test_constant.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test the best constant for generating random covariane matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from data import *\n",
    "\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import scienceplots\n",
    "\n",
    "plt.style.use(['science', 'ieee'])\n",
    "\n",
    "from matplotlib import cm\n",
    "from matplotlib.colors import ListedColormap, LinearSegmentedColormap\n",
    "\n",
    "top = cm.get_cmap('Oranges_r', 128)\n",
    "bottom = cm.get_cmap('Blues', 128)\n",
    "\n",
    "newcolors = np.vstack((top(np.linspace(0, 1, 128)),\n",
    "                       bottom(np.linspace(0, 1, 128))))\n",
    "newcmp = ListedColormap(newcolors, name='OrangeBlue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = generate_random_dag(20, 3, seed=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, cov, cov_prev, G_bi = generate_linear_sem_correlated(G, 1000, 0.5, seed=123, return_cov=True, return_graph=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "172613992503007.53"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matrix.trace(np.linalg.matrix_power(np.eye(20) + nx.to_numpy_array(G_bi) * nx.to_numpy_array(G_bi), 20)) - 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.17166031745094"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# L1 norm\n",
    "np.sum(np.abs(nx.to_numpy_array(G_bi)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.17166031745094"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.abs(nx.to_numpy_array(G)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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LIgCsss0N+KL3todb7BMOzaJwW9MsJnDQMvNZVB8ouC6lnA5dDwB76TcNy6Zmr4L7qT980NazgZtg9XUpxYzCHKr5DxVMIuJdfY90b3UgZ/Z7X29YF4xJVx8GXfSMvGmsGACA9snoATAG8nkwPBk9WIN8HgA9kdGDLcnnQSdk9GA78nl0RuMr2FzTrCDTlvbd9ALdNHsdANz4ccm6bbq7Txcsf7DFPuFgZOZxNN/Unxm4gbvqh743D3oNqADQlaaZP8xgCgPJzOdxe176YCmH7HzB8teZ+XaDmeVm93dlpkbYynTB8qaxYgAA2iejB8CukM+DHSWjB+uRzwOgRzJ6sCPk8+AOGT3YTdMFy+XzDojGV7C5vmeTm7S0bwD2UCnlKpoDNFellG0eEE8WLG/rPQ/2XdOMcWbKgmY3D31f1e9rANCFpmd6ws4wgPpDCDf3TE998IBDVodepgtWH0c1s9zrzJys2ldmvo7b97tp+OACTLb8fjPKAQAMS0YPgJ0gnwc7TUYP1iOfB0BfZPRgB8jnwV0yetCZyZbfL5+Hxlewhft27tzaBt1CATgsX0XEzQ34tP7zV1vuc9F7z7st9wt7LzOfxMezlVxHxKMByoGdVs8kchxVIPTF0PXAGGXmJDOf1IMtb+pZR97Vf36dmc/WGYSBfZaZTTPJRUT83LDtUX3uvMvMD5lZ6t/f1ssX7QtY302w+qyUcjFoJbAbvl2x/llE/EVmPlu0QWae19tFVM8HvxJa44BMO9rvgwXLjdsCAPRDRg+AXSKfBztGRg/WI58H25PPg/XI6MFOkc+Dj8noweamHe1XPg+Nr6Bl04737wUagIVKKdNSymkp5bP612kpZbrp/uqBl0XvPdvMUgd7rx5kOZ9bfBURj7Y5L2Efzc8kMmQtMEY3A/8R8SGq955nUYU6j6O6ljupl72OiA910MbMBxyqxwuW/zLYWIfUXkf1YYJncXtPNI1qNpLjevmbOmTzvLNqYY/V59lRREzNtg2VOmB2tmKzSUS8rkOev1zTZeZxZr6NiCf1oquI+FOzdXNgFgXIFgVj1jXZ8vsBAGjftOP9y+gB0Eg+D3aLjB6sRz4PtiOfB/cmowc7QD4PmsnowVbk8+iMxlewgR5mdfuog3Vt0vFxAWDWotkRpm7IoVk9CPMyIt7MrboopQjUQLObANoLsxzA/dSD+TcD/xHVIMzjiHhYSsmI+Kz+enamxpOIeFsPaMKhWRQqm0b88szvL6I6p64i4mkpJWc+vJBRnVM3HzSYRMTLOlwjsAZrqj+EcPPetWr2LDgoddBsnRkWj6O+pquv697G7fvcmWcQHKgfOtrvl4tW9DBmDABw0GT0ADgA8nmwARk9uDf5PNiQfB5sREYPBiafB8vJ6MHG5PPozKdDFwAjNRm6AADowTcLlq/qag17r75pPo6qI/UkIh5GdZM9P5hyGVVYQBgNGtQhtKOIuCqlvBq6HhiZ86jeg6YR8V3TOVQPpFxGxGVmntXfcxOefpaZX0bEVwZcOCCLZhN5X1/fvY3qvDotpTTe95RSbs6pJ3EbDp1ENbC58PuAO27Onet69ixgRinlaWbezAi8yrOZP19G9R7mAwscqssFy7cNvzxasm6y5b4BAFhuMnQBANAx+TxYQkYPtiefB1uRz4PNyOjB8OTzYAUZPdiIfB6d0fgKxmXRjT8AtKp+oPykYdU0Ir7rtxrYLfX58W6NTS/CDFmwUD3rzvP6y6dD1gIjNYmI64h4vM57TR2eeZyZszON3MxCYrYRDsVkybqbsNrTdQb6SykXmfk47s4i/DozQ7AGFqtnQ53UX74csBTYaaWUs8z8bdwNRq9iDImDVkq5yszr+DhIsywYs46vt/x+AADGx/0VAJ2Tz4PlZPRge/J5sLVJyOfBJiZL1snoQcfk82B9MnpwP/J5dOmToQuAkXJhAsC+W/Rw64VBFw5dPXj5KqrZFWd/XUTE7KxxTyLiXWa+q7vAA3fdzCRitgO4n/f179cR8WiD82c+yHYUt+cj7LtFs4mcRhU0e3Wf2a3qmeXmAzSvM3PdwU84KJk5ibvPG347UCkwCqWUaSnlcVTPINZxHNVzCKE1DtmLhmUbX5vV13WTJZsYMwYA6JbrLQD2mXweLCGjB62Qz4PNyOfBdmT0YCDyeXB/Mnpwb/J5dELjK2jX+9WbbGXS8f4B4OZmoWk2uTOzIkCllPKilHI69+tpKeVRRHwW1cDMtN78KKrBlQ+Z2XRuwcHJzNdRnRuX3lvg3q7iNlQzve8310Gc+fPuRACUA/csIq5LKU0DMas0fY+wGjSbHei/9MEdWC4zjzPzPG5n4l7X8/oDPkKeHJw6IH01t/hoi/NhVUit67FhAACayegBMGryebAeGT3YnHwebEU+D7ohowfdk8+De5LRg/uRz6MrGl9Bu3QNBGAfvG5YdllKOe29Ehihutv7WUT8ady9kZ9ExHn9QAwOVv0w61lUwbP5ma2AFeoQ58MtByObrvfMOsJeq2eyWmajc6A+F+dnoJuYyQfuqs/B2RDnm4FKgVGoP4zwNm4//HYR1Yd4PouP33eaHEXEm3o/cGiexu2H3W7c+9qs/nDccXz8wYRZ88cBAKAfMnoAjJ18HmxJRg8Wk8+D7cjnweZk9GA48nlwfzJ6sDH5PFqn8RVsZqjugNOBjgvAgagH+4/mFl+XUh4PUQ+MWT3A8lVUs/7MepKZHiJzkOoBlZtg2bdmEYFhlFKu4uNnDJPMvO9MJTAaa7zn/HaL3Tdd2z1fI8gDh+Q3c1+vEwqAg1PPIPcuboNoNzMJP60/xDMtpTyNiMfx8fOGJs8y821X9cIuqmfRnv8gz/F9Qs+ZeRzV84vpsg+c1scCAKA7MnoA7B35PGiXjB7cJZ8Hu0E+j0MloweDks+DNcnowXbk8+iCxlcAAERERGY+i9sO1TeuIuLRAOXAXqgHb5puvk/MKseB+j6qmRUvSikGU2BYPzYsM4Mwh+pqy7Bn0/kUEfH1FvuEfTM7m5yBSGhQz779Nm4/9HYVVaDman7bUsplKeVhRLxYY9fHPtzDoSmlXEYVPpvOLH6+zocJZs7FiOoDcwAAAACtkM+DbsjowR3yebA75PPgLhk96JZ8HqxBRg/aIZ9H2zS+gs1MBzruULPYAbDn6puF13OLr0opj8z2A9upb+Q/egAW1axyzxqWw17KzCdRBTinEfHtsNUA0Tz7yJHZrzhQi0Ix61oUEDAzN8QvH+SZzCxquj+Cg1Y/m5sNvqz1XK6U8ioiPouIyxWHOPEMgkNTP5N7FHffd15m5tv6GcUdmXlSB9BuzsXHTaG2GdPWigUAYJHpQMeV0QOgdfJ50C0ZPZDPgx0knwd3yehBR+TzYD0yetAu+TzapPEVbGZRuGXS0v4/X7B82tL+AeAXmXkUd2/aIyIuSylmkoP2fLdg+cteq4CB1AP139dfPhXahJ1m9iv22aLwy7uOjvfRgA0cqPkZS80mBzPqZ3OzM85f3+e5XCllWkp5HB/PnjXPMwgOTinl5nx6GrfvP8cRcZ6ZJTM/1L9KVM/IT6IKqT2sgzmx5MMH2wazAQBYTUYPgL0gnwe9kdHjYMnnwajI57HvZPSgf/J5sIKMHnRDPo+2aHwFGxjwIbAbDgBaVd8UvJ1b/Kq+EQfas6ir+yQzn/daCQzjPKoPIZzdPJgCBjddsHzSYw3Qt+k9l69l2bNCszRy6Opz4Hhu8e8HKAV22eu4ew32dJOdlFIuSymfRcSrBZtMzCjHoSqlXJRSHkY1w9yrqGaZu47q3JvUf76IiEellMellNkx2aMFu53/sCoAAC2T0QNgH8jnQa9k9Dhk8nmwe6YLlk96rAGGML3n8rXI6EEz+TxYm4wedEg+j219OnQBMGLT+Phh04OW9j2/3xuLZrEDgHubCdVMZhY/LaVcDFIQ7LFSyjQzp9F8nfdNLH7gBaNXP7Q9iWpGhPnZRIA1ZeZJVDOE/BxVSG265S5/XrD84Zb7hV12HR8P8Ed0+8ztQWwZ2oGRaxrA9+FRqGXmcVT3SzcuSilX2+yzlPIiM99E86D/aUScbbN/GLP6/LrvObYoWOODQwAA/ZiGjB4AIyWfB/2S0eNQyedBO+TzoDUyetAv+TxYQUYP+iOfx6Y+GboAGLGmi/9JS/tuDOcMOIsdAHtmJlRzc1NwHREPhWqgU4seHjcN7MBeyMyjqGZGiNhwRgQgIjNfRzUo8jwiXkbEh3oApgttfWAIdtGiWay6/H8/6XDfMAbfNCwTrIFb8x8+eN241T3VM3k/aljlGQTcX2OwZtsAHAAAa5PRA2CU5PNgMDJ6HBT5PGiHfB60SkYP+iWfB6vJ6MFuk88jPh26ABixy/j44qPL2eR0JQSgFXWo5ndxe0NwFRFfCW/Crcx8EhG/iep67zoiXpZStu22vnCWksw8KqV4uMw+Oq9/v4iIaR20adNxZjaucE6xL+rzpmk2nvPoZvY35w77bIjBj+kAx4Rd0jSA770Gbn05+0UdhmlFKeUqM19FFc7+RWZOPAeEe/l1wzLjtgAA/ZHRA2B05PNgPTJ60Ar5PNiSfB60TkYP+iWfB6vJ6MFuk89D4yvYwk0n91mTlvbd9LBZV0IAtjYTqrl5sHVZSnk8XEWwe+pAzfnMoqOIeF0/dHq1xa6nS9ZNttgv7LKb95sn9a+2nS9akZmPdHdnT5wsWL5tUO3zBcvfbblf2FmllMsFgcwuQmo3xxQg4GBlZuN7mMF8uGP2mq71+5dSyovMnB/LOuriWLDHmt7PWpn5EQCAtcjoATAq8nmwHhk9aI18HmxPPg9aJKMH/ZHPg7XJ6MFuk88jPhm6ABixH5sWtjRDQtM+ft/CfgE4YA2hmrP7hmoy80lmvmm4GYd98vKey9c1WbJuuuW+AeC+Fj2/EABg3zUNIk622WF9rwV8zAd5YLXJzJ8XzkK/pYu5r6cdHQf2Tj3uO5lbfF1KmT+vAADojoweAKMhnwf3IqM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",
      "text/plain": [
       "<Figure size 6000x6000 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 2, figsize=(10, 10))\n",
    "\n",
    "sns.heatmap(cov_prev, ax=axes.ravel()[0], cmap=newcmp, vmin=-1, vmax=1)\n",
    "axes.ravel()[0].set_title('Before positive definite transform', fontsize=14)\n",
    "axes.ravel()[0].collections[0].colorbar.remove()\n",
    "# axes.ravel()[0].axis('off')\n",
    "for _, spine in axes[0, 0].spines.items():\n",
    "    spine.set_visible(True)\n",
    "\n",
    "for idx, c in enumerate([1.0, 1.5, 2.0, 4.0, 8.0]):\n",
    "    X, cov, cov_prev = generate_linear_sem_correlated(G, 1000, 0.5, seed=123, return_cov=True, const=c)\n",
    "    sns.heatmap(cov, ax=axes.ravel()[idx+1], cmap=newcmp, vmin=-1, vmax=1)\n",
    "    axes.ravel()[idx+1].set_title(f'c = {c}', fontsize=14)\n",
    "    # remove the colorbar\n",
    "    axes.ravel()[idx+1].collections[0].colorbar.remove()\n",
    "    # remove the axis\n",
    "    # axes.ravel()[idx+1].axis('off')\n",
    "    # remove the frame\n",
    "    for _, spine in axes.ravel()[idx+1].spines.items():\n",
    "        spine.set_visible(True)\n",
    "\n",
    "\n",
    "plt.savefig('plots/const_psd_transform.png', dpi=300, bbox_inches='tight', facecolor='white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "G1 = generate_random_dag(10, 3, seed=123)\n",
    "\n",
    "X, G2 = generate_linear_sem_correlated(G1, 1000, 0.3, seed=123, return_graph=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = nx.circular_layout(G1)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 5))\n",
    "\n",
    "nx.draw_networkx_nodes(G1, pos, node_size=200, ax=axes[0], )\n",
    "nx.draw_networkx_edges(G1, pos, ax=axes[0])\n",
    "nx.draw_networkx_labels(G1, pos, labels={node: node for node in G1.nodes()}, font_size=10, font_color='w', ax=axes[0])\n",
    "\n",
    "axes[0].set_title('Original graph')\n",
    "\n",
    "# create a list of edge colors based on the edge type\n",
    "edge_colors = ['r' if G2.has_edge(u, v) and G2.has_edge(v, u) else 'k' for u, v in G2.edges()]\n",
    "\n",
    "nx.draw_networkx_nodes(G2, pos, node_size=200, ax=axes[1])\n",
    "nx.draw_networkx_edges(G2, pos, edge_color=edge_colors, ax=axes[1])\n",
    "nx.draw_networkx_labels(G2, pos, labels={node: node for node in G2.nodes()}, font_size=10, font_color='w', ax=axes[1])\n",
    "\n",
    "axes[1].set_title('Mixed graph with proportion 0.3')\n",
    "\n",
    "plt.savefig('plots/mixed_graph_example.png', dpi=300, bbox_inches='tight', facecolor='white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Heatmap of G1 and G2 adjacency matrix\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 5))\n",
    "\n",
    "sns.heatmap(nx.to_numpy_array(G1), ax=axes[0], cmap=newcmp, vmin=-1, vmax=1)\n",
    "axes[0].set_title('Original graph', fontsize=14)\n",
    "for _, spine in axes[0].spines.items():\n",
    "    spine.set_visible(True)\n",
    "\n",
    "sns.heatmap(nx.to_numpy_array(G2), ax=axes[1], cmap=newcmp, vmin=-1, vmax=1)\n",
    "axes[1].set_title('Mixed graph with proportion 0.3', fontsize=14)\n",
    "for _, spine in axes[1].spines.items():\n",
    "    spine.set_visible(True)\n",
    "\n",
    "\n",
    "axes[0].collections[0].colorbar.remove()\n",
    "axes[1].collections[0].colorbar.remove()\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.savefig('plots/mixed_graph_adjacency.png', dpi=300, bbox_inches='tight', facecolor='white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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