boundary_matrix_cohomology.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "bf0a36bd",
   "metadata": {},
   "source": [
    "## This notebook is for the development of the function get_boundary_matrix:\n",
    " ***This function returns the matrix boundary before reduction***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e3d1d139",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gudhi as gd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.sparse import lil_matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6f06fe0f",
   "metadata": {},
   "source": [
    "### Class: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "15fe0636",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SimplexTree(gd.SimplexTree):\n",
    "    \n",
    "    def get_boundary_matrix(self, sparse=False):\n",
    "        \n",
    "        \"\"\"\n",
    "        This function returns the matrix boundary before reduction.\n",
    "\n",
    "        :param sparse: Indicate if the returned matrix should be sparse or dense.\n",
    "        :param homology_coeff_field: The homology coefficient field. Must be a prime number. Default value is 2.\n",
    "        :returns: The boundary matrix in sparse format by default.\n",
    "        \"\"\"\n",
    "\n",
    "        filtration=self.get_filtration()  \n",
    "        filtration_list=list(filtration)\n",
    "        dim=len(filtration_list) # Dimension of the boundary matrix\n",
    "        dics={} # Dictionary to store each simplex and corresponding index \n",
    "\n",
    "        # Initialize the matrix boundary based on whether sparse is True or False\n",
    "        if sparse:\n",
    "            Matrice_bord = lil_matrix((dim, dim), dtype=int) \n",
    "        else:\n",
    "            Matrice_bord = np.zeros((dim, dim), dtype=int) \n",
    "\n",
    "        for i, (smpx,_) in  enumerate(filtration_list): # loop through the simplex and its order of apparition\n",
    "            dics[tuple(smpx)]=i   # assign an index to each simplex in the filtration\n",
    "            sign= 1 - 2 * (len(smpx) % 2) # \\in {-1,1} provides the sign in the  alternate sum in the boundary.\n",
    "            for n, _ in self.get_boundaries(smpx):\n",
    "                index = dics.get(tuple(n))\n",
    "                Matrice_bord[index, i] = sign\n",
    "                sign = -sign  # alternate the sign moving into the next boundary of the simplex\n",
    "\n",
    "        if sparse:\n",
    "            Matrice_bord = Matrice_bord.tocsr() # Convert the boundary matrix to compressed sparse format if sparse is True\n",
    "\n",
    "        return Matrice_bord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4b2ae4ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st=gd.SimplexTree()\n",
    "st.insert([0])\n",
    "st.insert([1],0.01)\n",
    "st.insert([2],0.02)\n",
    "st.insert([3],0.03)\n",
    "st.insert([1,3],0.04)\n",
    "st.insert([5],0.05)\n",
    "st.insert([6],0.06)\n",
    "st.insert([7],0.07)\n",
    "st.insert([8],0.08)\n",
    "st.insert([1,8],0.09)\n",
    "st.insert([1,7],0.10)\n",
    "st.insert([11],0.11)\n",
    "st.insert([12],0.12)\n",
    "st.insert([8,11],0.13)\n",
    "st.insert([11,12],0.14)\n",
    "st.insert([3,12],0.15)\n",
    "st.insert([7,12],0.16)\n",
    "st.insert([3,11],0.17)\n",
    "st.insert([3,11,12],0.18)\n",
    "st.insert([0,12],0.19)\n",
    "st.insert([0,7],0.20)\n",
    "st.insert([6,7],0.205)\n",
    "st.insert([3,7],0.21)\n",
    "st.insert([1,3,7],0.22)\n",
    "st.insert([0,7,12],0.23)\n",
    "st.insert([3,8],0.24)\n",
    "st.insert([3,7,12],0.25)\n",
    "st.insert([1,3,8],26)\n",
    "st.insert([3,8,11],27)\n",
    "st.insert([2,5],28)\n",
    "st.insert([5,6],29)\n",
    "st.insert([2,6],30)\n",
    "st.insert([2,5,6],31)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8de87d24",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_boundary_matrix(self, sparse=False):\n",
    "\n",
    "        filtration=self.get_filtration()  \n",
    "        filtration_list=list(filtration)\n",
    "        dim=len(filtration_list) # Dimension of the boundary matrix\n",
    "        dics={} # Dictionary to store each simplex and corresponding index \n",
    "\n",
    "        # Initialize the matrix boundary based on whether sparse is True or False\n",
    "        if sparse:\n",
    "            Matrice_bord = lil_matrix((dim, dim), dtype=int) \n",
    "        else:\n",
    "            Matrice_bord = np.zeros((dim, dim), dtype=int) \n",
    "\n",
    "        for i, (smpx,_) in  enumerate(filtration_list): #loop through the simplex and its order of apparition\n",
    "            dics[tuple(smpx)]=i   # assign an index to each simplex in the filtration\n",
    "            sign= 1 - 2 * (len(smpx) % 2)  # Depending on the cohomology, the sign will altern with 1 for pair symplex and -1 for impair\n",
    "            for n, _ in self.get_boundaries(smpx): \n",
    "                index = dics.get(tuple(n))\n",
    "                Matrice_bord[index, i] = sign\n",
    "                sign = -sign # altern the sign regarding the direction in the simplex\n",
    "\n",
    "        if sparse:\n",
    "            Matrice_bord = Matrice_bord.tocsr() # Convert the boundary matrix to compressed sparse format if sparse is True\n",
    "\n",
    "        return Matrice_bord"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b63301ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_unitaire=get_boundary_matrix(st)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "24791cae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_indices_modified(matrix):\n",
    "    indices_dict = {}\n",
    "    for col_idx, column in enumerate(matrix.T):\n",
    "        indices_1 = [i for i, val in enumerate(column) if val == 1]\n",
    "        indices_minus_1 = [i for i, val in enumerate(column) if val == -1]\n",
    "        indices_dict[col_idx] = {'1': indices_1, '-1': indices_minus_1}\n",
    "    return indices_dict\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6e794794",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: {'1': [], '-1': []},\n",
       " 1: {'1': [], '-1': []},\n",
       " 2: {'1': [], '-1': []},\n",
       " 3: {'1': [], '-1': []},\n",
       " 4: {'1': [1], '-1': [3]},\n",
       " 5: {'1': [], '-1': []},\n",
       " 6: {'1': [], '-1': []},\n",
       " 7: {'1': [], '-1': []},\n",
       " 8: {'1': [], '-1': []},\n",
       " 9: {'1': [1], '-1': [8]},\n",
       " 10: {'1': [1], '-1': [7]},\n",
       " 11: {'1': [], '-1': []},\n",
       " 12: {'1': [], '-1': []},\n",
       " 13: {'1': [8], '-1': [11]},\n",
       " 14: {'1': [11], '-1': [12]},\n",
       " 15: {'1': [3], '-1': [12]},\n",
       " 16: {'1': [7], '-1': [12]},\n",
       " 17: {'1': [3], '-1': [11]},\n",
       " 18: {'1': [15], '-1': [14, 17]},\n",
       " 19: {'1': [0], '-1': [12]},\n",
       " 20: {'1': [0], '-1': [7]},\n",
       " 21: {'1': [6], '-1': [7]},\n",
       " 22: {'1': [3], '-1': [7]},\n",
       " 23: {'1': [10], '-1': [4, 22]},\n",
       " 24: {'1': [19], '-1': [16, 20]},\n",
       " 25: {'1': [3], '-1': [8]},\n",
       " 26: {'1': [15], '-1': [16, 22]},\n",
       " 27: {'1': [9], '-1': [4, 25]},\n",
       " 28: {'1': [17], '-1': [13, 25]},\n",
       " 29: {'1': [2], '-1': [5]},\n",
       " 30: {'1': [5], '-1': [6]},\n",
       " 31: {'1': [2], '-1': [6]},\n",
       " 32: {'1': [31], '-1': [29, 30]}}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_indices_modified(test_unitaire)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "93bc5b5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "dense_matrix = test_unitaire\n",
    "\n",
    "# Create a bigger figure with a grid-like structure\n",
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "ax.set_aspect('equal')\n",
    "ax.set_facecolor('lightgray')\n",
    "\n",
    "# Plot the dense matrix with a grayscale colormap\n",
    "ax.imshow(dense_matrix, cmap='gray')\n",
    "\n",
    "# Get the indices where the values are +1 and -1\n",
    "indices_1 = np.argwhere(dense_matrix == 1)\n",
    "indices_minus_1 = np.argwhere(dense_matrix == -1)\n",
    "indices_0 = np.argwhere(dense_matrix == 0)\n",
    "\n",
    "# Highlight the positions of +1 and -1 values with black and white squares, respectively\n",
    "ax.plot(indices_1[:, 1], indices_1[:, 0], 's', markersize=12, label='+1', color='black')\n",
    "ax.plot(indices_minus_1[:, 1], indices_minus_1[:, 0], 's', markersize=12, label='-1', color='white')\n",
    "ax.plot(indices_0[:, 1], indices_0[:, 0], 's', markersize=12, label='0', color='gray')\n",
    "\n",
    "# Add gridlines\n",
    "ax.set_xticks(np.arange(dense_matrix.shape[1]+1)-0.5, minor=True)\n",
    "ax.set_yticks(np.arange(dense_matrix.shape[0]+1)-0.5, minor=True)\n",
    "ax.grid(which='minor', color='black', linestyle='-', linewidth=1)\n",
    "\n",
    "# Set the tick labels and remove ticks\n",
    "ax.set_xticks(np.arange(dense_matrix.shape[1]))\n",
    "ax.set_yticks(np.arange(dense_matrix.shape[0]))\n",
    "ax.set_xticklabels(np.arange(0, dense_matrix.shape[1] ))\n",
    "ax.set_yticklabels(np.arange(0, dense_matrix.shape[0] ))\n",
    "ax.tick_params(bottom=False, left=False)\n",
    "\n",
    "# Add a legend\n",
    "ax.legend(loc=3, fontsize=10)\n",
    "\n",
    "# Set the title\n",
    "ax.set_title('Boundary Matrix')\n",
    "\n",
    "# Show the plot\n",
    "plt.tight_layout()\n",
    "plt.savefig('image', bbox_inches='tight')\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b42b2534",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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