Sensitivity Plot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1eea7b07-7366-4639-a6d1-64cf0c1bfd80",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MaxNLocator\n",
    "import numpy as np\n",
    "\n",
    "assert np.allclose(np.arange(0.001, 0.1+0.001, 0.001), \n",
    "                   np.array([0.001*(1+v) for v in range(100)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5377f459",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_groups_with_same_values(lst):\n",
    "    value_indices = {}\n",
    "    for idx, value in enumerate(lst):\n",
    "        if value in value_indices: value_indices[value].append(idx)\n",
    "        else: value_indices[value] = [idx]\n",
    "    for v in value_indices:\n",
    "        value_indices[v] = (min(value_indices[v]), max(value_indices[v]))\n",
    "    return value_indices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "868280c4",
   "metadata": {},
   "source": [
    "#### KdV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9321e63d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x189 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.arange(0.001, 0.1+0.001, 0.001)\n",
    "kdv = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
    "groups = find_groups_with_same_values(kdv)\n",
    "\n",
    "with plt.style.context(['science', 'grid']):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "    for v in groups:\n",
    "        mini, maxi = groups[v]\n",
    "        thres = thresholds[mini:maxi+1]\n",
    "        vals = [v+1 for _ in range(len(thres))]\n",
    "        if v == 1:\n",
    "            ax.plot(thres, vals, '-o', c='black', label='True complexity')\n",
    "        else:\n",
    "            ax.plot(thres, vals, '-s')\n",
    "    ax.set_ylabel(\"Support sizes ($s_{k}$)\", fontsize=12)\n",
    "    ax.set_xlabel(\"Improvement threshold ($\\\\tau_{0}$)\", fontsize=12)\n",
    "    ax.legend(fontsize=12, title=\"Success rate = 90.0\\%\")\n",
    "    ax.set_title(\"$1^{\\\\textrm{st}}$ Strategy\", fontsize=12)\n",
    "    fig.savefig(\"./Figures/KdV/kdv_sensitivity.pdf\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "721f9fa2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x189 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.arange(50+5, 100+5, 5, dtype=np.int32)\n",
    "kdv = [4, 4, 1, 1, 1, 1, 1, 1, 1, 1]\n",
    "groups = find_groups_with_same_values(kdv)\n",
    "\n",
    "with plt.style.context(['science', 'grid']):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "    for v in groups:\n",
    "        mini, maxi = groups[v]\n",
    "        thres = thresholds[mini:maxi+1]\n",
    "        vals = [v+1 for _ in range(len(thres))]\n",
    "        if v == 1:\n",
    "            ax.plot(thres, vals, '-o', c='black', label='True complexity')\n",
    "        else:\n",
    "            ax.plot(thres, vals, '-s')\n",
    "    ax.set_xticks(thresholds)\n",
    "    ax.set_ylabel(\"Support sizes ($s_{k}$)\", fontsize=12)\n",
    "    ax.set_xlabel(\"$i^{\\\\textrm{th}}$ percentile ($P_{i}$)\", fontsize=12)\n",
    "    ax.set_title(\"$2^{\\\\textrm{nd}}$ Strategy\", fontsize=12)\n",
    "    ax.legend(fontsize=12, title=\"Success rate = 80.0\\%\")\n",
    "    fig.savefig(\"./Figures/KdV/kdv_percentile_sensitivity.pdf\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8347ef24",
   "metadata": {},
   "source": [
    "#### NV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e7116f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x189 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.arange(0.001, 0.1+0.001, 0.001)\n",
    "nv = [9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n",
    "groups = find_groups_with_same_values(nv)\n",
    "\n",
    "with plt.style.context(['science', 'grid']):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "    for v in groups:\n",
    "        mini, maxi = groups[v]\n",
    "        thres = thresholds[mini:maxi+1]\n",
    "        vals = [v+1 for _ in range(len(thres))]\n",
    "        if v == 3:\n",
    "            ax.plot(thres, vals, '-o', c='black', label='True complexity')\n",
    "        else:\n",
    "            ax.plot(thres, vals, '-s')\n",
    "    ax.set_ylabel(\"Support sizes ($s_{k}$)\", fontsize=12)\n",
    "    ax.set_xlabel(\"Improvement threshold ($\\\\tau_{0}$)\", fontsize=12)\n",
    "    ax.set_title(\"$1^{\\\\textrm{st}}$ Strategy\", fontsize=12)\n",
    "    ax.legend(fontsize=12, title=\"Success rate = 82.0\\%\")\n",
    "    fig.savefig(\"./Figures/NV/nv_sensitivity.pdf\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "69e48afc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x189 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.arange(50+5, 100+5, 5, dtype=np.int32)\n",
    "nv = [4, 4, 3, 3, 3, 3, 3, 3, 3, 3]\n",
    "groups = find_groups_with_same_values(nv)\n",
    "\n",
    "with plt.style.context(['science', 'grid']):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "    for v in groups:\n",
    "        mini, maxi = groups[v]\n",
    "        thres = thresholds[mini:maxi+1]\n",
    "        vals = [v+1 for _ in range(len(thres))]\n",
    "        if v == 3:\n",
    "            ax.plot(thres, vals, '-o', c='black', label='True complexity')\n",
    "        else:\n",
    "            ax.plot(thres, vals, '-s')\n",
    "    ax.set_xticks(thresholds)\n",
    "    ax.set_ylabel(\"Support sizes ($s_{k}$)\", fontsize=12)\n",
    "    ax.set_xlabel(\"$i^{\\\\textrm{th}}$ percentile ($P_{i}$)\", fontsize=12)\n",
    "    ax.set_title(\"$2^{\\\\textrm{nd}}$ Strategy\", fontsize=12)\n",
    "    ax.legend(fontsize=12, title=\"Success rate = 80.0\\%\")\n",
    "    fig.savefig(\"./Figures/NV/nv_percentile_sensitivity.pdf\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "994be845",
   "metadata": {},
   "source": [
    "#### RD2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "894735ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01  0.011 0.012\n",
      " 0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.02  0.021 0.022 0.023 0.024\n",
      " 0.025 0.026 0.027 0.028 0.029 0.03 ]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 252x189 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.arange(0.001, 0.1+0.001, 0.001)\n",
    "rd = [7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n",
    "groups = find_groups_with_same_values(rd)\n",
    "print(thresholds[:len(rd)])\n",
    "\n",
    "with plt.style.context(['science', 'grid']):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "    for v in groups:\n",
    "        mini, maxi = groups[v]\n",
    "        thres = thresholds[mini:maxi+1]\n",
    "        vals = [v+1 for _ in range(len(thres))]\n",
    "        if v == 6:\n",
    "            ax.plot(thres, vals, '-o', c='black', label='True complexity')\n",
    "        else:\n",
    "            ax.plot(thres, vals, '-s')\n",
    "    ax.set_ylabel(\"Support sizes ($s_{k}$)\", fontsize=12)\n",
    "    ax.set_xlabel(\"Improvement threshold ($\\\\tau_{0}$)\", fontsize=12)\n",
    "    ax.set_title(\"$1^{\\\\textrm{st}}$ Strategy\", fontsize=12)\n",
    "    ax.legend(fontsize=12, title=\"Success rate = 93.33\\% (Target: $u_t$)\")\n",
    "    fig.savefig(\"./Figures/RD2D/rd2d_sensitivity.pdf\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e5c9201a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 252x189 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.arange(50+5, 100+5, 5, dtype=np.int32)\n",
    "rd = [6, 6, 6, 6, 6]\n",
    "groups = find_groups_with_same_values(rd)\n",
    "\n",
    "with plt.style.context(['science', 'grid']):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.yaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "    for v in groups:\n",
    "        mini, maxi = groups[v]\n",
    "        thres = thresholds[mini:maxi+1]\n",
    "        vals = [v+1 for _ in range(len(thres))]\n",
    "        if v == 6:\n",
    "            ax.plot(thres, vals, '-o', c='black', label='True complexity')\n",
    "        else:\n",
    "            ax.plot(thres, vals, '-s')\n",
    "    ax.set_yticks([6+1])\n",
    "    ax.set_xticks(thresholds[:len(rd)])\n",
    "    ax.set_ylabel(\"Support sizes ($s_{k}$)\", fontsize=12)\n",
    "    ax.set_xlabel(\"$i^{\\\\textrm{th}}$ percentile ($P_{i}$)\", fontsize=12)\n",
    "    ax.set_title(\"$2^{\\\\textrm{nd}}$ Strategy\", fontsize=12)\n",
    "    ax.legend(fontsize=12, title=\"Success rate = 100.0\\% (Target: $u_t$ and $v_t$)\", loc=\"upper center\")\n",
    "    fig.savefig(\"./Figures/RD2D/rd2d_percentile_sensitivity.pdf\")\n",
    "    plt.show()"
   ]
  }
 ],
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