notebooks/Example1_Two_Component_Polymer_Ensemble_Colab.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qJN4M4IQfWlV"
   },
   "source": [
    "<a target=\"_blank\" href=\"https://colab.research.google.com/github/olsenlabmit/Polymer-Ensemble-Similarity/blob/main/notebooks/Example1_Two_Component_Polymer_Ensemble_Colab.ipynb\">\n",
    "  <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "zMN73XuAfrN0"
   },
   "outputs": [],
   "source": [
    "# @title Copyright & License (click to expand)\n",
    "\n",
    "# MIT License\n",
    "\n",
    "# Copyright (c) 2023 olsenlabmit\n",
    "\n",
    "# Permission is hereby granted, free of charge, to any person obtaining a copy\n",
    "# of this software and associated documentation files (the \"Software\"), to deal\n",
    "# in the Software without restriction, including without limitation the rights\n",
    "# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n",
    "# copies of the Software, and to permit persons to whom the Software is\n",
    "# furnished to do so, subject to the following conditions:\n",
    "\n",
    "# The above copyright notice and this permission notice shall be included in all\n",
    "# copies or substantial portions of the Software.\n",
    "\n",
    "# THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n",
    "# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n",
    "# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n",
    "# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n",
    "# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n",
    "# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\n",
    "# SOFTWARE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_iZyqlBRb7ce"
   },
   "source": [
    "# Download Necessary Files\n",
    "\n",
    "Downloading local python functions, tables, and dataset\n",
    "from Github Repo [Polymer-Ensemble-Similarity](https://github.com/olsenlabmit/Polymer-Ensemble-Similarity.git)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "_o8vi_-QrKij"
   },
   "outputs": [],
   "source": [
    "!git clone https://github.com/olsenlabmit/Polymer-Ensemble-Similarity.git\n",
    "!mv Polymer-Ensemble-Similarity/dataset .\n",
    "!mv Polymer-Ensemble-Similarity/tables .\n",
    "!mv Polymer-Ensemble-Similarity/utils ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mSdNpNOZcEdk"
   },
   "source": [
    "# Import Required Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "veQ7XTe5KHgx",
    "outputId": "98b74d31-1faa-4425-d6ae-fd4cf0834acb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: grakel in /usr/local/lib/python3.10/dist-packages (0.1.9)\n",
      "Requirement already satisfied: numpy>=1.14.0 in /usr/local/lib/python3.10/dist-packages (from grakel) (1.23.5)\n",
      "Requirement already satisfied: cython>=0.27.3 in /usr/local/lib/python3.10/dist-packages (from grakel) (0.29.36)\n",
      "Requirement already satisfied: scikit-learn>=0.19 in /usr/local/lib/python3.10/dist-packages (from grakel) (1.2.2)\n",
      "Requirement already satisfied: six>=1.11.0 in /usr/local/lib/python3.10/dist-packages (from grakel) (1.16.0)\n",
      "Requirement already satisfied: future>=0.16.0 in /usr/local/lib/python3.10/dist-packages (from grakel) (0.18.3)\n",
      "Requirement already satisfied: joblib in /usr/local/lib/python3.10/dist-packages (from grakel) (1.3.2)\n",
      "Requirement already satisfied: scipy>=1.3.2 in /usr/local/lib/python3.10/dist-packages (from scikit-learn>=0.19->grakel) (1.10.1)\n",
      "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn>=0.19->grakel) (3.2.0)\n",
      "Requirement already satisfied: dgl in /usr/local/lib/python3.10/dist-packages (1.1.2)\n",
      "Requirement already satisfied: numpy>=1.14.0 in /usr/local/lib/python3.10/dist-packages (from dgl) (1.23.5)\n",
      "Requirement already satisfied: scipy>=1.1.0 in /usr/local/lib/python3.10/dist-packages (from dgl) (1.10.1)\n",
      "Requirement already satisfied: networkx>=2.1 in /usr/local/lib/python3.10/dist-packages (from dgl) (3.1)\n",
      "Requirement already satisfied: requests>=2.19.0 in /usr/local/lib/python3.10/dist-packages (from dgl) (2.31.0)\n",
      "Requirement already satisfied: tqdm in /usr/local/lib/python3.10/dist-packages (from dgl) (4.66.1)\n",
      "Requirement already satisfied: psutil>=5.8.0 in /usr/local/lib/python3.10/dist-packages (from dgl) (5.9.5)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19.0->dgl) (3.2.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19.0->dgl) (3.4)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19.0->dgl) (2.0.4)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19.0->dgl) (2023.7.22)\n",
      "Requirement already satisfied: umap-learn in /usr/local/lib/python3.10/dist-packages (0.5.3)\n",
      "Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.10/dist-packages (from umap-learn) (1.23.5)\n",
      "Requirement already satisfied: scikit-learn>=0.22 in /usr/local/lib/python3.10/dist-packages (from umap-learn) (1.2.2)\n",
      "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.10/dist-packages (from umap-learn) (1.10.1)\n",
      "Requirement already satisfied: numba>=0.49 in /usr/local/lib/python3.10/dist-packages (from umap-learn) (0.56.4)\n",
      "Requirement already satisfied: pynndescent>=0.5 in /usr/local/lib/python3.10/dist-packages (from umap-learn) (0.5.10)\n",
      "Requirement already satisfied: tqdm in /usr/local/lib/python3.10/dist-packages (from umap-learn) (4.66.1)\n",
      "Requirement already satisfied: llvmlite<0.40,>=0.39.0dev0 in /usr/local/lib/python3.10/dist-packages (from numba>=0.49->umap-learn) (0.39.1)\n",
      "Requirement already satisfied: setuptools in /usr/local/lib/python3.10/dist-packages (from numba>=0.49->umap-learn) (67.7.2)\n",
      "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.10/dist-packages (from pynndescent>=0.5->umap-learn) (1.3.2)\n",
      "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn>=0.22->umap-learn) (3.2.0)\n",
      "Import Required Libraries Done!\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "import shutil\n",
    "import sys\n",
    "import os.path\n",
    "import json\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "if not shutil.which(\"rdkit\"):\n",
    "    !pip install -q rdkit\n",
    "\n",
    "from rdkit import Chem\n",
    "from rdkit.Chem import Draw\n",
    "from rdkit.Chem.Draw import IPythonConsole\n",
    "\n",
    "if not shutil.which(\"grakel\"):\n",
    "    !pip install grakel\n",
    "\n",
    "if not shutil.which(\"dgl\"):\n",
    "    !pip install dgl\n",
    "\n",
    "if not shutil.which(\"umap\"):\n",
    "    !pip install umap-learn\n",
    "\n",
    "if not shutil.which(\"pyomo\"):\n",
    "    !pip install -q pyomo\n",
    "    assert shutil.which(\"pyomo\")\n",
    "\n",
    "from pyomo.environ import *\n",
    "\n",
    "if not (shutil.which(\"cbc\") or os.path.isfile(\"cbc\")):\n",
    "    if \"google.colab\" in sys.modules:\n",
    "        !apt-get install -y -qq coinor-cbc\n",
    "    else:\n",
    "        try:\n",
    "            !conda install -c conda-forge coincbc\n",
    "        except:\n",
    "            pass\n",
    "\n",
    "assert shutil.which(\"cbc\") or os.path.isfile(\"cbc\")\n",
    "\n",
    "from utils.load_networkx import networkx_feat\n",
    "from utils import macro_unsupervised as unsup\n",
    "from utils import plot\n",
    "\n",
    "print(\"Import Required Libraries Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YteAN12TdcD2"
   },
   "source": [
    "# Load the Ensemble P and Ensemble Q in Example 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2DvcglBLxssN"
   },
   "source": [
    "## Graph Representation Index Sort Function\n",
    "\n",
    "P = \\{\"p1\": graph representatioon of p1, \"p2\", graph representatioon of p2}.\n",
    "\n",
    "Q = \\{\"q1\": graph representatioon of q1, \"q2\", graph representatioon of q2}.\n",
    "\n",
    "These graph representations are stored in dict format, which is a python dictionary. The dictionary does not have order. Therefore, we need to have some sort functions to call them in order according their labels (keys).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "id": "wloBCboDsPhM"
   },
   "outputs": [],
   "source": [
    "# \"p1\", \"p2\" (or \"q1\", \"q2\")\n",
    "# These graph representation labels (keys) are one alphabet and one number.\n",
    "# In one specific polymer ensemble,\n",
    "# the alphabet is constant, and the number is varying.\n",
    "# Therefore, we use the number for sort function.\n",
    "# The sort function depends on how the graph labels are created.\n",
    "def sortFunc(index):\n",
    "    return int(index[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7S0J7uqPxxpL"
   },
   "source": [
    "## Load Ensemble P\n",
    "\n",
    "<img src=\"https://drive.google.com/uc?export=view&id=1b0wnyachSnJKj1pSajL5GT0erMGUwx3p\"  width=\"50%\">\n",
    "\n",
    "where blue sphere is R0, red sphere is R1.\n",
    "\n",
    "\n",
    "$w_{p_{1}} = 0.5, w_ {p_{2}} = 0.5$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hzjj-4AEssfC"
   },
   "source": [
    "### Load Graph Representations in Ensemble P\n",
    "\n",
    "**Variables**:\n",
    "\n",
    "networkx_feat: the function for loading the graph representations of each type polymer chain in one polymer ensemble.\n",
    "\n",
    "TXT_DATA_PATH: the path for ensemble dataset where each polymer chain graph representation is stored as a txt file.\n",
    "\n",
    "MON_SMILES: the text file for repeat units\n",
    "\n",
    "FEAT: Type of features for polymer chain repeat units -- one-hot encoding ('onehot') or fingerprints ('fp')\n",
    "\n",
    "To understand how to generate the txt files for polymer chains, please check the dataset [README.md](https://github.com/olsenlabmit/Polymer-Ensemble-Similarity/blob/main/dataset/README.md)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "uwJvO6PjYKeK"
   },
   "outputs": [],
   "source": [
    "Ensemble_P = networkx_feat(\n",
    "    TXT_DATA_PATH=\"./dataset/Example1/Ensemble_P/\",\n",
    "    MON_SMILES=\"tables/SMILES_monomer.txt\",\n",
    "    FEAT=\"onehot\",\n",
    ")\n",
    "\n",
    "Ensemble_P_indexs = list(Ensemble_P.keys())\n",
    "Ensemble_P_indexs.sort(key=sortFunc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JMKoSdX-tSBb"
   },
   "source": [
    "### Load Weights of Graph Representations in Ensemble P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "keoxCBtftLMd",
    "outputId": "703cab03-c65a-440c-b1cb-cf454653b11f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'p1': 0.5, 'p2': 0.5}\n"
     ]
    }
   ],
   "source": [
    "with open(\"./dataset/Example1/Ensemble_P_weight.json\", \"r\") as json_file:\n",
    "    Ensemble_P_weight = json.load(json_file)\n",
    "print(Ensemble_P_weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5rhj0oj6tag8"
   },
   "source": [
    "### Visualize Ensemble P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "pAIdxDmcMTCY",
    "outputId": "83fa0c0b-b531-4f5f-dc52-974d2eae6c25"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p1: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 'R0', 1: 'R1', 2: 'R0', 3: 'R1', 4: 'R0', 5: 'R1', 6: 'R0', 7: 'R1', 8: 'R0'}\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "p2: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 'R1', 1: 'R0', 2: 'R1', 3: 'R0', 4: 'R1', 5: 'R0', 6: 'R1', 7: 'R0', 8: 'R1'}\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, len(Ensemble_P_indexs)):\n",
    "    print(Ensemble_P_indexs[i] + \": \")\n",
    "    plot.graph(Ensemble_P[Ensemble_P_indexs[i]])\n",
    "    print(\"\\n\")\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0Q_hj4Wdx1uS"
   },
   "source": [
    "## Load Ensemble Q\n",
    "\n",
    "<img src=\"https://drive.google.com/uc?export=view&id=1N3J7IsU4bSUDWdDFi4LuBqETT0pMj8WD\"  width=\"50%\">\n",
    "\n",
    "where blue sphere is R0, red sphere is R1.\n",
    "\n",
    "$w_{q_{1}} = 0.5, w_ {q_{2}} = 0.5$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c6ZJJFTStnUh"
   },
   "source": [
    "### Load Graph Representations in Ensemble Q\n",
    "\n",
    "**Variables**:\n",
    "\n",
    "networkx_feat: the function for loading the graph representations of each type polymer chain in one polymer ensemble.\n",
    "\n",
    "TXT_DATA_PATH: the path for ensemble dataset\n",
    "\n",
    "MON_SMILES: the text file for repeat units\n",
    "\n",
    "FEAT: Type of fatures for polymer chain repeat units -- one-hot encoding ('onehot') or fingerprints ('fp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "Z5KXPff8eI75"
   },
   "outputs": [],
   "source": [
    "Ensemble_Q = networkx_feat(\n",
    "    TXT_DATA_PATH=\"./dataset/Example1/Ensemble_Q/\",\n",
    "    MON_SMILES=\"tables/SMILES_repeatunit.txt\",\n",
    "    FEAT=\"onehot\",\n",
    ")\n",
    "\n",
    "Ensemble_Q_indexs = list(Ensemble_Q.keys())\n",
    "Ensemble_Q_indexs.sort(key=sortFunc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aSKuSUNItsKd"
   },
   "source": [
    "### Load Weights of Graph Representations in Ensemble Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rLgUo1zkdpcE",
    "outputId": "7e933882-7eee-4d8c-ee8d-06884447a4a7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'q1': 0.5, 'q2': 0.5}\n"
     ]
    }
   ],
   "source": [
    "with open(\"./dataset/Example1/Ensemble_Q_weight.json\", \"r\") as json_file:\n",
    "    Ensemble_Q_weight = json.load(json_file)\n",
    "print(Ensemble_Q_weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ldtcRxZRt7Jz"
   },
   "source": [
    "### Visualize Ensemble Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "c1Sje3dHdpfM",
    "outputId": "b771f6ac-8f19-4a9e-9c75-2cf8a4d9d32b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q1: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 'R0', 1: 'R0', 2: 'R0', 3: 'R1', 4: 'R1', 5: 'R1', 6: 'R0', 7: 'R0', 8: 'R0'}\n",
      "\n",
      "\n",
      "q2: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 'R1', 1: 'R1', 2: 'R1', 3: 'R0', 4: 'R0', 5: 'R0', 6: 'R1', 7: 'R1', 8: 'R1'}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, len(Ensemble_Q_indexs)):\n",
    "    print(Ensemble_Q_indexs[i] + \": \")\n",
    "    plot.graph(Ensemble_Q[Ensemble_Q_indexs[i]])\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e0uCMi7Udzb9"
   },
   "source": [
    "# Polymer Ensembles Similarity Function via Earth Mover's Distance\n",
    "\n",
    "Use the earth mover's distance (EMD) to compute pairwise similarity scores between polymer ensembles.\n",
    "\n",
    "\n",
    "$ EMD (P,Q)= \\min_{F}\\sum_{i=1}^{m}\\sum_{j=1}^{n}f_{i,j}d_{i,j}$\n",
    "\n",
    "$ {\\rm subject\\ to\\ } f_{i,j} \\geq 0, {\\rm\\ for\\ any\\ } \\ 1 \\leq i \\leq m, 1 \\leq j \\leq n $\n",
    "\n",
    "$     \\sum_{j=1}^{n}f_{i,j} =w_{pi}, {\\rm for\\ any} \\ 1 \\leq i \\leq m $\n",
    "\n",
    "$     \\sum_{i=1}^{m}f_{i,j} =w_{qj}, {\\rm for\\ any} \\ 1 \\leq j \\leq n $\n",
    "\n",
    "$     \\sum_{i=1}^{m}\\sum_{j=1}^{n}f_{i,j} = \\sum_{i}^{m} w_{pi} = \\sum_{j}^{n} w_{qj} = 1 $\n",
    "\n",
    "\n",
    "One polymer ensemble is defined as $P = \\{(p_1,w_{p_1}) ,(p_2,w_{p_2}),...,(p_i,w_{p_i}),...,(p_m,w_{p_m})\\}$ has $m$ types of polymer chains, where $p_i$ represents a type of polymer chain and  $w_{p_i}>0$ is its corresponding weight, which can be the mole fraction of this polymer chain in the polymer ensemble. Similarly, the second ensemble $Q = {(q_1,w_{q_1}),(q_2,w_{q_2}),...,(q_j,w_{q_j}),...,(q_n,w_{q_n})}$ has $n$ types of polymer chains. The sums of the weights for $P$ and $Q$ are both normalized and equal to one.\n",
    "\n",
    "The EMD linear optimization code  refers to [Transportation Networks, ND Pyomo Notebook](https://jckantor.github.io/ND-Pyomo-Cookbook/notebooks/03.01-Transportation-Networks.html)\n",
    "\n",
    "Once $EMD (P,Q)$ is calculated, the similarity score between $P$ and $Q$ is\n",
    "\n",
    "$S(P,Q) = 1- EMD (P,Q)$\n",
    "\n",
    "\n",
    "The distance ($d_{i,j}$) between one polymer molecule $p_i$ and another polymer molecule $q_j$ is calculated through graph edit distance. This part of the code builds on [GLAMOUR](https://github.com/learningmatter-mit/GLAMOUR) and networkx function [graph_edit_distance](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.similarity.graph_edit_distance.html).\n",
    "\n",
    "$d(g_1, g_2) = 1- \\exp(-\\frac{\\alpha \\cdot GED(g_1, g_2)}{(N_1 + N_2)/2})$\n",
    "\n",
    "where $g_i$ is the graph representation of one polymer molecule, $N_i$ is the number of nodes in graph $g_i$, $\\alpha$ is a tunable parameter with the default value being 1. [Reference1](https://arxiv.org/abs/1808.05689), [Reference2](https://doi.org/10.1021/acs.macromol.3c00761)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "VkvicUCoMTFZ"
   },
   "outputs": [],
   "source": [
    "def Similarity_Score_EMD_Calculation(\n",
    "    ensembleP=None,\n",
    "    ensembleP_weight=None,\n",
    "    ensembleQ=None,\n",
    "    ensembleQ_weight=None,\n",
    "    alpha=1,\n",
    "    print_details=False,\n",
    "):\n",
    "    \"\"\"\n",
    "    Pairwise Similarity calculation between two polymer ensembles using EMD\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    ensembleP: dict-like of shape (m graphs), Ensemble P\n",
    "    ensembleP_weight: dict-like of shape (m weights), Ensemble P weight\n",
    "    ensembleQ: dict-like of shape (n graphs), Ensemble Q\n",
    "    ensembleQ_weight: dict-like of shape (n graphs), Ensemble Q weight\n",
    "    alpha: float, a tuning parameter for d_{i,j} calculation, default is 1\n",
    "    print_details: bool, print the details of EMD calculation, default is False\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float, pairwise similarity score between two polymer ensembles, range from 0 to 1.\n",
    "    0 means two polymer ensembles are totally different.\n",
    "    1 means two polymer ensembles are identical.\n",
    "    The larger the similarity score, the more similar between two polymer ensembles.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    # Data loading w_i, w_j, d_ij\n",
    "\n",
    "    ## load the weight w_i of Ensemble P\n",
    "    Demand = {}\n",
    "\n",
    "    ensembleP_number = len(ensembleP_weight)\n",
    "\n",
    "    ensembleP_weight_sum = sum(ensembleP_weight.values())\n",
    "\n",
    "    ensembleP_indexs = list(ensembleP.keys())\n",
    "    ensembleP_indexs.sort(key=sortFunc)\n",
    "\n",
    "    for i in range(0, ensembleP_number):\n",
    "        Demand[\"p\" + str(i + 1)] = (\n",
    "            ensembleP_weight[ensembleP_indexs[i]] / ensembleP_weight_sum\n",
    "        )\n",
    "\n",
    "    ## load the weight w_j of Ensemble Q\n",
    "    Supply = {}\n",
    "\n",
    "    ensembleQ_number = len(ensembleQ_weight)\n",
    "\n",
    "    ensembleQ_weight_sum = sum(ensembleQ_weight.values())\n",
    "\n",
    "    ensembleQ_indexs = list(ensembleQ.keys())\n",
    "    ensembleQ_indexs.sort(key=sortFunc)\n",
    "\n",
    "    for j in range(0, ensembleQ_number):\n",
    "        Supply[\"q\" + str(j + 1)] = (\n",
    "            ensembleQ_weight[ensembleQ_indexs[j]] / ensembleQ_weight_sum\n",
    "        )\n",
    "\n",
    "    ## load the distance matrix D = [d_ij]\n",
    "    D = {}\n",
    "    for i in range(0, ensembleP_number):\n",
    "        for j in range(0, ensembleQ_number):\n",
    "            ### calculate the GED between two graph representations\n",
    "            GED = unsup.edit_distance(\n",
    "                ensembleP[ensembleP_indexs[i]],\n",
    "                ensembleQ[ensembleQ_indexs[j]],\n",
    "                node_attr=\"h\",\n",
    "                indel_mul=1,\n",
    "                sub_mul=1,\n",
    "            )\n",
    "\n",
    "            ### calculate the number of nodes in graph N_i\n",
    "            N_i = ensembleP[ensembleP_indexs[i]].number_of_nodes()\n",
    "\n",
    "            ### calculate the number of nodes in graph N_j\n",
    "            N_j = ensembleQ[ensembleQ_indexs[j]].number_of_nodes()\n",
    "\n",
    "            D[(\"p\" + str(i + 1), \"q\" + str(j + 1))] = 1 - np.exp(\n",
    "                -alpha * GED / (0.5 * (N_i + N_j))\n",
    "            )\n",
    "\n",
    "    # The following are optimization steps\n",
    "    ## Step 0: Create an instance of the model\n",
    "    model = ConcreteModel()\n",
    "    model.dual = Suffix(direction=Suffix.IMPORT)\n",
    "\n",
    "    ## Step 1: Define index sets\n",
    "    CUS = list(Demand.keys())\n",
    "    SRC = list(Supply.keys())\n",
    "\n",
    "    ## Step 2: Define the decision\n",
    "    model.x = Var(CUS, SRC, domain=NonNegativeReals)\n",
    "\n",
    "    ## Step 3: Define the objective\n",
    "    model.Cost = Objective(\n",
    "        expr=sum([D[c, s] * model.x[c, s] for c in CUS for s in SRC]), sense=minimize\n",
    "    )\n",
    "\n",
    "    ## Step 4: Add constraints\n",
    "    model.src = ConstraintList()\n",
    "    for s in SRC:\n",
    "        model.src.add(sum([model.x[c, s] for c in CUS]) <= Supply[s])\n",
    "\n",
    "    model.dmd = ConstraintList()\n",
    "    for c in CUS:\n",
    "        model.dmd.add(sum([model.x[c, s] for s in SRC]) == Demand[c])\n",
    "\n",
    "    ## Step 5: Call the cbc solver to solve this EMD problem\n",
    "    results = SolverFactory(\"cbc\").solve(model)\n",
    "\n",
    "    ## Step 6: Return EMD result\n",
    "    if \"ok\" == str(results.Solver.status):\n",
    "        if print_details == True:\n",
    "            for s in SRC:\n",
    "                for c in CUS:\n",
    "                    if model.x[c, s]() > 0:\n",
    "                        print(\n",
    "                            \"Ship from \",\n",
    "                            s,\n",
    "                            \" to \",\n",
    "                            c,\n",
    "                            \":\",\n",
    "                            model.x[c, s](),\n",
    "                            \"*\",\n",
    "                            D[c, s],\n",
    "                        )\n",
    "        return 1 - model.Cost()\n",
    "\n",
    "    else:\n",
    "        print(\"No Valid Solution Found\")\n",
    "        return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lpFPLOC7d3DI"
   },
   "source": [
    "# Calculation of $S(P,Q)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "id": "ziOxwdOrwerL"
   },
   "outputs": [],
   "source": [
    "Similarity_Score = Similarity_Score_EMD_Calculation(\n",
    "    ensembleP=Ensemble_P,\n",
    "    ensembleP_weight=Ensemble_P_weight,\n",
    "    ensembleQ=Ensemble_Q,\n",
    "    ensembleQ_weight=Ensemble_Q_weight,\n",
    "    alpha=1,\n",
    "    print_details=False,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_Z2phPpt1hr5",
    "outputId": "1cad6f06-264e-4de8-d839-538449f70722"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity Score between P and Q = 0.72\n"
     ]
    }
   ],
   "source": [
    "print(\"Similarity Score between P and Q = %.2f\" % Similarity_Score)"
   ]
  }
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