Calculate and compare MMJ distance matrix.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d8c341f4-72ec-41d9-8094-82d124d0d245",
   "metadata": {},
   "outputs": [],
   "source": [
    "exec(open(\"./funcs/mmj_cal_functions.py\").read())\n",
    "exec(open(\"./funcs/variant_of_Floyd_Warshall.py\").read())\n",
    "exec(open(\"./funcs/Prim_Minimum_Spanning_Tree.py\").read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2baeabee-a859-49f8-a070-cf2135ae5563",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x12e0651f0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_data_145 = pickle.load(  open( \"./data/test_data_145.p\", \"rb\" ) ) \n",
    " \n",
    "X = test_data_145[1][:100]\n",
    "    \n",
    "plt.scatter(X[:,0],X[:,1], s= 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "25a50f7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "21e69962",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Calculate Min-Max-Jump distance (MMJ distance) matrix with Algorithm 1 and implemented with C++, \n",
    "# the dynamic-link library (DLL) only compiled for macOS and linux, \n",
    "# readers can compile their own DLL with the C++ source code in the \"mmj_so\" folder.\n",
    "# Min-Max-Jump distance is equivalent to minimax path distance, or longest leg path distance (LLPD).\n",
    "# See the paper:\n",
    "# https://arxiv.org/abs/2301.05994\n",
    "\n",
    "X_mmj_matrix_algo_1_cpp = cal_mmj_matrix_algo_1_cpp(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4d4d83ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate MMJ distance matrix with Algorithm 1 and implemented with python, \n",
    " \n",
    "\n",
    "X_mmj_matrix_algo_1_python = cal_mmj_matrix_algo_1_python(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "25bea969",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2461fc54",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "7.277511926417901e-13\n"
     ]
    }
   ],
   "source": [
    "# Result of C++ version is equal to python version.\n",
    "\n",
    "\n",
    "print(np.allclose(X_mmj_matrix_algo_1_python, X_mmj_matrix_algo_1_cpp))\n",
    "print(np.sum(np.abs(X_mmj_matrix_algo_1_python - X_mmj_matrix_algo_1_cpp)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb26caca-58d6-43ab-8268-85467c8d67ef",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "53ce5d23",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Min-Max-Jump distance (MMJ distance) matrix with a variant of Floyd-Warshall algorithm \n",
    "# implemented with C++, the dynamic-link library (DLL) only compiled for macOS, \n",
    "# readers can compile their own DLL with the C++ source code in the \"mmj_so\" folder.\n",
    "\n",
    "\n",
    "X_mmj_matrix_Floyd_Warshall_cpp = cal_mmj_matrix_Floyd_Warshall_cpp(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "596be579",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# Result of Algorithm 1 is equal to X_mmj_matrix calculated with variant of Floyd-Warshall algorithm.\n",
    "\n",
    "\n",
    "print(np.allclose(X_mmj_matrix_algo_1_python, X_mmj_matrix_Floyd_Warshall_cpp))\n",
    "print(np.sum(np.abs(X_mmj_matrix_algo_1_python - X_mmj_matrix_Floyd_Warshall_cpp)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "60e14788",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Calculate MMJ distance matrix with variant of Floyd-Warshall algorithm implemented with python.\n",
    "\n",
    "X_mmj_matrix_Floyd_Warshall_python = cal_mmj_variant_of_Floyd_Warshall_python(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "78032084",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# Result is equal to previous calculations.\n",
    "\n",
    "\n",
    "print(np.allclose(X_mmj_matrix_algo_1_python, X_mmj_matrix_Floyd_Warshall_python))\n",
    "print(np.sum(np.abs(X_mmj_matrix_algo_1_python - X_mmj_matrix_Floyd_Warshall_python)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96f4ef8e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "32829cb3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Calculate Min-Max-Jump distance (MMJ distance) matrix by pairwise shortest path \n",
    "# in the minimum spanning tree of graph G.\n",
    " \n",
    "X_mmj_matrix_MST_shortest_path = cal_mmj_matrix_by_shortest_path_on_minimum_spanning_tree(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5f287e45",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "7.277511926417901e-13\n"
     ]
    }
   ],
   "source": [
    "# Result is equal to previous calculations.\n",
    "\n",
    "print(np.allclose(X_mmj_matrix_algo_1_python, X_mmj_matrix_MST_shortest_path))\n",
    "print(np.sum(np.abs(X_mmj_matrix_algo_1_python - X_mmj_matrix_MST_shortest_path)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a9fc22fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Min-Max-Jump distance (MMJ distance) matrix by Algorithm 4, Calculation and Copy.\n",
    "# Min-Max-Jump distance is equivalent to minimax path distance and longest leg path distance (LLPD). \n",
    "# See the paper:\n",
    "# https://arxiv.org/abs/2301.05994 \n",
    "\n",
    "X_mmj_matrix_algo_4 = cal_mmj_matrix_by_algo_4_Calculation_and_Copy(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "548c4d05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "7.277511926417901e-13\n"
     ]
    }
   ],
   "source": [
    "# Result is equal to previous calculations.\n",
    "\n",
    "print(np.allclose(X_mmj_matrix_algo_1_python, X_mmj_matrix_algo_4))\n",
    "print(np.sum(np.abs(X_mmj_matrix_algo_1_python - X_mmj_matrix_algo_4)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "676ea46f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "697a90fb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "64106fde",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "abeea006",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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