{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bipartite collaboration graph to simplicial complex and cochains\n",
    "\n",
    "\n",
    "In this notebook we show how to build a collaboration complex (where each collaboration of authors is represented by a simplex) and citation cochains (which are the number of citations attributed to the collaborations). \n",
    "\n",
    "As point 3 of Section [Data], we will follow the following steps:\n",
    "\n",
    "[Data]:https://github.com/stefaniaebli/simplicial_neural_networks#data\n",
    "\n",
    "1) Downsample the bipartite graph to have a connected simplicial complex.\n",
    "\n",
    "2) From a bipartite graph to a simplicial complex with k-cochains.\n",
    "\n",
    "3) From a simplicial complex to k-degree Laplacians.\n",
    "\n",
    "4) Artificially insert missing data on k-cochains.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy import sparse\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "import sys\n",
    "sys.path.append('..')\n",
    "from data.s2_4_bipartite_to_downsampled import subsample_node_x,starting_node_random_walk\n",
    "from data.s2_5_bipartite_to_complex import bipart2simpcochain\n",
    "from data.s2_6_complex_to_laplacians import build_boundaries, build_laplacians\n",
    "from data.s2_7_cochains_to_missingdata import build_missing_values, build_damaged_dataset,built_known_values\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) Downsample the bipartite graph to have a connected simplicial complex.\n",
    "\n",
    "First we load the bipartite graph from the Semantic Scholar dataset together with the citations of the articles. Then we will downasample the set of papers to obtain a connected simplicial complex,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "adjacency_papers = sparse.load_npz('../data/s2_2_bipartite_graph/papers_adjacency.npz')\n",
    "adjacency = scipy.sparse.load_npz('../data/s2_2_bipartite_graph/paper_author_biadjacency.npz')\n",
    "papers = pd.read_csv('../data/s2_2_bipartite_graph/papers.csv', index_col=0)\n",
    "citations=np.array(papers['citations_2019'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting node of the random walk has ID 134702\n",
      "The number of downsampled papers is 109\n"
     ]
    }
   ],
   "source": [
    "starting_node=starting_node_random_walk(adjacency,weights_x=citations, min_weight=100, max_dim=10 )\n",
    "print(\"The starting node of the random walk has ID {}\".format(starting_node))\n",
    "downsample= subsample_node_x(adjacency_papers,adjacency,weights_x=citations, min_weight=5, max_dim=10,length_walk=80)\n",
    "print(\"The number of downsampled papers is {}\".format(len(downsample)))\n",
    "#np.save('../data/s2_3_collaboration_complex/'+str(starting_node)+'_downsampled.npy',downsample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2) From a bipartite graph to a simplicial complex with k-cochains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "##load downsampling\n",
    "s_node=150250 ###starting node of the random walk\n",
    "\n",
    "output=str(s_node)\n",
    "downsample_papers=np.load('../data/s2_3_collaboration_complex/'+str(s_node)+'_downsampled.npy')\n",
    "\n",
    "simplices, cochains, signals_top = bipart2simpcochain(adjacency, citations, indices_x=downsample_papers, dimension=10)\n",
    "#np.save('../data/s2_3_collaboration_complex/'+output+'_cochains.npy',cochains)\n",
    "#np.save('../data/s2_3_collaboration_complex/'+output+'_simplices.npy',simplices)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Printing the number of simplices of the simplicial complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of 0-simplices is 352\n",
      "The number of 1-simplices is 1,474\n",
      "The number of 2-simplices is 3,285\n",
      "The number of 3-simplices is 5,019\n",
      "The number of 4-simplices is 5,559\n",
      "The number of 5-simplices is 4,547\n",
      "The number of 6-simplices is 2,732\n",
      "The number of 7-simplices is 1,175\n",
      "The number of 8-simplices is 343\n",
      "The number of 9-simplices is 61\n",
      "The number of 10-simplices is 5\n"
     ]
    }
   ],
   "source": [
    "for k, simp in enumerate(simplices):\n",
    "    print('The number of {}-simplices is {:,}'.format(k, len(simp)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the distribution of the values of the cochains in dimension $1$, $2$ and $3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "target_cochain=np.load('../data/s2_3_collaboration_complex/'+output+'_cochains.npy',allow_pickle=True)\n",
    "target_cochain_0=np.array(list(target_cochain[0].values()))  \n",
    "target_cochain_1=np.array(list(target_cochain[1].values()))  \n",
    "target_cochain_2=np.array(list(target_cochain[2].values()))     \n",
    "n_bins = 50\n",
    "\n",
    "#plt.figure(figsize=(8,4))\n",
    "fig, axs = plt.subplots(1, 3, sharey=True, tight_layout=True,figsize=(12,5))\n",
    "\n",
    "axs[0].hist(target_cochain_0, bins=n_bins,color = \"lightgreen\", ec='black',lw=0.2)\n",
    "axs[0].set_xlabel(\"Citations\")\n",
    "axs[0].set_ylabel(\"Count\")\n",
    "axs[0].set_title('Dimension 0')\n",
    "axs[1].hist(target_cochain_1, bins=n_bins,color = \"skyblue\", ec='black',lw=0.2)\n",
    "axs[1].set_title('Dimension 1')\n",
    "axs[1].set_xlabel(\"Citations\")\n",
    "axs[1].set_ylabel(\"Count\")\n",
    "axs[2].hist(target_cochain_2, bins=n_bins,color = \"lightsalmon\", ec='black',lw=0.2)\n",
    "axs[2].set_title('Dimension 2')\n",
    "axs[2].set_xlabel(\"Citations\")\n",
    "axs[2].set_ylabel(\"Count\")\n",
    "fig.suptitle('Distribution citations for seed {} '.format(s_node), y=1.05,fontsize=\"x-large\");\n",
    "#plt.savefig('distribution_cochains_{}.png'.format(s_node))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3) From a simplicial complex to k-degree Laplacians."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "simplices=np.load(f'../data/s2_3_collaboration_complex/{s_node}_simplices.npy',allow_pickle=True)\n",
    "\n",
    "boundaries=build_boundaries(simplices)\n",
    "laplacians=build_laplacians(boundaries)\n",
    "#np.save(f'../data/s2_3_collaboration_complex/{s_node}_laplacians.npy', laplacians)\n",
    "#np.save(f'../data/s2_3_collaboration_complex/{s_node}_boundaries.npy', boundaries)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot density Laplacians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0-simplices: 352 simplices, 2.66335% dense\n",
      "1-simplices: 1,474 simplices, 1.17210% dense\n",
      "2-simplices: 3,285 simplices, 0.04353% dense\n",
      "3-simplices: 5,019 simplices, 0.02151% dense\n",
      "4-simplices: 5,559 simplices, 0.01812% dense\n",
      "5-simplices: 4,547 simplices, 0.02199% dense\n",
      "6-simplices: 2,732 simplices, 0.03660% dense\n",
      "7-simplices: 1,175 simplices, 0.08511% dense\n",
      "8-simplices: 343 simplices, 0.29155% dense\n",
      "9-simplices: 61 simplices, 1.63934% dense\n",
      "10-simplices: 5 simplices, 20.00000% dense\n"
     ]
    }
   ],
   "source": [
    "laplacians = np.load(f'../data/s2_3_collaboration_complex/{s_node}_laplacians.npy',allow_pickle=True)\n",
    "\n",
    "for k, laplacian in enumerate(laplacians):\n",
    "    print('{}-simplices: {:,} simplices, {:.5%} dense'.format(k, laplacian.shape[0], laplacian.nnz/np.prod(laplacian.shape)))\n",
    "    assert laplacian.shape == (len(simplices[k]), len(simplices[k]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4) Artificially insert missing data on k-cochains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "percentage_missing_data=[10,20,30,40,50]\n",
    "for percentage in percentage_missing_data:\n",
    "\n",
    "    output=str(s_node)+'_percentage_'+str(percentage)\n",
    "   \n",
    "    missing_values=build_missing_values(simplices,percentage_missing_values=percentage,max_dim=10)\n",
    "    damaged_dataset=build_damaged_dataset(cochains,missing_values,function=np.median)\n",
    "    known_values=built_known_values(missing_values,simplices)\n",
    "    #np.save(f'../data/s2_3_collaboration_complex/{s_node}_percentage_{percentage}_missing_values.npy', missing_values)\n",
    "    #np.save(f'../data/s2_3_collaboration_complex/{s_node}_percentage_{percentage}_input_damaged.npy', damaged_dataset)\n",
    "    #np.save(f'../data/s2_3_collaboration_complex/{s_node}_percentage_{percentage}_known_values.npy', known_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Plot distribution misisng citations  and known citations in dimension $0$, $1$ and $2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gtqP1e0bEPhHx/VbrG+V7NmtfO/fNQWzLSFp/l9CKi8wcdBnUISKuBTYB7gceAH4DfAM4MjMfXI51vSkzfzCG11wAHJ+ZY/5iGxGHAFtl5uvH+trleK9jgAWZefB4v9fKMtb6qwfT4zNz8/Es18q0PPvs6i4ingZ8BngWsFFmxoCLpNWU7Y96iYg3Uj7LF4xy+ZnAH4E1M/P+8SvZyrMi++aqLCJeDbwT2Ba4NDN3GmyJVh32YE1Mu2fm+sAWwGHAe4GjWr9JRExpvU5Jzd0HnArsP+iCaFKw/ZE05Fbg85RjgcYiM/2ZQD/AtcBLu6btADwIPK0+PwY4tD7eGDgTWEz5Q/ghJTgfV1/zF+BO4D3ATCApX9SuBy7qmDalru8C4BPApcAS4AxgwzpvJ0qv0TLlBXYB/kr5Mngn8IuO9b2pPn4EcDBwHXAT5czoo+u8oXLMrmW7GfjAMPXUWQfrA+cDhwNR5x0BnAXcAVwCPLHjtc8DLqvbdxnwvDr9xcCvOpb7AeWMzdDzi4E9O7b7XcAv63pOAdYeprz/DFxVy/MbYLtR1t9+Ha+7BviXOn3d+tk+WJe/E9gMOIRylm3ofV8JXEnZPy4AntL12fXcBvrsV322LSlnjoc+l7513+O1+9b94RbgA3Ts/z22ZUfgx7VMvwB26ph3AXBonX8n8B1gI+AE4Pb6Oc/sWP7JwDl1234HvLpr3+q5DZT963OU/XdJrbtl/i47PvN59T3mAJt11dmbgauB2+r7xQjHhq2AHPQxyp/V9wfbn7G0P18Cvlvf70fA4yhfRG8Dfgs8s1e91vqcSzku3Qh8tk5fGziecixcTDlmbdJjO95IaYs+Xd/rj8CuHe+1Za3bOyht2BF0HEd7bMsewM9ref4A7NL5nsBTgHsoPZp3Aovr/N2AK+rr5gOHdKzz+lqfQ23Tc4fK3bFMz3a4470/Vuv1DuD7wMYj1dNw+zOlPTm1fu53UNrF7Yepl7+vn+MS4IvAhd2fQceyCbyVcjy/o5b9icBPav2cCqzVsfysWueLKW3W07vKPOZ2uWtbH0nZFxfWn88Dj+z8OwIOpPwd3ADsN4pjw5uACwZ9jFqVfuzBWgVk5qWUP4i/6zH7wDpvGmVox/vLS3JfykFu98xcLzM/1fGaF1EOmi/v85ZvAP4f5Qv7/ZTgMlIZvwf8J3BKfb9n9FjsjfXnxcATgPUoB65OLwCeBOwMfCginjLc+0bERsC5wI8y8+1ZjwTAa4GPAI+hfMn9eF1+Q8oX58MpX8A/C5xV1/MTYKuI2LieXX0asHlErB8Rj6IM0fphx9u/mtKwbwk8vW5brzLuRTm4vwHYgBJ6bulcZpj6u4lyMN6AErY+FxHbZeZdwK7Awrr8epm5sOt9/wY4idK9Pw04G/hORKw1im3ouV/12r4eetZ9j3rZBvgyJWRtRvk8eg53jIjplM/tUGBDSgP0rYiY1rHY3nVd03m4cft6Xf4q4MN1XetSwtWJwGNreb8UEU8dxTa8DHgh8DfAVOA1dH2W9T1eQvmi+GpgU8qXupO7FpsFPBt4Rl2u39+jNDC2P329mhLYNgbupRxvflafn0ZpW3r5AvCFzNyAcpw6tU6fDTwamEE5Fr6ZElB7eQ7lxNDGwKeAoyJiaOjwiZSAuhGl3dm33wZExA6UwPFuyvHshZQv6g/JzKtqWX5S63ZqnXUX5bOaSglbb4mIPeu8F9bfU+trftL1vsO1w0NeR2nzHgusRTnmw9jqqdsrKcfhqZSTXt2f/1D5Nga+xcOf7x+A54+w7l0o3xF2pJxQOBLYp5bzaZQ2hYjYDjga+Jda/v8B5kTEIzvWtaLt8gdqObaltC871G0Z8jhKHU6nnPA4IiIeM8L2aYwMWKuOhZQvit3uo3yB2yIz78vMH3aEjH4Oycy7MrPfQem4zPx1/RL/QeDVQxchr6B9KGfrrsnMO4H3AXt3DRX5SGb+JTN/Qeml6NVQDtmMclbpm7nstVjfzsxLs4z/PoFyoIHSEFydmcdl5v2ZeRLlLNXumXkP5cziC4HtKWeQLqYcWHesr+v8Mn14Zi7MzFspPSbb0tubgE9l5mVZzMvM64bZrodk5lmZ+Yf6ugspZ/J6fdHp5TXAWZl5TmbeRznj+SjKmcORtmF59qsh/eq+26uAMzPzosy8l7Kv9bvO4/XA2Zl5dmY+mJnnUD6rV3Qs8/VaV0soZ5b/kJk/qOX4JvDMutws4NrM/HrdB35GaUxfNYptuI/SY/pkSo/TVZl5Q4/y7gMcnZk/q9v2PuC59dqEIYdl5uLMvJ7SA9uvnqRBs/1Z1umZeXltN04H7snMb2TmA5Reh2f2ed191BN5mXlnZv60Y/pGlNEAD9R1395nHddl5lfrex1L+Qw2iYjHU07afCgz/5qZF1OCRD/7U45T59Tj6p8y87fDLP+QzLwgM39VX/dLysm8F43mtQzTDncs8/XM/H3dT05l6WPwaOup28W1DXmA0sva7/N9BfCbzDyttp2fB/48wro/mZm3Z+aVwK+B79d9bag9Gtof/hn4n8y8pJb/WEpA37FjXSvaLu8DfDQzb8rMRZSThZ1B+746/77MPJvSy/ikEbZPY2TAWnVMp3QJd/svyhn270fENRFx0CjWNX8M868D1qScxVlRm9X1da57CuVMzJDOg9jdlLOM/exGCQxf6TGv33q6yzBUjun18YWULvQX1scXUBqNF9Xno3mPbjMoZ8DGLCJ2jYifRsStEbGYcuAf7Wex1LZmuUh9Pg9vK/TfhuXZr0ZaZ6/yPbSv1S9Uy/QGVVsAe0XE4qEfytnmTTuWubHj8V96PB8qxxbAc7rWtQ/lrN6w25CZ51HOeh4B3BgRR0bEBn22rbPu76zbNpq6lyYa259ljfZ4021/Sg/4byPisoiYVacfB/wfcHJELIyIT0XEmn3W8VA5M/Pu+nA9yjbe2jENhq/vFWmbnhMR50fEoohYQulJWq62qepsh6H/ZzGWeurWvc61+1wL2N02JSPvt2Npfw7san9m1PfsV86xtsu99vXO9d+SS998xPZnHBiwVgER8WzKgefi7nmZeUdmHpiZT6Cc/fmPiNh5aHafVY50hnFGx+PHU8523EwZErBOR7nWoHRVj3a9CykHl85138/SB6Kx+CrwPeDsOuxrNLrLMFSOP9XH3QHrQvoHrNGaTxkKMpKl6q8OGfgWpedpkyxDM86mXAe0zPI9LLWtdQjJDB7e1v4FGX6/auUGOva1iFiHcmayl/mUM9tTO37WzczlufB2PnBh17rWy8y3jObFmXl4Zj4LeCrli9K7eyzWXffrUrZtxLqXJhLbn7Yy8+rMfC1l6NsngdMiYt3am/CRzNyGMspgFmUI3ljcAGxYj6VDZvRbmOVsm6oTKb1jMzLz0ZQTncvVNlWd7XD/grSpp5F0t03B8PU4FvOBj3e1P+vUXrxhjaFd7rWvL+yxnMaRAWsCi4gN6tmtkykXqf6qxzKzImKregC4nXIh6gN19o2UseZj9fqI2KYepD8KnFa71H9POeOzWz1jdDDlYsohNwIzI6LffnUS8O8RsWVErMfDY+ZX5Dau/0oZi35mvU5qJGcDfxMRr4uIKRHxGmAbyoWjUC44fRJlzPKltbt/C8qY94uWs4xfA94VEc+KYquI6G5cYNn6W4tSv4uA+yNiV8o1QJ3LbxQRj+7zvqcCu0XEzvXzOpAyFOHHIxV4hP2qldOAWRHxgnpd2Efpf0w6Htg9Il4eEWtExNoRsVNELM8t6s+k7AP7RsSa9efZI1xvAZQvm/XM7ZqUL3xDF393OxHYLyK2rUH5P4FLMvPasRa27jNrU/YH6rY/coSXSSvE9md8RMTrI2JaHVGwuE5+ICJeHBF/W4Pj7ZRgOaZjbpah53OBQyJirYh4LksPu+t2FOU4tXNEPCIipkfEk3ssdyPleuTO63fXp/SW3RPlWq7XdcxbRBnu3e/zH6kd7qtFPY3CWcBTI+Ifaw/X21l6hMOK+Crw5tqORESsW/fp9Ud64Rja5ZOAgyNiWpTryT5EaUPHbKi9pfT2PqK2P6PtMZzUDFgT03ci4g7KmY4PUC4A3a/PsltT7hR0J+Ui2y9l5gV13icof2SLI+JdfV7fy3GUuyT9mXLHnrcD1LHEb6UEhj9RvmAu6HjdN+vvWyLiZz3We3Rd90WUOx/dA/zbGMq1jNp1fwClrs6oB4Lhlr+FcsbrQMqQrfcAszLz5jr/LsqFyldm5l/ry35CGfN+03KW8ZuUmyScSLnD0P/S+3qGpeovM++g1P2plLtFvY6O8fR1rPxJwDX1M+4cAkBm/o5y7dJ/U84A70651uyvjGy4/aqJGl7fRqmXGyjbuKDPsvMpd7t6P6Xxnk/pORrzMazW68soN8VYSNnPP8nSX9b62YDSQN7Gw3c//HSP9ziXcv3Ityjb9sT6fstjC8oQkyvr879QTipI48H2Z3ztAlwZEXdSbnixd5bruB5HOel0O+WmPBeyfF+K96Hcte8Wyk2BTqGcWFtGlhuY7Ee5M+qS+p69Tv6dRzn+/Dkibq7T3gp8tO4rH+Lhm3UMDVv8OPCj+vl3Xl80Yjs8glb11Fctx16UW5PfQtnPf9Ro3XMp12F9kdKOzKPPDbJ6GG27fCglaP8S+BXlO82hy1nkfSltzpcp13//hdIGagT+o2FJkqTVUEScAvw2Mz886LJIk4k9WJIkSauBOoz5iXXI3y6Unv//HXS5pMnG/6QuSZK0engc8G3KTXUWAG/JzCsGWyRp8nGIoCRJkiQ14hBBSZIkSWpkQgwR3HjjjXPmzJmDLoYkaRV0+eWX35yZ00Zecmm2PZKkFdGv/ZkQAWvmzJnMnTt30MWQJK2CIuK65XmdbY8kaUX0a38cIihJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktTIlEEXoKWZB5017PxrD9ttJZVEkiRJ0mRkD5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoZVcCKiGsj4lcR8fOImFunbRgR50TE1fX3Y+r0iIjDI2JeRPwyIrYbzw2QJEmSpIliLD1YL87MbTNz+/r8IODczNwaOLc+B9gV2Lr+HAB8uVVhJUmSJGkiW5EhgnsAx9bHxwJ7dkz/RhY/BaZGxKYr8D6SJEmStEoYbcBK4PsRcXlEHFCnbZKZNwDU34+t06cD8zteu6BOW0pEHBARcyNi7qJFi5av9JIkjYFtjyRpvI02YD0/M7ejDP97W0S8cJhlo8e0XGZC5pGZuX1mbj9t2rRRFkOSpOVn2yNJGm+jCliZubD+vgk4HdgBuHFo6F/9fVNdfAEwo+PlmwMLWxVYkiRJkiaqEQNWRKwbEesPPQZeBvwamAPMrovNBs6oj+cAb6h3E9wRWDI0lFCSJEmSVmdTRrHMJsDpETG0/ImZ+b2IuAw4NSL2B64H9qrLnw28ApgH3A3s17zUkiRJkjQBjRiwMvMa4Bk9pt8C7NxjegJva1I6SZIkSVqFrMht2iVJkiRJHQxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoxYEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoxYCJMNpIAABHVSURBVEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiOjDlgRsUZEXBERZ9bnW0bEJRFxdUScEhFr1emPrM/n1fkzx6fokiRJkjSxjKUH6x3AVR3PPwl8LjO3Bm4D9q/T9wduy8ytgM/V5SRJkiRptTeqgBURmwO7AV+rzwN4CXBaXeRYYM/6eI/6nDp/57q8JEmSJK3WRtuD9XngPcCD9flGwOLMvL8+XwBMr4+nA/MB6vwldXlJkiRJWq2NGLAiYhZwU2Ze3jm5x6I5inmd6z0gIuZGxNxFixaNqrCSJK0I2x5J0ngbTQ/W84FXRsS1wMmUoYGfB6ZGxJS6zObAwvp4ATADoM5/NHBr90oz88jM3D4zt582bdoKbYQkSaNh2yNJGm8jBqzMfF9mbp6ZM4G9gfMycx/gfOBVdbHZwBn18Zz6nDr/vMxcpgdLkiRJklY3K/J/sN4L/EdEzKNcY3VUnX4UsFGd/h/AQStWREmSJElaNUwZeZGHZeYFwAX18TXADj2WuQfYq0HZJEmSJGmVsiI9WJIkSZKkDgYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoxYEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1MmLAioi1I+LSiPhFRFwZER+p07eMiEsi4uqIOCUi1qrTH1mfz6vzZ47vJkiSJEnSxDCaHqx7gZdk5jOAbYFdImJH4JPA5zJza+A2YP+6/P7AbZm5FfC5upwkSZIkrfZGDFhZ3Fmfrll/EngJcFqdfiywZ328R31Onb9zRESzEkuSJEnSBDWqa7AiYo2I+DlwE3AO8AdgcWbeXxdZAEyvj6cD8wHq/CXARj3WeUBEzI2IuYsWLVqxrZAkaRRseyRJ421UASszH8jMbYHNgR2Ap/RarP7u1VuVy0zIPDIzt8/M7adNmzba8kqStNxseyRJ421MdxHMzMXABcCOwNSImFJnbQ4srI8XADMA6vxHA7e2KKwkSZIkTWSjuYvgtIiYWh8/CngpcBVwPvCquths4Iz6eE59Tp1/XmYu04MlSZIkSaubKSMvwqbAsRGxBiWQnZqZZ0bEb4CTI+JQ4ArgqLr8UcBxETGP0nO19ziUW5IkSZImnBEDVmb+Enhmj+nXUK7H6p5+D7BXk9JJkiRJ0ipkTNdgSZIkSZL6M2BJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoxYEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1MiUQRdAkqRV3cyDzuo779rDdluJJZEkDZo9WJIkSZLUiAFLkiRJkhoxYEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjIwasiJgREedHxFURcWVEvKNO3zAizomIq+vvx9TpERGHR8S8iPhlRGw33hshSZIkSRPBaHqw7gcOzMynADsCb4uIbYCDgHMzc2vg3PocYFdg6/pzAPDl5qWWJEmSpAloxICVmTdk5s/q4zuAq4DpwB7AsXWxY4E96+M9gG9k8VNgakRs2rzkkiRJkjTBjOkarIiYCTwTuATYJDNvgBLCgMfWxaYD8ztetqBO617XARExNyLmLlq0aOwllyRpjGx7JEnjbdQBKyLWA74FvDMzbx9u0R7TcpkJmUdm5vaZuf20adNGWwxJkpabbY8kabyNKmBFxJqUcHVCZn67Tr5xaOhf/X1Tnb4AmNHx8s2BhW2KK0mSJEkT12juIhjAUcBVmfnZjllzgNn18WzgjI7pb6h3E9wRWDI0lFCSJEmSVmdTRrHM84F9gV9FxM/rtPcDhwGnRsT+wPXAXnXe2cArgHnA3cB+TUssSZIkSRPUiAErMy+m93VVADv3WD6Bt61guSRJkiRplTOmuwhKkiRJkvozYEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDUyZdAFWJlmHnRW33nXHrbbSiyJJEmSpNWRPViSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoxYEmSJElSIwYsSZIkSWrEgCVJkiRJjRiwJEmSJKkRA5YkSZIkNWLAkiRJkqRGDFiSJEmS1IgBS5IkSZIaMWBJkiRJUiMGLEmSJElqxIAlSZIkSY2MGLAi4uiIuCkift0xbcOIOCcirq6/H1OnR0QcHhHzIuKXEbHdeBZekiRJkiaS0fRgHQPs0jXtIODczNwaOLc+B9gV2Lr+HAB8uU0xJUmSJGniGzFgZeZFwK1dk/cAjq2PjwX27Jj+jSx+CkyNiE1bFVaSJEmSJrLlvQZrk8y8AaD+fmydPh2Y37HcgjpNkiRJklZ7rW9yET2mZc8FIw6IiLkRMXfRokWNiyFJ0rJseyRJ4215A9aNQ0P/6u+b6vQFwIyO5TYHFvZaQWYemZnbZ+b206ZNW85iSJI0erY9kqTxtrwBaw4wuz6eDZzRMf0N9W6COwJLhoYSSpIkSdLqbspIC0TEScBOwMYRsQD4MHAYcGpE7A9cD+xVFz8beAUwD7gb2G8cyixJkiRJE9KIASszX9tn1s49lk3gbStaKEmSJElaFbW+yYUkSZIkTVoGLEmSJElqxIAlSZIkSY0YsCRJkiSpEQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJamTKoAsgSdLqbOZBZ/Wdd+1hu63EkkiSVgZ7sCRJkiSpEQOWJEmSJDXiEMFx5tAQSZIkafKwB0uSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmNGLAkSZIkqREDliRJkiQ1YsCSJEmSpEYMWJIkSZLUiAFLkiRJkhoxYEmSJElSI1MGXYBV3cyDzhp0ESRJkiRNEPZgSZIkSVIjBixJkiRJasQhgpVD/SRJkiStKAOWljJc0Lz2sN1WYkkkSZKkVY9DBCVJkiSpEXuwBsjeIkmSJGn1Yg+WJEmSJDViwJIkSZKkRhwiKEnSasYh6JI0OPZgSZIkSVIj9mBNUCP9Xy7PQEqSJEkTjz1YkiRJktSIPViSJA2IoxUkafVjD5YkSZIkNWLAkiRJkqRGHCKoSclbGEta1Y00vHB5X+cxUJJWjAFLkiQ9xBNQkrRiDFiSpHHjl3WNhvuJpNWJAUuSpAlqeYcBSpIGZ1wCVkTsAnwBWAP4WmYeNh7vo948EyhJ0sTj9W/S5NA8YEXEGsARwN8DC4DLImJOZv6m9XtJkiRJUqdBdzaMRw/WDsC8zLwGICJOBvYADFiruEHvrJIkSdJENx4Bazowv+P5AuA54/A+WkU4JKIwoErS2NmGFMvbhlh/K872W2MVmdl2hRF7AS/PzDfV5/sCO2Tmv3UtdwBwQH36JOAW4OamhVk9bIz10ov10pv10pv10tvqUi9bZOa00Sxo2zNqq8u+0Zr10p9105v10tvqUi8925/xCFjPBQ7JzJfX5+8DyMxPjPC6uZm5fdPCrAasl96sl96sl96sl96sF+ugH+ulN+ulP+umN+ult9W9Xh4xDuu8DNg6IraMiLWAvYE54/A+kiRJkjShNL8GKzPvj4h/Bf6Pcpv2ozPzytbvI0mSJEkTzbj8H6zMPBs4e4wvO3I8yrIasF56s156s156s156s16sg36sl96sl/6sm96sl95W63ppfg2WJEmSJE1W43ENliRJkiRNSgMPWBGxS0T8LiLmRcRBgy7PoETEjIg4PyKuiogrI+IddfqGEXFORFxdfz9m0GUdhIhYIyKuiIgz6/MtI+KSWi+n1BuqTDoRMTUiTouI39Z957nuMxAR/17/jn4dESdFxNqTcZ+JiKMj4qaI+HXHtJ77RxSH12PxLyNiu8GVfOWw/Slsf4Zn+7Ms257ebHsK254BB6yIWAM4AtgV2AZ4bURsM8gyDdD9wIGZ+RRgR+BttS4OAs7NzK2Bc+vzyegdwFUdzz8JfK7Wy23A/gMp1eB9AfheZj4ZeAaljib1PhMR04G3A9tn5tMoN9vZm8m5zxwD7NI1rd/+sSuwdf05APjySirjQNj+LMX2Z3i2P8uy7eli27OUY5jkbc+ge7B2AOZl5jWZ+VfgZGCPAZdpIDLzhsz8WX18B+VgNZ1SH8fWxY4F9hxMCQcnIjYHdgO+Vp8H8BLgtLrIZK2XDYAXAkcBZOZfM3Mx7jNQbuDzqIiYAqwD3MAk3Gcy8yLg1q7J/faPPYBvZPFTYGpEbLpySjoQtj+V7U9/tj/Lsu0Zlm0Ptj0w+IA1HZjf8XxBnTapRcRM4JnAJcAmmXkDlEYQeOzgSjYwnwfeAzxYn28ELM7M++vzybrfPAFYBHy9Dl/5WkSsyyTfZzLzT8CngespjdsS4HLcZ4b02z8m2/F4sm3vqNj+LMP2Z1m2PT3Y9oxoUrU9gw5Y0WPapL6tYUSsB3wLeGdm3j7o8gxaRMwCbsrMyzsn91h0Mu43U4DtgC9n5jOBu5hkQzJ6qeO69wC2BDYD1qUMQeg2GfeZ4Uy2v6vJtr0jsv1Zmu1PX7Y9Pdj2LLfV8m9q0AFrATCj4/nmwMIBlWXgImJNSuN2QmZ+u06+cairtP6+aVDlG5DnA6+MiGspQ3heQjmjOLV2wcPk3W8WAAsy85L6/DRKozfZ95mXAn/MzEWZeR/wbeB5uM8M6bd/TLbj8WTb3mHZ/vRk+9ObbU9vtj3Dm1Rtz6AD1mXA1vUOK2tRLgacM+AyDUQd130UcFVmfrZj1hxgdn08GzhjZZdtkDLzfZm5eWbOpOwf52XmPsD5wKvqYpOuXgAy88/A/Ih4Up20M/AbJvk+QxmesWNErFP/robqZdLvM1W//WMO8IZ6R6cdgSVDwzlWU7Y/le1Pb7Y/vdn29GXbM7xJ1fYM/B8NR8QrKGeE1gCOzsyPD7RAAxIRLwB+CPyKh8d6v58yDv5U4PGUP969MrP7wsFJISJ2At6VmbMi4gmUM4obAlcAr8/MewdZvkGIiG0pF1+vBVwD7Ec5cTKp95mI+AjwGsrd0a4A3kQZ0z2p9pmIOAnYCdgYuBH4MPC/9Ng/6heCL1Lu/HQ3sF9mzh1EuVcW25/C9mdktj9Ls+3pzbansO2ZAAFLkiRJklYXgx4iKEmSJEmrDQOWJEmSJDViwJIkSZKkRgxYkiRJktSIAUuSJEmSGjFgSZIkSVIjBixJkiRJasSAJUmSJEmN/H/vC2GcgiV3ZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for percentage in [30]:\n",
    "    for dim in range(0,3):\n",
    "        \n",
    "        output=str(s_node)\n",
    "        target_cochain=np.load('../data/s2_3_collaboration_complex/'+output+'_cochains.npy',allow_pickle=True)\n",
    "        target_cochain=np.array(list(target_cochain[dim].values()))\n",
    "        mask_seen=np.load(f'../data/s2_3_collaboration_complex/{s_node}_percentage_{percentage}_known_values.npy',allow_pickle=True)\n",
    "        mask_seen=list(mask_seen[dim].values())\n",
    "        mask_unseen=np.load(f'../data/s2_3_collaboration_complex/{s_node}_percentage_{percentage}_missing_values.npy',allow_pickle=True)\n",
    "        mask_unseen=list(mask_unseen[dim].values())\n",
    "\n",
    "        n_bins = 50\n",
    "        # Generate a normal distribution, center at x=0 and y=5\n",
    "        x=target_cochain[mask_seen]\n",
    "        y = target_cochain[mask_unseen]\n",
    "\n",
    "        #plt.figure(figsize=(8,4))\n",
    "        fig, axs = plt.subplots(1, 2, sharey=True, tight_layout=True,figsize=(12,5))\n",
    "\n",
    "        # We can set the number of bins with the `bins` kwarg\n",
    "        axs[0].hist(x, bins=n_bins)\n",
    "        axs[0].set_title('Distribution known citations in diemension {}'.format(dim))\n",
    "        axs[1].hist(y, bins=n_bins)\n",
    "        plt.title('Distribution missing citations in dimension {}'.format(dim))\n",
    "        fig.suptitle(\"Distribution percentage of unknown values {0}% \".format(percentage),y=1.1)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}