GutCP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GutCP (Gut Cross-feeding Predictor) - Ecology-guided prediction of cross-feeding interactions in the human gut microbiome\n",
    "The predictive power of the trophic model heavily on a manually curated metabolic interaction network [NJS16](https://www.nature.com/articles/ncomms15393). However, the manually curated network derived from the past experiments and literature is incomplete because not all exchange reactions were revealed by experiments. The number of links in this network is only roughly one-sixth of that in a potentially over-complete cross-feeding network obtained from the genomic annotation. Here, we proposed an ecologically guided machine learning algorithm to cleverly discover metabolite exchange reactions that help to improve the predictions of the trophic level. Later, we demonstrated that the prevalent exchange reactions statistically discovered from many independent simulations are supported by the genomic evidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from collections import Counter\n",
    "from scipy.stats import sem\n",
    "\n",
    "#%% Plot Tong's default setting\n",
    "SMALL_SIZE = 12\n",
    "MEDIUM_SIZE = 15\n",
    "BIGGER_SIZE = 15\n",
    "\n",
    "plt.rc('font', size=SMALL_SIZE, family='sans-serif', serif='Arial')          # controls default text sizes\n",
    "plt.rc('axes', titlesize=BIGGER_SIZE)     # fontsize of the axes title\n",
    "plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels\n",
    "plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize\n",
    "plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "plt.rc('text')\n",
    "\n",
    "from matplotlib.ticker import MaxNLocator\n",
    "my_locator = MaxNLocator(6)\n",
    "\n",
    "color_list = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd']\n",
    "\n",
    "def figure_size_setting(WIDTH):\n",
    "    #WIDTH = 700.0  # the number latex spits out\n",
    "    FACTOR = 0.8  # the fraction of the width you'd like the figure to occupy\n",
    "    fig_width_pt  = WIDTH * FACTOR\n",
    "    inches_per_pt = 1.0 / 72.27\n",
    "    golden_ratio  = (np.sqrt(5) - 1.0) / 2.0  # because it looks good\n",
    "    fig_width_in  = fig_width_pt * inches_per_pt  # figure width in inches\n",
    "    fig_height_in = fig_width_in * golden_ratio   # figure height in inches\n",
    "    fig_dims    = [fig_width_in, fig_height_in] # fig dims as a list\n",
    "    return fig_dims"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "########### import the pickled file containing all processed data which are useful for simulations (the processing is\n",
    "########### done in \"Trophic_model_for_gut_data_processing.ipynb\")\n",
    "import pickle\n",
    "pickle_in = open(\"Chia_network.pickle\",\"rb\")\n",
    "net, i_selfish, i_intake, names = pickle.load(pickle_in)\n",
    "\n",
    "pickle_in = open(\"data.pickle\",\"rb\")\n",
    "metagenome_ID, metagenome, metabolome_ID, metabolome = pickle.load(pickle_in)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trophic model for the gut microbiome\n",
    "The human gut microbial community is complex because of 3 reasons: (1) many microbial species ($\\approx$ 570); (2) many metabolites involved ($\\approx$ 244); and (3) many microbe-metabolite interactions/links (>4400). Of all types of microbe-metabolite interactions/links, the cross-feeding makes the system more complicated to interpret. Previously, a literature-curated interspecies network of the human gut microbiota, called [NJS16](https://www.nature.com/articles/ncomms15393) is reported. This is an extensive data resource composed of ∼570 microbial species and 3 human cell types metabolically interacting through >4,400 small-molecule transport and macromolecule degradation events.\n",
    "\n",
    "Here, we devoted to building a Consumer-Resource model (CRM) with trophic levels posted in the paper \"[an evidence for a multi-level trophic organization of the human gut microbiome](https://www.biorxiv.org/content/10.1101/603365v1.full-text)\". The model is devoted to studying the complex microbe-metabolite network in human guts.\n",
    "\n",
    "In concise, a trophic level is considered as one round of carbon processing and is composed of two processes: resource allocation to microbes and the following resource/byproduct generation by microbes. The simulation is stopped after several trophic levels because the residence time of resources in the human gut is assumed to be finite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create maps of microbes and metabolites to their reduced matrix forms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#i_nonzero_microbes = net['microbes_ID'].unique()\n",
    "#i_nonzero_microbes = np.sort(i_nonzero_microbes)\n",
    "i_nonzero_microbes = metagenome_ID.values.copy()\n",
    "i_nonzero_metabolites = net['metabolites_ID'].unique()\n",
    "i_nonzero_metabolites = np.sort(i_nonzero_metabolites)\n",
    "\n",
    "\n",
    "df_metabolites = pd.DataFrame.from_dict({'oldID': i_nonzero_metabolites, 'newID':list(range(len(i_nonzero_metabolites)))})\n",
    "df_metabolites.set_index('oldID', inplace=True)\n",
    "df_microbes = pd.DataFrame.from_dict({'oldID': i_nonzero_microbes, 'newID':list(range(len(i_nonzero_microbes)))})\n",
    "df_microbes.set_index('oldID', inplace=True)\n",
    "\n",
    "\n",
    "outgoingNodes = df_metabolites.reindex(net['metabolites_ID'].values).values.flatten()\n",
    "ingoingNodesTemp = df_microbes.reindex(net['microbes_ID'].values).values.flatten()\n",
    "edge_types = net.iloc[~np.isnan(ingoingNodesTemp),2].values\n",
    "outgoingNodes = outgoingNodes[~np.isnan(ingoingNodesTemp)]\n",
    "ingoingNodes = ingoingNodesTemp[~np.isnan(ingoingNodesTemp)].astype(int)\n",
    "\n",
    "net_reduced = pd.DataFrame.from_dict({'metabolites': outgoingNodes, 'microbes':ingoingNodes, 'edgeType':edge_types})\n",
    "net = net_reduced.copy()\n",
    "net_temp = net.copy()\n",
    "net['edgeType'][net['edgeType']==5] = 2\n",
    "net_temp['edgeType'][net_temp['edgeType']==5] = 3\n",
    "net = net.append(net_temp).drop_duplicates()\n",
    "net_ori = net.copy()\n",
    "\n",
    "metagenome_ID_reduced = df_microbes.reindex(metagenome_ID).values.flatten()\n",
    "metagenome_ID = metagenome_ID_reduced[~np.isnan(metagenome_ID_reduced)].astype(int)\n",
    "\n",
    "metabolome_ID_reduced = df_metabolites.reindex(metabolome_ID).values.flatten()\n",
    "metabolome_ID = metabolome_ID_reduced[~np.isnan(metabolome_ID_reduced)].astype(int)\n",
    "\n",
    "\n",
    "i_selfish_reduced = df_microbes.reindex(i_selfish).values.flatten()\n",
    "i_selfish = i_selfish_reduced[~np.isnan(i_selfish_reduced)].astype(int)\n",
    "\n",
    "i_intake_reduced = df_metabolites.loc[i_intake].values.flatten()\n",
    "i_intake = i_intake_reduced[~np.isnan(i_intake_reduced)].astype(int)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1075"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(net_ori)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the simulation with reduced matrix forms for one individual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 3.150813280364595\n",
      "            Iterations: 16\n",
      "            Function evaluations: 354\n",
      "            Gradient evaluations: 16\n",
      "     fun: 3.150813280364595\n",
      "     jac: array([ 0.        ,  0.00985742,  0.00507501,  0.00553936,  0.06272534,\n",
      "        0.01278245,  0.03304654,  0.00766429, -0.00600919,  0.01459843,\n",
      "        0.00206965,  0.01478863,  0.12712216,  0.08330959, -0.00155345,\n",
      "        0.01078972,  0.08886304,  0.02255568, -0.01123685,  0.01378873])\n",
      " message: 'Optimization terminated successfully.'\n",
      "    nfev: 354\n",
      "     nit: 16\n",
      "    njev: 16\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([5.00000000e-02, 1.10194613e-01, 4.62982166e+00, 3.86162425e-01,\n",
      "       0.00000000e+00, 1.47368555e-16, 0.00000000e+00, 7.21666785e-02,\n",
      "       3.79356843e-02, 5.02151329e-17, 4.71539162e-01, 1.65348559e-02,\n",
      "       0.00000000e+00, 4.01310415e-16, 3.52982093e-01, 2.22130587e-01,\n",
      "       0.00000000e+00, 0.00000000e+00, 2.19499696e-01, 0.00000000e+00])\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "(0.8765075672949567, 1.1692577742998602e-12)\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "(0.750209548742103, 0.00021599588533741842)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+64SxnxKwGPgxcL6Z/amFtjmOU0E3iQ+kXwd0GMEd6/lmdmcL7XEcpwbdJj6QogsWndD/CDivqOIjabyk2yStlDQlb3scJ2u6UXwghQDFbRYnApu33pwBsxp4H3Bh3oY4TtZ0q/hA+kHo24HdW2nIYDCzl8xsed52OE7WdLP4QHoB+iJwjKTjJO0oaYyk0cmU9oaxjj5JayUtqCjbQtLFklZJ6pd0eBPfxXG6im4XH0gvQL8DXg98hzAL9hzwfEVKy1LgFMK4UiVnAS8Swv7MJKy2Lju/30bSTVXSNk3c2ykAlc7Szz333LxNKhxDQXwg/SzYUYBlcUMzuwhA0lRg+3J+3OrxIWBKjDl/k6RLCS5AZpvZY8C+Wdjg5Ec1Z+mzZs0CKPy+pXYxVMQHCP5C8kiEVtCCxPFbgTUV5xwPXJayvisJratbgCNrnDML6AP6enp6zGk/pVLJCP+ZbZBKpVLephWCpUuX2i677GJjxoyxG264IW9zBg3QZ3V+t82uhH6DpCMkfbnc9ZE0WdJmg5NBAMYSfE8nWQGkqtvM3mtm25nZ3ma2oMY5vWY21cymbrWVexbJg1qOs2rlt4oidgPLLZ+HHnqIsWPHMm3atMLY1jLqqZO92nIYS1iIuB5YC6wDdotlFwCnpamnos5qLaDVFed8gZQtoCbuOx3onTx5cjYS7zRFEVpACxcutNGjR29w/9GjR9vChQvbZkMl5ZbPyJEjbeTIkYWybTCQUQvoDODtBHesm7FhXLArgXc3pXrVeQAYISm5r+wtZBwK2nw3fK7Mnz+f0aM3nDRtt+Osav6TV69ezZw5c9pmQ5LkmM/mm2/O2rUbejjO07aWU0+d7NVWw5PAzPh5OKElVG4B/T3wfJp64vkjgFHAfwDnxM8jYtn5wHnAGGAfQhfsjWnrTnl/bwHlzMKFC61UKpkkK5VKbf/fXVLVVhjQdlsqx3xq2SaprXZlBQ1aQGl/tKuAd1t1AXo/8GyaeuL586o84HmxbAvgkni/JcDhaettNu2+++4ZP2qnU6jVDaTN3Z1qA85F6KJmSVYCtAj4qVUXoJ8AV6appwjJW0BOtTGgdv/Ya812FXF8ajBkJUD7Ai8A1xBiw68D5sYu1BpgjzT1FCl5C2hos3DhwpoC1OruTqOp9ry7qFnSSIAUzmmMpH2ArwNvi60gA24FvmRmN6eqpEBMnTrV+vr68jbDyZFJkyZVDWVTKpV4+OGHW3LPIbXIEJB0h5lNrVXejE/om81sP2AcYQXzZma2T6eJj8eGd8q0e0ZuqIlPGpr2CW1ma8xsKTBS0q7RX1DHYD4N70RmzpxJb28vpVKp5aFsXHyqk6oLJukrwEgzmx2PDwR+AYwmRMR4l5llul6n1XgXzGkXQ1l8suqCzQTuSxyfDtxEWKtzH2FNT0fgXTCnnQxl8UlDWgHaDvgLgKS/IaxQPtnMbiWskn5ba8zLHu+COe3CxacxaQXoeaD8iz0QeMbMbovHLxC6Yo7jRFx80pFWgK4HZkt6H8FFxi8SZTsDj2RtmOOUKeLO9Xq4+DRBvUVC5QS8DriO0BK6Edg2UXYL8P009RQh4SuhO4pOWxncbf58BgtZLUSshaRxwAtm9uKgKmozPgvWGeSxWHCgeMtnYxrNgqV1yZqscHtgW2CZmT1qZs8NxkDHqUdRHJg1wsVnYKReiCjpGEmPAP2ELRj9kh6VdGzLrHOGPD09PU3l54GLz8BJJUCSTgLOBK4iBADcI/69CvhOLHeczCmCA7N6uPgMknoDRPbqwO3jwNdqlJ0CPJ6mniIkfBC64yjq7nAfcG4MGbnjeA44qEbZQcCKNPUUKXW7O46i/mi7BRefdDQSoLRjQJcAh9Yo+xBw+YCaX05LKMfe6u/vx8xeib1V9PUznYJ3u7Kj5jS8pPcmDscDpwJ3E8ToCWAi8EHgjQSfQOe11tRs6eZp+E6auu40XHyao9E0fD0BWk9Y+KWqJ2yImdnwgZmYD90sQMOGDaPae5XE+vXrc7CoO3DxaZ7BrAPaoQX2OG2gp6enaguoSFPXnYaLT2uoKUBmtvG/YKcjmD9//gbx16FYU9edhotP60i9ElrSCMKA876E8DlPE/aFXWRmL7fGvOyRNB2YPnny5LxNaRllj35z5sxhyZIl9PT0MH/+/JZ4+ut2XHxaS1qPiBOBXwNvBh4mrAvaGpgE3EXwiLi8ZVa2gG4eA3KywcVn8GTlEfEMYAKwl5ntaGZ7m9mOwF4x/4zBm+o4xcHFpz2kFaD3AieY2e3JzHh8ImFbhuN0BS4+7SOtAI0k+AKqxvPAJtmY4zj50uni02nO29IK0K3ACZLGJDPj8Qmx3HE6mm4Qn05bAZ92EHpX4DeEhYm/JgxCTwQOJixUPMDM7mqhnQ2RtDdhLOpFYCnwcTN7qdb5PgjtJOl08YFiroDPZBDazO4EdgJ6ga0IG1AnAt8DdspbfCL9wIFmNo0QweOQnO1xOoRuEB/oHOdtSVKvAzKzJ4HZLbRlUFiI1lrmZcD3HDgN6Rbxgc5cAd90aOYskHScpD5JayUtqCjbQtLFklZJ6pd0eJN17wC8B9+h7zSgm8QHiu+8rRpN+4TOiKUER2YHA5tWlJ1FGMfZGtgVuELSXWZ2j6RtgAur1DfDzB6LDvLPBo6wDnOS77SXbhMf6MwV8IOOijGom0unANub2ZHxeAzwDDDFzB6IeecAf7UYl75OXSMI8cpON7PrGt3bB6GHLt0oPkUlq5XQ7WJnYF1ZfCJ3EXwONeKjhJXZJ0laJOkjlSdImhW7fn3Ll3fUzhEnI1x8ikWqLpik4Wa2rtXGAGOBFRV5K4DNGl1oZucA5zQ4p5cwk8fUqVPza/o5ueDiUzzStoD+KulUSX/XUmtgJTCuIm8ctVdhN42k6ZJ6V6yo1Dmnm3HxKSZpBej7wAzgbkm/i12ZSqHIggeAEZJ2SuS9BbgnqxuY2WVmNmv8+PFZVek0QR5bBVx8Ckw9j/WVCTgQ+AmhpbIKOBd4ZzN1xHpGAKOA/yB0m0YBI2LZ+cB5wBhgH0IX7I3N3qPOvT0sT07kEefdo1fkC1mE5dnoojBWcxTQB6wj+AiaB2yX8vp5yX+EMc2LZVsQHN+vApYAhw/Exkap28PyFJFSqVT5zg2wUqnUkvu5+ORPIwEa0DS8pAOAIwndshcIEVL/PorHLDNb2HSlbSLhEfHoxYsX523OkKKdzvK921UMMpuGl1SSdLKkPwPXAtsSWkHbmdkRQIkwVvTNQdrcUszHgHKjXXHeXXw6h7Sx4a8D/gx8kjBms6OZHWxmF1hccWxhmv6nhBXMhcVnwfKjHVsFXHw6i7QtoCcJXhF3MLN5Vjtixp0UPJyPt4DyY+bMmfT29jJhwoRX8jbdtHInzsBx8ek8Ui1ENLPDUp73EsEthuPUZM2aNa98fuqpp5g1axbAoPYsufh0JjVbQJLe0Exqp9FDhU5zr5mGOXPmbBCvDGD16tXMmTNnwHW6+HQwtabHCP501qVI6wn7tzKfKm9FokPWAeWxZqYdSKo6FS9pQPX5VHuxYaDT8JKmNSlk1zdzft4UfTd8Ed1rZkGW38tbPsVnwLHhO01Quo1OdK+ZhqzCRrv4dAdFc8fRcjplGr5da2baTXkmrFQqIYlSqURvb29TA9AuPt1DvS7YckL/PBVmNjEro9pB0btg5RArlS2FZn+s3YaLT2cx4C4YwTWq+8zJiU50r9lqXHy6kHoj1N2cfDNqZzHY2a6FCxdaqVQySVYqlTp+NrFToMEsWF5O6R0nNYNt+VR2Z8sRQ2Fwix+dwZN6N3yMPPopgt/mUZXlZrZntqa1Bt8N31lk0e3q1iUNnUAmu+ElHQTcAGwP7AssJzglewswAbh78Ka2B/O9YB3DQMSn2urxbl3S0BXU65+VE3ALcBownLDyebeYXwLuI8Rhz31cp5nkY0DFZiBjPrVWj0+YMKGtjtCcV6HBGFDadUBvIDgdWx9f3pgoXv0E74YD38jjOBUMtNtVa58Z0HERQ4cKaQXoBWBYVLRlwOsTZc8RumaOM2gGM+ZTq0v19NNPD3rxYxZ04+biQVOveVROwK+B4+Lns4H7gYOAaQS/0LemqadIybtgxWOwU+3t9jndDN26ubgRZOGUnuCM7DPx8+uA3xO6Y+sJjuN3T1NPkZILULHIYld7kX/kRRbHVpKJAG10EQjYCXgzsMlA6sgr0SHuOIYSWbrUKOqCw6zdkHQKjQQo1TogSScBPzSzpVXKtgWONrOvNqyoQBR9L9hQYahsrxiqa5GyiopxMrUHmreL5Y7TFENFfKA9Dvk7kbQCJGpvTN0eeCYbc5yhwlASH8jGDUk3Us8dxyeAT8TDacAfCFPuSUYBbwJ+bWYfapWRrcC7YPkx1MRnKDMYdxyrgafK9RBitD9dcc6LhAWK/zUYI52hg4uPk6SeS9afAz8HkPRj4Gtm9pd2GdYMkrYGLgZeIjjKn2lmy/K1yqnExcepJNUYkJl9sqjiE3kS2NfMpgE/IezadwqEi49TjdT+gCRNBQ4lDDpXc8eRKnhhK7AQFrrMZsA9ednibIyLj1OLtO44jgFuA/6JsA9sqyopFZKOk9Qnaa2kBRVlW0i6WNIqSf2SDm+i3l0l/Q44jrBS2ykALj5OPdK2gI4HfgR82sxeHuQ9lwKnAAcDlYHBzyIMbG8N7ApcIekuM7tH0jbAhVXqm2Fmj5nZncBekg4DTgQ+PUg7nUHi4uM0Iq0ATQTOy0B8MLOL4JUu3SuLGyWNAT4ETDGzlcBNki4FjgBmm9ljBGdoGyFppJmtjYcrCDN4To64+DhpSCtAVwF7Ade20JadCSGeH0jk3UVYg9SI3SR9gzAD9gJwVLWTJM0CZkHnx9cqMi4+TlrSCtBZQK+k1wBXA89WnmBm9w7SlrGE1kuSFYRB5bqY2S3A/inO6wV6ISxEHICNTgNcfJxmSCtAv4l/TwZOqigrb9MYPkhbVgLjKvLGAc8Pst4NSDilz7JaBxcfp3nSCtDft9SKwAPACEk7mVk5XMVbyHhK3cwuAy6bOnXq0VnWO9Rx8XEGQioBMrPrs7qhpBHxvsOB4ZJGAS+b2SpJFwFflfRPhFmwQ4C3Z3XveH9vAWWMi48zUNLuhgdA0nsk/ZukXkk9MW9/Sds1Uc1cYA0wG/hY/Dw3lh1LmJp/AjgPOMbMMm8BmYflyQwXH2cwpHVItjVwKbA78DCwA7CHmf0+7hN7wcyOaaWhWeGBCbPDxcdpRFYOyb5LmKXaJSYlyq4B3jFgC9uMt4CywcXHyYK0g9DvBj5hZg9KqpztepTgqN4ZIrj4OFnRzBjQuhr5WxLGcToCSdMl9a5YUbnkyEmDi4+TJWkF6EbgXypaP+XBo6OA6zK1qoUMhS5YqwLgufg4WZO2C3YCcBNwN8HxlwFHS5oCTAHe1hrznGY599xzmTVr1ishifv7+5k1axbAoPwPu/g4rSDVLBiApNcT4sC/g9DtepqwN2xeYuFg4en2WbBWhH9x8XEGSqNZsNQC1G10q1P6YcOGUe2dSmL9+vVN1+fi4wyGrKbhnQ6h1i7/gez+d/FxWk1qAZJ0mKTzJN0g6bbK1EojnfRkFQDPxcdpB6kGoSV9HfgScDvwIMFrYUfS7XvBygPNc+bMYcmSJfT09DB//vymBqBdfJy2US9wfDkR9madmObcTkm77767ORuzdOlS22WXXWzMmDF2ww031Dxv4cKFViqVTJKVSiVbuHBhG610OgWgz+r8DtN2wV4C7miVCDrFIG3LpzzV39/fj5m9MtWf1XqjWrRqfZOTI/XUqZwI3a8LiLNm3ZC8BbQhaVs+ZmalUskIa8E2SKVSqWX2LVy40EaPHr3B/UaPHu0tr4JDgxZQM+uATgOmA9ezsUtWM7MTBi+H7aNbp+EHQrNjPllP9aehFeubnNYzmNjwyUpmAp8H1hN2xVcOQhthtXTh6fZB6GYZyIBzT09PVTFopaP/JUuWNJXvdAZpx4C+DvwMmGBmrzOzHSrSji20MVNsCOwFS8tAZ7uymupvhizXNznFIa0AjQN+ZGaZOoh38mMwU+0zZ86kt7eXUqmEJEqlEr29vYPaa9aIPETPaQP1BojKiRAV9ZQ055mxGb0AAA6RSURBVHZKGsqD0M0MOBcJn/rvPMhiEFrSRwjdsGsJrjeqxQW7MlNlbDFDdRDaFxk67SSTQWiCg3gIvn+qRR3NIi6Y02JcfJyikVaAdmipFU7LcfFxikjauGAbz7l2KENxGt7FxykqNWfBJI1Ofm6U2mPu4LEhNg3v4uMUmXotoOcl7W1mtxHitjcarfYxoILh4uMUnXoCdBTw5/j5k22wxckQFx+nE6gpQGZ2NoCk1xB8AD1kZkvbZZgzcFx8nE4hzUrodYS1P3/XYlucDFi2bBlTp07l/vvvZ9WqVRxxxBHutsIpLA0FyMzWA4uBrVtvzuCQ9FFJy/O2Iy/K4rN06dJXdqu3y1eP4wyEtHvB5gAnSXpTK40ZDJKGATOAR/K2JQ/K3a5ly5ZtVLZ69WrmzJmTg1WOU5+0CxHnAhOAOyX9FXicilkxM9szY9ua5XDgQuALOdvRdpJjPrW21rjbCqeIpG0B3Q1cDvyEsB/sbuCeipQKScdJ6pO0VtKCirItJF0saZWkfkmHp6xzOHAYwWXIkKJywLlUKlU9z91WOEUk7UroLKfhlwKnAAcDm1aUnUVwdrY1sCtwhaS7zOweSdsQWjiVzIh1XWBm6yVlaGqxqTbbNX/+/A1CM4O7rXAKTL2t8pUJEPA3wNuBMc1cW6WuU4AFieMxBPHZOZF3DvD1FHV9A/g18EtgBfCdRtd0ujuOei413G2FUxRo4I6jGcE4ltB6WU+Ymt8t5l8EfD5tPYn6KgXorcCainOOBy5rst6aXxiYBfQBfT09Pdk+6TbSqf58nKFHIwFKNQYk6YvAGcAPgANjS6jMIuAjaeppwFhC6yXJCmCzZiqxOr5HzKzXzKaa2dStttpqACbmjy8ydLqJtLNgnwFOMrNT44BvkvuBnTOwZSXB9WuScUCmbmA7eTe8i4/TbaSdBduG2oEJ1wOjMrDlAWCEpJ0SeW+hiRm2NFiH7oZ38XG6kbQC9CAwrUbZ/sC9aW8oaYSkUYTd88MljZI0wsxWEcaTvippjKR9gEMIA9GZIWm6pN4VKyp7e8XFxcfpVtIK0LeB2ZLmAuUWykRJnwL+H/CtJu45F1gDzAY+Fj/PjWXHEqbmnyC4gT3GzIZ0C8jFx+lmmomM+kXgJGA0rw5Crwa+YmbfbI152ZMYAzp68eLFeZtTFxcfp9Np5JQ+tQDFyjYjrAGaADwN3GJmndOXSVD0qBguPk43kFVUDAAsBCb81aCtcuri4uMMFVILkKSJhPjwewLbAsuA3xFWHT/eGvOyp+jT8C4+zlAi7ULEfQg+gf4ZeJKwIfVJ4NPA4ljeERR5ENrFxxlqpG0BnUlYBzQ9TpcDIGksYZf8d4Hdsjdv6ODi4wxF0k7D7wKcnhQfADNbCZxGB7lrLeI6IBcfZ6iSVoDuJayGrsa2wH3ZmNN6itYFc/FxhjJpu2D/ApwjaSVwiZmtlTQS+CBhQeHHW2VgN+Pi4wx10grQLwgLEH8KEIVobCx7Abg46QjMzCZmaGNX4uLjOOkF6CwaR0btCIowDe/i4ziBplZCdxN5rYR28XGGEo1WQqddB1R3lkvS+5o1bCji4uM4G5J2Fuz3ko5Xhcd3SZtJ+jFwafamdRcuPo6zMWkFaC7wVeAGSTsCSDqIEJ7nXcD01piXPXmsA3LxcZzqpBIgMzsd2B0YCfyfpIsJEShuBKaY2ZWtMzFb2r0OyMXHcWqTtgWEmf2JsOZnOMFT4R+AY83smRbZ1vG4+DhOfdIOQo+UdAYh9tZlwIeALYG7Y1fMqcDFx3Eak7YFdCdwBPAxMzvMzC4G3gRcA/xS0n+3ysBOxMXHcdLRjFP6N5nZ+eUMM3vezI4idMfe3wrjOhEXH8dJT9rY8DVnuczscklTsjOpc3HxcZzmSD0IDSDpDZKOkPRlSdvEvMnAyy2xrgW0ahrexcdxmiftIPRYSRcAfwR+CHwN2C4W/ztwcmvMy55WTMO7+DjOwEjbAjqDEA3jnYRY7ckV0VcC787Yro7BxcdxBk7a3fCHAp8zs99UiQ3fD5SyNaszcPFxnMGRtgW0KfBUjbLNgHXZmNM5uPg4zuBJK0C3U9vr4Qzgt9mY0xm4+DhONqTtgs0FrpF0DfBzgnOy90r6V4IA7d8i+1IhaRJBJMtx5D9sZstbcS8XH8fJjrSbUW8C3kHYjHomYRD6K8COwDvN7PaWWZie683sgJhcfBynA0gdGdXMbgb2k7Qp8FrgWTNb3TLLmmcfSTcSdujPsYxdPbr4OE72NLUQEcDM1pjZ0oGKj6TjJPVJWitpQUXZFpIulrRKUr+kw1NWuwyYTOgKTiTM2mWGi4/jtIbULaAMWQqcAhxMmF1LchbwIrA1sCtwhaS7zOyeuPL6wir1zTCzx4C1AJIuAt4G/G8Wxrr4OE7raLsAmdlFAJKmAtuX8yWNIbj5mBIjrt4k6VLCLvzZUWT2rVanpHFm9lw83A/4Uxa2uvg4TmtpugvWQnYG1pnZA4m8u4A3prh2mqQ74hjQ64jxyyqRNCt2//qWL288Tn322We7+DhOC8mjC1aLsUDlDtEVhIWOdTGzywiO0hqd1wv0QgjL0+j8E044gRkzZpBnDDHH6WaK1AJaCYyryBsHPJ/lTZrZDS/JxcdxWkiRBOgBYISknRJ5b+HVxYWZ0G6n9I7j1KbtAiRphKRRBOf2wyWNkjTCzFYBFwFflTRG0j4Eb4vnZHz/toflcRynOnm0gOYCawgRNj4WP8+NZccSpuafAM4DjjEzbwE5Tpcy5GLDS5oOTJ88efLRixcvztscx+lqMokN3014C8hxisOQEyDHcYrDkBMgH4R2nOIw5MaAykhaTnAn2+lsCTyZtxEdij+7gZP22ZXMbKtahUNWgLoFSX31Bvmc2vizGzhZPbsh1wVzHKc4uAA5jpMbLkCdT2/eBnQw/uwGTibPzseAHMfJDW8BOY6TGy5AjuPkhgvQEEHSR+PaJyclkvaWdIuk6yWdJ+k1edtUdCTNl3SjpAsljW50vgvQEEDSMEIAyUfytqXD6AcONLNpwF8I7mGcGkiaArzezPYDrgGOanSNC9DQ4HBCRJH1eRvSScTwU2vi4cv482vEfsBV8fNV1AgikcQFqEC0ImaapOHAYcDPWmByYWhRvLny9TsA7wEuz9DkwjKIZ/laXvXrvgLYotG9iuSU3mlBzLRY1wVmtl5S6yzPn5bEm5M0DjgbOMLMXmyd+YViQM8SeAYo+7kZDzzd6Ea+DqiASDoF2N7MjozHYwgvd0o5bJGkc4C/mtnsBnV9A3grofuwN3C2mX22hebnSsbPbgTwC+B0M7uupYYXkGafpaQ3ASea2eGSZgEjzey79e7hXbDOYMAx08zsBDN7l5m9G1jczeJTg8HEm/sosBdwkqRFkj7SCgM7iLrP0sz+CPTH+HwHAz9qVKF3wTqDAcdMSzJEd34PJt7cOWQcFKHDafgszezEZir0FlBn0JaYaV2KP7vsyPxZugB1Bm2Jmdal+LPLjsyfpQtQgcg7Zlon488uO9r6LM3MU0ESMA+wijQvlm0BXAKsApYAh+dtb5GSP7vOfJY+De84Tm54F8xxnNxwAXIcJzdcgBzHyQ0XIMdxcsMFyHGc3HABchwnN1yAHMfJDRcgp5BIGivJJB2ZyHtY0mlN1LGnpHkZ29VX6aTLGTguQE4n8UHgO02cvydwcotscTLA3XE4LUHSpvaqP+VMMLM/ZFmfkz/eAnIaImlB7Hp8QNJ9kl6QdJOkNyTOMUn/T9K3Y/ifPybKDonXvyDpMUmnVoa4kfQhSQ9IWiPpBmCXKnZs1AWTtL+k30haKWlFdBz21th1+27CNpO0KHHdFElXSHo+pp9H96xUnHNztPtPkt4/qAfpbIQLkJOWEnAG8DVClI3xwK/irukyXwS2BY4APgsg6TDCDurbgPcDXwFmAf9RvkjSbgSn+XcBhwKXAhc0MkjSAcC1wEvAJ4CPADcCrwOuAE6Pp+4d07HxusnAzcCoaOuRBK9+lyk6zpa0KfArghOuwwk+kr8N9DSyy2mCvHfeeip+AhYQdkS/PZFXIoSq+XQ8NuAPFdeJEFvrxxX5RwFrgAnx+ALgXqKP8pg3J9Z5ZCLvYeC0xPEtQF/yuor7HBf+iW+Ufw5wP7BJIm8nYB3wvnh8LEHYtk+cs0+0aUHe76RbkreAnLQ8YWa/LR+YWT9wB2Ggt8wVFdfsTGgxXBB9zIyIjt6vI7Q+psTz9gQutfgrj1xUz5joIH0vgpP9Zl06vBO4GFifsOkhgsCV3dbuCdxhZo+WLzKzm4EnmryXUwcXICct1X54TxC6XGUeryjfMv69ktCaKKeHYv7fxL/bVKm/0Q/9tYQW1rIG51VjS+CECpteAnZsYFMau5wm8FkwJy0Ta+Ql3XFWtkTKcaFmAdVmsMpC9FiV+qvdL8kzhFBD2zY4rxpPE1pAP6xS9mTCpo0GwlPY5TSBC5CTlomS3l7uhknqAXYDflznmvuBvwKTzOwHdc67HXi/pBMT3alD6xljZqsk/Q74uKQza3TDXoy2jjKzFxL51xK6f3fU6b7dDsyUtH25GxZdkLoAZYgLkJOWJ4FzJP0bYQD5q4TuyIJaF1iIxvqFeN04QrzwFwldnQ8Qoo+uBr4B/I4wVvQ/BHH4VAqbZgPXAFdJ6iW4Cd0b6DOzy4H74nmfk3Qd8JyZ3U9wOXobIarnj+J3ex1wEGGAeRFBWOfGc+YRIoR+jVdbSE4W5D0K7qn4iSAyfYRWyQPAWsI09pTEOQYcV+P69xCmx1cBzwF3Eqa1RyTO+TDwIPACcBOwBw1mwWLeNOAGYDXwLPAbYNdYJuBUQqjh9cCixHW7EEIyP00Q1AeB77PhrNebgd/G73s/QTT78FmwzJL7hHYaEvc+TbGhGdjQaSE+C+Y4Tm64ADmOkxveBXMcJze8BeQ4Tm64ADmOkxsuQI7j5IYLkOM4ueEC5DhObrgAOY6TG/8fSe1KwTWHiGEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "################################# Predict metabolome from individual's metagenome.\n",
    "from numpy import array\n",
    "from scipy.sparse import csr_matrix\n",
    "import numpy.matlib\n",
    "from scipy.optimize import minimize, rosen, rosen_der\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "MAX_ID_microbes = len(i_nonzero_microbes)  # MAX_ID_microbes is the maximum of ID labels for microbes.\n",
    "MAX_ID_metabolites = len(i_nonzero_metabolites)  # MAX_ID_metabolites is the maximum of ID labels for metabolites.\n",
    "\n",
    "def Ain_out(b_real, net):\n",
    "    '''\n",
    "    Ain_out is a function used to create sparse matrices made of metabolites and microbes \n",
    "    where metabolite consumption and production is considered. The matrices created are \"m2b\" and \"b2m\":\n",
    "    (1) m2b is a matrix determines the nutrient splitting among microbes, and\n",
    "    (2) b2m is a matrix determines the byproducts generation.\n",
    "    Both matrices have rows representing bacterial species and columns representing metablolites.\n",
    "    Two matrices are created based on (1) the metabolite consumption and production network which is \n",
    "    encode in \"net\" as a dataframe, and (2) the experimentally measured bacterial abundance \"b_real\".\n",
    "    '''\n",
    "    valid_index = np.where((net['edgeType']==2) | (net['edgeType']==5))[0]\n",
    "    row = net['metabolites'].iloc[valid_index]\n",
    "    col = net['microbes'].iloc[valid_index]\n",
    "    data = np.ones((len(valid_index),))\n",
    "    m2b = csr_matrix( (data,(row,col)), shape=(MAX_ID_metabolites, MAX_ID_microbes)).toarray()#.todense()\n",
    "\n",
    "    valid_index = np.where((net['edgeType']==3) | (net['edgeType']==5))[0]\n",
    "    row = net['metabolites'].iloc[valid_index]\n",
    "    col = net['microbes'].iloc[valid_index]\n",
    "    data = np.ones((len(valid_index),))\n",
    "    b2m = csr_matrix( (data,(row,col)), shape=(MAX_ID_metabolites, MAX_ID_microbes)).toarray()#.todense()\n",
    "\n",
    "    ########## Normalize the b2m by out_degree\n",
    "    out_degree = b2m.sum(0).copy()\n",
    "    out_degree[out_degree==0]=100\n",
    "    b2m = (b2m / out_degree)\n",
    "\n",
    "    ########## Normalize the m2b by proportion of microbial abundance in each individual\n",
    "    b_real_repmat = numpy.matlib.repmat(b_real[np.newaxis,:], MAX_ID_metabolites, 1)\n",
    "    m2b = m2b * b_real_repmat\n",
    "    in_degree = m2b.sum(1)\n",
    "    in_degree[in_degree==0]=100\n",
    "    m2b = m2b / numpy.matlib.repmat(in_degree[:,np.newaxis], 1, MAX_ID_microbes)\n",
    "    m2b = np.float32(m2b)\n",
    "    b2m = np.float32(b2m)\n",
    "    return [m2b, b2m]\n",
    "\n",
    "def m2b_multiple_levels(f, m2b, b2m, numLevels_max):\n",
    "    '''\n",
    "    m2b_multiple_levels is a function used to generate matrices involving the calculation of metabolite \n",
    "    byproducts and microbial biomass after several trophic levels/layers. Those matrices are:\n",
    "    (1) m2m_layer is a conversion matrix from the nutrient intake to the metabolite byproducts at a trophic\n",
    "    level or layer.\n",
    "    (2) m2m_total is a conversion matrix from the nutrient intake to a summation of metabolite byproducts at\n",
    "    all trophic levels or layers.\n",
    "    (3) m2b_total is a conversion matrix from the nutrient intake to a summation of all microbial/bacterial \n",
    "    biomass gain at all trophic levels or layers.\n",
    "    Those matrices are computed based on (1) metabolite consumption matrix \"m2b\", (2) metabolite byproduct\n",
    "    generation matrix \"b2m\", (3) byproduct/leakage fraction \"f\", and (4) number of trophic levels/layers in the \n",
    "    simulation \"numLevels_max\".\n",
    "    '''\n",
    "    m2m_layer = np.zeros((MAX_ID_metabolites, MAX_ID_metabolites, numLevels_max));  \n",
    "    #m2b_total = np.zeros((MAX_ID_metabolites, MAX_ID_microbes));  \n",
    "    m2b_total = np.zeros((MAX_ID_metabolites, MAX_ID_metabolites));  \n",
    "    \n",
    "    f_mul = numpy.matlib.repmat(f, 1, MAX_ID_metabolites)\n",
    "    #s_step =  np.dot(b2m, m2b.T) # s_step is the conversion matrix of each trophic level/layer\n",
    "    s_step =  np.dot(b2m, f_mul*m2b.T) # s_step is the conversion matrix of each trophic level/layer\n",
    "    s_step_ii = np.eye(MAX_ID_metabolites, MAX_ID_metabolites);\n",
    "    #f_mul = numpy.matlib.repmat(f[np.newaxis,:], MAX_ID, 1)#numpy.matlib.repmat(f, 1, MAX_ID)\n",
    "    #f_mul = numpy.matlib.repmat(f, 1, MAX_ID_metabolites)\n",
    "    \n",
    "    for ii in range(numLevels_max):\n",
    "        # m2b_total is a series made of s_step of each layer\n",
    "        #m2b_total = m2b_total + f_mul**(ii) * s_step_ii\n",
    "        #m2m_layer[:,:,ii] = f_mul**(ii) * s_step_ii\n",
    "        m2b_total = m2b_total + s_step_ii\n",
    "        m2m_layer[:,:,ii] = s_step_ii\n",
    "        s_step_ii = np.dot(s_step_ii, s_step);  \n",
    "    m2m_total = m2b_total;\n",
    "    m2b_total = np.dot((1 - f_mul) * m2b.T, m2b_total) # m2b_total has an extra multiplication of m2b and (1-f).\n",
    "    return [m2b_total, m2m_total, m2m_layer]\n",
    "\n",
    "def pred_error(x, b_real, m2b_total, i_intake):\n",
    "    '''\n",
    "    pred_error is a function used to compute the logarithmic error between experimentally measured\n",
    "    metagenome and predicted metagenome computed from the model for a certain nutrient intake. It relies on \n",
    "    (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2b_total: a conversion matrix \n",
    "    from thenutrient intake to the total biomass, and (4) b_real: experimentally measured metagenome. The \n",
    "    first three is used to compute the metagenome predicted by the model \"ba_pred\" and compare it with the \n",
    "    experimentally measured metagenome \"b_real\".\n",
    "    '''\n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = x;\n",
    "    \n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "    pred_error = (np.log10(ba_pred + 1e-6) - np.log10(b_real +1e-6)) / np.log10(b_real +1e-6);\n",
    "    pred_error = np.sqrt(np.dot(pred_error, pred_error.T)) #np.sqrt(np.sum(pred_error**2))\n",
    "    return pred_error\n",
    "\n",
    "def calc_metabolome(x, m2m_layer, numLevels_max, i_intake):\n",
    "    '''\n",
    "    calc_metabolome is a function used to calculate the metabolome from the fitted nutrient intake from the\n",
    "    model. It relies on (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2m_layer: \n",
    "    a conversion matrix from the nutrient intake to the metabolite byproducts at a trophic level or layer, \n",
    "    and (4) numLevels_max: the number of trophic levels/layers in the model. The metabolome in the model is \n",
    "    assumed to be composed of two parts: (1) met_levels: all metabolites in the final trophic level/layer \n",
    "    (which is considered to be reaching the end of the gut because of the finite gut length and gut motility.),\n",
    "    and (2) met_leftover_levels: all unusable metabolites from all previous trophic levels/layers. \n",
    "    '''\n",
    "    i_unused = np.where(np.sum(m2b.T,0) == 0)[0]\n",
    "    met_levels = np.zeros((MAX_ID_metabolites, numLevels_max));  \n",
    "    met_leftover_levels = np.zeros((MAX_ID_metabolites, numLevels_max));\n",
    "    \n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = x;\n",
    "    \n",
    "    for ii in range(numLevels_max):\n",
    "        met_levels[:,ii] = np.dot(m2m_layer[:,:,ii], x_full)\n",
    "        if ii==0:\n",
    "            met_leftover_levels[i_unused,ii] = x_full[i_unused]\n",
    "        else:\n",
    "            met_leftover_levels[i_unused,ii] = met_levels[i_unused,ii-1]\n",
    "            \n",
    "    return [met_levels, met_leftover_levels]\n",
    "\n",
    "f_byproduct = 0.9\n",
    "f = f_byproduct * np.ones((MAX_ID_microbes,1));\n",
    "f[i_selfish] = 0.0;  # The byproduct/leakage fraction f for microbes that don't generate byproducts is set as 0.\n",
    "\n",
    "numLevels_max = 4\n",
    "\n",
    "######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "pa = 5; \n",
    "b_real = np.zeros((MAX_ID_microbes,))\n",
    "b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "######## Compute matrices involving the metabolite consumption and generation:\n",
    "m2b, b2m = Ain_out(b_real, net)\n",
    "m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "#m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(i_nonzero_microbes, i_nonzero_metabolites, f, m2b, b2m, numLevels_max)\n",
    "\n",
    "######## Assign diet\n",
    "x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "# minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "# from the model for a certain nutrient intake.\n",
    "fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "bnds = ((0, 100), ) * len(x0)\n",
    "res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'disp': True, 'maxiter': 1000}, tol=1e-3)\n",
    "#res = minimize(fun, x0, method='Nelder-Mead', bounds=bnds, options={'disp': True})\n",
    "#res = minimize(fun, x0, method='TNC', bounds=bnds, options={'disp': True, 'maxiter': 1000})\n",
    "print(res)\n",
    "\n",
    "######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "# optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "# visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "x_full = np.zeros((MAX_ID_metabolites,));\n",
    "x_full[i_intake] = res.x;\n",
    "ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "#### Metagenome comparison\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(ba_pred+1e-5, b_real+1e-5, 'ko')\n",
    "ax.plot([1e-5, 1], [1e-5, 1],'k-')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlabel('predicted')\n",
    "ax.set_ylabel('experimentally observed')\n",
    "ax.set_title('Metagenome comparison')\n",
    "\n",
    "met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "#metabolome_measured[metabolome_ID.values] = metabolome.iloc[:,pa]\n",
    "metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "#metabolome_pred = np.dot(m2m_total, x_full)\n",
    "i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "\n",
    "#### Metabolome comparison\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(metabolome_pred_common+1e-5, metabolome_measured_common+1e-5, 'ko')\n",
    "ax.plot([1e-5, 1], [1e-5, 1],'k-')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlabel('predicted')\n",
    "ax.set_ylabel('experimentally observed')\n",
    "ax.set_title('Metabolome comparison')\n",
    "\n",
    "print('-------------------------------------------------------------------------------------------------------------')\n",
    "print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:')\n",
    "print(pearsonr(ba_pred[b_real>0], b_real[b_real>0]))\n",
    "print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:')\n",
    "print(pearsonr(metabolome_pred_common, metabolome_measured_common))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the simulation with reduced matrix forms for all individuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.4264852667826321\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6529538363213333\n",
      "1\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9011443329682665\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5125408038131118\n",
      "2\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8058052669743445\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7508803126168367\n",
      "3\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8249327931599912\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7689774595704626\n",
      "4\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8544471602442482\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6821088227787729\n",
      "5\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8765075672949567\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5699517741034683\n",
      "6\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8164448836125086\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5656970755260629\n",
      "7\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7801013613352173\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5218332316209638\n",
      "8\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6825814005294661\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7817900908468021\n",
      "9\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.973041274509723\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5418894661381514\n",
      "10\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.67932598507259\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6677578636511161\n",
      "11\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8246508928704608\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5653770777636512\n",
      "12\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9783264660568008\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5549021866319443\n",
      "13\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6875887135567134\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.48940313780094374\n",
      "14\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6573005189824788\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.4223893032881786\n",
      "15\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9694045651225953\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.565441535724876\n",
      "16\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6592519651360947\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7310204753865066\n",
      "17\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9537854660357964\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5519901974198363\n",
      "18\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7565291161563833\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7304309608075413\n",
      "19\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9031879719590015\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6832822581256159\n",
      "20\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7630536992550145\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5774059668273381\n",
      "21\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7700035345916794\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6679272882344237\n",
      "22\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9026760902451338\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.710211975303134\n",
      "23\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8927271146910619\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7756813440676168\n",
      "24\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9693578076516381\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.535209432735657\n",
      "25\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.4050883391885774\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.3812994999489509\n",
      "26\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9698716332434417\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7019312780667835\n",
      "27\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8330614829914302\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.593930214527131\n",
      "28\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8997635841728259\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5305577952165181\n",
      "29\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7790605010599706\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7376868205411262\n",
      "30\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.1768997163940344\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5040594387290794\n",
      "31\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.710890898273119\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5878886164360281\n",
      "32\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8864630456016162\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6961391679267546\n",
      "33\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9861768761913714\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5929523332779914\n",
      "34\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.5908428407805811\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5871530829466426\n",
      "35\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.33541479365343585\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.45756681663310445\n",
      "36\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.902967507706118\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7655944118690443\n",
      "37\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.1659252573138252\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.4624534356331108\n",
      "38\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8287701400789014\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5758689681420956\n",
      "39\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8528324670201044\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6230555581702404\n",
      "40\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8433786629817083\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.668119375076076\n"
     ]
    }
   ],
   "source": [
    "corr_list = np.zeros((metabolome.shape[1],2))\n",
    "diet_list = np.zeros((metabolome.shape[1], 20))\n",
    "for pa in range(metabolome.shape[1]):\n",
    "    print(pa)\n",
    "    ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "    b_real = np.zeros((MAX_ID_microbes,))\n",
    "    b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "    ######## Compute matrices involving the metabolite consumption and generation:\n",
    "    m2b, b2m = Ain_out(b_real, net)\n",
    "    #m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "    m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "    ######## Assign diet\n",
    "    x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "    ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "    # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "    # from the model for a certain nutrient intake.\n",
    "    fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "    bnds = ((0, 100), ) * len(x0)\n",
    "    res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'maxiter': 1000}, tol=1e-3)\n",
    "\n",
    "    ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "    # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "    # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "    met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "    metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "    metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "    metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "    i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "    metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "    metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "    if i_common.shape[0] >= 2:\n",
    "        corr_list[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "        corr_list[pa, 1] = pearsonr(np.log10(metabolome_pred_common+1e-5), np.log10(metabolome_measured_common+1e-5))[0]\n",
    "    else:\n",
    "        corr_list[pa, 0] = -1\n",
    "        corr_list[pa, 1] = -1\n",
    "    \n",
    "    diet_list[pa, :] = res.x\n",
    "\n",
    "    print('-------------------------------------------------------------------------------------------------------------')\n",
    "    print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:')\n",
    "    print(corr_list[pa, 0])\n",
    "    print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:')\n",
    "    print(corr_list[pa, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean Pearson correlation coefficient is 0.6108124558596347\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean Pearson correlation coefficient is\", np.mean(corr_list[:,1]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 557.908x344.806 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_of_species = np.sum(metagenome>0, 0)\n",
    "corr_metabolome = corr_list[:,1]\n",
    "df_individual_performance = pd.DataFrame({\"num_of_species\":num_of_species, \"corr_metabolome\":corr_metabolome})\n",
    "\n",
    "fig_dims = figure_size_setting(700)\n",
    "fig, axes = plt.subplots(1, 1, figsize=fig_dims, sharex=True)\n",
    "g = sns.regplot(x=\"num_of_species\", y=\"corr_metabolome\", color='black', data=df_individual_performance, ax=axes);\n",
    "#g.set_ax_joint.text(145, 95, 'r = 0.45, p < .001', fontstyle='italic')\n",
    "[r, p] = pearsonr(num_of_species, corr_metabolome)\n",
    "axes.text(38, 0.4, 'r = '+str(np.round(r,2))+', p = '+str(np.round(p,2)), fontstyle='italic', fontsize=14)\n",
    "#g.set_ax_joint.text\n",
    "#axes.plot(num_of_species, corr_metabolome,'ko')\n",
    "axes.set_xlabel('Number of microbial species')\n",
    "axes.set_ylabel('Correlation between predicted and \\n experimentally measured metabolome')\n",
    "fig.subplots_adjust(left=.13, bottom=.12, right=.97, top=.97, hspace=0.2)\n",
    "fig.savefig(\"./no_correlation_between_#species_performance.pdf\", dpi=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GutCP: Markov Chain Monte Carlo algorithm of proposing random links (exchange reactions) to add and accepting according to the change in performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## No training-test splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The original error is 0.9062371391507545\n",
      "0\n",
      "accepted, error is 0.8883846092256427\n",
      "accepted, error is 0.8388496823014399\n",
      "accepted, error is 0.8387497436332605\n",
      "50\n",
      "accepted, error is 0.8390501318839914\n",
      "accepted, error is 0.8345180512793308\n",
      "accepted, error is 0.8143832348880207\n",
      "accepted, error is 0.8115617746855315\n",
      "100\n",
      "accepted, error is 0.808743068608957\n",
      "accepted, error is 0.8080000639371394\n",
      "accepted, error is 0.8065180243055451\n",
      "accepted, error is 0.7975061026414058\n",
      "150\n",
      "accepted, error is 0.7985061026414058\n",
      "accepted, error is 0.794198385723165\n",
      "accepted, error is 0.7862606389436068\n",
      "accepted, error is 0.7841549060541706\n",
      "accepted, error is 0.7811913369453213\n",
      "accepted, error is 0.7793071757245614\n",
      "200\n",
      "accepted, error is 0.7794457663459718\n",
      "accepted, error is 0.7794114040696847\n",
      "accepted, error is 0.7774533800317437\n",
      "accepted, error is 0.7782891505236835\n",
      "accepted, error is 0.7746807272543957\n",
      "accepted, error is 0.7741774650504365\n",
      "accepted, error is 0.7720866481838791\n",
      "accepted, error is 0.7719499219235452\n",
      "accepted, error is 0.7716619622322879\n",
      "accepted, error is 0.768964399043218\n",
      "250\n",
      "accepted, error is 0.7651151833282063\n",
      "accepted, error is 0.7628652618258592\n",
      "accepted, error is 0.7629976539939094\n",
      "accepted, error is 0.7626949425241573\n",
      "accepted, error is 0.75462439974705\n",
      "300\n",
      "accepted, error is 0.7527220699114797\n",
      "accepted, error is 0.7412822527213818\n",
      "accepted, error is 0.7409470304422768\n",
      "accepted, error is 0.7332750973036483\n",
      "accepted, error is 0.7332376738494295\n",
      "accepted, error is 0.7336398466180978\n",
      "350\n",
      "accepted, error is 0.733524001589953\n",
      "accepted, error is 0.7308267435509084\n",
      "accepted, error is 0.730095312846181\n",
      "accepted, error is 0.7224771617973639\n",
      "400\n",
      "accepted, error is 0.7217486203615994\n",
      "450\n",
      "accepted, error is 0.7208382452276099\n",
      "accepted, error is 0.7218046803387049\n",
      "accepted, error is 0.7166689504411068\n",
      "500\n",
      "accepted, error is 0.7144546630268984\n",
      "accepted, error is 0.715259728963528\n",
      "accepted, error is 0.7023406751413082\n",
      "550\n",
      "accepted, error is 0.7004894459762239\n",
      "accepted, error is 0.7014894459762239\n",
      "accepted, error is 0.7024894459762239\n",
      "600\n",
      "accepted, error is 0.7034894459762239\n",
      "accepted, error is 0.6987441485847549\n",
      "650\n",
      "accepted, error is 0.6988218076256698\n",
      "accepted, error is 0.6986439903916779\n",
      "accepted, error is 0.6951903792481877\n",
      "700\n",
      "accepted, error is 0.695351763785148\n",
      "accepted, error is 0.6949314039491551\n",
      "accepted, error is 0.6923441857570398\n",
      "750\n",
      "accepted, error is 0.6923334318677223\n",
      "accepted, error is 0.6923469361704757\n",
      "800\n",
      "accepted, error is 0.6917010970304558\n",
      "accepted, error is 0.6917385868922986\n",
      "850\n",
      "accepted, error is 0.690994787895998\n",
      "accepted, error is 0.688175276368817\n",
      "accepted, error is 0.6868198798742718\n",
      "accepted, error is 0.6825125218222325\n",
      "900\n",
      "accepted, error is 0.682538049207129\n",
      "950\n",
      "accepted, error is 0.6821383395285209\n",
      "accepted, error is 0.6807523425758036\n",
      "1000\n",
      "accepted, error is 0.6735606440247297\n",
      "accepted, error is 0.673577989235822\n",
      "1050\n",
      "accepted, error is 0.6724587795350071\n",
      "accepted, error is 0.6724984996594402\n",
      "1100\n",
      "accepted, error is 0.6724832369243112\n",
      "accepted, error is 0.6701951966696159\n",
      "accepted, error is 0.6701766643275674\n",
      "1150\n",
      "accepted, error is 0.669464515186459\n",
      "accepted, error is 0.6689278392008016\n",
      "accepted, error is 0.6689195802920744\n",
      "accepted, error is 0.6701041875561524\n",
      "1200\n",
      "accepted, error is 0.6699730023734211\n",
      "1250\n",
      "accepted, error is 0.6697128716830796\n",
      "1300\n",
      "accepted, error is 0.6692263904128507\n",
      "accepted, error is 0.6572556336323033\n",
      "accepted, error is 0.6550886861858299\n",
      "accepted, error is 0.6550576124787509\n",
      "1350\n",
      "accepted, error is 0.6546309589776381\n",
      "accepted, error is 0.6553829090955865\n",
      "1400\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
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      "\u001b[0;32m<ipython-input-10-5b4dafd31c2f>\u001b[0m in \u001b[0;36mpred_error_addingLinks\u001b[0;34m(x, m2b_ori, b2m_ori, x_ori)\u001b[0m\n\u001b[1;32m     85\u001b[0m         \u001b[0mfun2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mpred_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb_real\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b_total\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi_intake\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m         \u001b[0mbnds\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'SLSQP'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbnds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'disp'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'maxiter'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m         \u001b[0;31m#res = minimize(fun, x0, method='Nelder-Mead', bounds=bnds, options={'disp': True})\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m         \u001b[0;31m#res = minimize(fun, x0, method='TNC', bounds=bnds, options={'disp': True, 'maxiter': 1000})\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    606\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'slsqp'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    607\u001b[0m         return _minimize_slsqp(fun, x0, args, jac, bounds,\n\u001b[0;32m--> 608\u001b[0;31m                                constraints, callback=callback, **options)\n\u001b[0m\u001b[1;32m    609\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'trust-constr'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    610\u001b[0m         return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/slsqp.py\u001b[0m in \u001b[0;36m_minimize_slsqp\u001b[0;34m(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)\u001b[0m\n\u001b[1;32m    421\u001b[0m             \u001b[0;31m# Compute the derivatives of the objective function\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    422\u001b[0m             \u001b[0;31m# For some reason SLSQP wants g dimensioned to n+1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 423\u001b[0;31m             \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfprime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    424\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    425\u001b[0m             \u001b[0;31m# Compute the normals of the constraints\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    324\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    325\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 326\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    327\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    328\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/slsqp.py\u001b[0m in \u001b[0;36mapprox_jacobian\u001b[0;34m(x, func, epsilon, *args)\u001b[0m\n\u001b[1;32m     61\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m         \u001b[0mdx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 63\u001b[0;31m         \u001b[0mjac\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mdx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mf0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mepsilon\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     64\u001b[0m         \u001b[0mdx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "import random\n",
    "######## Select all microbes in the Thai data:\n",
    "b_real = np.zeros((MAX_ID_microbes,))\n",
    "b_real[metagenome_ID] = 0.05\n",
    "\n",
    "######## Compute matrices involving the metabolite consumption and generation:\n",
    "m2b, b2m = Ain_out(b_real, net)\n",
    "\n",
    "######## Keep a record of the original network\n",
    "m2b_ori = (m2b!=0).astype(int).copy()\n",
    "b2m_ori = (b2m!=0).astype(int).copy()\n",
    "x_ori = np.concatenate([m2b_ori.flatten(), b2m_ori.flatten()])\n",
    "net_ori = net.copy()\n",
    "\n",
    "def pred_error_addingLinks(x, m2b_ori, b2m_ori, x_ori):\n",
    "    '''\n",
    "    pred_error_addingLinks is a function used to compute the logarithmic error between experimentally measured\n",
    "    metagenome and predicted metagenome computed from the model for a certain nutrient intake. It relies on \n",
    "    (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2b_total: a conversion matrix \n",
    "    from thenutrient intake to the total biomass, and (4) b_real: experimentally measured metagenome. The \n",
    "    first three is used to compute the metagenome predicted by the model \"ba_pred\" and compare it with the \n",
    "    experimentally measured metagenome \"b_real\".\n",
    "    '''\n",
    "    max_links = m2b_ori.shape[0] * m2b_ori.shape[1] # maximal number of links = numberr of specis * number of metabolites\n",
    "    \n",
    "    ######## Convert x to net structure (convert the adjacency matrix into the edge list):\n",
    "    thres = 0.1\n",
    "    x = x - x_ori\n",
    "    ### consumption links:\n",
    "    m2b_added = x[:max_links].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(m2b_added >= thres)[0]]\n",
    "    b = metagenome_ID[np.where(m2b_added >= thres)[1]]\n",
    "    c = [2] * np.where(m2b_added >= thres)[1].shape[0]\n",
    "    net_added_consumption = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    ### production links:\n",
    "    b2m_added = x[max_links:].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(b2m_added >= thres)[0]]\n",
    "    b = metagenome_ID[np.where(b2m_added >= thres)[1]]\n",
    "    c = [3] * np.where(b2m_added >= thres)[1].shape[0]\n",
    "    net_added_production = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    ### overall edge list of the new network\n",
    "    net = pd.concat([net_ori, net_added_consumption, net_added_production])\n",
    "    \n",
    "    f_byproduct = 0.9\n",
    "    f = f_byproduct * np.ones((MAX_ID_microbes,1));\n",
    "    f[i_selfish] = 0.0;  # The byproduct/leakage fraction f for microbes that don't generate byproducts is set as 0.\n",
    "\n",
    "    numLevels_max = 4\n",
    "\n",
    "    corr_list_aveDiet = np.zeros((metabolome.shape[1],2))\n",
    "    log_list_aveDiet = np.zeros((metabolome.shape[1],2))\n",
    "    order_dev_list = np.zeros((metabolome.shape[1], MAX_ID_metabolites))\n",
    "    order_dev_metagenome_list = np.zeros((metabolome.shape[1], MAX_ID_microbes))\n",
    "    numMetabolites_list = np.zeros((metabolome.shape[1]))\n",
    "    for pa in range(metabolome.shape[1]):\n",
    "        ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "        b_real = np.zeros((MAX_ID_microbes,))\n",
    "        b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "        ######## Compute matrices involving the metabolite consumption and generation:\n",
    "        m2b, b2m = Ain_out(b_real, net)\n",
    "        #m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "        m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        \n",
    "        ######## Assign diet\n",
    "        x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "        ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "        # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "        # from the model for a certain nutrient intake.\n",
    "        fun2 = lambda y: pred_error(y, b_real, m2b_total, i_intake)\n",
    "        bnds = ((0, 100), ) * len(x0)\n",
    "        res = minimize(fun2, x0, method='SLSQP', bounds=bnds, options={'disp': False, 'maxiter': 1000}, tol=1e-3, callback=None)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        x_full = np.zeros((MAX_ID_metabolites,));\n",
    "        x_full[i_intake] = res.x;\n",
    "        ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "        met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "        metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "        metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "        metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "        i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "        metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "        metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "        ######## compute the bias of the order of magnitude\n",
    "        order_dev_metagenome_list[pa, :] = np.log10(b_real + 1e-5) - np.log10(ba_pred + 1e-5)\n",
    "        order_dev_list[pa, i_common] = np.log10(metabolome_measured_common + 1e-5) - np.log10(metabolome_pred_common + 1e-5)\n",
    "        numMetabolites_list[pa] = i_common.shape[0]\n",
    "            \n",
    "        if i_common.shape[0] >= 2:\n",
    "            corr_list_aveDiet[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "            corr_list_aveDiet[pa, 1] = pearsonr(metabolome_pred_common, metabolome_measured_common)[0]\n",
    "            log_list_aveDiet[pa, 0] = np.mean(np.abs(np.log10(ba_pred[b_real>0]+1e-6) - np.log10(b_real[b_real>0]+1e-6)))\n",
    "            log_list_aveDiet[pa, 1] = np.mean(np.abs(np.log10(metabolome_pred_common+1e-6) - np.log10(metabolome_measured_common+1e-6)))\n",
    "\n",
    "        else:\n",
    "            corr_list_aveDiet[pa, 0] = -1\n",
    "            corr_list_aveDiet[pa, 1] = -1\n",
    "            log_list_aveDiet[pa, 0] = 5\n",
    "            log_list_aveDiet[pa, 1] = 5\n",
    "            \n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    \n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "    \n",
    "    pred_error1 = np.mean(log_list_aveDiet[:,0])\n",
    "    pred_error2 = np.mean(log_list_aveDiet[:,1])\n",
    "    pred_error3 = np.sum(np.abs(x))\n",
    "    pred_error4 = np.mean(numMetabolites_list)\n",
    "    hyper_reg = 0.001\n",
    "    pred_errorTotal = pred_error2 + hyper_reg * pred_error3 - (pred_error4 - 20) * 0.003 # with reward\n",
    "    \n",
    "    return [pred_errorTotal, np.abs(np.sum(order_dev_list, 0)), np.sum(order_dev_metagenome_list, 0)]\n",
    "\n",
    "error_list = []\n",
    "current_step_list = []\n",
    "pos_x_list = []\n",
    "metID_list = []\n",
    "microbeID_list = []\n",
    "prior_list = []\n",
    "fun = lambda x: pred_error_addingLinks(x, m2b_ori, b2m_ori, x_ori)\n",
    "max_links = m2b.shape[0]*m2b.shape[1]\n",
    "x = x_ori.copy()\n",
    "error_before, bias_metabolome, bias_metagenome = fun(x)\n",
    "bias_metabolome_ori = bias_metabolome.copy()\n",
    "prior_prob1 = np.matlib.repmat(np.exp(3 * (bias_metagenome) / metabolome.shape[1])[np.newaxis, :], m2b.shape[0], 1) * np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "prior_prob2 = np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "prior_prob = np.concatenate([prior_prob1.flatten(), prior_prob2.flatten()]) + 0.1\n",
    "prior_prob = prior_prob / np.sum(prior_prob)\n",
    "print('The original error is', error_before)\n",
    "error_list.append(error_before)\n",
    "\n",
    "inverseKT = 5000\n",
    "Twindow = 500\n",
    "numStepsNotAdded = 0\n",
    "error_window = []\n",
    "for i in range(10000):\n",
    "    if i%50==0:\n",
    "        print(i)\n",
    "    i_x = np.random.choice(np.where(x==0)[0], 1, p=prior_prob[x==0]/np.sum(prior_prob[x==0]))[0]\n",
    "    x[i_x] = 1\n",
    "    #x[i_x] = 1 - x[i_x]\n",
    "    error_after, bias_metabolome, bias_metagenome = fun(x)\n",
    "    ## Consumption links:\n",
    "    prior_prob1 = np.matlib.repmat(np.exp(3 * (bias_metagenome) / metabolome.shape[1])[np.newaxis, :], m2b.shape[0], 1) * np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "    ## Production links:\n",
    "    prior_prob2 = np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "    prior_prob = np.concatenate([prior_prob1.flatten(), prior_prob2.flatten()]) + 0.1\n",
    "    prior_prob = prior_prob / np.sum(prior_prob)\n",
    "    \n",
    "    if np.random.uniform(0,1,1)[0] <= np.min([1, np.exp((inverseKT)*(error_before - error_after))]): \n",
    "        error_before = error_after\n",
    "        print('accepted, error is', error_before)\n",
    "        error_list.append(error_before)\n",
    "        current_step_list.append(i)\n",
    "        pos_x_list.append(i_x)\n",
    "        prior_list.append(prior_prob[i_x])\n",
    "        if i_x < max_links:\n",
    "            row_num = i_x // m2b_ori.shape[1]\n",
    "            col_num = i_x - row_num * m2b_ori.shape[1]\n",
    "        elif i_x >= max_links:\n",
    "            i_x = i_x - m2b_ori.shape[0] * m2b_ori.shape[1]\n",
    "            row_num = i_x // b2m_ori.shape[1]\n",
    "            col_num = i_x - row_num * b2m_ori.shape[1]\n",
    "        metID_list.append(row_num)\n",
    "        microbeID_list.append(col_num)\n",
    "        numStepsNotAdded = 0\n",
    "    else:  ## not accepted   \n",
    "        x[i_x] = 0\n",
    "        numStepsNotAdded += 1\n",
    "        #x[i_x] = 1 - x[i_x]\n",
    "    error_window.append(error_before)\n",
    "    if (i > Twindow) and ((error_window[-1] - error_window[-Twindow]) > -(np.sqrt(Twindow) / inverseKT)):\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training-test splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The original error is 0.9100794876623948\n",
      "0\n",
      "accepted, error is 0.8920295965906664\n",
      "accepted, error is 0.8908768292450164\n",
      "accepted, error is 0.8776617241515577\n",
      "accepted, error is 0.8699701330439435\n",
      "accepted, error is 0.8685225705759596\n",
      "accepted, error is 0.8676825681757004\n",
      "accepted, error is 0.8686825681757004\n",
      "accepted, error is 0.8685437868597373\n",
      "accepted, error is 0.8193766784747477\n",
      "50\n",
      "accepted, error is 0.819020114547384\n",
      "accepted, error is 0.8184001472921364\n",
      "accepted, error is 0.8177516293907373\n",
      "accepted, error is 0.81629185498725\n",
      "accepted, error is 0.8151433851374235\n",
      "accepted, error is 0.8153534096447655\n",
      "accepted, error is 0.8106819470285683\n",
      "accepted, error is 0.8089580867932288\n",
      "accepted, error is 0.8072552321594202\n",
      "100\n",
      "accepted, error is 0.807043439993324\n",
      "accepted, error is 0.7993093063791119\n",
      "accepted, error is 0.771707465470248\n",
      "accepted, error is 0.7666597628597699\n",
      "accepted, error is 0.7659453740950384\n",
      "accepted, error is 0.7645920667129432\n",
      "150\n",
      "accepted, error is 0.7633853632017348\n",
      "accepted, error is 0.7630662908824402\n",
      "accepted, error is 0.7607337022575585\n",
      "accepted, error is 0.7607856452629654\n",
      "accepted, error is 0.7608902995345787\n",
      "accepted, error is 0.7583768603105948\n",
      "200\n",
      "accepted, error is 0.7578815446739001\n",
      "accepted, error is 0.7471223378658433\n",
      "accepted, error is 0.7448612587485115\n",
      "accepted, error is 0.7430635141135095\n",
      "accepted, error is 0.7397813318515405\n",
      "accepted, error is 0.7380775557222167\n",
      "accepted, error is 0.7380131522034689\n",
      "accepted, error is 0.7367509441842116\n",
      "250\n",
      "accepted, error is 0.7363648696480193\n",
      "accepted, error is 0.7358790844532178\n",
      "accepted, error is 0.7327739320240759\n",
      "accepted, error is 0.7305856486008643\n",
      "300\n",
      "accepted, error is 0.7129050210088379\n",
      "accepted, error is 0.7107789932740817\n",
      "accepted, error is 0.7078285981650677\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-2b440ecceb6e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    175\u001b[0m     \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi_x\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    176\u001b[0m     \u001b[0;31m#x[i_x] = 1 - x[i_x]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 177\u001b[0;31m     \u001b[0merror_after\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbias_metabolome\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbias_metagenome\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    178\u001b[0m     \u001b[0mprior_prob1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrepmat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbias_metagenome\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mmetabolome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnewaxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrepmat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mbias_metabolome_ori\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mmetabolome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnewaxis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    179\u001b[0m     \u001b[0mprior_prob2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrepmat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mbias_metabolome_ori\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mmetabolome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnewaxis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-44-2b440ecceb6e>\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m    149\u001b[0m \u001b[0mmicrobeID_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    150\u001b[0m \u001b[0mprior_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 151\u001b[0;31m \u001b[0mfun\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mpred_error_addingLinks\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b_ori\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb2m_ori\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_ori\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    152\u001b[0m \u001b[0mmax_links\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm2b\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mm2b\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    153\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx_ori\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-44-2b440ecceb6e>\u001b[0m in \u001b[0;36mpred_error_addingLinks\u001b[0;34m(i_train, x, m2b_ori, b2m_ori, x_ori)\u001b[0m\n\u001b[1;32m     78\u001b[0m         \u001b[0mfun2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mpred_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb_real\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b_total\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi_intake\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     79\u001b[0m         \u001b[0mbnds\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 80\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'SLSQP'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbnds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'disp'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'maxiter'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     81\u001b[0m         \u001b[0;31m#res = minimize(fun, x0, method='Nelder-Mead', bounds=bnds, options={'disp': True})\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     82\u001b[0m         \u001b[0;31m#res = minimize(fun, x0, method='TNC', bounds=bnds, options={'disp': True, 'maxiter': 1000})\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    606\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'slsqp'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    607\u001b[0m         return _minimize_slsqp(fun, x0, args, jac, bounds,\n\u001b[0;32m--> 608\u001b[0;31m                                constraints, callback=callback, **options)\n\u001b[0m\u001b[1;32m    609\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'trust-constr'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    610\u001b[0m         return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/slsqp.py\u001b[0m in \u001b[0;36m_minimize_slsqp\u001b[0;34m(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)\u001b[0m\n\u001b[1;32m    397\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    398\u001b[0m             \u001b[0;31m# Compute objective function\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 399\u001b[0;31m             \u001b[0mfx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    400\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    401\u001b[0m                 \u001b[0mfx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    324\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    325\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 326\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    327\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    328\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-44-2b440ecceb6e>\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(y)\u001b[0m\n\u001b[1;32m     76\u001b[0m         \u001b[0;31m# minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     77\u001b[0m         \u001b[0;31m# from the model for a certain nutrient intake.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 78\u001b[0;31m         \u001b[0mfun2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mpred_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb_real\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm2b_total\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi_intake\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     79\u001b[0m         \u001b[0mbnds\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'SLSQP'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbnds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'disp'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'maxiter'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-40-c81097cac7ce>\u001b[0m in \u001b[0;36mpred_error\u001b[0;34m(x, b_real, m2b_total, i_intake)\u001b[0m\n\u001b[1;32m     95\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     96\u001b[0m     \u001b[0mba_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm2b_total\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_full\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 97\u001b[0;31m     \u001b[0mpred_error\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog10\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mba_pred\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1e-6\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog10\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb_real\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0;36m1e-6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog10\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb_real\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0;36m1e-6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     98\u001b[0m     \u001b[0mpred_error\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpred_error\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpred_error\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#np.sqrt(np.sum(pred_error**2))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     99\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mpred_error\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "import random\n",
    "######## Select all microbes in the Thai data:\n",
    "b_real = np.zeros((MAX_ID_microbes,))\n",
    "b_real[metagenome_ID] = 0.05\n",
    "\n",
    "######## Compute matrices involving the metabolite consumption and generation:\n",
    "m2b, b2m = Ain_out(b_real, net)\n",
    "\n",
    "m2b_ori = (m2b!=0).astype(int).copy()\n",
    "b2m_ori = (b2m!=0).astype(int).copy()\n",
    "x_ori = np.concatenate([m2b_ori.flatten(), b2m_ori.flatten()])\n",
    "net_ori = net.copy()\n",
    "\n",
    "def pred_error_addingLinks(i_train, x, m2b_ori, b2m_ori, x_ori):\n",
    "    '''\n",
    "    pred_error_addingLinks is a function used to compute the logarithmic error between experimentally measured\n",
    "    metagenome and predicted metagenome computed from the model for a certain nutrient intake. It relies on \n",
    "    (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2b_total: a conversion matrix \n",
    "    from thenutrient intake to the total biomass, and (4) b_real: experimentally measured metagenome. The \n",
    "    first three is used to compute the metagenome predicted by the model \"ba_pred\" and compare it with the \n",
    "    experimentally measured metagenome \"b_real\".\n",
    "    '''\n",
    "    max_links = m2b_ori.shape[0] * m2b_ori.shape[1] # maximal number of links = numberr of specis * number of metabolites\n",
    "    \n",
    "    ######## Convert x to net structure (convert the adjacency matrix into the edge list):\n",
    "    thres = 0.1\n",
    "    x = x - x_ori\n",
    "    ### consumption links:\n",
    "    m2b_added = x[:max_links].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(m2b_added >= thres)[0]]\n",
    "    b = metagenome_ID[np.where(m2b_added >= thres)[1]]\n",
    "    c = [2] * np.where(m2b_added >= thres)[1].shape[0]\n",
    "    net_added_consumption = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    ### production links:\n",
    "    b2m_added = x[max_links:].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(b2m_added >= thres)[0]]\n",
    "    b = metagenome_ID[np.where(b2m_added >= thres)[1]]\n",
    "    c = [3] * np.where(b2m_added >= thres)[1].shape[0]\n",
    "    net_added_production = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    ### overall edge list of the new network\n",
    "    net = pd.concat([net_ori, net_added_consumption, net_added_production])\n",
    "    \n",
    "    f_byproduct = 0.9\n",
    "    f = f_byproduct * np.ones((MAX_ID_microbes,1));\n",
    "    f[i_selfish] = 0.0;  # The byproduct/leakage fraction f for microbes that don't generate byproducts is set as 0.\n",
    "\n",
    "    numLevels_max = 4\n",
    "\n",
    "    corr_list_aveDiet = np.zeros((i_train.shape[0], 2))\n",
    "    log_list_aveDiet = np.zeros((i_train.shape[0], 2))\n",
    "    order_dev_list = np.zeros((i_train.shape[0], MAX_ID_metabolites)) ## order difference in metabolome\n",
    "    order_dev_metagenome_list = np.zeros((i_train.shape[0], MAX_ID_microbes)) ## order difference in metagenome\n",
    "    numMetabolites_list = np.zeros((i_train.shape[0]))\n",
    "    for pa in range(i_train.shape[0]):\n",
    "        ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "        b_real = np.zeros((MAX_ID_microbes,))\n",
    "        b_real[metagenome_ID] = metagenome.iloc[:, i_train[pa]] / np.sum(metagenome.iloc[:, i_train[pa]])\n",
    "\n",
    "        ######## Compute matrices involving the metabolite consumption and generation:\n",
    "        m2b, b2m = Ain_out(b_real, net)\n",
    "        #m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "        m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        \n",
    "        ######## Assign diet\n",
    "        x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "        ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "        # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "        # from the model for a certain nutrient intake.\n",
    "        fun2 = lambda y: pred_error(y, b_real, m2b_total, i_intake)\n",
    "        bnds = ((0, 100), ) * len(x0)\n",
    "        res = minimize(fun2, x0, method='SLSQP', bounds=bnds, options={'disp': False, 'maxiter': 1000}, tol=1e-3, callback=None)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        x_full = np.zeros((MAX_ID_metabolites,));\n",
    "        x_full[i_intake] = res.x;\n",
    "        ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "        met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "        metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "        metabolome_measured[metabolome_ID] = metabolome.iloc[:, i_train[pa]]\n",
    "        metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "        i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "        metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "        metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "        ######## compute the bias of the order of magnitude\n",
    "        order_dev_metagenome_list[pa, :] = np.log10(b_real + 1e-5) - np.log10(ba_pred + 1e-5)\n",
    "        order_dev_list[pa, i_common] = np.log10(metabolome_measured_common + 1e-5) - np.log10(metabolome_pred_common + 1e-5)\n",
    "        numMetabolites_list[pa] = i_common.shape[0]\n",
    "\n",
    "        if i_common.shape[0] >= 2:\n",
    "            corr_list_aveDiet[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "            corr_list_aveDiet[pa, 1] = pearsonr(metabolome_pred_common, metabolome_measured_common)[0]\n",
    "            log_list_aveDiet[pa, 0] = np.mean(np.abs(np.log10(ba_pred[b_real>0]+1e-6) - np.log10(b_real[b_real>0]+1e-6)))\n",
    "            log_list_aveDiet[pa, 1] = np.mean(np.abs(np.log10(metabolome_pred_common+1e-6) - np.log10(metabolome_measured_common+1e-6)))\n",
    "\n",
    "        else:\n",
    "            corr_list_aveDiet[pa, 0] = -1\n",
    "            corr_list_aveDiet[pa, 1] = -1\n",
    "            log_list_aveDiet[pa, 0] = 5\n",
    "            log_list_aveDiet[pa, 1] = 5\n",
    "            \n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    \n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "    \n",
    "    pred_error1 = np.mean(log_list_aveDiet[:,0])\n",
    "    pred_error2 = np.mean(log_list_aveDiet[:,1])\n",
    "    pred_error3 = np.sum(np.abs(x))\n",
    "    pred_error4 = np.mean(numMetabolites_list)\n",
    "    hyper_reg = 0.001\n",
    "    pred_errorTotal = pred_error2 + hyper_reg * pred_error3 - (pred_error4 - 20) * 0.003 # with reward\n",
    "    \n",
    "    return [pred_errorTotal, np.abs(np.sum(order_dev_list, 0)), np.sum(order_dev_metagenome_list, 0)]\n",
    "\n",
    "i_train = np.sort(np.random.choice(range(metabolome.shape[1]), 30, replace=False))\n",
    "i_test = np.setdiff1d(range(metabolome.shape[1]), i_train)\n",
    "\n",
    "error_list = []\n",
    "current_step_list = []\n",
    "pos_x_list = []\n",
    "metID_list = []\n",
    "microbeID_list = []\n",
    "prior_list = []\n",
    "fun = lambda x: pred_error_addingLinks(i_train, x, m2b_ori, b2m_ori, x_ori)\n",
    "max_links = m2b.shape[0]*m2b.shape[1]\n",
    "x = x_ori.copy()\n",
    "error_before, bias_metabolome, bias_metagenome = fun(x)\n",
    "bias_metabolome_ori = bias_metabolome.copy()\n",
    "prior_prob1 = np.matlib.repmat(np.exp(3 * (bias_metagenome) / metabolome.shape[1])[np.newaxis, :], m2b.shape[0], 1) * np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "prior_prob2 = np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "prior_prob = np.concatenate([prior_prob1.flatten(), prior_prob2.flatten()]) + 0.1\n",
    "prior_prob = prior_prob / np.sum(prior_prob)\n",
    "print('The original error is', error_before)\n",
    "error_list.append(error_before)\n",
    "\n",
    "inverseKT = 5000\n",
    "Twindow = 500\n",
    "numStepsNotAdded = 0\n",
    "error_window = []\n",
    "# MCMC\n",
    "for i in range(10000):\n",
    "    if i%50==0:\n",
    "        print(i)\n",
    "    i_x = np.random.choice(np.where(x==0)[0], 1, p=prior_prob[x==0]/np.sum(prior_prob[x==0]))[0]\n",
    "    x[i_x] = 1\n",
    "    #x[i_x] = 1 - x[i_x]\n",
    "    error_after, bias_metabolome, bias_metagenome = fun(x)\n",
    "    ## Consumption links:\n",
    "    prior_prob1 = np.matlib.repmat(np.exp(3 * (bias_metagenome) / metabolome.shape[1])[np.newaxis, :], m2b.shape[0], 1) * np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "    ## Production links:\n",
    "    prior_prob2 = np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "    prior_prob = np.concatenate([prior_prob1.flatten(), prior_prob2.flatten()]) + 0.1\n",
    "    prior_prob = prior_prob / np.sum(prior_prob)\n",
    "    if np.random.uniform(0,1,1)[0] <= np.min([1, np.exp((inverseKT)*(error_before - error_after))]): \n",
    "        error_before = error_after\n",
    "        print('accepted, error is', error_before)\n",
    "        error_list.append(error_before)\n",
    "        current_step_list.append(i)\n",
    "        pos_x_list.append(i_x)\n",
    "        prior_list.append(prior_prob[i_x])\n",
    "        if i_x < max_links:\n",
    "            row_num = i_x // m2b_ori.shape[1]\n",
    "            col_num = i_x - row_num * m2b_ori.shape[1]\n",
    "        elif i_x >= max_links:\n",
    "            i_x = i_x - m2b_ori.shape[0] * m2b_ori.shape[1]\n",
    "            row_num = i_x // b2m_ori.shape[1]\n",
    "            col_num = i_x - row_num * b2m_ori.shape[1]\n",
    "        metID_list.append(row_num)\n",
    "        microbeID_list.append(col_num)\n",
    "        numStepsNotAdded = 0\n",
    "    else:  ## not accepted   \n",
    "        x[i_x] = 0\n",
    "        numStepsNotAdded += 1\n",
    "        #x[i_x] = 1 - x[i_x]\n",
    "    error_window.append(error_before)\n",
    "    if (i > Twindow) and ((error_window[-1] - error_window[-Twindow]) > -(np.sqrt(Twindow) / inverseKT)):\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convert x to network structure and add it to *net*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The original network has  1037 links\n",
      "The improved network has  1082 links\n"
     ]
    }
   ],
   "source": [
    "######## Convert x to net structure:\n",
    "a = np.array(metID_list)\n",
    "b = np.array(microbeID_list)\n",
    "c = np.ones([len(metID_list)], dtype = int) * 3\n",
    "c[np.where(np.array(pos_x_list) < max_links)[0]] = 2\n",
    "net_added = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "net_new = pd.concat([net_ori, net_added])\n",
    "\n",
    "print('The original network has ',len(net_ori),'links')\n",
    "print('The improved network has ',len(net_new),'links')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show the performance on the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average Pearson correlation coefficient for the test set:\n",
      "0.6533940617104443\n",
      "The average log error for the test set:\n",
      "0.7159941234213341\n"
     ]
    }
   ],
   "source": [
    "corr_list = np.zeros((i_test.shape[0], 2))\n",
    "diet_list = np.zeros((i_test.shape[0], 20))\n",
    "log_list = np.zeros((i_test.shape[0], 2))\n",
    "for pa in range(i_test.shape[0]):\n",
    "    ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "    b_real = np.zeros((MAX_ID_microbes,))\n",
    "    b_real[metagenome_ID] = metagenome.iloc[:, i_test[pa]] / np.sum(metagenome.iloc[:, i_test[pa]])\n",
    "\n",
    "    ######## Compute matrices involving the metabolite consumption and generation:\n",
    "    m2b, b2m = Ain_out(b_real, net_new)\n",
    "    m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "    ######## Assign diet\n",
    "    x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "    ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "    # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "    # from the model for a certain nutrient intake.\n",
    "    fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "    bnds = ((0, 100), ) * len(x0)\n",
    "    res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'maxiter': 1000}, tol=1e-3)\n",
    "\n",
    "    ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "    # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "    # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "    met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "    metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "    metabolome_measured[metabolome_ID] = metabolome.iloc[:, i_test[pa]]\n",
    "    metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "    i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "    metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "    metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "\n",
    "    if i_common.shape[0] >= 2:\n",
    "        corr_list[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "        corr_list[pa, 1] = pearsonr(np.log10(metabolome_pred_common+1e-5), np.log10(metabolome_measured_common+1e-5))[0]\n",
    "    else:\n",
    "        corr_list[pa, 0] = -1\n",
    "        corr_list[pa, 1] = -1\n",
    "    \n",
    "    log_list[pa, 0] = np.mean(np.abs(np.log10(ba_pred[b_real>0]+1e-6) - np.log10(b_real[b_real>0]+1e-6)))\n",
    "    log_list[pa, 1] = np.mean(np.abs(np.log10(metabolome_pred_common+1e-6) - np.log10(metabolome_measured_common+1e-6)))\n",
    "    diet_list[pa, :] = res.x\n",
    "    \n",
    "print('The average Pearson correlation coefficient for the test set:')\n",
    "print(np.mean(corr_list[:,1]))\n",
    "print('The average log error for the test set:')\n",
    "print(np.mean(log_list[:,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct the added links to a pandas data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>metabolite ID</th>\n",
       "      <th>metabolite names</th>\n",
       "      <th>microbes ID</th>\n",
       "      <th>microbes names</th>\n",
       "      <th>edgeType</th>\n",
       "      <th>error reduced</th>\n",
       "      <th>step added</th>\n",
       "      <th>position in x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>161</td>\n",
       "      <td>Blautia hansenii (Ruminococcus hansenii)</td>\n",
       "      <td>3</td>\n",
       "      <td>0.049167</td>\n",
       "      <td>46</td>\n",
       "      <td>23642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>464</td>\n",
       "      <td>Faecalibacterium prausnitzii</td>\n",
       "      <td>3</td>\n",
       "      <td>0.027602</td>\n",
       "      <td>131</td>\n",
       "      <td>24380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>54</td>\n",
       "      <td>Alistipes putredinis</td>\n",
       "      <td>2</td>\n",
       "      <td>0.018050</td>\n",
       "      <td>0</td>\n",
       "      <td>8426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>2179</td>\n",
       "      <td>Niacin (Vitamin B3, Nicotinic acid, Nicotinate...</td>\n",
       "      <td>135</td>\n",
       "      <td>Bacteroides uniformis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.017681</td>\n",
       "      <td>306</td>\n",
       "      <td>27449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2125</td>\n",
       "      <td>L-Alanine (D-Alanine, Alanine)</td>\n",
       "      <td>425</td>\n",
       "      <td>Eggerthella lenta</td>\n",
       "      <td>2</td>\n",
       "      <td>0.013215</td>\n",
       "      <td>16</td>\n",
       "      <td>7885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2217</td>\n",
       "      <td>Succinate</td>\n",
       "      <td>953</td>\n",
       "      <td>Roseburia inulinivorans</td>\n",
       "      <td>2</td>\n",
       "      <td>0.010759</td>\n",
       "      <td>202</td>\n",
       "      <td>14100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2129</td>\n",
       "      <td>L-Aspartate (Aspartate, D-Aspartate)</td>\n",
       "      <td>953</td>\n",
       "      <td>Roseburia inulinivorans</td>\n",
       "      <td>3</td>\n",
       "      <td>0.007734</td>\n",
       "      <td>126</td>\n",
       "      <td>24108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2145</td>\n",
       "      <td>L-Methionine (D-Methionine)</td>\n",
       "      <td>551</td>\n",
       "      <td>Holdemania filiformis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.007692</td>\n",
       "      <td>19</td>\n",
       "      <td>25248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2132</td>\n",
       "      <td>L-Fucose</td>\n",
       "      <td>1064</td>\n",
       "      <td>Streptococcus salivarius</td>\n",
       "      <td>3</td>\n",
       "      <td>0.005048</td>\n",
       "      <td>133</td>\n",
       "      <td>24333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2037</td>\n",
       "      <td>Butylamine</td>\n",
       "      <td>157</td>\n",
       "      <td>Bifidobacterium longum (Bifidobacterium infant...</td>\n",
       "      <td>2</td>\n",
       "      <td>0.004671</td>\n",
       "      <td>95</td>\n",
       "      <td>2471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2141</td>\n",
       "      <td>L-Lactate ([S]-Lactate, Lactate, D-Lactate, [R...</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>2</td>\n",
       "      <td>0.003282</td>\n",
       "      <td>219</td>\n",
       "      <td>9064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>2240</td>\n",
       "      <td>Valerate (Pentanoic acid, Pentanoate)</td>\n",
       "      <td>129</td>\n",
       "      <td>Bacteroides ovatus</td>\n",
       "      <td>3</td>\n",
       "      <td>0.003105</td>\n",
       "      <td>285</td>\n",
       "      <td>31549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2155</td>\n",
       "      <td>L-Tyrosine (Tyrosine)</td>\n",
       "      <td>133</td>\n",
       "      <td>Bacteroides stercoris</td>\n",
       "      <td>3</td>\n",
       "      <td>0.002950</td>\n",
       "      <td>344</td>\n",
       "      <td>25935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>1007</td>\n",
       "      <td>Shigella sonnei</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002513</td>\n",
       "      <td>194</td>\n",
       "      <td>8490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2055</td>\n",
       "      <td>CO2</td>\n",
       "      <td>157</td>\n",
       "      <td>Bifidobacterium longum (Bifidobacterium infant...</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002333</td>\n",
       "      <td>179</td>\n",
       "      <td>3407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>2147</td>\n",
       "      <td>L-Phenylalanine (Phenylalanine, D-Phenylalanine)</td>\n",
       "      <td>159</td>\n",
       "      <td>Bilophila wadsworthia</td>\n",
       "      <td>3</td>\n",
       "      <td>0.002261</td>\n",
       "      <td>209</td>\n",
       "      <td>25369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>2012</td>\n",
       "      <td>5-Aminovalerate</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>3</td>\n",
       "      <td>0.002188</td>\n",
       "      <td>287</td>\n",
       "      <td>16765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>2129</td>\n",
       "      <td>L-Aspartate (Aspartate, D-Aspartate)</td>\n",
       "      <td>135</td>\n",
       "      <td>Bacteroides uniformis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.002126</td>\n",
       "      <td>339</td>\n",
       "      <td>24065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2139</td>\n",
       "      <td>L-iduronate</td>\n",
       "      <td>161</td>\n",
       "      <td>Blautia hansenii (Ruminococcus hansenii)</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001798</td>\n",
       "      <td>218</td>\n",
       "      <td>24794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2242</td>\n",
       "      <td>XOS (Xylooligosaccharide)</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001724</td>\n",
       "      <td>97</td>\n",
       "      <td>31739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>878</td>\n",
       "      <td>Prevotella salivae</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001704</td>\n",
       "      <td>229</td>\n",
       "      <td>23672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2142</td>\n",
       "      <td>L-Leucine (Leucine)</td>\n",
       "      <td>122</td>\n",
       "      <td>Bacteroides coprophilus</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001703</td>\n",
       "      <td>98</td>\n",
       "      <td>24992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2109</td>\n",
       "      <td>H2S (HS-)</td>\n",
       "      <td>338</td>\n",
       "      <td>Coprococcus comes</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001460</td>\n",
       "      <td>88</td>\n",
       "      <td>7017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2185</td>\n",
       "      <td>Orotic acid (Orotate)</td>\n",
       "      <td>1052</td>\n",
       "      <td>Streptococcus gallolyticus</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001448</td>\n",
       "      <td>22</td>\n",
       "      <td>27931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2162</td>\n",
       "      <td>Melibiose</td>\n",
       "      <td>870</td>\n",
       "      <td>Prevotella copri</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001353</td>\n",
       "      <td>149</td>\n",
       "      <td>26479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>2238</td>\n",
       "      <td>Urea</td>\n",
       "      <td>157</td>\n",
       "      <td>Bifidobacterium longum (Bifidobacterium infant...</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001262</td>\n",
       "      <td>249</td>\n",
       "      <td>31415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2011</td>\n",
       "      <td>4-Aminobutyrate (GABA)</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001207</td>\n",
       "      <td>162</td>\n",
       "      <td>16691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2233</td>\n",
       "      <td>Trimethylamine</td>\n",
       "      <td>878</td>\n",
       "      <td>Prevotella salivae</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001153</td>\n",
       "      <td>1</td>\n",
       "      <td>15176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2115</td>\n",
       "      <td>Indole-3-acetate (Indoleacetate)</td>\n",
       "      <td>9</td>\n",
       "      <td>Acidaminococcus fermentans</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001148</td>\n",
       "      <td>89</td>\n",
       "      <td>23112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2093</td>\n",
       "      <td>Formate</td>\n",
       "      <td>966</td>\n",
       "      <td>Ruminococcus gnavus</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000840</td>\n",
       "      <td>32</td>\n",
       "      <td>6039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2158</td>\n",
       "      <td>Linoleic acid (Omega-6 fatty acid)</td>\n",
       "      <td>1007</td>\n",
       "      <td>Shigella sonnei</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000714</td>\n",
       "      <td>141</td>\n",
       "      <td>26202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2201</td>\n",
       "      <td>Propanoate (Propionate)</td>\n",
       "      <td>484</td>\n",
       "      <td>Fusobacterium varium</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000649</td>\n",
       "      <td>77</td>\n",
       "      <td>13005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2091</td>\n",
       "      <td>Folic acid (Folate, Vitamin B9)</td>\n",
       "      <td>126</td>\n",
       "      <td>Bacteroides fragilis</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000620</td>\n",
       "      <td>69</td>\n",
       "      <td>5844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>2204</td>\n",
       "      <td>Pyridoxal (Vitamin B6, Pyridoxine, Pyridoxamin...</td>\n",
       "      <td>460</td>\n",
       "      <td>Eubacterium siraeum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000495</td>\n",
       "      <td>200</td>\n",
       "      <td>29130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>2154</td>\n",
       "      <td>L-Tryptophan (Tryptophan)</td>\n",
       "      <td>551</td>\n",
       "      <td>Holdemania filiformis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000486</td>\n",
       "      <td>272</td>\n",
       "      <td>25896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>2167</td>\n",
       "      <td>Methylamine (Monomethylamine)</td>\n",
       "      <td>159</td>\n",
       "      <td>Bilophila wadsworthia</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000386</td>\n",
       "      <td>256</td>\n",
       "      <td>26809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2065</td>\n",
       "      <td>D-Galacturonate</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000357</td>\n",
       "      <td>67</td>\n",
       "      <td>20008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2125</td>\n",
       "      <td>L-Alanine (D-Alanine, Alanine)</td>\n",
       "      <td>456</td>\n",
       "      <td>Eubacterium limosum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000319</td>\n",
       "      <td>168</td>\n",
       "      <td>23800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2056</td>\n",
       "      <td>Crotonate (2-Butenoate, 2-Butenoic acid, Croto...</td>\n",
       "      <td>260</td>\n",
       "      <td>Catenibacterium mitsuokai</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000212</td>\n",
       "      <td>110</td>\n",
       "      <td>19395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2228</td>\n",
       "      <td>Thymidine</td>\n",
       "      <td>9</td>\n",
       "      <td>Acidaminococcus fermentans</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000139</td>\n",
       "      <td>45</td>\n",
       "      <td>30744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>796</td>\n",
       "      <td>Odoribacter splanchnicus</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000064</td>\n",
       "      <td>235</td>\n",
       "      <td>7754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2190</td>\n",
       "      <td>Pantothenic acid (Vitamin B5, Pantothenate)</td>\n",
       "      <td>122</td>\n",
       "      <td>Bacteroides coprophilus</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.000052</td>\n",
       "      <td>184</td>\n",
       "      <td>28232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2236</td>\n",
       "      <td>Tyramine</td>\n",
       "      <td>969</td>\n",
       "      <td>Ruminococcus torques</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000105</td>\n",
       "      <td>187</td>\n",
       "      <td>15401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2141</td>\n",
       "      <td>L-Lactate ([S]-Lactate, Lactate, D-Lactate, [R...</td>\n",
       "      <td>608</td>\n",
       "      <td>Lactococcus lactis</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000210</td>\n",
       "      <td>93</td>\n",
       "      <td>9049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2186</td>\n",
       "      <td>Oxalate</td>\n",
       "      <td>122</td>\n",
       "      <td>Bacteroides coprophilus</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>35</td>\n",
       "      <td>12032</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    metabolite ID                                   metabolite names  \\\n",
       "8            2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "20           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "0            2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "42           2179  Niacin (Vitamin B3, Nicotinic acid, Nicotinate...   \n",
       "2            2125                     L-Alanine (D-Alanine, Alanine)   \n",
       "31           2217                                          Succinate   \n",
       "19           2129               L-Aspartate (Aspartate, D-Aspartate)   \n",
       "3            2145                        L-Methionine (D-Methionine)   \n",
       "21           2132                                           L-Fucose   \n",
       "15           2037                                         Butylamine   \n",
       "34           2141  L-Lactate ([S]-Lactate, Lactate, D-Lactate, [R...   \n",
       "40           2240              Valerate (Pentanoic acid, Pentanoate)   \n",
       "44           2155                              L-Tyrosine (Tyrosine)   \n",
       "29           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "26           2055                                                CO2   \n",
       "32           2147   L-Phenylalanine (Phenylalanine, D-Phenylalanine)   \n",
       "41           2012                                    5-Aminovalerate   \n",
       "43           2129               L-Aspartate (Aspartate, D-Aspartate)   \n",
       "33           2139                                        L-iduronate   \n",
       "16           2242                          XOS (Xylooligosaccharide)   \n",
       "35           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "17           2142                                L-Leucine (Leucine)   \n",
       "12           2109                                          H2S (HS-)   \n",
       "4            2185                              Orotic acid (Orotate)   \n",
       "23           2162                                          Melibiose   \n",
       "37           2238                                               Urea   \n",
       "24           2011                             4-Aminobutyrate (GABA)   \n",
       "1            2233                                     Trimethylamine   \n",
       "13           2115                   Indole-3-acetate (Indoleacetate)   \n",
       "5            2093                                            Formate   \n",
       "22           2158                 Linoleic acid (Omega-6 fatty acid)   \n",
       "11           2201                            Propanoate (Propionate)   \n",
       "10           2091                    Folic acid (Folate, Vitamin B9)   \n",
       "30           2204  Pyridoxal (Vitamin B6, Pyridoxine, Pyridoxamin...   \n",
       "39           2154                          L-Tryptophan (Tryptophan)   \n",
       "38           2167                      Methylamine (Monomethylamine)   \n",
       "9            2065                                    D-Galacturonate   \n",
       "25           2125                     L-Alanine (D-Alanine, Alanine)   \n",
       "18           2056  Crotonate (2-Butenoate, 2-Butenoic acid, Croto...   \n",
       "7            2228                                          Thymidine   \n",
       "36           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "27           2190        Pantothenic acid (Vitamin B5, Pantothenate)   \n",
       "28           2236                                           Tyramine   \n",
       "14           2141  L-Lactate ([S]-Lactate, Lactate, D-Lactate, [R...   \n",
       "6            2186                                            Oxalate   \n",
       "\n",
       "    microbes ID                                     microbes names  edgeType  \\\n",
       "8           161           Blautia hansenii (Ruminococcus hansenii)         3   \n",
       "20          464                       Faecalibacterium prausnitzii         3   \n",
       "0            54                               Alistipes putredinis         2   \n",
       "42          135                              Bacteroides uniformis         3   \n",
       "2           425                                  Eggerthella lenta         2   \n",
       "31          953                            Roseburia inulinivorans         2   \n",
       "19          953                            Roseburia inulinivorans         3   \n",
       "3           551                              Holdemania filiformis         3   \n",
       "21         1064                           Streptococcus salivarius         3   \n",
       "15          157  Bifidobacterium longum (Bifidobacterium infant...         2   \n",
       "34          968                                 Ruminococcus obeum         2   \n",
       "40          129                                 Bacteroides ovatus         3   \n",
       "44          133                              Bacteroides stercoris         3   \n",
       "29         1007                                    Shigella sonnei         2   \n",
       "26          157  Bifidobacterium longum (Bifidobacterium infant...         2   \n",
       "32          159                              Bilophila wadsworthia         3   \n",
       "41          964                                Ruminococcus bromii         3   \n",
       "43          135                              Bacteroides uniformis         3   \n",
       "33          161           Blautia hansenii (Ruminococcus hansenii)         3   \n",
       "16          952                             Roseburia intestinalis         3   \n",
       "35          878                                 Prevotella salivae         3   \n",
       "17          122                            Bacteroides coprophilus         3   \n",
       "12          338                                  Coprococcus comes         2   \n",
       "4          1052                         Streptococcus gallolyticus         3   \n",
       "23          870                                   Prevotella copri         3   \n",
       "37          157  Bifidobacterium longum (Bifidobacterium infant...         3   \n",
       "24          952                             Roseburia intestinalis         3   \n",
       "1           878                                 Prevotella salivae         2   \n",
       "13            9                         Acidaminococcus fermentans         3   \n",
       "5           966                                Ruminococcus gnavus         2   \n",
       "22         1007                                    Shigella sonnei         3   \n",
       "11          484                               Fusobacterium varium         2   \n",
       "10          126                               Bacteroides fragilis         2   \n",
       "30          460                                Eubacterium siraeum         3   \n",
       "39          551                              Holdemania filiformis         3   \n",
       "38          159                              Bilophila wadsworthia         3   \n",
       "9           968                                 Ruminococcus obeum         3   \n",
       "25          456                                Eubacterium limosum         3   \n",
       "18          260                          Catenibacterium mitsuokai         3   \n",
       "7             9                         Acidaminococcus fermentans         3   \n",
       "36          796                           Odoribacter splanchnicus         2   \n",
       "27          122                            Bacteroides coprophilus         3   \n",
       "28          969                               Ruminococcus torques         2   \n",
       "14          608                                 Lactococcus lactis         2   \n",
       "6           122                            Bacteroides coprophilus         2   \n",
       "\n",
       "    error reduced  step added  position in x  \n",
       "8        0.049167          46          23642  \n",
       "20       0.027602         131          24380  \n",
       "0        0.018050           0           8426  \n",
       "42       0.017681         306          27449  \n",
       "2        0.013215          16           7885  \n",
       "31       0.010759         202          14100  \n",
       "19       0.007734         126          24108  \n",
       "3        0.007692          19          25248  \n",
       "21       0.005048         133          24333  \n",
       "15       0.004671          95           2471  \n",
       "34       0.003282         219           9064  \n",
       "40       0.003105         285          31549  \n",
       "44       0.002950         344          25935  \n",
       "29       0.002513         194           8490  \n",
       "26       0.002333         179           3407  \n",
       "32       0.002261         209          25369  \n",
       "41       0.002188         287          16765  \n",
       "43       0.002126         339          24065  \n",
       "33       0.001798         218          24794  \n",
       "16       0.001724          97          31739  \n",
       "35       0.001704         229          23672  \n",
       "17       0.001703          98          24992  \n",
       "12       0.001460          88           7017  \n",
       "4        0.001448          22          27931  \n",
       "23       0.001353         149          26479  \n",
       "37       0.001262         249          31415  \n",
       "24       0.001207         162          16691  \n",
       "1        0.001153           1          15176  \n",
       "13       0.001148          89          23112  \n",
       "5        0.000840          32           6039  \n",
       "22       0.000714         141          26202  \n",
       "11       0.000649          77          13005  \n",
       "10       0.000620          69           5844  \n",
       "30       0.000495         200          29130  \n",
       "39       0.000486         272          25896  \n",
       "38       0.000386         256          26809  \n",
       "9        0.000357          67          20008  \n",
       "25       0.000319         168          23800  \n",
       "18       0.000212         110          19395  \n",
       "7        0.000139          45          30744  \n",
       "36       0.000064         235           7754  \n",
       "27      -0.000052         184          28232  \n",
       "28      -0.000105         187          15401  \n",
       "14      -0.000210          93           9049  \n",
       "6       -0.001000          35          12032  "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NUMADDED = len(net_new) - len(net_ori)\n",
    "\n",
    "df_added_metabolites = names.loc[df_metabolites.reset_index().set_index('newID').loc[net_new.iloc[-NUMADDED:,0]].values.flatten()]\n",
    "df_added_metabolites.reset_index(inplace=True)\n",
    "df_added_metabolites.columns = ['metabolite ID', 'metabolite names'] \n",
    "\n",
    "df_added_microbes = names.loc[df_microbes.reset_index().set_index('newID').loc[net_new.iloc[-NUMADDED:,1]].values.flatten()]\n",
    "df_added_microbes.reset_index(inplace=True)\n",
    "df_added_microbes.columns = ['microbes ID', 'microbes names'] \n",
    "\n",
    "df_added_edgeTypes = net_new.iloc[-NUMADDED:,2]\n",
    "df_added_edgeTypes = pd.DataFrame(df_added_edgeTypes)\n",
    "df_added_edgeTypes.index = range(NUMADDED)\n",
    "\n",
    "df_added_errorReduced = -np.diff(error_list)\n",
    "df_added_errorReduced = pd.DataFrame(df_added_errorReduced)\n",
    "df_added_errorReduced.index = range(NUMADDED)\n",
    "df_added_errorReduced.columns = ['error reduced'] \n",
    "\n",
    "df_added_step = np.array(current_step_list)\n",
    "df_added_step = pd.DataFrame(df_added_step)\n",
    "df_added_step.index = range(NUMADDED)\n",
    "df_added_step.columns = ['step added'] \n",
    "\n",
    "df_added_pos = np.array(pos_x_list)\n",
    "df_added_pos = pd.DataFrame(df_added_pos)\n",
    "df_added_pos.index = range(NUMADDED)\n",
    "df_added_pos.columns = ['position in x'] \n",
    "\n",
    "df_added_tables = pd.concat([df_added_metabolites, df_added_microbes, df_added_edgeTypes,  df_added_errorReduced, df_added_step, df_added_pos], axis=1, sort=False)\n",
    "df_added_tables.sort_values(by = 'error reduced', ascending=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize error reduction over time and rank plot of error reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'number of links added')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(np.cumsum(np.sort(df_added_tables['error reduced'].values))[::-1])\n",
    "plt.yscale('log')\n",
    "plt.ylabel('per link error reduction')\n",
    "plt.xlabel('rank of links')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(error_list)\n",
    "plt.ylabel('error')\n",
    "plt.xlabel('number of links added')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate p-value by comparing the added links to links in the MAMBO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3230 30787\n",
      "0.1049144119271121\n",
      "Of 30 valid links existing in MAMBO, there are 16 found by the GutCP.\n",
      "The p-value of this is 7.831660628898618e-06\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "chia_microbes_in_Thai = df_microbes.reset_index().set_index('newID').loc[metagenome_ID].values.flatten()\n",
    "chia_metabolites_in_Thai = df_metabolites.reset_index().set_index('newID').loc[df_metabolites['newID']].values.flatten()\n",
    "\n",
    "df_MAMBO = pd.read_csv(\"mambo_curated.txt\", sep = '\\t')\n",
    "df_MAMBO_filtered = df_MAMBO[df_MAMBO['microbe_ID'].apply(lambda x: x in chia_microbes_in_Thai)]\n",
    "df_MAMBO_filtered = df_MAMBO_filtered[df_MAMBO_filtered['metabolite_ID'].apply(lambda x: x in chia_metabolites_in_Thai)]\n",
    "\n",
    "df_MAMBO_filtered_newID = df_MAMBO_filtered[['microbe_ID', 'metabolite_ID']].copy()\n",
    "df_MAMBO_filtered_newID.columns = ['microbes', 'metabolites']\n",
    "df_MAMBO_filtered_newID['microbes'] = df_microbes.loc[df_MAMBO_filtered_newID['microbes']].values\n",
    "df_MAMBO_filtered_newID['metabolites'] = df_metabolites.loc[df_MAMBO_filtered_newID['metabolites']].values\n",
    "s1 = df_MAMBO_filtered_newID\n",
    "s2 = net[['metabolites', 'microbes']]\n",
    "numOverlap = len(pd.merge(s1, s2, how='inner'))\n",
    "\n",
    "print((len(df_MAMBO_filtered)-numOverlap), (x.shape[0] - len(net_ori)))\n",
    "print((len(df_MAMBO_filtered)-numOverlap) / (x.shape[0] - len(net_ori)) )\n",
    "\n",
    "k = 0\n",
    "l = 0\n",
    "ifIncluded = np.zeros((NUMADDED))\n",
    "ifCovered = np.zeros((NUMADDED))\n",
    "for i in range(NUMADDED):\n",
    "    if (np.sum((df_MAMBO['microbe_ID'] == df_added_tables['microbes ID'].iloc[i])) >=1 and \n",
    "       np.sum((df_MAMBO['metabolite_ID'] == df_added_tables['metabolite ID'].iloc[i]))>=1):\n",
    "        ifCovered[i] = 1\n",
    "        l += 1\n",
    "    if np.sum((df_MAMBO['microbe_ID'] == df_added_tables['microbes ID'].iloc[i]) & \n",
    "       (df_MAMBO['metabolite_ID'] == df_added_tables['metabolite ID'].iloc[i]))>=1:\n",
    "        ifIncluded[i] = 1\n",
    "        k += 1\n",
    "print('Of '+str(l)+' valid links existing in MAMBO, there are '+str(k)+' found by the GutCP.')\n",
    "\n",
    "from scipy.stats import bernoulli, binom\n",
    "xx = range(NUMADDED)\n",
    "p = len(df_MAMBO_filtered) / x.shape[0]\n",
    "#prob = bernoulli.cdf(xx, p)\n",
    "probCum = binom.cdf(xx, NUMADDED, p)\n",
    "prob = binom.pmf(xx, NUMADDED, p)\n",
    "plt.plot(xx, prob, 'o')\n",
    "plt.plot([k, k], [0, np.max(prob)], '-.')\n",
    "plt.xlabel('Number of predicted links in MAMBO')\n",
    "plt.ylabel('Probability')\n",
    "p_value = 1 - probCum[k]\n",
    "print('The p-value of this is',str(p_value))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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