code/paper-Supplement-sensitivity-to-data-sampling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=top-page></a>\n",
    "\n",
    "# Cost function response to data sampling\n",
    "\n",
    "In this notebook, we explore the response of the cost function, $\\mathcal{L}$, to random data sampling.\n",
    "\n",
    "Datasets are sampled at:\n",
    "\n",
    "- 5%\n",
    "- 20%\n",
    "- 50%\n",
    "- 80%\n",
    "- 100% (full data)\n",
    "\n",
    "The analysis in this notebook is performed in the following steps:\n",
    "\n",
    "- [Load the reacting flow data](#reacting)\n",
    "    - [Hydrogen/air combustion](#reacting-hydrogen)\n",
    "        - [Plot the result of data sampling on 2D projections](#reacting-hydrogen-2D)\n",
    "        - [Plot the result of data sampling on 3D projections](#reacting-hydrogen-3D)\n",
    "    - [Syngas/air combustion](#reacting-syngas)\n",
    "        - [Plot the result of data sampling on 2D projections](#reacting-syngas-2D)\n",
    "        - [Plot the result of data sampling on 3D projections](#reacting-syngas-3D)\n",
    "- [Load the plasma data](#plasma)\n",
    "    - [Plot the result of data sampling on 2D projections](#plasma-2D)\n",
    "    - [Plot the result of data sampling on 3D projections](#plasma-3D)\n",
    "- [Load the atmospheric dispersion data](#atmo)\n",
    "    - [Plot the result of data sampling on 2D projections](#atmo-2D)\n",
    "    - [Plot the result of data sampling on 3D projections](#atmo-3D)\n",
    "    \n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run -i imports.py\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "bandwidth_values = np.logspace(-7, 3, 200)\n",
    "penalty_function = 'log-sigma-over-peak'\n",
    "norm = 'cumulative'\n",
    "power = 1\n",
    "save_csv = True\n",
    "color_map_colors = cm.get_cmap('Greys')\n",
    "colors = np.flipud(color_map_colors(np.linspace(0.1, 1, 5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting></a>\n",
    "***\n",
    "\n",
    "## Load the reacting flow data\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_percentage_list = [5, 20, 50, 80, 100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "scalings_list = ['none', 'auto', 'pareto', 'vast', 'range', '0to1', '-1to1', 'level', 'max', 'poisson', 'vast_2', 'vast_3', 'vast_4']\n",
    "tex_scalings_list = ['None', 'Auto', 'Pareto', 'VAST', 'Range', '$\\\\langle 0, 1 \\\\rangle$', '$\\\\langle -1, 1 \\\\rangle$', 'Level', 'Max', 'Poisson', 'S1', 'S2', 'S3']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting-hydrogen></a>\n",
    "\n",
    "### Hydrogen/air combustion\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_space = pd.read_csv('../data/reacting-flow-hydrogen-air-steady-state-space.csv', header=None).to_numpy()\n",
    "state_space_names = pd.read_csv('../data/reacting-flow-hydrogen-air-steady-state-space-names.csv', header=None).to_numpy().ravel()\n",
    "mixture_fraction = pd.read_csv('../data/reacting-flow-hydrogen-air-steady-mixture-fraction.csv', header=None).to_numpy()\n",
    "dissipation_rates = pd.read_csv('../data/reacting-flow-hydrogen-air-steady-dissipation-rates.csv', header=None).to_numpy()\n",
    "\n",
    "target_variables_idx = [0, 2, 4, 5, 6]\n",
    "target_variables = state_space[:,target_variables_idx]\n",
    "target_variables_names = state_space_names[target_variables_idx]\n",
    "\n",
    "(n_observations, n_variables) = np.shape(state_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green;\">► You only need to run this once to generate the `csv` files in `../results/`:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n_components in [2,3]:\n",
    "\n",
    "    for sample_percentage in sample_percentage_list:\n",
    "\n",
    "        print('\\nRunning for ' + str(n_components) + 'D LDM, for ' + str(sample_percentage) + '% of data\\n')\n",
    "\n",
    "        costs = []\n",
    "\n",
    "        idx = np.zeros((n_observations,)).astype(int)\n",
    "        sample_random = preprocess.DataSampler(idx, random_seed=random_seed, verbose=False)\n",
    "        (idx_test, _) = sample_random.random(sample_percentage)\n",
    "\n",
    "        for scaling in scalings_list:\n",
    "\n",
    "            print(scaling)\n",
    "\n",
    "            tic = time.perf_counter()\n",
    "\n",
    "            pca = reduction.PCA(state_space, scaling=scaling, n_components=n_components)\n",
    "            PCs = pca.transform(state_space)\n",
    "\n",
    "            variance_data = analysis.compute_normalized_variance(PCs[idx_test,:],\n",
    "                                                                 target_variables[idx_test,:],\n",
    "                                                                 depvar_names=target_variables_names,\n",
    "                                                                 bandwidth_values=bandwidth_values)\n",
    "\n",
    "            cost = analysis.cost_function_normalized_variance_derivative(variance_data, \n",
    "                                                                         penalty_function=penalty_function, \n",
    "                                                                         power=power,\n",
    "                                                                         norm=norm)\n",
    "\n",
    "            costs.append(cost)\n",
    "\n",
    "            print('Pure scaling cost:\\t' + str(round(cost,4)))\n",
    "\n",
    "            toc = time.perf_counter()\n",
    "\n",
    "            print(f'\\tTime it took: {(toc - tic)/60:0.1f} minutes.\\n' + '-'*40)\n",
    "\n",
    "        if save_csv:\n",
    "\n",
    "            np.savetxt('../results/SUPPLEMENT-reacting-flow-hydrogen-air-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-' + '-'.join(target_variables_names) + '-pure-scaling-cost-' + norm + '.csv', (costs), delimiter=',', fmt='%.16e')\n",
    "            np.savetxt('../results/SUPPLEMENT-reacting-flow-hydrogen-air-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-' + '-'.join(target_variables_names) + '-scalings-list.csv', (scalings_list), delimiter=',', fmt='%s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting-hydrogen-2D></a>\n",
    "#### Plot the result of data sampling on 2D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 655.2x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-reacting-flow-hydrogen-air-perc-of-data-' + str(sample_percentage) + '-2D-LDM-optimizing-on-T-H2-OH-H2O-O2-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage ==100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, [], fontsize=16)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([5,6,7,8,9,10,11,12,13,14,15])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([5,16])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Reacting flow hydrogen/air, 2D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-reacting-flow-hydrogen-air-data-sampling-2D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting-hydrogen-3D></a>\n",
    "#### Plot the result of data sampling on 3D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 655.2x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-reacting-flow-hydrogen-air-perc-of-data-' + str(sample_percentage) + '-3D-LDM-optimizing-on-T-H2-OH-H2O-O2-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage ==100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, [], fontsize=16)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([4,5,6,7,8,9,10,11,12,13])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([4,13])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Reacting flow hydrogen/air, 3D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-reacting-flow-hydrogen-air-data-sampling-3D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting-syngas></a>\n",
    "\n",
    "### Syngas/air combustion\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_space = pd.read_csv('../data/reacting-flow-syngas-air-steady-state-space.csv', header=None).to_numpy()\n",
    "state_space_names = pd.read_csv('../data/reacting-flow-syngas-air-steady-state-space-names.csv', header=None).to_numpy().ravel()\n",
    "mixture_fraction = pd.read_csv('../data/reacting-flow-syngas-air-steady-mixture-fraction.csv', header=None).to_numpy()\n",
    "dissipation_rates = pd.read_csv('../data/reacting-flow-syngas-air-steady-dissipation-rates.csv', header=None).to_numpy()\n",
    "\n",
    "state_space = state_space[:,0:-1]\n",
    "state_space_names = state_space_names[0:-1]\n",
    "\n",
    "target_variables_idx = [0, 1, 2, 4, 5, 8, 9]\n",
    "target_variables = state_space[:,target_variables_idx]\n",
    "target_variables_names = state_space_names[target_variables_idx]\n",
    "\n",
    "(n_observations, n_variables) = np.shape(state_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green;\">► You only need to run this once to generate the `csv` files in `../results/`:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n_components in [2,3]:\n",
    "\n",
    "    for sample_percentage in sample_percentage_list:\n",
    "\n",
    "        print('\\nRunning for ' + str(n_components) + 'D LDM, for ' + str(sample_percentage) + '% of data\\n')\n",
    "\n",
    "        costs = []\n",
    "\n",
    "        idx = np.zeros((n_observations,)).astype(int)\n",
    "        sample_random = preprocess.DataSampler(idx, random_seed=random_seed, verbose=False)\n",
    "        (idx_test, _) = sample_random.random(sample_percentage)\n",
    "\n",
    "        for scaling in scalings_list:\n",
    "\n",
    "            print(scaling)\n",
    "\n",
    "            tic = time.perf_counter()\n",
    "\n",
    "            pca = reduction.PCA(state_space, scaling=scaling, n_components=n_components)\n",
    "            PCs = pca.transform(state_space)\n",
    "\n",
    "            variance_data = analysis.compute_normalized_variance(PCs[idx_test,:],\n",
    "                                                                 target_variables[idx_test,:],\n",
    "                                                                 depvar_names=target_variables_names,\n",
    "                                                                 bandwidth_values=bandwidth_values)\n",
    "\n",
    "            cost = analysis.cost_function_normalized_variance_derivative(variance_data, \n",
    "                                                                         penalty_function=penalty_function, \n",
    "                                                                         power=power,\n",
    "                                                                         norm=norm)\n",
    "\n",
    "            costs.append(cost)\n",
    "\n",
    "            print('Pure scaling cost:\\t' + str(round(cost,4)))\n",
    "\n",
    "            toc = time.perf_counter()\n",
    "\n",
    "            print(f'\\tTime it took: {(toc - tic)/60:0.1f} minutes.\\n' + '-'*40)\n",
    "\n",
    "        if save_csv:\n",
    "\n",
    "            np.savetxt('../results/SUPPLEMENT-reacting-flow-syngas-air-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-' + '-'.join(target_variables_names) + '-pure-scaling-cost-' + norm + '.csv', (costs), delimiter=',', fmt='%.16e')\n",
    "            np.savetxt('../results/SUPPLEMENT-reacting-flow-syngas-air-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-' + '-'.join(target_variables_names) + '-scalings-list.csv', (scalings_list), delimiter=',', fmt='%s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting-syngas-2D></a>\n",
    "#### Plot the result of data sampling on 2D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 655.2x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-reacting-flow-syngas-air-perc-of-data-' + str(sample_percentage) + '-2D-LDM-optimizing-on-T-H2-O2-OH-H2O-CO-CO2-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage ==100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, [], fontsize=16)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([6,7,8,9,10,11,12,13,14])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([7,14])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Reacting flow syngas/air, 2D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-reacting-flow-syngas-air-data-sampling-2D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=reacting-syngas-3D></a>\n",
    "#### Plot the result of data sampling on 3D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 655.2x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-reacting-flow-syngas-air-perc-of-data-' + str(sample_percentage) + '-3D-LDM-optimizing-on-T-H2-O2-OH-H2O-CO-CO2-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage ==100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, tex_scalings_list, fontsize=16, rotation=90)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([6,7,8,9,10])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([6,10])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Reacting flow syngas/air, 3D PCA projections', fontsize=18)\n",
    "# plt.legend(frameon=False, ncol=5, bbox_to_anchor=(1,1), fontsize=18, handletextpad=0)\n",
    "# plt.savefig('../figures/data-sampling-legend.svg', dpi=200, bbox_inches='tight')\n",
    "           \n",
    "plt.savefig('../figures/supplement-reacting-flow-syngas-air-data-sampling-3D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=plasma></a>\n",
    "***\n",
    "\n",
    "## Load the plasma data\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_percentage_list = [5, 20, 50]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "scalings_list = ['none', 'auto', 'pareto', 'vast', 'range', '0to1', '-1to1', 'level', 'max']\n",
    "tex_scalings_list = ['None', 'Auto', 'Pareto', 'VAST', 'Range', '$\\\\langle 0, 1 \\\\rangle$', '$\\\\langle -1, 1 \\\\rangle$', 'Level', 'Max']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = pd.read_csv('../data/plasma-physics-argon-plasma-state-space.csv', header=None).to_numpy()\n",
    "X_names = pd.read_csv('../data/plasma-physics-argon-plasma-state-space-names.csv', header=None).to_numpy().ravel()\n",
    "\n",
    "target_variables_idx = [0, 1, 2, 3]\n",
    "target_variables = X[:,target_variables_idx]\n",
    "target_variables_names = X_names[target_variables_idx]\n",
    "\n",
    "(n_observations, n_variables) = np.shape(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green;\">► You only need to run this once to generate the `csv` files in `../results/`:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n_components in [2,3]:\n",
    "\n",
    "    for sample_percentage in sample_percentage_list:\n",
    "\n",
    "        print('\\nRunning for ' + str(n_components) + 'D LDM, for ' + str(sample_percentage) + '% of data\\n')\n",
    "\n",
    "        costs = []\n",
    "\n",
    "        idx = np.zeros((n_observations,)).astype(int)\n",
    "        sample_random = preprocess.DataSampler(idx, random_seed=random_seed, verbose=False)\n",
    "        (idx_test, _) = sample_random.random(sample_percentage)\n",
    "\n",
    "        for scaling in scalings_list:\n",
    "\n",
    "            print(scaling)\n",
    "\n",
    "            tic = time.perf_counter()\n",
    "\n",
    "            pca = reduction.PCA(X, scaling=scaling, n_components=n_components)\n",
    "            PCs = pca.transform(X)  \n",
    "\n",
    "            variance_data = analysis.compute_normalized_variance(PCs[idx_test,:],\n",
    "                                                        target_variables[idx_test,:],\n",
    "                                                        depvar_names=target_variables_names,\n",
    "                                                        bandwidth_values=bandwidth_values)\n",
    "\n",
    "            cost = analysis.cost_function_normalized_variance_derivative(variance_data, \n",
    "                                                                         penalty_function=penalty_function, \n",
    "                                                                         power=power,\n",
    "                                                                         norm=norm)\n",
    "\n",
    "            costs.append(cost)\n",
    "\n",
    "            print('Pure scaling cost:\\t' + str(round(cost,4)))\n",
    "\n",
    "            toc = time.perf_counter()\n",
    "\n",
    "            print(f'\\tTime it took: {(toc - tic)/60:0.1f} minutes.\\n' + '-'*40)\n",
    "\n",
    "        if save_csv:\n",
    "\n",
    "            np.savetxt('../results/SUPPLEMENT-plasma-physics-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-Te-Th-Ye-YAr-pure-scaling-cost-' + norm + '.csv', (costs), delimiter=',', fmt='%.16e')\n",
    "            np.savetxt('../results/SUPPLEMENT-plasma-physics-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-Te-Th-Ye-YAr-scalings-list.csv', (scalings_list), delimiter=',', fmt='%s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=plasma-2D></a>\n",
    "\n",
    "### Plot the result of data sampling on 2D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 453.6x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-plasma-physics-perc-of-data-' + str(sample_percentage) + '-2D-LDM-optimizing-on-Te-Th-Ye-YAr-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage == 100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, [], fontsize=16)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([4,5,6,7,8,9,10,11])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([4,11])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Argon plasma, 2D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-plasma-physics-data-sampling-2D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=plasma-3D></a>\n",
    "\n",
    "### Plot the result of data sampling on 3D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 453.6x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-plasma-physics-perc-of-data-' + str(sample_percentage) + '-3D-LDM-optimizing-on-Te-Th-Ye-YAr-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage == 100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, tex_scalings_list, fontsize=16, rotation=90)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([3,4,5,6,7,8,9])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([3,9])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Argon plasma, 3D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-plasma-physics-data-sampling-3D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=atmo></a>\n",
    "***\n",
    "\n",
    "## Load the atmospheric physics data\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_percentage_list = [5, 20, 50, 80, 100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "scalings_list = ['none', 'auto', 'pareto', 'vast', 'range', '0to1', '-1to1', 'level', 'max', 'vast_2', 'vast_3', 'vast_4']\n",
    "tex_scalings_list = ['None', 'Auto', 'Pareto', 'VAST', 'Range', '$\\\\langle 0, 1 \\\\rangle$', '$\\\\langle -1, 1 \\\\rangle$', 'Level', 'Max', 'S1', 'S2', 'S3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = pd.read_csv('../data/atmospheric-physics-state-space.csv', header=None).to_numpy()\n",
    "X_names = pd.read_csv('../data/atmospheric-physics-state-space-names.csv', header=None).to_numpy().ravel()\n",
    "X_Sct = pd.read_csv('../data/atmospheric-physics-turbulent-Schmidt-number.csv', header=None).to_numpy().ravel()\n",
    "(n_observations, n_variables) = X.shape\n",
    "\n",
    "(idx_outliers_removed, idx_outliers) = preprocess.outlier_detection(X, \n",
    "                                                                    'auto', \n",
    "                                                                    method='PC CLASSIFIER', \n",
    "                                                                    quantile_threshold=0.98,\n",
    "                                                                    verbose=True)\n",
    "\n",
    "X = X[idx_outliers_removed,:]\n",
    "X_Sct = X_Sct[idx_outliers_removed]\n",
    "\n",
    "(n_observations, n_variables) = np.shape(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green;\">► You only need to run this once to generate the `csv` files in `../results/`:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n_components in [2,3]:\n",
    "\n",
    "    for sample_percentage in sample_percentage_list:\n",
    "\n",
    "        print('\\nRunning for ' + str(n_components) + 'D LDM, for ' + str(sample_percentage) + '% of data\\n')\n",
    "\n",
    "        costs = []\n",
    "\n",
    "        idx = np.zeros((n_observations,)).astype(int)\n",
    "        sample_random = preprocess.DataSampler(idx, random_seed=random_seed, verbose=False)\n",
    "        (idx_test, _) = sample_random.random(sample_percentage)\n",
    "\n",
    "        for scaling in scalings_list:\n",
    "\n",
    "            print(scaling)\n",
    "\n",
    "            tic = time.perf_counter()\n",
    "\n",
    "            pca = reduction.PCA(X, scaling=scaling, n_components=n_components)\n",
    "            PCs = pca.transform(X)  \n",
    "\n",
    "            variance_data = analysis.compute_normalized_variance(PCs[idx_test,:],\n",
    "                                                        X_Sct[idx_test,None],\n",
    "                                                        depvar_names=['Sct'],\n",
    "                                                        bandwidth_values=bandwidth_values)\n",
    "\n",
    "            cost = analysis.cost_function_normalized_variance_derivative(variance_data, \n",
    "                                                                         penalty_function=penalty_function, \n",
    "                                                                         power=power,\n",
    "                                                                         norm=norm)\n",
    "\n",
    "            costs.append(cost)\n",
    "\n",
    "            print('Pure scaling cost:\\t' + str(round(cost,4)))\n",
    "\n",
    "            toc = time.perf_counter()\n",
    "\n",
    "            print(f'\\tTime it took: {(toc - tic)/60:0.1f} minutes.\\n' + '-'*40)\n",
    "\n",
    "        if save_csv:\n",
    "\n",
    "            np.savetxt('../results/SUPPLEMENT-atmospheric-physics-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-Sct-pure-scaling-cost-' + norm + '.csv', (costs), delimiter=',', fmt='%.16e')\n",
    "            np.savetxt('../results/SUPPLEMENT-atmospheric-physics-perc-of-data-' + str(sample_percentage) + '-' + str(n_components) + 'D-LDM-optimizing-on-Sct-scalings-list.csv', (scalings_list), delimiter=',', fmt='%s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=atmo-2D></a>\n",
    "\n",
    "### Plot the result of data sampling on 2D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 604.8x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-atmospheric-physics-perc-of-data-' + str(sample_percentage) + '-2D-LDM-optimizing-on-Sct-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage ==100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, [], fontsize=16)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([1,2,3,4,5,6])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([0.7,6])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Atmospheric pollutant dispersion, 2D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-atmospheric-physics-data-sampling-2D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=atmo-3D></a>\n",
    "\n",
    "### Plot the result of data sampling on 3D projections\n",
    "\n",
    "[Go to the top](#top-page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 604.8x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(len(tex_scalings_list)*0.7, 2))\n",
    "fig.tight_layout(pad=-30)\n",
    "widths = [1]\n",
    "heights = [1]\n",
    "spec = fig.add_gridspec(ncols=1, nrows=1, width_ratios=widths, height_ratios=heights)\n",
    "x_range = np.array([i for i in range(0,len(tex_scalings_list))])\n",
    "ax = fig.add_subplot(spec[0,0])\n",
    "\n",
    "for i, sample_percentage in enumerate(sample_percentage_list):\n",
    "    costs = pd.read_csv('../results/SUPPLEMENT-atmospheric-physics-perc-of-data-' + str(sample_percentage) + '-3D-LDM-optimizing-on-Sct-pure-scaling-cost-cumulative.csv', sep = ',', header=None).to_numpy()\n",
    "    if sample_percentage ==100:\n",
    "        plt.scatter(x_range, costs, c='r', marker='x', s=100, linewidths=2, label=str(sample_percentage) + '%')\n",
    "    else:\n",
    "        plt.scatter(x_range, costs, c=colors[i], marker='o', s=400-80*i, label=str(sample_percentage) + '%')\n",
    "\n",
    "plt.xticks(x_range, tex_scalings_list, fontsize=16, rotation=90)\n",
    "plt.grid(alpha=0.3, zorder=0)\n",
    "plt.xlim([-0.5,len(tex_scalings_list)-0.5])\n",
    "ax.set_yscale('log')\n",
    "ax.set_yticks([1,2,3,4,5,6])\n",
    "ax.get_yaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n",
    "plt.ylim([0.7,6])\n",
    "plt.ylabel('$\\mathcal{L}$', fontsize=20, rotation=0, horizontalalignment='right')\n",
    "plt.gca().spines[\"top\"].set_visible(False)\n",
    "plt.gca().spines[\"right\"].set_visible(False)\n",
    "ax.xaxis.grid(False)\n",
    "ax.yaxis.grid(True)\n",
    "plt.title('Atmospheric pollutant dispersion, 3D PCA projections', fontsize=18)\n",
    "\n",
    "plt.savefig('../figures/supplement-atmospheric-physics-data-sampling-3D-LDM.svg', dpi=200, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}