsMswCiAxtik4BjWXHIarXWIxEkh2/kIMtxy9DpSrdt0hEcrEYiSRbuDUJAPBYR3+09dVKTkNELEYiifadvYbdZ67BSa3Cm5FtZMchIrAYiaQRQmDhr6VzAY/qGoAALzfJiYgIYDESSRN76gqOZN6Cq5Mab/RvJTsOEd3GYiSSwGQW+GBb6WhxTM8W8NG6SE5ERHewGIkk+OFIFlKu5MHdxRGv9mkpOw4RlcFiJKpjxUYzPtqeAgAY93BLeLg5SU5ERGXV6Ooaer2+Wuu5u7v/oTBE9cE38RnIvFGIJloNxjwUJDsOEf1OjYqxUaNGVU5VJYSASqWCyWS672BE9qig2IhPdqQCACb2bwVXZ16EmEhpalSMv/32m+V7IQSGDBmClStXwt+fF1Mlqo5Ve9NxLc+AAE83PN0lQHYcIqpAjYqxb9++5e6r1Wp0794dwcHBtRqKyB7dKijGsrizAIApA9vA2ZG7+ImUiO9MojqyLO4ccouMCPHVYviDfrLjEFElWIxEdSBbX4Sv9qUBAKZGtYWDAy8rRaRU912MvG4c0b198p8zKCoxo1NAIwwI9ZEdh4iqUKN9jCNHjix3v6ioCOPGjUODBg3KLf/+++/vPxmRnTh/PR/fHMwEwIsQE9mCGhWjh4dHufvPPfdcrYYhskcfxabAaBbo06YJugd7yY5DRPdQo2JctWqVtXIQ2aXTl/T44ehFAMA0XoSYyCbw4BsiK1rwaxKEAIY+0Azt/T3uvQERScdiJLKSfanXsDP5KhwdVPgbR4tENoPFSGQFZrNA9C9JAIDR3QLQwrvBPbYgIqVgMRJZweZjF3E8KwcNNY6YMKC17DhEVAMsRqJaZjCaLBchfrVPMLwbaiQnIqKaYDES1bK1B0ovK+Wj1WBsb15WisjWsBiJalFOYQk+/c8ZAKUThbs51+iMKCJSABYjUS1aFncWtwpK0MqnIZ6IaC47DhH9ATZVjNHR0VCpVJg8ebLsKER3uXirEP/aUzpR+IxHQuCotqm3FxHdZjPv3Pj4eKxYsQIdOnSQHYWoQotiU2AwmtG1hScnCieyYTZRjHl5eRg9ejS++OILNG7cWHYcorskXdbju0MXAAAzh3CicCJbZhPFOH78eAwdOhSRkZH3XNdgMECv15e7EVnbP3/539Rv4QH8zxuRLVP8IXPffPMNEhMTkZCQUK31o6Oj8e6771o5FdH/cOo3Ivui6BFjZmYmJk2ahHXr1sHFxaVa28ycORM5OTmWW2ZmppVTUn3Gqd+I7I+iR4yJiYnIzs5GRESEZZnJZMKuXbuwZMkSGAwGqNXqcttoNBpoNJxphOoGp34jsj+KLsYBAwbg+PHj5ZaNGTMGISEhmD59+l2lSFSXDEYT3t/Kqd+I7I2ii1Gr1aJ9+/blljVo0ABeXl53LSeqa2sPZODCTU79RmRvFL2PkUipOPUbkf2yuXfzzp07ZUcgwtKdnPqNyF5xxEhUQxdvFWLVXk79RmSv+I4mqqEPtiZz6jciO8ZiJKqBYxdu4fvDWQCAWUNDOfUbkR1iMRJVkxAC7/10CgDweLg/HtQ1kpyIiKyBxUhUTb+euIz49JtwcXLg1G9EdozFSFQNBqPJMvXbX3oHw6+Rq+RERGQtLEaiali9Lx0ZNwrgo9Xg1b4tZcchIitiMRLdw/U8Az7dkQoAmDqoLRpobO70XyKqARYj0T0s3n4GuQYjwvzc8UQnnsxPZO9YjERVOHMlF+sPZgAAZg9tBwcHnp5BZO9YjERVmLflNExmgah2TdGjpZfsOERUB1iMRJWIS7mKnclX4aRWYeaQUNlxiKiOsBiJKmA0mTHv59KT+V/o0QJB3g0kJyKiusJiJKrAhoRMpFzJQyM3J0zs31p2HCKqQyxGot/RF5Vg0bYUAMDkAa3h4eYkORER1SUWI9HvfP7bWVzPL0ZwkwYY3T1QdhwiqmMsRqIyMm8U4F97Sq+1OGtIKJx4rUWieofveqIy/vlrEopNZvRs5YX+IbzWIlF9xGIkui0h/QZ+PnYJKlXpyfy81iJR/cRiJAJgNgu89/NpAMDTnXUIbeYuORERycJiJALwbeIFHM28hQbOakyJaiM7DhFJxGKkei/jegHe3XwSADBhQGv4aF0kJyIimViMVK8ZTWZM+b8jyC82oUuLxnild7DsSEQkGYuR6rVlcWeRcP4mGmocseipjlDz6hlE9R6Lkeqto5m3sHj7GQDAnBFh0Hm6SU5ERErAYqR6qaDYiDc3HIHRLDC0QzM8Hu4vOxIRKQSLkeqleT+fxrlr+fB1d8G8x9rznEUismAxUr2z4/QVrPtvBgDgw6ceRCM3Z8mJiEhJWIxUr1zNNWDat8cAAC/3CkLPVt6SExGR0rAYqd4QQmDGd8dwPb8YIb5aTB3UVnYkIlIgFiPVG+sPZmBHUjac1Q5Y/ExHuDipZUciIgViMVK9cPZqHt776RQAYNojbRHiy7lQiahiii7G6OhodOnSBVqtFj4+PnjssceQnJwsOxbZmBKTGW9uOIKiktLLSb3UM0h2JCJSMEUXY1xcHMaPH48DBw4gNjYWRqMRUVFRyM/Plx2NbMgnO87g2IUceLg64YMnH4QDZ7choio4yg5QlV9//bXc/VWrVsHHxweJiYno06ePpFRkSxLSb+Cz31IBAPMffwDNPFwlJyIipVN0Mf5eTk4OAMDT07PSdQwGAwwGg+W+Xq+3ei5SptyiErz5f0dgFsCfOjXH0A7NZEciIhug6I9SyxJCYMqUKejVqxfat29f6XrR0dHw8PCw3HQ6XR2mJCVZsescMm8UonljV7wzvJ3sOERkI2ymGN944w0cO3YMMTExVa43c+ZM5OTkWG6ZmZl1lJCUpKDYiK8PnAcAzBoSCq2Lk+RERGQrbOKj1AkTJuDHH3/Erl270Lx58yrX1Wg00Gg0dZSMlOrfCRdwq6AEgV5uiArzlR2HiGyIootRCIEJEyZg48aN2LlzJ4KCeJg93ZvJLLByzzkApdO+8RqLRFQTii7G8ePHY/369fjhhx+g1Wpx+fJlAICHhwdcXXl0IVVs68nLyLxRiMZuTngigvuYiahmFL2PcenSpcjJycHDDz+MZs2aWW4bNmyQHY0USgiB5btKR4vP92gBV2dO+0ZENaPoEaMQQnYEsjHx6TdxNPMWnB0d8EKPQNlxiMgGKXrESFRTK26PFv/UqTm8G/IgLCKqORYj2Y3U7DxsP30FKhXwcm8eqEVEfwyLkezGl7ePRI0MbYqWTRpKTkNEtorFSHbhaq4B3x3KAgD8pU+w5DREZMtYjGQXvt6fjmKjGR11jdA5sLHsOERkw1iMZPMKio1Yc3v6t1f7BEOl4gn9RPTHsRjJ5n2bWDr9W4Anp38jovvHYiSbZjILrNydBqD0SFRO/0ZE94vFSDZt28nLyLhRgEZuTngiouoJ5omIqoPFSDar7PRvL3QPhJuzoidyIiIbwWIkm5Vw/iaO3J7+7fkeLWTHISI7wWIkm/W/6d/80UTL6d+IqHawGMkmnb1aOv0bALzcmyf0E1HtYTGSTVq5Ow1CcPo3Iqp9LEayOdfyDPju0AUAnP6NiGofi5Fszpr951FsNONBXSN0acHp34iodrEYyaYUFpvw9f50AJz+jYisg8VINmXN/nTcLCiBztMVgzj9GxFZAYuRbEbmjQIs3n4GADChf2tO/0ZEVsFiJJsghMDsTSdQWGJCtyBPPMnp34jISliMZBM2H7uEuJSrcFY7YP7IB7hvkYishsVIineroBhzNp8EALzRvxXPWyQiq2IxkuJFb0nCtbxitPZpiHF9W8qOQ0R2jsVIinbg3HVsSMgEAESPfADOjvwnS0TWxb8ypFhFJSb8feNxAMCz3QLQuYWn5EREVB+wGEmxPt95Fueu5qOJVoPpj4TIjkNE9QSLkRTpzJVcLN2ZCgB4d3gYPFydJCciovqCxUiKYzYLzPz+OEpMApGhPhjcnjPcEFHdYTGS4sTEZyDh/E00cFZjzoj2PGeRiOoUi5EUJVtfhH/+kgQAmDqoLfwauUpORET1DYuRFOXdzaeQW2TEg8098EKPFrLjEFE9ZBPF+PnnnyMoKAguLi6IiIjA7t27ZUciK9h+6gp+Pn4JagcV5o98gJOEE5EUii/GDRs2YPLkyZg1axYOHz6M3r17Y/DgwcjIyJAdjWpRnsGIt344AQB4uXcQwvw8JCciovpK8cW4aNEijB07Fi+//DJCQ0OxePFi6HQ6LF26VHY0qkUfbkvGxZwi6DxdMXlAG9lxiKgec5QdoCrFxcVITEzEjBkzyi2PiorCvn37KtzGYDDAYDBY7uv1+vvOsWpvGjbEZ97381DlUq7kAgDmPfYAXJ3VktMQUX2m6GK8du0aTCYTmjZtWm5506ZNcfny5Qq3iY6OxrvvvlurOa7mGpB0ObdWn5PuNrKTP/q0aSI7BhHVc4ouxjt+fx6bEKLSc9tmzpyJKVOmWO7r9XrodLr7ev2nOuvwUEvv+3oOqpqTWoXwgMayYxARKbsYvb29oVar7xodZmdn3zWKvEOj0UCj0dRqjhbeDdDCu0GtPicRESmTog++cXZ2RkREBGJjY8stj42NxUMPPSQpFRER2TNFjxgBYMqUKXj++efRuXNn9OjRAytWrEBGRgbGjRsnOxoREdkhxRfj008/jevXr2POnDm4dOkS2rdvjy1btiAwMFB2NCIiskMqIYSQHcKa9Ho9PDw8kJOTA3d3d9lxiIhIgpp0gaL3MRIREdU1FiMREVEZLEYiIqIyFH/wzf26swu1NqaGIyIi23SnA6pzWI3dF2NubulUbvc7+w0REdm+3NxceHhUffUeuz8q1Ww24+LFi9BqtZVOI1cdd6aWy8zMtImjW5nXupjXupjXuupjXiEEcnNz4efnBweHqvci2v2I0cHBAc2bN6+153N3d7eJf0h3MK91Ma91Ma911be89xop3sGDb4iIiMpgMRIREZWhfuedd96RHcJWqNVqPPzww3B0tI1PoJnXupjXupjXupi3cnZ/8A0REVFN8KNUIiKiMliMREREZbAYiYiIymAxEhERlcFi/ANSUlIwYsQIeHt7w93dHT179sRvv/0mO1aVfv75Z3Tr1g2urq7w9vbGyJEjZUe6J4PBgI4dO0KlUuHIkSOy41QoPT0dY8eORVBQEFxdXdGyZUu8/fbbKC4ulh3N4vPPP0dQUBBcXFwQERGB3bt3y45UoejoaHTp0gVarRY+Pj547LHHkJycLDtWtUVHR0OlUmHy5Mmyo1QqKysLzz33HLy8vODm5oaOHTsiMTFRdqwKGY1GzJ492/LeCg4Oxpw5c2A2m63+2izGP2Do0KEwGo34z3/+g8TERHTs2BGPPvooLl++LDtahb777js8//zzGDNmDI4ePYq9e/fi2WeflR3rnqZNmwY/Pz/ZMaqUlJQEs9mM5cuX4+TJk/joo4+wbNky/P3vf5cdDQCwYcMGTJ48GbNmzcLhw4fRu3dvDB48GBkZGbKj3SUuLg7jx4/HgQMHEBsbC6PRiKioKOTn58uOdk/x8fFYsWIFOnToIDtKpW7evImePXvCyckJv/zyC06dOoUPP/wQjRo1kh2tQgsWLMCyZcuwZMkSnD59GgsXLiuDeisAAAq6SURBVMT777+PTz/91PovLqhGrl69KgCIXbt2WZbp9XoBQGzfvl1isoqVlJQIf39/sXLlStlRamTLli0iJCREnDx5UgAQhw8flh2p2hYuXCiCgoJkxxBCCNG1a1cxbty4cstCQkLEjBkzJCWqvuzsbAFAxMXFyY5SpdzcXNG6dWsRGxsr+vbtKyZNmiQ7UoWmT58uevXqJTtGtQ0dOlS89NJL5ZaNHDlSPPfcc1Z/bY4Ya8jLywuhoaFYs2YN8vPzYTQasXz5cjRt2hQRERGy493l0KFDyMrKgoODA8LDw9GsWTMMHjwYJ0+elB2tUleuXMErr7yCr7/+Gm5ubrLj1FhOTg48PT1lx0BxcTESExMRFRVVbnlUVBT27dsnKVX15eTkAIAifpdVGT9+PIYOHYrIyEjZUar0448/onPnznjyySfh4+OD8PBwfPHFF7JjVapXr17YsWMHUlJSAABHjx7Fnj17MGTIEOu/uNWr1w5duHBBRERECJVKJdRqtfDz81PsiCYmJkYAEAEBAeLbb78VCQkJYtSoUcLLy0tcv35ddry7mM1m8cgjj4j33ntPCCFEWlqaTY0YU1NThbu7u/jiiy9kRxFZWVkCgNi7d2+55fPmzRNt2rSRlKp6zGazGDZsmOJHODExMSIsLEwUFhYKIYSiR4wajUZoNBoxc+ZMcejQIbFs2TLh4uIiVq9eLTtahcxms5gxY4ZQqVTC0dFRqFQqMX/+/Dp5bRbjbW+//bYAUOUtPj5emM1mMXz4cDF48GCxZ88ekZiYKF577TXh7+8vLl68qLi869atEwDE8uXLLdsWFRUJb29vsWzZMsXl/fjjj8VDDz0kjEajEEJeMVY3b1lZWVmiVatWYuzYsXWatTJ3inHfvn3lls+dO1e0bdtWUqrqef3110VgYKDIzMyUHaVSGRkZwsfHRxw5csSyTMnF6OTkJHr06FFu2YQJE0T37t0lJapaTEyMaN68uYiJiRHHjh0Ta9asEZ6enuKrr76y+mtzSrjbrl27hmvXrlW5TosWLbB3715ERUXh5s2b5S5/0rp1a4wdOxYzZsywdlQA1c+7f/9+9O/fH7t370avXr0sj3Xr1g2RkZGYN2+etaMCqH7eZ555Bps3by537UyTyQS1Wo3Ro0dj9erV1o4KoPp5XVxcAAAXL15Ev3790K1bN3z11Vf3vN5bXSguLoabmxv+/e9/4/HHH7csnzRpEo4cOYK4uDiJ6So3YcIEbNq0Cbt27UJQUJDsOJXatGkTHn/8cajVassyk8kElUoFBwcHGAyGco/JFhgYiIEDB2LlypWWZUuXLsXcuXORlZUlMVnFdDodZsyYgfHjx1uWzZ07F2vXrkVSUpJVX9s2Zo+tA97e3vD29r7negUFBQBw1x8+BweHOjmM+I7q5o2IiIBGo0FycrKlGEtKSpCeno7AwEBrx7Sobt5PPvkEc+fOtdy/ePEiBg0ahA0bNqBbt27WjFhOdfMCpYfA9+vXDxEREVi1apUiShEAnJ2dERERgdjY2HLFGBsbixEjRkhMVjEhBCZMmICNGzdi586dii5FABgwYACOHz9ebtmYMWMQEhKC6dOnK6oUAaBnz553nf6SkpJSp38HaqKgoOCu95Jara6bv7NWH5PamatXrwovLy8xcuRIceTIEZGcnCymTp0qnJycyn2koiSTJk0S/v7+YuvWrSIpKUmMHTtW+Pj4iBs3bsiOdk9K38d45+PT/v37iwsXLohLly5ZbkrwzTffCCcnJ/Hll1+KU6dOicmTJ4sGDRqI9PR02dHu8tprrwkPDw+xc+fOcr/HgoIC2dGqTckfpR48eFA4OjqKefPmiTNnzoh169YJNzc3sXbtWtnRKvTiiy8Kf39/8dNPP4m0tDTx/fffC29vbzFt2jSrvzaL8Q+Ij48XUVFRwtPTU2i1WtG9e3exZcsW2bEqVVxcLP76178KHx8fodVqRWRkpDhx4oTsWNWi9GJctWpVpfsgleKzzz4TgYGBwtnZWXTq1Emxpz9U9ntctWqV7GjVpuRiFEKIzZs3i/bt2wuNRiNCQkLEihUrZEeqlF6vF5MmTRIBAQHCxcVFBAcHi1mzZgmDwWD11+Y+RiIiojKUsTOEiIhIIViMREREZbAYiYiIymAxEhERlcFiJCIiKoPFSEREVAaLkYiIqAwWI5ENaNGiBRYvXlzrz1tcXIxWrVph79691Vp/6tSpmDhxYq3nIFISFiNRPbZixQoEBgaiZ8+e1Vp/2rRpWLVqFdLS0qycjEgeFiNRPfbpp5/i5Zdfrvb6Pj4+iIqKwrJly6yYikguFiORDcrIyMCIESPQsGFDuLu746mnnsKVK1fKrTN37lz4+PhAq9Xi5ZdfxowZM9CxY0fL44cOHUJqaiqGDh1abrsFCxYgKCgIGo0G3t7eGDZsWLnHhw8fjpiYGOv9cESSsRiJbIwQAo899hhu3LiBuLg4xMbG4uzZs3j66act66xbtw7z5s3DggULkJiYiICAACxdurTc8+zatQtt2rQpd13RuLg4zJ49G3PmzMGZM2ewe/fuu0aUXbt2RWZmJs6fP2/dH5RIEl6PkcjGbN++HceOHUNaWhp0Oh0A4Ouvv0ZYWBji4+PRpUsXfPrppxg7dizGjBkDAHjrrbewbds25OXlWZ4nPT0dfn5+5Z7bZDLB0dERoaGhCAgIAACEhoaWW8ff39+yvVKv5Ud0PzhiJFKYdevWoWHDhpbb7t27yz1++vRp6HQ6SykCQLt27dCoUSOcPn0aAJCcnIyuXbuW2+739wsLC+Hi4lJuWf/+/fGPf/wD3bt3h4uLC0aNGnVXPldXVwD/u2g3kb3hiJFIYYYPH45u3bpZ7t8Zod0hhIBKpbpru98v//06v7/CnLe3911XoD958iQ+/PBDLFq0CJGRkfD09LzrdW7cuAEAaNKkSTV/IiLbwhEjkcJotVq0atXKcrszQrujXbt2yMjIQGZmpmXZqVOnkJOTY/nYs23btjh48GC57RISEsrdDw8PR1JSUrnC/OWXXxAQEICJEyeiXbt28PX1vSvfiRMn4OTkhLCwsPv+WYmUiMVIZGMiIyPRoUMHjB49GocOHcLBgwfxwgsvoG/fvujcuTMAYMKECfjyyy+xevVqnDlzBnPnzsWxY8fKjSL79euH/Px8nDx50rIsPDwcJ06cwMcff4yzZ88iOTkZa9euxaVLlyzr7N69G717976rsInsBYuRyMaoVCps2rQJjRs3Rp8+fRAZGYng4GBs2LDBss7o0aMxc+ZMTJ06FZ06dUJaWhr+/Oc/l9un6OXlhZEjR2LdunWWZQMGDMDy5cvxr3/9Cx06dECXLl2wdOlSmM1myzoxMTF45ZVX6uaHJZJAJX6/44GI7NLAgQPh6+uLr7/+2rLs+PHjiIyMRGpqKrRa7T2f4+eff8bf/vY3HDt2DI6OPESB7BP/ZRPZoYKCAixbtgyDBg2CWq1GTEwMtm/fjtjY2HLrPfDAA1i4cCHS09PxwAMP3PN58/PzsWrVKpYi2TWOGInsUGFhIYYNG4ZDhw7BYDCgbdu2mD17NkaOHCk7GpHisRiJiIjK4ME3REREZbAYiYiIymAxEhERlcFiJCIiKoPFSEREVAaLkYiIqAwWIxERURksRiIiojJYjERERGX8Pxg2ievGmE1sAAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = -log.(εs)\n",
    "plot(xs, Hs)\n",
    "xlabel(\"-log(ε)\"); ylabel(\"H\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And one can clearly identify a region in the middle which has the slope of `D`, the fractal dimension of `tr`. But in case you are not really happy with eyeballing this, you can use the function `linear_regions(x, y)` which takes in the curve `y(x)` and decomposes it to approximately independent linear regions.\n",
    "\n",
    "Let's see the result with some nice color coding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrs, slopes = linear_regions(xs, Hs, tol = 0.25)\n",
    "\n",
    "for i in 1:length(lrs)-1\n",
    "    plot(xs[lrs[i]:lrs[i+1]], Hs[lrs[i]:lrs[i+1]], marker = \"o\", \n",
    "        label = i > 7 ? \"slope $(round(slopes[i]; digits = 3))\" : \"\")\n",
    "end\n",
    "xlabel(\"-log(ε)\"); ylabel(\"H\"); legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So here we would get the value `1.939` as the fractal dimension, which is easily accessible as "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9387874361172148"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = maximum(slopes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Distributions.jl\n",
    "\n",
    "The [`Distributions`](https://juliastats.org/Distributions.jl/stable/) package provides an interface for writing distribution-agnostic code: sampling distributions and getting pdfs, using moments, and more. This means that you can write any code that uses a probability distribution without having to care about the distribution's specifics. The result: your code can be run with _any_ probability distribution!\n",
    "\n",
    "The way it works is quite straightforward: `Distributions` provides a unified API around abstract types representing probability distributions. To keep things simple here we (a) limit ourselfes to univariate distributions and (b) assume that the highest level of this abstract hierarchy is `UnivariateDistribution`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Distribution{Univariate,S} where S<:ValueSupport"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Distributions\n",
    "x = -1:0.01:1\n",
    "UnivariateDistribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some example univariate distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Normal{Float64}(μ=0.1, σ=0.25)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Normal(0.1, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, pdf.(d, x)); # pdf(::Distribution, x) gives the pdf at x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cauchy = Cauchy(0.5, 0.25)\n",
    "plot(x, pdf.(cauchy, x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also create your own distribution by extending a small amount of methods. \n",
    "\n",
    "Okay, so where are these distributions useful? Well, you can for example use `rand(::Distribution, ...)` and sample random numbers from an arbitrary distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6411208610416594"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(cauchy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×10 Array{Float64,2}:\n",
       " -0.0945251   0.684076  0.466336   …  0.422561   0.522409   -1.76902 \n",
       "  4.8943     -1.42156   0.533809      0.659961   0.500381    0.339564\n",
       "  0.496773    1.76202   0.623583      1.38527    0.509958    0.476158\n",
       "  0.153889    0.309391  0.706236      0.526716  -0.658566  -31.2724  \n",
       "  1.18274     0.938097  0.49508       0.553075   0.313847    0.34469 \n",
       "  0.619908    0.4957    0.349988   …  2.06727    0.355546    0.848048\n",
       "  0.52721     0.247744  0.477669      0.772037   0.93203     0.511023\n",
       "  0.214352    0.83484   2.49486       0.404149   0.834677    0.753976\n",
       "  0.352015    2.12321   0.690749      0.186116   0.644478    0.414438\n",
       "  0.739386    0.366461  0.0252278     0.229541   1.4945     -1.28772 "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(cauchy, 10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, you can use the `fit` function, to fit a distribution to an e.g. experimental measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Normal{Float64}(μ=-0.008417643639840577, σ=0.9899834868193246)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = randn(5000);\n",
    "fit(Normal, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cauchy{Float64}(μ=-0.006922149389176409, σ=0.6748085966702937)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cauchyfit = fit(Cauchy, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.006922149389176409, 0.6748085966702937)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params(cauchyfit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x300 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(x, 50, alpha = 0.5, density = true)\n",
    "scatter(x, pdf.(cauchyfit, x), color = \"C1\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, other fundamental statistical measures, e.g. means, stds, quantiles, work out of the box for any distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.006922149389176409"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantile(cauchyfit, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " -4.267495948731982\n",
       "  4.253651649953623"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantile.(cauchyfit, [0.05, 0.95])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NaN"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std(cauchyfit) # Cauchy distr. is known for NOT having finite std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. DrWatson\n",
    "\n",
    "[DrWatson](https://juliadynamics.github.io/DrWatson.jl/dev/) is a scientific project assistant software. It helps people deal with their scientific code base, allowing them to focus more on the science and less on the code management. DrWatson offers a lot of tools and functionality for this purpose, but here I'll only show a couple of them. \n",
    "\n",
    "*Disclaimer: I am one of the developers of DrWatson.*\n",
    "\n",
    "## FileIO\n",
    "\n",
    "Obviously, in order to do science, it is necessary to be able to save files to arbitrary formats and to be able to read them later. `FileIO` (which is used by `DrWatson`) is a Julia package that provides a unified API to save and load files to disk, without caring about their actual file ending type.\n",
    "\n",
    "The interface is as simple as:\n",
    "```julia\n",
    "using FileIO\n",
    "object = load(filename)\n",
    "save(filename, object)\n",
    "```\n",
    "where `filename` is a `String` (arbitrary path) that *includes* the file ending, e.g. `.hdf5`.\n",
    "\n",
    "`FileIO` does not actually install any packages that can save or load files! It provides the interface. If you try to save/load a file with an unsupported ending, `FileIO` will tell you that's impossible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"C:\\\\Users\\\\m300808\\\\ownCloud\\\\Zero2Hero-JuliaWorkshop\""
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using FileIO\n",
    "pwd() # state current working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most packages that can save data of arbitrary format expect the final object-to-be saved as a dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"b\" => 4\n",
       "  \"a\" => 5"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testdata = Dict(\"a\" => 5, \"b\" => 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Error encountered while saving \"test.jld2\".\n",
      "\n",
      "Fatal error:\n"
     ]
    },
    {
     "ename": "ArgumentError",
     "evalue": "ArgumentError: Package JLD2 not found in current path:\n- Run `import Pkg; Pkg.add(\"JLD2\")` to install the JLD2 package.\n",
     "output_type": "error",
     "traceback": [
      "ArgumentError: Package JLD2 not found in current path:\n- Run `import Pkg; Pkg.add(\"JLD2\")` to install the JLD2 package.\n",
      "",
      "Stacktrace:",
      " [1] handle_error(::ArgumentError, ::File{DataFormat{:JLD2}}) at C:\\Users\\m300808\\.julia\\packages\\FileIO\\BcdlR\\src\\error_handling.jl:82",
      " [2] handle_exceptions(::Array{Any,1}, ::String) at C:\\Users\\m300808\\.julia\\packages\\FileIO\\BcdlR\\src\\error_handling.jl:77",
      " [3] #save#30(::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::typeof(save), ::Formatted, ::Any) at C:\\Users\\m300808\\.julia\\packages\\FileIO\\BcdlR\\src\\loadsave.jl:213",
      " [4] save at C:\\Users\\m300808\\.julia\\packages\\FileIO\\BcdlR\\src\\loadsave.jl:196 [inlined]",
      " [5] #save#15 at C:\\Users\\m300808\\.julia\\packages\\FileIO\\BcdlR\\src\\loadsave.jl:118 [inlined]",
      " [6] save(::String, ::Dict{String,Int64}) at C:\\Users\\m300808\\.julia\\packages\\FileIO\\BcdlR\\src\\loadsave.jl:118",
      " [7] top-level scope at In[55]:1"
     ]
    }
   ],
   "source": [
    "# I don't have JLD2 installed:\n",
    "save(\"test.jld2\", testdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here I use BSON, which I have installed\n",
    "save(\"test.bson\", testdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"b\" => 4\n",
       "  \"a\" => 5"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testdata = load(\"test.bson\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "rm(\"test.bson\") # delete the file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Savename\n",
    "\n",
    "When saving files, scientists often want to include the parameter values of the simulations in the name of the file. For example, If I had run a simulation with parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 2, 3)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b, c = 1, 2, 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I would like to save my simulation as e.g. `sim_a=1_b=2_c=3.bson`. This can be achieved with string interpolation like so"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"sim_a=1_b=2_c=3.bson\""
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filename = \"sim_a=$(a)_b=$(b)_c=$(c).bson\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This works, but besides being tedius, it is not extendable: if I have a different simulation, with different parameter names, I have to modify this command.\n",
    "\n",
    "This is where DrWatson comes in: it provides a tool, called `savename`, that takes as an input **any Julia container** and converts it into a `key=value` chain. It works with dictionaries and arbitrary Julia composite types (it would work with the `Animal` we defined in the previous session). For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Symbol,Int64} with 3 entries:\n",
       "  :a => 1\n",
       "  :b => 2\n",
       "  :c => 3"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DrWatson\n",
    "# the @dict command makes a dictionary from the given variable names\n",
    "# @dict is a \"macro\", something we won't talk about in this workshop\n",
    "pars = @dict a b c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a=1_b=2_c=3\""
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savename(pars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also call `savename` with prefix and suffix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"prefix_a=1_b=2_c=3_model=linear.bson\""
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = \"linear\"\n",
    "pars = @dict a b c model\n",
    "savename(\"prefix\", pars, \"bson\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`savename` is highly customizable, and also extendable for your own types, while by default it makes some reasonable assumptions about what should and should not be put into the this name. For example, if you had a vector of numbers as part of your parameters, you probably don't want to include it into the savename (by default)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Symbol,Any} with 5 entries:\n",
       "  :a     => 1\n",
       "  :b     => 2\n",
       "  :v     => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
       "  :c     => 3\n",
       "  :model => \"linear\""
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pars[:v] = collect(1:10)\n",
    "pars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a=1_b=2_c=3_model=linear\""
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savename(pars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But you _could_ if you really wanted to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a=1_b=2_c=3_model=linear_v=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10].bson\""
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savename(pars, \"bson\"; allowedtypes = (Real, String, Vector))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`savename` is also convenient for creating titles for figures, by using a different connector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Simulation, a=1, b=2, c=3, model=linear\""
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savename(\"Simulation\", pars; connector = \", \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saving tools\n",
    "\n",
    "DrWatson offers some tools that are useful when saving files. The first is\n",
    "`tagsave`, which modifies the dictionary-to-be-saved by adding additional infromation about the current status of the Git repository of the project (if there exists a Git repository). This allows for reproducibility. For example (notice that `pwd()` is the path of a Git repository)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: The Git repository is dirty! Appending _dirty to the commit ID\n",
      "└ @ DrWatson C:\\Users\\m300808\\.julia\\dev\\DrWatson\\src\\saving_tools.jl:60\n",
      "┌ Warning: `gitpatch` failed with error Base.IOError(\"could not spawn `git --git-dir=C:/Users/m300808/ownCloud/Zero2Hero-JuliaWorkshop/.git --work-tree=C:/Users/m300808/ownCloud/Zero2Hero-JuliaWorkshop diff HEAD`: no such file or directory (ENOENT)\", -4058), returning `nothing` instead.\n",
      "└ @ DrWatson C:\\Users\\m300808\\.julia\\dev\\DrWatson\\src\\saving_tools.jl:97\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{Symbol,Any} with 7 entries:\n",
       "  :a         => 1\n",
       "  :b         => 2\n",
       "  :v         => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
       "  :c         => 3\n",
       "  :gitcommit => \"ff94fd2b9208e5849bd5e7c12781ffd49a8f9755_dirty\"\n",
       "  :model     => \"linear\"\n",
       "  :gitpatch  => nothing"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tagsave(\"test.bson\", copy(pars); gitpath = pwd())\n",
    "load(\"test.bson\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the Git commit ID was included in the saved file!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another useful tool is `safesave`. We all know how **devastating** it can be to by-mistake overwrite an existing simulation because you saved a new simulation with the same name... `safesave` comes to the rescue because it ensures that no files are overwritten but also all files are saved!\n",
    "\n",
    "It works like this:\n",
    "```julia\n",
    "safesave(\"test.bson\", ...)\n",
    "```\n",
    "if `\"test.bson\"` exists, rename it to `test_#1.bson` (and do this recursively if `test_#1.bson` also exists, by incrementing the number after the `#`). Then, save the current data as `test.bson`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "safesave(\"test.bson\", pars)\n",
    "safesave(\"test.bson\", pars)\n",
    "safesave(\"test.bson\", pars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16-element Array{String,1}:\n",
       " \".git\"                    \n",
       " \".gitignore\"              \n",
       " \".ipynb_checkpoints\"      \n",
       " \"1-JuliaBasics.ipynb\"     \n",
       " \"2-MultipleDispatch.ipynb\"\n",
       " \"3-Ecosystem.ipynb\"       \n",
       " \"add.jpg\"                 \n",
       " \"Julia advertisement.pdf\" \n",
       " \"Julia advertisement.pptx\"\n",
       " \"LICENSE.md\"              \n",
       " \"README.md\"               \n",
       " \"solutions.jl\"            \n",
       " \"test.bson\"               \n",
       " \"test_#1.bson\"            \n",
       " \"test_#2.bson\"            \n",
       " \"test_#3.bson\"            "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readdir(pwd())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# delete all files that end in \"bson\"\n",
    "[rm(f) for f in readdir(pwd()) if f[end-3:end] == \"bson\"];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Collecting results\n",
    "\n",
    "If you run several similar simulations with different parameters, you typically want to collect all of them in a tabular datastrcture to analyze further. You can use `collect_results` to automate the data collection process. \n",
    "\n",
    "Let's say we run first some simulations with varying parameters like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = \"linear\"\n",
    "for a in 1:2\n",
    "    for b in [2, 3]\n",
    "        # perform a fake simulation\n",
    "        r = a + b\n",
    "        # save it:\n",
    "        p = @dict a b r model\n",
    "        s = @dict a b model # the result \"r\" doesn't take part in the name\n",
    "        wsave(joinpath(\"data\", savename(s, \"bson\")), p)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we run a different model, which does not necessarily have the same parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = \"cubic\"\n",
    "for a in 1:2\n",
    "    for d in [5, 6]\n",
    "        # perform a fake simulation\n",
    "        r = a + d^3\n",
    "        # save it:\n",
    "        p = @dict a d r model\n",
    "        s = @dict a d model # the result \"r\" doesn't take part in the name\n",
    "        wsave(joinpath(\"data\", savename(s, \"bson\")), p)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the idea is that we want to collect all of this results in a single tabular structure. We do with `collect_results(folder)`, which collects all results of the `folder` into a `DataFrame`. This is a tabular data structure (and thus we need the Julia package `DataFrames` to use it):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling DataFrames [a93c6f00-e57d-5684-b7b6-d8193f3e46c0]\n",
      "└ @ Base loading.jl:1273\n",
      "┌ Info: Scanning folder data for result files.\n",
      "└ @ DrWatson C:\\Users\\m300808\\.julia\\dev\\DrWatson\\src\\result_collection.jl:79\n",
      "┌ Info: Added 8 entries.\n",
      "└ @ DrWatson C:\\Users\\m300808\\.julia\\dev\\DrWatson\\src\\result_collection.jl:107\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th><th>model</th><th>path</th><th>d</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th><th>String⍰</th><th>String⍰</th><th>Int64⍰</th></tr></thead><tbody><p>8 rows × 6 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td><td>linear</td><td>data\\\\a=1_b=2_model=linear.bson</td><td>missing</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td><td>linear</td><td>data\\\\a=1_b=3_model=linear.bson</td><td>missing</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td><td>cubic</td><td>data\\\\a=1_d=5_model=cubic.bson</td><td>5</td></tr><tr><th>4</th><td>1</td><td>missing</td><td>217</td><td>cubic</td><td>data\\\\a=1_d=6_model=cubic.bson</td><td>6</td></tr><tr><th>5</th><td>2</td><td>2</td><td>4</td><td>linear</td><td>data\\\\a=2_b=2_model=linear.bson</td><td>missing</td></tr><tr><th>6</th><td>2</td><td>3</td><td>5</td><td>linear</td><td>data\\\\a=2_b=3_model=linear.bson</td><td>missing</td></tr><tr><th>7</th><td>2</td><td>missing</td><td>127</td><td>cubic</td><td>data\\\\a=2_d=5_model=cubic.bson</td><td>5</td></tr><tr><th>8</th><td>2</td><td>missing</td><td>218</td><td>cubic</td><td>data\\\\a=2_d=6_model=cubic.bson</td><td>6</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& a & b & r & model & path & d\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰ & String⍰ & String⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 & linear & data\\textbackslash{}\\textbackslash{}a=1\\_b=2\\_model=linear.bson &  \\\\\n",
       "\t2 & 1 & 3 & 4 & linear & data\\textbackslash{}\\textbackslash{}a=1\\_b=3\\_model=linear.bson &  \\\\\n",
       "\t3 & 1 &  & 126 & cubic & data\\textbackslash{}\\textbackslash{}a=1\\_d=5\\_model=cubic.bson & 5 \\\\\n",
       "\t4 & 1 &  & 217 & cubic & data\\textbackslash{}\\textbackslash{}a=1\\_d=6\\_model=cubic.bson & 6 \\\\\n",
       "\t5 & 2 & 2 & 4 & linear & data\\textbackslash{}\\textbackslash{}a=2\\_b=2\\_model=linear.bson &  \\\\\n",
       "\t6 & 2 & 3 & 5 & linear & data\\textbackslash{}\\textbackslash{}a=2\\_b=3\\_model=linear.bson &  \\\\\n",
       "\t7 & 2 &  & 127 & cubic & data\\textbackslash{}\\textbackslash{}a=2\\_d=5\\_model=cubic.bson & 5 \\\\\n",
       "\t8 & 2 &  & 218 & cubic & data\\textbackslash{}\\textbackslash{}a=2\\_d=6\\_model=cubic.bson & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "8×6 DataFrame. Omitted printing of 1 columns\n",
       "│ Row │ a      │ b       │ r      │ model   │ path                            │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mString⍰\u001b[39m │ \u001b[90mUnion{Missing, String}\u001b[39m          │\n",
       "├─────┼────────┼─────────┼────────┼─────────┼─────────────────────────────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │ linear  │ data\\\\a=1_b=2_model=linear.bson │\n",
       "│ 2   │ 1      │ 3       │ 4      │ linear  │ data\\\\a=1_b=3_model=linear.bson │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │ cubic   │ data\\\\a=1_d=5_model=cubic.bson  │\n",
       "│ 4   │ 1      │ \u001b[90mmissing\u001b[39m │ 217    │ cubic   │ data\\\\a=1_d=6_model=cubic.bson  │\n",
       "│ 5   │ 2      │ 2       │ 4      │ linear  │ data\\\\a=2_b=2_model=linear.bson │\n",
       "│ 6   │ 2      │ 3       │ 5      │ linear  │ data\\\\a=2_b=3_model=linear.bson │\n",
       "│ 7   │ 2      │ \u001b[90mmissing\u001b[39m │ 127    │ cubic   │ data\\\\a=2_d=5_model=cubic.bson  │\n",
       "│ 8   │ 2      │ \u001b[90mmissing\u001b[39m │ 218    │ cubic   │ data\\\\a=2_d=6_model=cubic.bson  │"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DataFrames\n",
    "results = collect_results(\"data\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So `collect_results` collected all files, but also did something extra, something very useful. Simulation parameters that do not exist in one run (see `b` vs `d`) have the value `missing`. `missing` is how Julia represents missing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# delete all fake data (they are loaded in memory)\n",
    "rm(\"data\"; recursive = true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Tabular data\n",
    "\n",
    "The `result` that we got above is a `DataFrame` from [DataFrames.jl](http://juliadata.github.io/DataFrames.jl/stable/), one of the major Julia packages for tabular data. \n",
    "\n",
    "## Basic stuff\n",
    "One can do basic selection of these data, for example selecting specific columns, removing columns, adding new columns or rows, etc. The `path` column of the `results` is not so useful, so let's remove it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th><th>model</th><th>d</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th><th>String⍰</th><th>Int64⍰</th></tr></thead><tbody><p>8 rows × 5 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td><td>linear</td><td>missing</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td><td>linear</td><td>missing</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td><td>cubic</td><td>5</td></tr><tr><th>4</th><td>1</td><td>missing</td><td>217</td><td>cubic</td><td>6</td></tr><tr><th>5</th><td>2</td><td>2</td><td>4</td><td>linear</td><td>missing</td></tr><tr><th>6</th><td>2</td><td>3</td><td>5</td><td>linear</td><td>missing</td></tr><tr><th>7</th><td>2</td><td>missing</td><td>127</td><td>cubic</td><td>5</td></tr><tr><th>8</th><td>2</td><td>missing</td><td>218</td><td>cubic</td><td>6</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& a & b & r & model & d\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰ & String⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 & linear &  \\\\\n",
       "\t2 & 1 & 3 & 4 & linear &  \\\\\n",
       "\t3 & 1 &  & 126 & cubic & 5 \\\\\n",
       "\t4 & 1 &  & 217 & cubic & 6 \\\\\n",
       "\t5 & 2 & 2 & 4 & linear &  \\\\\n",
       "\t6 & 2 & 3 & 5 & linear &  \\\\\n",
       "\t7 & 2 &  & 127 & cubic & 5 \\\\\n",
       "\t8 & 2 &  & 218 & cubic & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "8×5 DataFrame\n",
       "│ Row │ a      │ b       │ r      │ model   │ d       │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mString⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │\n",
       "├─────┼────────┼─────────┼────────┼─────────┼─────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 2   │ 1      │ 3       │ 4      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │ cubic   │ 5       │\n",
       "│ 4   │ 1      │ \u001b[90mmissing\u001b[39m │ 217    │ cubic   │ 6       │\n",
       "│ 5   │ 2      │ 2       │ 4      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 6   │ 2      │ 3       │ 5      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 7   │ 2      │ \u001b[90mmissing\u001b[39m │ 127    │ cubic   │ 5       │\n",
       "│ 8   │ 2      │ \u001b[90mmissing\u001b[39m │ 218    │ cubic   │ 6       │"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select!(results, Not(:path))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To access specific rows or colums you can access a dataframe like a matrix, e.g. `df[:, 1:3]` gives the first three rows while `df[:, [:a, :b]]` gives the rows selected by name.\n",
    "\n",
    "Adding new data to a dataframe is also straight forward. One can add new rows or new columns. New rows are added by either providing a vector (where the vector's length matches the number of columns), or by providing a named tuple that explicitly names which column gets which new value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th></tr></thead><tbody><p>3 rows × 3 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& a & b & r\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 \\\\\n",
       "\t2 & 1 & 3 & 4 \\\\\n",
       "\t3 & 1 &  & 126 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "3×3 DataFrame\n",
       "│ Row │ a      │ b       │ r      │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │\n",
       "├─────┼────────┼─────────┼────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │\n",
       "│ 2   │ 1      │ 3       │ 4      │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = results[1:3, 1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th></tr></thead><tbody><p>4 rows × 3 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td></tr><tr><th>4</th><td>5</td><td>5</td><td>5</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& a & b & r\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 \\\\\n",
       "\t2 & 1 & 3 & 4 \\\\\n",
       "\t3 & 1 &  & 126 \\\\\n",
       "\t4 & 5 & 5 & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×3 DataFrame\n",
       "│ Row │ a      │ b       │ r      │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │\n",
       "├─────┼────────┼─────────┼────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │\n",
       "│ 2   │ 1      │ 3       │ 4      │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │\n",
       "│ 4   │ 5      │ 5       │ 5      │"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add new row by order of columns\n",
    "push!(df1, [5, 5, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th></tr></thead><tbody><p>5 rows × 3 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td></tr><tr><th>4</th><td>5</td><td>5</td><td>5</td></tr><tr><th>5</th><td>-5</td><td>7</td><td>89</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& a & b & r\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 \\\\\n",
       "\t2 & 1 & 3 & 4 \\\\\n",
       "\t3 & 1 &  & 126 \\\\\n",
       "\t4 & 5 & 5 & 5 \\\\\n",
       "\t5 & -5 & 7 & 89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "5×3 DataFrame\n",
       "│ Row │ a      │ b       │ r      │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │\n",
       "├─────┼────────┼─────────┼────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │\n",
       "│ 2   │ 1      │ 3       │ 4      │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │\n",
       "│ 4   │ 5      │ 5       │ 5      │\n",
       "│ 5   │ -5     │ 7       │ 89     │"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add new row by name of columnns\n",
    "push!(df1, (b = 7, r=89, a = -5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th><th>z</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th><th>Float64</th></tr></thead><tbody><p>5 rows × 4 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td><td>0.574353</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td><td>0.579092</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td><td>0.0584591</td></tr><tr><th>4</th><td>5</td><td>5</td><td>5</td><td>0.973551</td></tr><tr><th>5</th><td>-5</td><td>7</td><td>89</td><td>0.63589</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& a & b & r & z\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰ & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 & 0.574353 \\\\\n",
       "\t2 & 1 & 3 & 4 & 0.579092 \\\\\n",
       "\t3 & 1 &  & 126 & 0.0584591 \\\\\n",
       "\t4 & 5 & 5 & 5 & 0.973551 \\\\\n",
       "\t5 & -5 & 7 & 89 & 0.63589 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "5×4 DataFrame\n",
       "│ Row │ a      │ b       │ r      │ z         │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mFloat64\u001b[39m   │\n",
       "├─────┼────────┼─────────┼────────┼───────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │ 0.574353  │\n",
       "│ 2   │ 1      │ 3       │ 4      │ 0.579092  │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │ 0.0584591 │\n",
       "│ 4   │ 5      │ 5       │ 5      │ 0.973551  │\n",
       "│ 5   │ -5     │ 7       │ 89     │ 0.63589   │"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.z = rand(size(df1, 1))\n",
    "# equivalent syntax: df1.z == df1[!, :z]\n",
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Querying a DataFrame\n",
    "\n",
    "Querying a dataframe is done with the [Query.jl](https://www.queryverse.org/Query.jl/stable/) package (alternatives also exist). `Query` allows you to query many different Julia data sources with two styles of syntax: \n",
    "\n",
    "1. Composable standalone operations \n",
    "2. \"LINQ\" style\n",
    "\n",
    "Here I'll show the LINQ syntax because it involves less new symbols. \n",
    "\n",
    "Query is extremely powerful and general, because in principle it can query almost everything that is iterable. E.g. a dataframe is in principle an iterable of NamedTuples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Query [1a8c2f83-1ff3-5112-b086-8aa67b057ba1]\n",
      "└ @ Base loading.jl:1273\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>b</th><th>r</th><th>model</th><th>d</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th><th>Int64⍰</th><th>String⍰</th><th>Int64⍰</th></tr></thead><tbody><p>8 rows × 5 columns</p><tr><th>1</th><td>1</td><td>2</td><td>3</td><td>linear</td><td>missing</td></tr><tr><th>2</th><td>1</td><td>3</td><td>4</td><td>linear</td><td>missing</td></tr><tr><th>3</th><td>1</td><td>missing</td><td>126</td><td>cubic</td><td>5</td></tr><tr><th>4</th><td>1</td><td>missing</td><td>217</td><td>cubic</td><td>6</td></tr><tr><th>5</th><td>2</td><td>2</td><td>4</td><td>linear</td><td>missing</td></tr><tr><th>6</th><td>2</td><td>3</td><td>5</td><td>linear</td><td>missing</td></tr><tr><th>7</th><td>2</td><td>missing</td><td>127</td><td>cubic</td><td>5</td></tr><tr><th>8</th><td>2</td><td>missing</td><td>218</td><td>cubic</td><td>6</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& a & b & r & model & d\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰ & Int64⍰ & String⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 & linear &  \\\\\n",
       "\t2 & 1 & 3 & 4 & linear &  \\\\\n",
       "\t3 & 1 &  & 126 & cubic & 5 \\\\\n",
       "\t4 & 1 &  & 217 & cubic & 6 \\\\\n",
       "\t5 & 2 & 2 & 4 & linear &  \\\\\n",
       "\t6 & 2 & 3 & 5 & linear &  \\\\\n",
       "\t7 & 2 &  & 127 & cubic & 5 \\\\\n",
       "\t8 & 2 &  & 218 & cubic & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "8×5 DataFrame\n",
       "│ Row │ a      │ b       │ r      │ model   │ d       │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mString⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m  │\n",
       "├─────┼────────┼─────────┼────────┼─────────┼─────────┤\n",
       "│ 1   │ 1      │ 2       │ 3      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 2   │ 1      │ 3       │ 4      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 3   │ 1      │ \u001b[90mmissing\u001b[39m │ 126    │ cubic   │ 5       │\n",
       "│ 4   │ 1      │ \u001b[90mmissing\u001b[39m │ 217    │ cubic   │ 6       │\n",
       "│ 5   │ 2      │ 2       │ 4      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 6   │ 2      │ 3       │ 5      │ linear  │ \u001b[90mmissing\u001b[39m │\n",
       "│ 7   │ 2      │ \u001b[90mmissing\u001b[39m │ 127    │ cubic   │ 5       │\n",
       "│ 8   │ 2      │ \u001b[90mmissing\u001b[39m │ 218    │ cubic   │ 6       │"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Query\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's perform some basic queries and then explain them. The basic query syntax is as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>r</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th></tr></thead><tbody><p>4 rows × 2 columns</p><tr><th>1</th><td>1</td><td>3</td></tr><tr><th>2</th><td>1</td><td>4</td></tr><tr><th>3</th><td>2</td><td>4</td></tr><tr><th>4</th><td>2</td><td>5</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& a & r\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3 \\\\\n",
       "\t2 & 1 & 4 \\\\\n",
       "\t3 & 2 & 4 \\\\\n",
       "\t4 & 2 & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×2 DataFrame\n",
       "│ Row │ a      │ r      │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m │\n",
       "├─────┼────────┼────────┤\n",
       "│ 1   │ 1      │ 3      │\n",
       "│ 2   │ 1      │ 4      │\n",
       "│ 3   │ 2      │ 4      │\n",
       "│ 4   │ 2      │ 5      │"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = @from row in results begin\n",
    "    @where row.model == \"linear\"\n",
    "    @select {row.a, row.r}\n",
    "    @collect DataFrame\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "same command, with comments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>a</th><th>r</th></tr><tr><th></th><th>Int64⍰</th><th>Int64⍰</th></tr></thead><tbody><p>4 rows × 2 columns</p><tr><th>1</th><td>1</td><td>3</td></tr><tr><th>2</th><td>1</td><td>4</td></tr><tr><th>3</th><td>2</td><td>4</td></tr><tr><th>4</th><td>2</td><td>5</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& a & r\\\\\n",
       "\t\\hline\n",
       "\t& Int64⍰ & Int64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3 \\\\\n",
       "\t2 & 1 & 4 \\\\\n",
       "\t3 & 2 & 4 \\\\\n",
       "\t4 & 2 & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×2 DataFrame\n",
       "│ Row │ a      │ r      │\n",
       "│     │ \u001b[90mInt64⍰\u001b[39m │ \u001b[90mInt64⍰\u001b[39m │\n",
       "├─────┼────────┼────────┤\n",
       "│ 1   │ 1      │ 3      │\n",
       "│ 2   │ 1      │ 4      │\n",
       "│ 3   │ 2      │ 4      │\n",
       "│ 4   │ 2      │ 5      │"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# `@from ... begin` initializes a query\n",
    "# here `row` (any name would be fine) is the \n",
    "# iterable of the tabular data. Think of it as a \n",
    "# NamedTuple. You can access its values by name.\n",
    "q = @from row in results begin\n",
    "    # `@where` filters elements where the following\n",
    "    # expression is true. \n",
    "    @where row.model == \"linear\"\n",
    "    # `@select { stuf... }  creates a new named tuple\n",
    "    @select {row.a, row.r}\n",
    "    # `@collect` collects the selected results into\n",
    "    # the specified data structure\n",
    "    @collect DataFrame\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is another query but with different contents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>sin</th><th>cos</th></tr><tr><th></th><th>Float64⍰</th><th>Float64⍰</th></tr></thead><tbody><p>7 rows × 2 columns</p><tr><th>1</th><td>0.841471</td><td>-0.989992</td></tr><tr><th>2</th><td>0.841471</td><td>-0.653644</td></tr><tr><th>3</th><td>0.841471</td><td>-0.973642</td></tr><tr><th>4</th><td>0.909297</td><td>-0.653644</td></tr><tr><th>5</th><td>0.909297</td><td>0.283662</td></tr><tr><th>6</th><td>0.909297</td><td>0.232359</td></tr><tr><th>7</th><td>0.909297</td><td>-0.334137</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& sin & cos\\\\\n",
       "\t\\hline\n",
       "\t& Float64⍰ & Float64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 0.841471 & -0.989992 \\\\\n",
       "\t2 & 0.841471 & -0.653644 \\\\\n",
       "\t3 & 0.841471 & -0.973642 \\\\\n",
       "\t4 & 0.909297 & -0.653644 \\\\\n",
       "\t5 & 0.909297 & 0.283662 \\\\\n",
       "\t6 & 0.909297 & 0.232359 \\\\\n",
       "\t7 & 0.909297 & -0.334137 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "7×2 DataFrame\n",
       "│ Row │ sin      │ cos       │\n",
       "│     │ \u001b[90mFloat64⍰\u001b[39m │ \u001b[90mFloat64⍰\u001b[39m  │\n",
       "├─────┼──────────┼───────────┤\n",
       "│ 1   │ 0.841471 │ -0.989992 │\n",
       "│ 2   │ 0.841471 │ -0.653644 │\n",
       "│ 3   │ 0.841471 │ -0.973642 │\n",
       "│ 4   │ 0.909297 │ -0.653644 │\n",
       "│ 5   │ 0.909297 │ 0.283662  │\n",
       "│ 6   │ 0.909297 │ 0.232359  │\n",
       "│ 7   │ 0.909297 │ -0.334137 │"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = @from row in results begin\n",
    "    @where cos(row.r) < 0.5\n",
    "    @select {sin = sin(row.a), cos = cos(row.r)}\n",
    "    @collect DataFrame\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, you don't have to necessarily collect existing columns, you can even create new ones (specified by name).\n",
    "\n",
    "Of course, much, much more things are possible to do in such a query. For more, see the documentation of Query.jl."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A final take-home message\n",
    "\n",
    "One thing that should really, _really_ be added a lot of weight, is how simple, transparent, and high level are the interfaces of everything that you have seen so far. Both base Julia, as well as most packages for it, have such a simple interface which means that people can learn the software faster and spend more time actually doing science than trying to figure out how to write the code.\n",
    "\n",
    "This is something that \"old\" programming languages typically fail at: most (young) people that use codebases written in C/FORTRAN without any high level API defined on top (in e.g. Python) always complain that it is \"so hard to use this stuff\".\n",
    "\n",
    "Julia = answer :) \n",
    "\n",
    "# Exercises\n",
    "\n",
    "These exercises will require you to search things on the internet (because this is part of the process of \"learning a Julia package\").\n",
    "\n",
    "## Make a basic plot\n",
    "\n",
    "There are many (perhaps too many) packages you can use to plot things with Julia. Some of them are entirely trivial to install, some of them not so much. I'd recommend to use PyPlot.jl, as it always installs and works without problems and a huge list of features as well as excellent documentation. \n",
    "\n",
    "After installing a plotting package, plot `1:5` versus `rand(5)` and then scatter plot `1:5` versus `rand(5)`, in a different color. Then make the x and y axis to have labels have \"x\" and \"y\", and add a title to your plot. Plotting will be used in subesequent exercises.\n",
    "\n",
    "## Bouncing ball\n",
    "\n",
    "Using the callback functionality of DifferentialEquations.jl, implement the bouncing ball physical system:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= v \\\\\n",
    "\\dot{v} &= -g - \\gamma v \n",
    "\\end{aligned}\n",
    "$$\n",
    "and at $x=0$ there is a table that the ball bounces from. $g$ is the gravity constant and $\\gamma$ the air friction (use e.g. $g=10, \\gamma = 0.99, x = 1, v = 0$). Implement this problem for elastic collisions (elastic collisions preserve velocity measure), and plot the time evolution of $x, v$ versus time.\n",
    "\n",
    "*Hint: whenever the ball reaches the level $x=0$, its velocity should be reversed.*\n",
    "\n",
    "\n",
    "## Distribution quantile\n",
    "\n",
    "To find the $q$-th quantile of a distribution, one can use a Newton method\n",
    "\n",
    "$$\\theta_{n+1} = \\theta_n -\\frac{\\text{cdf}(\\theta)−q}{\\text{pdf}(\\theta)}$$\n",
    "\n",
    "where $\\theta_n$ converges to the value of the $q$-th quantile.\n",
    "\n",
    "Use multiple dispatch to write a generic algorithm for which calculates the qth quantile of any `UnivariateDistribution` in Distributions.jl, and test your result against the `quantile(d::UnivariateDistribution, q::Number)` function from Distributions.jl using the following distributions: `[Gamma(5, 1), Normal(0, 1), Beta(2, 4)]`.\n",
    "\n",
    "*Hint: use `θ0 = mean(distribution)`*\n",
    "\n",
    "## Plotting subsets of a dataframe\n",
    "\n",
    "`DataFrames` has a default dataset that is used in its test suite. Install the `CSV` package, and load this dataset with the command:\n",
    "```julia\n",
    "using DataFrames, CSV\n",
    "iris = DataFrame(CSV.File(\n",
    "    joinpath(dirname(pathof(DataFrames)), \n",
    "    \"../docs/src/assets/iris.csv\")\n",
    "))\n",
    "```\n",
    "\n",
    "This dataset has various flower species (column `:Species`). For every species create a 1x2 figure with the following plots:\n",
    "\n",
    "* [1,1] = scatter plot of `SepalLength` vs `SepalWidth`. \n",
    "2. [1,2] = scatter plot of `PetalLength` vs `PetalWidth`.\n",
    "\n",
    "for each of these sub-scatter plots, calculate and print the Pearson correlaton coefficient.\n",
    "\n",
    "## DataFrame of chaos\n",
    "\n",
    "Define the Roessler system as a `DynamicalSystem`:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= -y-z \\\\\n",
    "\\dot{y} &= x+ay \\\\\n",
    "\\dot{z} &= b + z(x-c)\n",
    "\\end{aligned}\n",
    "$$\n",
    "with initial condition `ones(3)`. Loop over all three of the following parameter ranges:\n",
    "```julia\n",
    "as = 0.15:0.025:0.25\n",
    "bs = 0.15:0.025:0.25\n",
    "cs = 4:0.1:6.0\n",
    "```\n",
    "and for each parameter combination calculate (1) the Lyapunov spectrum and (2) the shannon entropy of the system's trajectory. (For the entropy, evolve the system with `dt=0.1` and use `ε=0.1` for the box size. For changing parameters you have to use `set_parameter!`).\n",
    "\n",
    "Collect this analysis into a dataframe, with columns `a, b, c, λ1, λ2, H`. Then use the querying framework to query into this dataframe and do the following processes:\n",
    "\n",
    "####  find chaotic parameter sets\n",
    "Select all values `a, b, c` where `λ1 > 0.01` (which indicates chaotic dynamics).\n",
    "\n",
    "####  λ vs H\n",
    "For all chaotic cases, select the `λ1, H` values and then perform a scatter plot of these two.\n",
    "\n",
    "#### heatmap of H\n",
    "For `a` fixed to `0.2`, plot a heatmap of the value of `H` with axis the values of `c` and the values of `b`. Provided that you have a dataframe with columns `:b, :c, :H`, then these commands:\n",
    "```julia\n",
    "unstacked = unstack(heatdf, :b,  :H; renamecols = (x -> \"H for b=$(x)\"))\n",
    "heat = Matrix(unstacked[:, Not(:c)])\n",
    "```\n",
    "will create a matrix with the values of `H` where the row index is the values of `c` and the column index is the values of `b`.\n",
    "\n",
    "*Hint: you can initiallize an empty dataframe with `df = DataFrame()`, and then start pushing into it arbitrary named tuples like `push!(df, (a = 0.5, b = 0.5))`.*\n",
    "\n",
    "*Hint 2: this all sounds like a lot of computation, but if you do the exercise correct running all code should not take more than 10 seconds.*\n",
    "\n",
    "\n",
    "## Reproducible scientific project\n",
    "*this exercise only applies to participants that already know Git*\n",
    "\n",
    "* Use DrWatson's `initialize_project` to start a scientific project somewhere on your computer. \n",
    "* Add the package `BSON` to this project. \n",
    "* In the `scripts` folder create a new Julia script that uses three parameters `a, b, c ∈ Reals` and creates a random result `r`. Save this result into disk by using `savename` to produce a name from `a, b, c`, and using `tagsave` to do the actual saving.\n",
    "* Save your script, and commit it into Git. Then run the script, load the saved file, and confirm that the saved git commit ID matches that of your Git repo.\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.3.1",
   "language": "julia",
   "name": "julia-1.3"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.3.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}