I3_vs_SAP_s5n5m3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a004ce6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Patch\n",
    "from numpy import pi, e\n",
    "from numpy.linalg import inv, det\n",
    "from numpy.linalg import norm as LA_norm\n",
    "from numpy.random import random\n",
    "from scipy.stats import norm\n",
    "from sklearn.datasets import make_spd_matrix\n",
    "from termcolor import colored\n",
    "import itertools\n",
    "from itertools import combinations, product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c48c1abf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_matrix(m, n):\n",
    "    return np.random.rand(m, n)\n",
    "\n",
    "def initial_inputs(flag):\n",
    "    if flag == 0:\n",
    "        # Create initial encoder inputs (B, Sigma_W)\n",
    "        B = create_matrix(m, n)\n",
    "        Sigma_W = make_spd_matrix(m)\n",
    "        return np.concatenate(([flag], B.reshape((m*n)), Sigma_W.reshape((m*m))))\n",
    "    else:\n",
    "        # Create initial decoder inputs (A, Sigma_Z)\n",
    "        A = create_matrix(n, m)\n",
    "        Sigma_Z = np.diag(random(n))\n",
    "        return np.concatenate(([flag], A.reshape((n*m)), Sigma_Z.reshape((n*n))))\n",
    "\n",
    "def is_close_to_zero(arr, etol):\n",
    "    return np.allclose(arr, 0, atol=etol)\n",
    "\n",
    "def is_singular(matrix):\n",
    "    is_singular = np.linalg.matrix_rank(matrix) < min(matrix.shape)\n",
    "    if is_singular:\n",
    "        print(colored('The matrix is singular.', 'red', attrs=['bold']))\n",
    "    else:\n",
    "        print(colored('The matrix is not singular.', 'red', attrs=['bold']))\n",
    "\n",
    "def is_positive_definite(matrix):\n",
    "    if np.all(np.linalg.eigvals(matrix) > 0):\n",
    "        print(colored('The matrix is positive definite.', 'red', attrs=['bold']))\n",
    "    else:\n",
    "        print(colored('The matrix is not positive definite.', 'red', attrs=['bold']))\n",
    "\n",
    "def matrix_B(A, Sigma_Z):\n",
    "    inv_Sigma_Z_hat = gamma * inv(Sigma_Z) + 2 * lamda * np.identity(n)\n",
    "    B = inv(np.identity(m) + A.T @ inv_Sigma_Z_hat @ A) @ A.T @ inv_Sigma_Z_hat\n",
    "    return B\n",
    "\n",
    "def covariance_matrix_W(A, Sigma_Z):\n",
    "    inv_Sigma_Z_hat = gamma * inv(Sigma_Z) + 2 * lamda * np.identity(n)\n",
    "    Sigma_W = inv(np.identity(m) + A.T @ inv_Sigma_Z_hat @ A)\n",
    "    return Sigma_W\n",
    "\n",
    "def matrix_A(B, Sigma_W):\n",
    "    A = inv(inv(Sigma_Y) + B.T @ inv(Sigma_W) @ B) @ B.T @ inv(Sigma_W)\n",
    "    return A\n",
    "\n",
    "def covariance_matrix_Z(B, Sigma_W):\n",
    "    Sigma_Z = inv(inv(Sigma_Y) + B.T @ inv(Sigma_W) @ B)\n",
    "    diagonalized_Sigma_Z = np.diag(Sigma_Z.diagonal())\n",
    "    return diagonalized_Sigma_Z\n",
    "\n",
    "def covariance_matrix_XV(B):\n",
    "    cov_XV = np.block([[np.identity(m), B @ eigenvectors @ Sigma_V],\n",
    "                       [(B @ eigenvectors @ Sigma_V).T, Sigma_V]])\n",
    "    return cov_XV\n",
    "\n",
    "def encoder_mi(B, Sigma_W):\n",
    "    return 0.5 * np.log(det(B @ Sigma_Y @ B.T + Sigma_W) / det(Sigma_W))\n",
    "\n",
    "def decoder_mi(A, Sigma_Z):\n",
    "    return 0.5 * np.log(det(A @ A.T + Sigma_Z) / det(Sigma_Z))\n",
    "\n",
    "def mi_VX(B, Sigma_W):\n",
    "    return 0.5 * np.log(det(B @ Sigma_Y @ B.T + Sigma_W) / det(sigma_squared * B @ B.T + Sigma_W))\n",
    "\n",
    "def reconstruction_error(recon, orig):\n",
    "    norm_diff = LA_norm(orig - recon, 2)\n",
    "    orig_norm = LA_norm(orig, 2)\n",
    "    recon_err = norm_diff / orig_norm\n",
    "    return recon_err\n",
    "\n",
    "def objective_function(A, B, Sigma_Z, Sigma_W):\n",
    "    Sigma_X = B @ Sigma_Y @ B.T + Sigma_W\n",
    "    \n",
    "    regularizer = 0.5 * (np.trace(Sigma_X) - np.log(det(Sigma_W)) - m)\n",
    "    reconstruction = 0.5 * (np.trace(Sigma_X) + \\\n",
    "                            np.trace(A.T @ inv(Sigma_Z) @ Sigma_Y @ B.T) + \\\n",
    "                            np.trace(inv(Sigma_Z) @ A @ B @ Sigma_Y) - \\\n",
    "                            np.trace(inv(Sigma_Z) @ Sigma_Y) - \\\n",
    "                            np.trace((np.identity(m) + A.T @ inv(Sigma_Z) @ A) @ Sigma_X) - \\\n",
    "                            n * np.log(2 * pi) - np.log(det(Sigma_Z)))\n",
    "    lambda_term = lamda * np.trace((np.identity(n) - A @ B) @ Sigma_Y @ ((np.identity(n) - A @ B).T) + A @ Sigma_W @ A.T)\n",
    "    \n",
    "    return regularizer - gamma * reconstruction + lambda_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "87c4fdae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_cost_function(cf_arr):\n",
    "    \"\"\"\n",
    "    Plot values of objective function against iterations t\n",
    "    \"\"\"\n",
    "    plt.plot(range(1, len(cf_arr) + 1), cf_arr)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('Cost Function', fontsize=10)\n",
    "    plt.show()\n",
    "\n",
    "def plot_encoder_mi(en_mi_arr):\n",
    "    \"\"\"\n",
    "    Plot mutual information of encoder against iterations t\n",
    "    \"\"\"\n",
    "    plt.plot(range(1, len(en_mi_arr) + 1), en_mi_arr)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('Mutual Information of Encoder', fontsize=10)\n",
    "    plt.show()\n",
    "\n",
    "def plot_decoder_mi(de_mi_arr):\n",
    "    \"\"\"\n",
    "    Plot mutual information of decoder against iterations t\n",
    "    \"\"\"\n",
    "    plt.plot(range(1, len(de_mi_arr) + 1), de_mi_arr)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('Mutual Information of Decoder', fontsize=10)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "00ae4c9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_optimal_solution(sol, m):\n",
    "    A_arr = sol[:n*m] \n",
    "    B_arr = sol[n*m:2*n*m]\n",
    "    Sigma_Z_arr = sol[2*n*m:2*n*m+n*n]\n",
    "    Sigma_Z = Sigma_Z_arr.reshape((n, n))\n",
    "    Sigma_W_arr = sol[2*n*m+n*n:2*n*m+n*n+m*m]\n",
    "    Sigma_W = Sigma_W_arr.reshape((m, m))\n",
    "    cost_function = sol[2*n*m+n*n+m*m:2*n*m+n*n+m*m+1][0]\n",
    "    en_mi = sol[2*n*m+n*n+m*m+1:2*n*m+n*n+m*m+2][0]\n",
    "    de_mi = sol[2*n*m+n*n+m*m+2:2*n*m+n*n+m*m+3][0]\n",
    "    recon_err = sol[-1]\n",
    "    len_cf_mi_arr = sol[2*n*m+n*n+m*m+3:2*n*m+n*n+m*m+6]\n",
    "    Sigma_X = sol[2*n*m+n*n+m*m+6:2*n*m+n*n+2*m*m+6].reshape((m, m))\n",
    "    Sigma_Y_hat = sol[2*n*m+n*n+2*m*m+6:2*n*m+2*n*n+2*m*m+6].reshape((n, n))\n",
    "    \n",
    "    print(colored('At optimal solution:', attrs=['bold']))\n",
    "    \n",
    "    if m > 1:\n",
    "        print('\\nMutual information of the encoder:\\n{}'.format(round(en_mi, 4)))\n",
    "        print('\\nReconstruction error:\\n{}'.format(round(recon_err, 8)))\n",
    "    else:\n",
    "        print('\\nMutual information of the encoder:\\n{}'.format(round(en_mi, 4)))     \n",
    "        print('\\nReconstruction error:\\n{}'.format(round(recon_err, 8)))\n",
    "        \n",
    "    return len_cf_mi_arr\n",
    "\n",
    "def print_comprehensive_results(gamma, lamda, flag, m, n, is_arr):\n",
    "    if flag == 0:\n",
    "        # Generate random initial encoder inputs (B, Sigma_W)\n",
    "        B, Sigma_W = initial_inputs(flag)[1:1+m*n].reshape((m, n)), initial_inputs(flag)[1+m*n:1+m*n+m*m].reshape((m, m))\n",
    "    else:\n",
    "        # Generate random initial decoder inputs (A, Sigma_Z)\n",
    "        A, Sigma_Z = initial_inputs(flag)[1:1+n*m].reshape((n, m)), initial_inputs(flag)[1+n*m:1+n*m+n*n].reshape((n, n))\n",
    "    \n",
    "    # Print given inputs\n",
    "    if is_arr == 0:\n",
    "        if m > 1 and flag == 0:\n",
    "            print(colored('Given encoder X:', attrs=['bold']))\n",
    "            print('Initial matrix B:')\n",
    "            print(np.round(B.reshape((m, n)), 4))\n",
    "            print('\\nInitial covariance matrix of W:')\n",
    "            print(np.round(Sigma_W, 4))\n",
    "        elif m == 1 and flag == 0:\n",
    "            print(colored('Given encoder X:', attrs=['bold']))\n",
    "            print('Initial vector b:')\n",
    "            print(np.round(B.reshape((m, n)), 4)[0])\n",
    "            print('\\nInitial variance of W:')\n",
    "            print(np.round(Sigma_W, 4)[0][0])\n",
    "        elif m > 1 and flag == 1:\n",
    "            print(colored('Given decoder Y_hat:', attrs=['bold']))\n",
    "            print('Initial matrix A:')\n",
    "            print(np.round(A.reshape((n, m)), 4))\n",
    "            print('\\nInitial covariance matrix of Z:')\n",
    "            print(np.round(Sigma_Z, 4))\n",
    "        else:\n",
    "            print(colored('Given decoder Y_hat:', attrs=['bold']))\n",
    "            print('Initial vector a:')\n",
    "            print(np.round(A.reshape((n, m)), 4))\n",
    "            print('\\nInitial covariance matrix of Z:')\n",
    "            print(np.round(Sigma_Z, 4))    \n",
    "    \n",
    "        # Print results\n",
    "        if flag == 0:\n",
    "            # Compute optimal solution given encoder inputs\n",
    "            opt_sol = rate_distortion(initial_inputs(flag), is_arr)\n",
    "    \n",
    "            # Extract length of arrays for cost function and mutual information of encoder and decoder\n",
    "            len_all_arrs = print_optimal_solution(opt_sol, m).astype(int)\n",
    "            len_cf_arr, len_en_mi_arr = len_all_arrs[:2]\n",
    "            len_cf_en_mi_arr = len_cf_arr + len_en_mi_arr\n",
    "        \n",
    "            # Plot values of cost function and mutual information against iterations\n",
    "            cf_arr = opt_sol[2*n*m+2*n*n+2*m*m+6 : 2*n*m+2*n*n+2*m*m+6+len_cf_arr]\n",
    "            plot_cost_function(cf_arr)\n",
    "    \n",
    "            en_mi_arr = opt_sol[2*n*m+2*n*n+2*m*m+6+len_cf_arr : 2*n*m+2*n*n+2*m*m+6+len_cf_en_mi_arr]\n",
    "            plot_encoder_mi(en_mi_arr)\n",
    "    \n",
    "            de_mi_arr = opt_sol[2*n*m+2*n*n+2*m*m+6+len_cf_en_mi_arr:]\n",
    "            plot_decoder_mi(de_mi_arr)  \n",
    "        else:\n",
    "            opt_sol = rate_distortion(initial_inputs(flag), is_arr)\n",
    "        \n",
    "            len_all_arrs = print_optimal_solution(opt_sol, m).astype(int)\n",
    "            len_cf_arr, len_en_mi_arr = len_all_arrs[:2]\n",
    "            len_cf_en_mi_arr = len_cf_arr + len_en_mi_arr\n",
    "        \n",
    "            cf_arr = opt_sol[2*n*m+2*n*n+2*m*m+6 : 2*n*m+2*n*n+2*m*m+6+len_cf_arr]\n",
    "            plot_cost_function(cf_arr)\n",
    "    \n",
    "            en_mi_arr = opt_sol[2*n*m+2*n*n+2*m*m+6+len_cf_arr : 2*n*m+2*n*n+2*m*m+6+len_cf_en_mi_arr]\n",
    "            plot_encoder_mi(en_mi_arr)\n",
    "    \n",
    "            de_mi_arr = opt_sol[2*n*m+2*n*n+2*m*m+6+len_cf_en_mi_arr:]\n",
    "            plot_decoder_mi(de_mi_arr)\n",
    "    else:\n",
    "        if flag == 0:\n",
    "            opt_sol = rate_distortion(initial_inputs(flag), is_arr)\n",
    "            \n",
    "            en_mi = round(opt_sol[2*n*m+n*n+m*m+1:2*n*m+n*n+m*m+2][0], 8)\n",
    "            de_mi = round(opt_sol[2*n*m+n*n+m*m+2:2*n*m+n*n+m*m+3][0], 8)\n",
    "            recon_err = round(opt_sol[-1], 8)\n",
    "            \n",
    "            return [recon_err, en_mi, de_mi, opt_sol]\n",
    "        else:\n",
    "            opt_sol = rate_distortion(initial_inputs(flag), is_arr)\n",
    "            \n",
    "            en_mi = round(opt_sol[2*n*m+n*n+m*m+1:2*n*m+n*n+m*m+2][0], 8)\n",
    "            de_mi = round(opt_sol[2*n*m+n*n+m*m+2:2*n*m+n*n+m*m+3][0], 8)\n",
    "            recon_err = round(opt_sol[-1], 8)\n",
    "            \n",
    "            return [recon_err, en_mi, de_mi, opt_sol]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f2fbe240",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "\n",
    "*****************************************************************\n",
    "**                          ALGORITHM                          **\n",
    "*****************************************************************\n",
    "   \n",
    "Inputs:\n",
    "- MAX_ITERS: Maximum number of iterations\n",
    "- n, m: Dimensions of the matrix\n",
    "- TOL_ERR: Tolerable error\n",
    "- Sigma_Y: A random nxn positive definite matrix\n",
    "\n",
    "Algorithm:\n",
    "1. Initialize flag\n",
    "    a. If we start with the encoder, set flag = 0.\n",
    "    b. Otherwise, set flag = 1.\n",
    "    \n",
    "2. Generate initial inputs for the iteration step\n",
    "    a. If flag = 0, then do:\n",
    "        i. create random initial encoder inputs, including \n",
    "            - a random mxn matrix B\n",
    "            - a random mxm positive definite covariance matrix Sigma_W\n",
    "        ii. set flag = 1.\n",
    "    b. If flag = 1, then do:\n",
    "        i. create random initial decoder inputs, including \n",
    "            - a random nxm matrix A\n",
    "            - a random nxn positive definite covariance matrix Sigma_Z\n",
    "        ii. set flag = 0.\n",
    "        \n",
    "3. Set iteration counter i = 0. \n",
    "\n",
    "4. Iterative step\n",
    "    a. If flag = 0, given the decoder inputs (A, Sigma_Z) at iteration i,\n",
    "        i. compute the corresponding encoder inputs at iteration i+1:\n",
    "            B = matrix_B(A, Sigma_Z)\n",
    "            Sigma_W = covariance_matrix_W(A, Sigma_Z)\n",
    "        ii. set flag = 1.\n",
    "        iii. compute the resulting gamma-VAE cost function and mutual information of the encoder.\n",
    "        iv. check if the cost function is NaN:\n",
    "            - if it is, conclude that the algorithm fails to converge and skip to step 7.\n",
    "        v. check for convergence after the second iteration:\n",
    "            - if converges, conclude that the algorithm converges and skip to step 7.\n",
    "            - unless, check if the maximum number of iterations has been reached:\n",
    "                - if it is, conclude that the algorithm failed to converge and skip to step 7.\n",
    "                - otherwise, move to step 5.\n",
    "    b. If flag = 1, given the encoder inputs (B, Sigma_W) at iteration i,\n",
    "        i. compute the corresponding decoder inputs at iteration i:\n",
    "            A = matrix_A(B, Sigma_W)\n",
    "            Sigma_Z = covariance_matrix_Z(B, Sigma_W, is_diagonal)\n",
    "        ii. set flag = 0.\n",
    "        iii. compute the resulting gamma-VAE cost function, mutual information of the decoder, and reconstruction error.\n",
    "        iv. check if the cost function is NaN:\n",
    "            - if it is, conclude that the algorithm fails to converge and skip to step 7.\n",
    "        v. check for convergence after the second iteration:\n",
    "            - if converges, conclude that the algorithm converges and skip to step 7.\n",
    "            - unless, check if the maximum number of iterations has been reached:\n",
    "                - if it is, conclude that the algorithm failed to converge and skip to step 7.\n",
    "                - otherwise, move to step 5.\n",
    "            \n",
    "5. Increment iteration counter i <- i + 1.\n",
    "\n",
    "6. If the iteration counter i < MAX_ITERS, then move back to step 4.\n",
    "    Otherwise, move to step 7.\n",
    "    \n",
    "7. Compute the values of Sigma_X and Sigma_Y_hat.\n",
    "        \n",
    "8. Display results\n",
    "    a. display the optimal solution (A, B, Sigma_Z, Sigma_W).\n",
    "    b. display the corresponding minimum value of gamma-VAE cost function.\n",
    "    c. display the resulting mutual information of both encoder and decoder.\n",
    "    d. display the values of Sigma_X and Sigma_Y_hat.\n",
    "    e. display the value of reconstruction error.\n",
    "    f. move to step 9.\n",
    "    \n",
    "9. Stop.\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "def rate_distortion(inputs, is_arr):\n",
    "    flag = inputs[0]\n",
    "    if flag == 0:\n",
    "        B = inputs[1:1+m*n].reshape((m, n))\n",
    "        Sigma_W = inputs[1+m*n:1+m*n+m*m].reshape((m, m))\n",
    "        flag = 1\n",
    "        # Array of current encoder inputs (B_t, Sigma_W_t)\n",
    "        current_encoder_inputs = np.concatenate((B.reshape((m*n)), Sigma_W.reshape((m*m))))\n",
    "    else:\n",
    "        A = inputs[1:1+n*m].reshape((n, m))\n",
    "        Sigma_Z = inputs[1+n*m:1+n*m+n*n].reshape((n, n))\n",
    "        flag = 0\n",
    "        # Array of current decoder inputs (A_t, Sigma_Z_t)\n",
    "        current_decoder_inputs = np.concatenate((A.reshape((n*m)), Sigma_Z.reshape((n*n))))\n",
    "    \n",
    "    # Cost function and mutual information arrays\n",
    "    cf_arr = []\n",
    "    en_mi_arr = []\n",
    "    de_mi_arr = [] \n",
    "\n",
    "    # Iteration step\n",
    "    try:\n",
    "        for i in range(0, MAX_ITERS):\n",
    "            if  flag == 0:\n",
    "                B = matrix_B(A, Sigma_Z)\n",
    "                Sigma_W = covariance_matrix_W(A, Sigma_Z)\n",
    "                flag = 1\n",
    "                \n",
    "                # Check if the value of the cost function is not a number\n",
    "                current_obj = objective_function(A, B, Sigma_Z, Sigma_W)\n",
    "                if np.isnan(current_obj):\n",
    "                    if is_arr == 0:\n",
    "                        print(colored('\\nThe algorithm fails to converge after {} iterations due to NaN values.\\n'.format(i+1), 'red', attrs=['bold']))\n",
    "                    break\n",
    "                    \n",
    "                cf_arr = np.concatenate((cf_arr, [current_obj]))\n",
    "                current_en_mi = encoder_mi(B, Sigma_W)\n",
    "                en_mi_arr = np.concatenate((en_mi_arr, [current_en_mi]))\n",
    "                \n",
    "                # For the first iteration, update the current encoder inputs and value of the cost function\n",
    "                if i == 0:\n",
    "                    current_encoder_inputs = np.concatenate((B.reshape((m*n)), Sigma_W.reshape((m*m))))\n",
    "                    previous_obj = current_obj\n",
    "                # From the second iteration,\n",
    "                # 1. Compute the Frobenius norm of the difference between\n",
    "                #    i. B and itself in the previous iteration\n",
    "                #    ii. Sigma_W and itself in the previous iteration\n",
    "                # 2. Compute the difference between the cost function and itself in the previous iteration\n",
    "                # 3. Update the current encoder inputs and value of the cost function\n",
    "                else:\n",
    "                    B_diff = B - current_encoder_inputs[:m*n].reshape((m, n))\n",
    "                    B_norm_diff = LA_norm(B_diff, 'fro')\n",
    "                    Sigma_W_diff = Sigma_W - current_encoder_inputs[m*n:m*n+m*m].reshape((m, m))\n",
    "                    Sigma_W_norm_diff = LA_norm(Sigma_W_diff, 'fro')\n",
    "                    obj_diff = previous_obj - current_obj\n",
    "                    previous_obj = current_obj\n",
    "                    current_encoder_inputs = np.concatenate((B.reshape((m*n)), Sigma_W.reshape((m*m))))\n",
    "                    # Check for convergence\n",
    "                    if B_norm_diff <= TOL_ERR and Sigma_W_norm_diff <= TOL_ERR and round(obj_diff, 8) == 0 and \\\n",
    "                    is_close_to_zero(recon_err, 1e-6):\n",
    "                        if is_arr == 0:\n",
    "                            print(colored('\\nThe algorithm converges after {} iterations.\\n'.format(i+1), 'blue', attrs=['bold']))\n",
    "                        break\n",
    "            else:\n",
    "                A = matrix_A(B, Sigma_W)\n",
    "                Sigma_Z = covariance_matrix_Z(B, Sigma_W)\n",
    "                flag = 0\n",
    "                \n",
    "                current_obj = objective_function(A, B, Sigma_Z, Sigma_W)\n",
    "                if np.isnan(current_obj):\n",
    "                    if is_arr == 0:\n",
    "                        print(colored('\\nThe algorithm fails to converge after {} iterations due to NaN values.\\n'.format(i+1), 'red', attrs=['bold']))\n",
    "                    break\n",
    "                    \n",
    "                cf_arr = np.concatenate((cf_arr, [current_obj]))\n",
    "                current_de_mi = decoder_mi(A, Sigma_Z)\n",
    "                de_mi_arr = np.concatenate((de_mi_arr, [current_de_mi]))\n",
    "                \n",
    "                Sigma_Y_hat = A @ A.T + Sigma_Z\n",
    "                recon_err = reconstruction_error(Sigma_Y_hat, Sigma_Y)\n",
    "                \n",
    "                # For the first iteration, update the current decoder inputs and value of the cost function\n",
    "                if i == 0:\n",
    "                    current_decoder_inputs = np.concatenate((A.reshape((n*m)), Sigma_Z.reshape((n*n))))\n",
    "                    previous_obj = current_obj\n",
    "                # From the second iteration,\n",
    "                # 1. Compute the Frobenius norm of the difference between\n",
    "                #    i. A and itself in the previous iteration\n",
    "                #    ii. Sigma_Z and itself in the previous iteration\n",
    "                # 2. Compute the difference between the cost function and itself in the previous iteration\n",
    "                # 3. Update the current dencoder inputs and value of the cost function                \n",
    "                else:\n",
    "                    A_diff = A - current_decoder_inputs[:n*m].reshape((n, m))\n",
    "                    A_norm_diff = LA_norm(A_diff, 'fro')\n",
    "                    Sigma_Z_diff = Sigma_Z - current_decoder_inputs[n*m:n*m+n*n].reshape((n, n))\n",
    "                    Sigma_Z_norm_diff = LA_norm(Sigma_Z_diff, 'fro')\n",
    "                    obj_diff = previous_obj - current_obj\n",
    "                    previous_obj = current_obj\n",
    "                    current_decoder_inputs = np.concatenate((A.reshape((n*m)), Sigma_Z.reshape((n*n))))\n",
    "                    # Check for convergence\n",
    "                    if A_norm_diff <= TOL_ERR and Sigma_Z_norm_diff <= TOL_ERR and round(obj_diff, 8) == 0 and \\\n",
    "                    is_close_to_zero(recon_err, 1e-6):\n",
    "                        if is_arr == 0:\n",
    "                            print(colored('\\nThe algorithm converges after {} iterations.\\n'.format(i+1), 'blue', attrs=['bold']))\n",
    "                        break                       \n",
    "\n",
    "        # Compute Sigma_X and Sigma_Y_hat  \n",
    "        Sigma_X = B @ Sigma_Y @ B.T + Sigma_W\n",
    "        Sigma_Y_hat = A @ A.T + Sigma_Z\n",
    "        \n",
    "        sol = np.concatenate((A.reshape((n*m)), B.reshape((m*n)),\n",
    "                              Sigma_Z.reshape((n*n)), Sigma_W.reshape((m*m)),\n",
    "                              [current_obj], [current_en_mi], [current_de_mi],\n",
    "                              [len(cf_arr)], [len(en_mi_arr)], [len(de_mi_arr)],\n",
    "                              Sigma_X.reshape((m*m)), Sigma_Y_hat.reshape((n*n)),\n",
    "                              cf_arr, en_mi_arr, de_mi_arr, [recon_err]))\n",
    "          \n",
    "        if is_arr == 0 and i == MAX_ITERS - 1 and recon_err > MAX_RECON_ERR:\n",
    "            print(colored('\\nMax iterations was reached!', 'red', attrs=['bold']))\n",
    "            print('There is NO solutions that has reconstruction error statisfying the tolerance error = {}.\\n'.format(MAX_RECON_ERR))\n",
    "            \n",
    "        return sol\n",
    "    \n",
    "    except Exception as e:\n",
    "        if is_arr == 0:\n",
    "            print(colored('\\nThe algorithm fails to converge after {} iterations due to {}.\\n'.format(i+1, e), 'red', attrs=['bold']))\n",
    "         \n",
    "        Sigma_X = B @ Sigma_Y @ B.T + Sigma_W\n",
    "        Sigma_Y_hat = A @ A.T + Sigma_Z\n",
    "        \n",
    "        sol = np.concatenate((A.reshape((n*m)), B.reshape((m*n)),\n",
    "                              Sigma_Z.reshape((n*n)), Sigma_W.reshape((m*m)),\n",
    "                              [current_obj], [current_en_mi], [current_de_mi], \n",
    "                              [len(cf_arr)], [len(en_mi_arr)], [len(de_mi_arr)],\n",
    "                              Sigma_X.reshape((m*m)), Sigma_Y_hat.reshape((n*n)),\n",
    "                              cf_arr, en_mi_arr, de_mi_arr, [recon_err]))\n",
    "        return sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d3ee78d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_Sigma_V(case):\n",
    "    for case_idx in range(num_cases):\n",
    "        if case_idx == 0:\n",
    "            # Case 1: Linear dependence of v_1 and v_2, linear dependence of v_3 and v_4, with independence of v_5\n",
    "            v_1 = np.random.normal(mean, std_dev_v1, size=num_samples)\n",
    "            v_3 = np.random.normal(mean, std_dev_v3, size=num_samples)\n",
    "            v_5 = np.random.normal(mean, std_dev_v5, size=num_samples)\n",
    "\n",
    "            random_noise_z2 = np.random.normal(mean, std_dev_z2, num_samples)\n",
    "            random_noise_z4 = np.random.normal(mean, std_dev_z4, num_samples)\n",
    "            \n",
    "            v_2 = alpha * v_1 + random_noise_z2\n",
    "            v_4 = beta * v_3 + random_noise_z4\n",
    "\n",
    "            V_1 = np.array([v_1, v_2, v_3, v_4, v_5])\n",
    "            Sigma_V_1 = np.round(np.cov(V_1), 4)\n",
    "\n",
    "        elif case_idx == 1:\n",
    "            # Case 2: Linear dependence of v_1, v_2, v_3, and linear dependence of v_4 and v_5\n",
    "            v_1 = np.random.normal(mean, std_dev_v1, size=num_samples)\n",
    "            v_4 = np.random.normal(mean, std_dev_v4, size=num_samples)\n",
    "\n",
    "            random_noise_z2 = np.random.normal(mean, std_dev_z2, num_samples)\n",
    "            random_noise_z3 = np.random.normal(mean, std_dev_z3, num_samples)\n",
    "            random_noise_z5 = np.random.normal(mean, std_dev_z5, num_samples)\n",
    "            \n",
    "            v_2 = alpha * v_1 + random_noise_z2\n",
    "            v_3 = beta * v_1 + random_noise_z3\n",
    "            v_5 = delta * v_4 + random_noise_z5\n",
    "\n",
    "            V_2 = np.array([v_1, v_2, v_3, v_4, v_5])\n",
    "            Sigma_V_2 = np.round(np.cov(V_2), 4)  \n",
    "        \n",
    "        else:\n",
    "            # Case 3: Linear dependence of v_2, v_3, v_4, v_5, with v_1\n",
    "            v_1 = np.random.normal(mean, std_dev_v1, size=num_samples)\n",
    "\n",
    "            random_noise_z2 = np.random.normal(mean, std_dev_z2, num_samples)\n",
    "            random_noise_z3 = np.random.normal(mean, std_dev_z3, num_samples)\n",
    "            random_noise_z4 = np.random.normal(mean, std_dev_z4, num_samples)\n",
    "            random_noise_z5 = np.random.normal(mean, std_dev_z5, num_samples)\n",
    "            \n",
    "            v_2 = alpha * v_1 + random_noise_z2\n",
    "            v_3 = beta * v_1 + random_noise_z3\n",
    "            v_4 = delta * v_1 + random_noise_z4\n",
    "            v_5 = omega * v_1 + random_noise_z5\n",
    "\n",
    "            V_3 = np.array([v_1, v_2, v_3, v_4, v_5])\n",
    "            Sigma_V_3 = np.round(np.cov(V_3), 4)\n",
    "    \n",
    "    if case == 0:\n",
    "        print(colored('Scenario 1:', attrs=['bold','underline']))\n",
    "        print(colored('\\nCovariance matrix of generative variable V:', 'blue', attrs=['bold']))\n",
    "        print(Sigma_V_1)\n",
    "        is_singular(Sigma_V_1)\n",
    "        return Sigma_V_1\n",
    "    \n",
    "    elif case == 1:\n",
    "        print(colored('\\nScenario 2:', attrs=['bold','underline']))\n",
    "        print(colored('\\nCovariance matrix of generative variable V:', 'blue', attrs=['bold']))\n",
    "        print(Sigma_V_2)\n",
    "        is_singular(Sigma_V_2) \n",
    "        return Sigma_V_2\n",
    "    \n",
    "    else:\n",
    "        print(colored('\\nScenario 3:', attrs=['bold','underline']))\n",
    "        print(colored('\\nCovariance matrix of generative variable V:', 'blue', attrs=['bold']))\n",
    "        print(Sigma_V_3)\n",
    "        is_singular(Sigma_V_3)  \n",
    "        return Sigma_V_3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eff45dfc",
   "metadata": {},
   "source": [
    "## I. Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7cc2f26c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34mAn array of gamma:\u001b[0m\n",
      "[0.98 0.99 1.   1.01 1.02]\n",
      "\u001b[1m\u001b[34m\n",
      "An array of lambda:\u001b[0m\n",
      "[-0.02 -0.01  0.    0.01  0.02]\n",
      "\u001b[1m\u001b[34m\n",
      "Independent eigenvectors:\u001b[0m\n",
      "[[1 0 0 0 0]\n",
      " [0 0 0 1 0]\n",
      " [0 0 0 0 1]\n",
      " [0 0 1 0 0]\n",
      " [0 1 0 0 0]]\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance of noise Z_tilde:\u001b[0m\n",
      "[[0.0001 0.     0.     0.     0.    ]\n",
      " [0.     0.0001 0.     0.     0.    ]\n",
      " [0.     0.     0.0001 0.     0.    ]\n",
      " [0.     0.     0.     0.0001 0.    ]\n",
      " [0.     0.     0.     0.     0.0001]]\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Given:\n",
    "1. Maximum number of iterations: MAX_ITERS = 10,000\n",
    "2. Dimensions of the matrix: s = 5, n = 5, and m = 3\n",
    "3. Tolerable error: TOL_ERR = 1e-8\n",
    "4. Reconstruction error tolerance: MAX_RECON_ERR = 0.05\n",
    "5. A nxn positive definite matrix Sigma_Y = Gamma * Sigma_V * Gamma_T + Sigma_Z_tilde\n",
    "6. An array of gamma = [0.98, 1.02] with step size = 0.01\n",
    "7. An array of lambda = [-0.02, 0.02] with step size = 0.01\n",
    "\"\"\"\n",
    "\n",
    "# Constants\n",
    "MAX_ITERS = 10000\n",
    "s, n, m = 5, 5, 3\n",
    "TOL_ERR = 1e-8\n",
    "MAX_RECON_ERR = 0.05\n",
    "\n",
    "num_cases = 3\n",
    "num_samples = int(1e7)\n",
    "alpha = 0.1\n",
    "beta = 0.3\n",
    "delta = 0.4\n",
    "omega = 0.2\n",
    "\n",
    "mean = 0\n",
    "\n",
    "std_dev_v1 = 0.05\n",
    "std_dev_v2 = 0.01\n",
    "std_dev_v3 = 0.02\n",
    "std_dev_v4 = 0.04\n",
    "std_dev_v5 = 0.03\n",
    "\n",
    "std_dev_z2 = 0.02\n",
    "std_dev_z3 = 0.01\n",
    "std_dev_z4 = 0.03\n",
    "std_dev_z5 = 0.04\n",
    "\n",
    "# Arrays of gamma and lambda\n",
    "gamma_arr = np.round(np.arange(0.98, 1.02, 0.01), 2)\n",
    "print(colored('An array of gamma:', 'blue', attrs=['bold']))\n",
    "print('{}'.format(gamma_arr))\n",
    "\n",
    "lambda_arr = np.round(np.arange(-0.02, 0.03, 0.01), 2)\n",
    "print(colored('\\nAn array of lambda:', 'blue', attrs=['bold']))\n",
    "print('{}'.format(lambda_arr))\n",
    "\n",
    "# Independent eigenvectors\n",
    "eigenvectors = np.array([[1, 0, 0, 0, 0],\n",
    "                         [0, 0, 0, 1, 0],\n",
    "                         [0, 0, 0, 0, 1],\n",
    "                         [0, 0, 1, 0, 0],\n",
    "                         [0, 1, 0, 0, 0]])\n",
    "print(colored('\\nIndependent eigenvectors:', 'blue', attrs=['bold']))\n",
    "print(eigenvectors)\n",
    "\n",
    "# Covariance of noise Z_tilde\n",
    "sigma_squared = 0.01**2\n",
    "Sigma_Z_tilde = sigma_squared * np.identity(n)\n",
    "print(colored('\\nCovariance of noise Z_tilde:', 'blue', attrs=['bold']))\n",
    "print(np.round(Sigma_Z_tilde, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d132e67",
   "metadata": {},
   "source": [
    "## II. Partitioning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8d34c4c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1mAll ways to divide the indices of the generative parameters into three distinct groups:\n",
      "\u001b[0m\n",
      "Partition 1: Group 1: set(), Group 2: set(), Group 3: {4, 5, 6, 7, 8}\n",
      "Partition 2: Group 1: set(), Group 2: {4}, Group 3: {8, 5, 6, 7}\n",
      "Partition 3: Group 1: set(), Group 2: {5}, Group 3: {8, 4, 6, 7}\n",
      "Partition 4: Group 1: set(), Group 2: {6}, Group 3: {8, 4, 5, 7}\n",
      "Partition 5: Group 1: set(), Group 2: {7}, Group 3: {8, 4, 5, 6}\n",
      "Partition 6: Group 1: set(), Group 2: {8}, Group 3: {4, 5, 6, 7}\n",
      "Partition 7: Group 1: set(), Group 2: {4, 5}, Group 3: {8, 6, 7}\n",
      "Partition 8: Group 1: set(), Group 2: {4, 6}, Group 3: {8, 5, 7}\n",
      "Partition 9: Group 1: set(), Group 2: {4, 7}, Group 3: {8, 5, 6}\n",
      "Partition 10: Group 1: set(), Group 2: {8, 4}, Group 3: {5, 6, 7}\n",
      "Partition 11: Group 1: set(), Group 2: {5, 6}, Group 3: {8, 4, 7}\n",
      "Partition 12: Group 1: set(), Group 2: {5, 7}, Group 3: {8, 4, 6}\n",
      "Partition 13: Group 1: set(), Group 2: {8, 5}, Group 3: {4, 6, 7}\n",
      "Partition 14: Group 1: set(), Group 2: {6, 7}, Group 3: {8, 4, 5}\n",
      "Partition 15: Group 1: set(), Group 2: {8, 6}, Group 3: {4, 5, 7}\n",
      "Partition 16: Group 1: set(), Group 2: {8, 7}, Group 3: {4, 5, 6}\n",
      "Partition 17: Group 1: set(), Group 2: {4, 5, 6}, Group 3: {8, 7}\n",
      "Partition 18: Group 1: set(), Group 2: {4, 5, 7}, Group 3: {8, 6}\n",
      "Partition 19: Group 1: set(), Group 2: {8, 4, 5}, Group 3: {6, 7}\n",
      "Partition 20: Group 1: set(), Group 2: {4, 6, 7}, Group 3: {8, 5}\n",
      "Partition 21: Group 1: set(), Group 2: {8, 4, 6}, Group 3: {5, 7}\n",
      "Partition 22: Group 1: set(), Group 2: {8, 4, 7}, Group 3: {5, 6}\n",
      "Partition 23: Group 1: set(), Group 2: {5, 6, 7}, Group 3: {8, 4}\n",
      "Partition 24: Group 1: set(), Group 2: {8, 5, 6}, Group 3: {4, 7}\n",
      "Partition 25: Group 1: set(), Group 2: {8, 5, 7}, Group 3: {4, 6}\n",
      "Partition 26: Group 1: set(), Group 2: {8, 6, 7}, Group 3: {4, 5}\n",
      "Partition 27: Group 1: set(), Group 2: {4, 5, 6, 7}, Group 3: {8}\n",
      "Partition 28: Group 1: set(), Group 2: {8, 4, 5, 6}, Group 3: {7}\n",
      "Partition 29: Group 1: set(), Group 2: {8, 4, 5, 7}, Group 3: {6}\n",
      "Partition 30: Group 1: set(), Group 2: {8, 4, 6, 7}, Group 3: {5}\n",
      "Partition 31: Group 1: set(), Group 2: {8, 5, 6, 7}, Group 3: {4}\n",
      "Partition 32: Group 1: set(), Group 2: {4, 5, 6, 7, 8}, Group 3: set()\n",
      "Partition 33: Group 1: {4}, Group 2: set(), Group 3: {8, 5, 6, 7}\n",
      "Partition 34: Group 1: {5}, Group 2: set(), Group 3: {8, 4, 6, 7}\n",
      "Partition 35: Group 1: {6}, Group 2: set(), Group 3: {8, 4, 5, 7}\n",
      "Partition 36: Group 1: {7}, Group 2: set(), Group 3: {8, 4, 5, 6}\n",
      "Partition 37: Group 1: {8}, Group 2: set(), Group 3: {4, 5, 6, 7}\n",
      "Partition 38: Group 1: {4}, Group 2: {8}, Group 3: {5, 6, 7}\n",
      "Partition 39: Group 1: {4}, Group 2: {5}, Group 3: {8, 6, 7}\n",
      "Partition 40: Group 1: {4}, Group 2: {6}, Group 3: {8, 5, 7}\n",
      "Partition 41: Group 1: {4}, Group 2: {7}, Group 3: {8, 5, 6}\n",
      "Partition 42: Group 1: {5}, Group 2: {8}, Group 3: {4, 6, 7}\n",
      "Partition 43: Group 1: {5}, Group 2: {4}, Group 3: {8, 6, 7}\n",
      "Partition 44: Group 1: {5}, Group 2: {6}, Group 3: {8, 4, 7}\n",
      "Partition 45: Group 1: {5}, Group 2: {7}, Group 3: {8, 4, 6}\n",
      "Partition 46: Group 1: {6}, Group 2: {8}, Group 3: {4, 5, 7}\n",
      "Partition 47: Group 1: {6}, Group 2: {4}, Group 3: {8, 5, 7}\n",
      "Partition 48: Group 1: {6}, Group 2: {5}, Group 3: {8, 4, 7}\n",
      "Partition 49: Group 1: {6}, Group 2: {7}, Group 3: {8, 4, 5}\n",
      "Partition 50: Group 1: {7}, Group 2: {8}, Group 3: {4, 5, 6}\n",
      "Partition 51: Group 1: {7}, Group 2: {4}, Group 3: {8, 5, 6}\n",
      "Partition 52: Group 1: {7}, Group 2: {5}, Group 3: {8, 4, 6}\n",
      "Partition 53: Group 1: {7}, Group 2: {6}, Group 3: {8, 4, 5}\n",
      "Partition 54: Group 1: {8}, Group 2: {4}, Group 3: {5, 6, 7}\n",
      "Partition 55: Group 1: {8}, Group 2: {5}, Group 3: {4, 6, 7}\n",
      "Partition 56: Group 1: {8}, Group 2: {6}, Group 3: {4, 5, 7}\n",
      "Partition 57: Group 1: {8}, Group 2: {7}, Group 3: {4, 5, 6}\n",
      "Partition 58: Group 1: {4}, Group 2: {8, 5}, Group 3: {6, 7}\n",
      "Partition 59: Group 1: {4}, Group 2: {8, 6}, Group 3: {5, 7}\n",
      "Partition 60: Group 1: {4}, Group 2: {8, 7}, Group 3: {5, 6}\n",
      "Partition 61: Group 1: {4}, Group 2: {5, 6}, Group 3: {8, 7}\n",
      "Partition 62: Group 1: {4}, Group 2: {5, 7}, Group 3: {8, 6}\n",
      "Partition 63: Group 1: {4}, Group 2: {6, 7}, Group 3: {8, 5}\n",
      "Partition 64: Group 1: {5}, Group 2: {8, 4}, Group 3: {6, 7}\n",
      "Partition 65: Group 1: {5}, Group 2: {8, 6}, Group 3: {4, 7}\n",
      "Partition 66: Group 1: {5}, Group 2: {8, 7}, Group 3: {4, 6}\n",
      "Partition 67: Group 1: {5}, Group 2: {4, 6}, Group 3: {8, 7}\n",
      "Partition 68: Group 1: {5}, Group 2: {4, 7}, Group 3: {8, 6}\n",
      "Partition 69: Group 1: {5}, Group 2: {6, 7}, Group 3: {8, 4}\n",
      "Partition 70: Group 1: {6}, Group 2: {8, 4}, Group 3: {5, 7}\n",
      "Partition 71: Group 1: {6}, Group 2: {8, 5}, Group 3: {4, 7}\n",
      "Partition 72: Group 1: {6}, Group 2: {8, 7}, Group 3: {4, 5}\n",
      "Partition 73: Group 1: {6}, Group 2: {4, 5}, Group 3: {8, 7}\n",
      "Partition 74: Group 1: {6}, Group 2: {4, 7}, Group 3: {8, 5}\n",
      "Partition 75: Group 1: {6}, Group 2: {5, 7}, Group 3: {8, 4}\n",
      "Partition 76: Group 1: {7}, Group 2: {8, 4}, Group 3: {5, 6}\n",
      "Partition 77: Group 1: {7}, Group 2: {8, 5}, Group 3: {4, 6}\n",
      "Partition 78: Group 1: {7}, Group 2: {8, 6}, Group 3: {4, 5}\n",
      "Partition 79: Group 1: {7}, Group 2: {4, 5}, Group 3: {8, 6}\n",
      "Partition 80: Group 1: {7}, Group 2: {4, 6}, Group 3: {8, 5}\n",
      "Partition 81: Group 1: {7}, Group 2: {5, 6}, Group 3: {8, 4}\n",
      "Partition 82: Group 1: {8}, Group 2: {4, 5}, Group 3: {6, 7}\n",
      "Partition 83: Group 1: {8}, Group 2: {4, 6}, Group 3: {5, 7}\n",
      "Partition 84: Group 1: {8}, Group 2: {4, 7}, Group 3: {5, 6}\n",
      "Partition 85: Group 1: {8}, Group 2: {5, 6}, Group 3: {4, 7}\n",
      "Partition 86: Group 1: {8}, Group 2: {5, 7}, Group 3: {4, 6}\n",
      "Partition 87: Group 1: {8}, Group 2: {6, 7}, Group 3: {4, 5}\n",
      "Partition 88: Group 1: {4}, Group 2: {8, 5, 6}, Group 3: {7}\n",
      "Partition 89: Group 1: {4}, Group 2: {8, 5, 7}, Group 3: {6}\n",
      "Partition 90: Group 1: {4}, Group 2: {8, 6, 7}, Group 3: {5}\n",
      "Partition 91: Group 1: {4}, Group 2: {5, 6, 7}, Group 3: {8}\n",
      "Partition 92: Group 1: {5}, Group 2: {8, 4, 6}, Group 3: {7}\n",
      "Partition 93: Group 1: {5}, Group 2: {8, 4, 7}, Group 3: {6}\n",
      "Partition 94: Group 1: {5}, Group 2: {8, 6, 7}, Group 3: {4}\n",
      "Partition 95: Group 1: {5}, Group 2: {4, 6, 7}, Group 3: {8}\n",
      "Partition 96: Group 1: {6}, Group 2: {8, 4, 5}, Group 3: {7}\n",
      "Partition 97: Group 1: {6}, Group 2: {8, 4, 7}, Group 3: {5}\n",
      "Partition 98: Group 1: {6}, Group 2: {8, 5, 7}, Group 3: {4}\n",
      "Partition 99: Group 1: {6}, Group 2: {4, 5, 7}, Group 3: {8}\n",
      "Partition 100: Group 1: {7}, Group 2: {8, 4, 5}, Group 3: {6}\n",
      "Partition 101: Group 1: {7}, Group 2: {8, 4, 6}, Group 3: {5}\n",
      "Partition 102: Group 1: {7}, Group 2: {8, 5, 6}, Group 3: {4}\n",
      "Partition 103: Group 1: {7}, Group 2: {4, 5, 6}, Group 3: {8}\n",
      "Partition 104: Group 1: {8}, Group 2: {4, 5, 6}, Group 3: {7}\n",
      "Partition 105: Group 1: {8}, Group 2: {4, 5, 7}, Group 3: {6}\n",
      "Partition 106: Group 1: {8}, Group 2: {4, 6, 7}, Group 3: {5}\n",
      "Partition 107: Group 1: {8}, Group 2: {5, 6, 7}, Group 3: {4}\n",
      "Partition 108: Group 1: {4}, Group 2: {8, 5, 6, 7}, Group 3: set()\n",
      "Partition 109: Group 1: {5}, Group 2: {8, 4, 6, 7}, Group 3: set()\n",
      "Partition 110: Group 1: {6}, Group 2: {8, 4, 5, 7}, Group 3: set()\n",
      "Partition 111: Group 1: {7}, Group 2: {8, 4, 5, 6}, Group 3: set()\n",
      "Partition 112: Group 1: {8}, Group 2: {4, 5, 6, 7}, Group 3: set()\n",
      "Partition 113: Group 1: {4, 5}, Group 2: set(), Group 3: {8, 6, 7}\n",
      "Partition 114: Group 1: {4, 6}, Group 2: set(), Group 3: {8, 5, 7}\n",
      "Partition 115: Group 1: {4, 7}, Group 2: set(), Group 3: {8, 5, 6}\n",
      "Partition 116: Group 1: {8, 4}, Group 2: set(), Group 3: {5, 6, 7}\n",
      "Partition 117: Group 1: {5, 6}, Group 2: set(), Group 3: {8, 4, 7}\n",
      "Partition 118: Group 1: {5, 7}, Group 2: set(), Group 3: {8, 4, 6}\n",
      "Partition 119: Group 1: {8, 5}, Group 2: set(), Group 3: {4, 6, 7}\n",
      "Partition 120: Group 1: {6, 7}, Group 2: set(), Group 3: {8, 4, 5}\n",
      "Partition 121: Group 1: {8, 6}, Group 2: set(), Group 3: {4, 5, 7}\n",
      "Partition 122: Group 1: {8, 7}, Group 2: set(), Group 3: {4, 5, 6}\n",
      "Partition 123: Group 1: {4, 5}, Group 2: {8}, Group 3: {6, 7}\n",
      "Partition 124: Group 1: {4, 5}, Group 2: {6}, Group 3: {8, 7}\n",
      "Partition 125: Group 1: {4, 5}, Group 2: {7}, Group 3: {8, 6}\n",
      "Partition 126: Group 1: {4, 6}, Group 2: {8}, Group 3: {5, 7}\n",
      "Partition 127: Group 1: {4, 6}, Group 2: {5}, Group 3: {8, 7}\n",
      "Partition 128: Group 1: {4, 6}, Group 2: {7}, Group 3: {8, 5}\n",
      "Partition 129: Group 1: {4, 7}, Group 2: {8}, Group 3: {5, 6}\n",
      "Partition 130: Group 1: {4, 7}, Group 2: {5}, Group 3: {8, 6}\n",
      "Partition 131: Group 1: {4, 7}, Group 2: {6}, Group 3: {8, 5}\n",
      "Partition 132: Group 1: {8, 4}, Group 2: {5}, Group 3: {6, 7}\n",
      "Partition 133: Group 1: {8, 4}, Group 2: {6}, Group 3: {5, 7}\n",
      "Partition 134: Group 1: {8, 4}, Group 2: {7}, Group 3: {5, 6}\n",
      "Partition 135: Group 1: {5, 6}, Group 2: {8}, Group 3: {4, 7}\n",
      "Partition 136: Group 1: {5, 6}, Group 2: {4}, Group 3: {8, 7}\n",
      "Partition 137: Group 1: {5, 6}, Group 2: {7}, Group 3: {8, 4}\n",
      "Partition 138: Group 1: {5, 7}, Group 2: {8}, Group 3: {4, 6}\n",
      "Partition 139: Group 1: {5, 7}, Group 2: {4}, Group 3: {8, 6}\n",
      "Partition 140: Group 1: {5, 7}, Group 2: {6}, Group 3: {8, 4}\n",
      "Partition 141: Group 1: {8, 5}, Group 2: {4}, Group 3: {6, 7}\n",
      "Partition 142: Group 1: {8, 5}, Group 2: {6}, Group 3: {4, 7}\n",
      "Partition 143: Group 1: {8, 5}, Group 2: {7}, Group 3: {4, 6}\n",
      "Partition 144: Group 1: {6, 7}, Group 2: {8}, Group 3: {4, 5}\n",
      "Partition 145: Group 1: {6, 7}, Group 2: {4}, Group 3: {8, 5}\n",
      "Partition 146: Group 1: {6, 7}, Group 2: {5}, Group 3: {8, 4}\n",
      "Partition 147: Group 1: {8, 6}, Group 2: {4}, Group 3: {5, 7}\n",
      "Partition 148: Group 1: {8, 6}, Group 2: {5}, Group 3: {4, 7}\n",
      "Partition 149: Group 1: {8, 6}, Group 2: {7}, Group 3: {4, 5}\n",
      "Partition 150: Group 1: {8, 7}, Group 2: {4}, Group 3: {5, 6}\n",
      "Partition 151: Group 1: {8, 7}, Group 2: {5}, Group 3: {4, 6}\n",
      "Partition 152: Group 1: {8, 7}, Group 2: {6}, Group 3: {4, 5}\n",
      "Partition 153: Group 1: {4, 5}, Group 2: {8, 6}, Group 3: {7}\n",
      "Partition 154: Group 1: {4, 5}, Group 2: {8, 7}, Group 3: {6}\n",
      "Partition 155: Group 1: {4, 5}, Group 2: {6, 7}, Group 3: {8}\n",
      "Partition 156: Group 1: {4, 6}, Group 2: {8, 5}, Group 3: {7}\n",
      "Partition 157: Group 1: {4, 6}, Group 2: {8, 7}, Group 3: {5}\n",
      "Partition 158: Group 1: {4, 6}, Group 2: {5, 7}, Group 3: {8}\n",
      "Partition 159: Group 1: {4, 7}, Group 2: {8, 5}, Group 3: {6}\n",
      "Partition 160: Group 1: {4, 7}, Group 2: {8, 6}, Group 3: {5}\n",
      "Partition 161: Group 1: {4, 7}, Group 2: {5, 6}, Group 3: {8}\n",
      "Partition 162: Group 1: {8, 4}, Group 2: {5, 6}, Group 3: {7}\n",
      "Partition 163: Group 1: {8, 4}, Group 2: {5, 7}, Group 3: {6}\n",
      "Partition 164: Group 1: {8, 4}, Group 2: {6, 7}, Group 3: {5}\n",
      "Partition 165: Group 1: {5, 6}, Group 2: {8, 4}, Group 3: {7}\n",
      "Partition 166: Group 1: {5, 6}, Group 2: {8, 7}, Group 3: {4}\n",
      "Partition 167: Group 1: {5, 6}, Group 2: {4, 7}, Group 3: {8}\n",
      "Partition 168: Group 1: {5, 7}, Group 2: {8, 4}, Group 3: {6}\n",
      "Partition 169: Group 1: {5, 7}, Group 2: {8, 6}, Group 3: {4}\n",
      "Partition 170: Group 1: {5, 7}, Group 2: {4, 6}, Group 3: {8}\n",
      "Partition 171: Group 1: {8, 5}, Group 2: {4, 6}, Group 3: {7}\n",
      "Partition 172: Group 1: {8, 5}, Group 2: {4, 7}, Group 3: {6}\n",
      "Partition 173: Group 1: {8, 5}, Group 2: {6, 7}, Group 3: {4}\n",
      "Partition 174: Group 1: {6, 7}, Group 2: {8, 4}, Group 3: {5}\n",
      "Partition 175: Group 1: {6, 7}, Group 2: {8, 5}, Group 3: {4}\n",
      "Partition 176: Group 1: {6, 7}, Group 2: {4, 5}, Group 3: {8}\n",
      "Partition 177: Group 1: {8, 6}, Group 2: {4, 5}, Group 3: {7}\n",
      "Partition 178: Group 1: {8, 6}, Group 2: {4, 7}, Group 3: {5}\n",
      "Partition 179: Group 1: {8, 6}, Group 2: {5, 7}, Group 3: {4}\n",
      "Partition 180: Group 1: {8, 7}, Group 2: {4, 5}, Group 3: {6}\n",
      "Partition 181: Group 1: {8, 7}, Group 2: {4, 6}, Group 3: {5}\n",
      "Partition 182: Group 1: {8, 7}, Group 2: {5, 6}, Group 3: {4}\n",
      "Partition 183: Group 1: {4, 5}, Group 2: {8, 6, 7}, Group 3: set()\n",
      "Partition 184: Group 1: {4, 6}, Group 2: {8, 5, 7}, Group 3: set()\n",
      "Partition 185: Group 1: {4, 7}, Group 2: {8, 5, 6}, Group 3: set()\n",
      "Partition 186: Group 1: {8, 4}, Group 2: {5, 6, 7}, Group 3: set()\n",
      "Partition 187: Group 1: {5, 6}, Group 2: {8, 4, 7}, Group 3: set()\n",
      "Partition 188: Group 1: {5, 7}, Group 2: {8, 4, 6}, Group 3: set()\n",
      "Partition 189: Group 1: {8, 5}, Group 2: {4, 6, 7}, Group 3: set()\n",
      "Partition 190: Group 1: {6, 7}, Group 2: {8, 4, 5}, Group 3: set()\n",
      "Partition 191: Group 1: {8, 6}, Group 2: {4, 5, 7}, Group 3: set()\n",
      "Partition 192: Group 1: {8, 7}, Group 2: {4, 5, 6}, Group 3: set()\n",
      "Partition 193: Group 1: {4, 5, 6}, Group 2: set(), Group 3: {8, 7}\n",
      "Partition 194: Group 1: {4, 5, 7}, Group 2: set(), Group 3: {8, 6}\n",
      "Partition 195: Group 1: {8, 4, 5}, Group 2: set(), Group 3: {6, 7}\n",
      "Partition 196: Group 1: {4, 6, 7}, Group 2: set(), Group 3: {8, 5}\n",
      "Partition 197: Group 1: {8, 4, 6}, Group 2: set(), Group 3: {5, 7}\n",
      "Partition 198: Group 1: {8, 4, 7}, Group 2: set(), Group 3: {5, 6}\n",
      "Partition 199: Group 1: {5, 6, 7}, Group 2: set(), Group 3: {8, 4}\n",
      "Partition 200: Group 1: {8, 5, 6}, Group 2: set(), Group 3: {4, 7}\n",
      "Partition 201: Group 1: {8, 5, 7}, Group 2: set(), Group 3: {4, 6}\n",
      "Partition 202: Group 1: {8, 6, 7}, Group 2: set(), Group 3: {4, 5}\n",
      "Partition 203: Group 1: {4, 5, 6}, Group 2: {8}, Group 3: {7}\n",
      "Partition 204: Group 1: {4, 5, 6}, Group 2: {7}, Group 3: {8}\n",
      "Partition 205: Group 1: {4, 5, 7}, Group 2: {8}, Group 3: {6}\n",
      "Partition 206: Group 1: {4, 5, 7}, Group 2: {6}, Group 3: {8}\n",
      "Partition 207: Group 1: {8, 4, 5}, Group 2: {6}, Group 3: {7}\n",
      "Partition 208: Group 1: {8, 4, 5}, Group 2: {7}, Group 3: {6}\n",
      "Partition 209: Group 1: {4, 6, 7}, Group 2: {8}, Group 3: {5}\n",
      "Partition 210: Group 1: {4, 6, 7}, Group 2: {5}, Group 3: {8}\n",
      "Partition 211: Group 1: {8, 4, 6}, Group 2: {5}, Group 3: {7}\n",
      "Partition 212: Group 1: {8, 4, 6}, Group 2: {7}, Group 3: {5}\n",
      "Partition 213: Group 1: {8, 4, 7}, Group 2: {5}, Group 3: {6}\n",
      "Partition 214: Group 1: {8, 4, 7}, Group 2: {6}, Group 3: {5}\n",
      "Partition 215: Group 1: {5, 6, 7}, Group 2: {8}, Group 3: {4}\n",
      "Partition 216: Group 1: {5, 6, 7}, Group 2: {4}, Group 3: {8}\n",
      "Partition 217: Group 1: {8, 5, 6}, Group 2: {4}, Group 3: {7}\n",
      "Partition 218: Group 1: {8, 5, 6}, Group 2: {7}, Group 3: {4}\n",
      "Partition 219: Group 1: {8, 5, 7}, Group 2: {4}, Group 3: {6}\n",
      "Partition 220: Group 1: {8, 5, 7}, Group 2: {6}, Group 3: {4}\n",
      "Partition 221: Group 1: {8, 6, 7}, Group 2: {4}, Group 3: {5}\n",
      "Partition 222: Group 1: {8, 6, 7}, Group 2: {5}, Group 3: {4}\n",
      "Partition 223: Group 1: {4, 5, 6}, Group 2: {8, 7}, Group 3: set()\n",
      "Partition 224: Group 1: {4, 5, 7}, Group 2: {8, 6}, Group 3: set()\n",
      "Partition 225: Group 1: {8, 4, 5}, Group 2: {6, 7}, Group 3: set()\n",
      "Partition 226: Group 1: {4, 6, 7}, Group 2: {8, 5}, Group 3: set()\n",
      "Partition 227: Group 1: {8, 4, 6}, Group 2: {5, 7}, Group 3: set()\n",
      "Partition 228: Group 1: {8, 4, 7}, Group 2: {5, 6}, Group 3: set()\n",
      "Partition 229: Group 1: {5, 6, 7}, Group 2: {8, 4}, Group 3: set()\n",
      "Partition 230: Group 1: {8, 5, 6}, Group 2: {4, 7}, Group 3: set()\n",
      "Partition 231: Group 1: {8, 5, 7}, Group 2: {4, 6}, Group 3: set()\n",
      "Partition 232: Group 1: {8, 6, 7}, Group 2: {4, 5}, Group 3: set()\n",
      "Partition 233: Group 1: {4, 5, 6, 7}, Group 2: set(), Group 3: {8}\n",
      "Partition 234: Group 1: {8, 4, 5, 6}, Group 2: set(), Group 3: {7}\n",
      "Partition 235: Group 1: {8, 4, 5, 7}, Group 2: set(), Group 3: {6}\n",
      "Partition 236: Group 1: {8, 4, 6, 7}, Group 2: set(), Group 3: {5}\n",
      "Partition 237: Group 1: {8, 5, 6, 7}, Group 2: set(), Group 3: {4}\n",
      "Partition 238: Group 1: {4, 5, 6, 7}, Group 2: {8}, Group 3: set()\n",
      "Partition 239: Group 1: {8, 4, 5, 6}, Group 2: {7}, Group 3: set()\n",
      "Partition 240: Group 1: {8, 4, 5, 7}, Group 2: {6}, Group 3: set()\n",
      "Partition 241: Group 1: {8, 4, 6, 7}, Group 2: {5}, Group 3: set()\n",
      "Partition 242: Group 1: {8, 5, 6, 7}, Group 2: {4}, Group 3: set()\n",
      "Partition 243: Group 1: {4, 5, 6, 7, 8}, Group 2: set(), Group 3: set()\n"
     ]
    }
   ],
   "source": [
    "print(colored('All ways to divide the indices of the generative parameters into three distinct groups:\\n', attrs=['bold']))\n",
    "\n",
    "V_indices = np.arange(m+1, m+s+1)\n",
    "\n",
    "group_1_list_V = []\n",
    "group_2_list_V = []\n",
    "group_3_list_V = []\n",
    "group_1_list_XV = []\n",
    "group_2_list_XV = []\n",
    "group_3_list_XV = []\n",
    "\n",
    "# Initialize an empty list to store valid partitions\n",
    "valid_partitions = []\n",
    "\n",
    "# Generate all possible ways to divide the indices of parameters into 3 groups (may be empty)\n",
    "V_indices = np.arange(m+1, m+s+1)\n",
    "\n",
    "for i in range(len(V_indices) + 1):\n",
    "    for j in range(len(V_indices) + 1):\n",
    "        if i + j <= len(V_indices):\n",
    "            group_1_combinations = combinations(V_indices, i)\n",
    "            for group_1 in group_1_combinations:\n",
    "                remaining_indices_1 = set(V_indices) - set(group_1)\n",
    "                group_2_combinations = combinations(remaining_indices_1, j)\n",
    "                for group_2 in group_2_combinations:\n",
    "                    group_3 = tuple(index for index in V_indices if index not in group_1 and index not in group_2)\n",
    "                    valid_partitions.append((set(group_1), set(group_2), set(group_3)))\n",
    "\n",
    "for idx, partition in enumerate(valid_partitions, start=1):\n",
    "    group_1, group_2, group_3 = partition\n",
    "    print(f'Partition {idx}: Group 1: {group_1}, Group 2: {group_2}, Group 3: {group_3}')\n",
    "\n",
    "    # Add group information to respective lists\n",
    "    group_1_list_V.append(list(group_1))\n",
    "    group_2_list_V.append(list(group_2))\n",
    "    group_3_list_V.append(list(group_3))\n",
    "    \n",
    "    group_1_list_XV.append([1] + list(group_1))   \n",
    "    group_2_list_XV.append([2] + list(group_2))\n",
    "    group_3_list_XV.append([3] + list(group_3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7221e8f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the result arrays with empty lists\n",
    "group_list_v1v2 = [[] for _ in range(len(group_1_list_V))]\n",
    "group_list_v1v3 = [[] for _ in range(len(group_1_list_V))]\n",
    "group_list_v2v3 = [[] for _ in range(len(group_1_list_V))]\n",
    "\n",
    "# Function to combine arrays\n",
    "def combine_arrays(result, arr):\n",
    "    for i in range(len(arr)):\n",
    "        if arr[i]:\n",
    "            result[i].extend(arr[i])\n",
    "\n",
    "# Combine group_1_list_V and group_2_list_V\n",
    "combine_arrays(group_list_v1v2, group_1_list_V)\n",
    "combine_arrays(group_list_v1v2, group_2_list_V)\n",
    "\n",
    "# Combine group_1_list_V and group_3_list_V\n",
    "combine_arrays(group_list_v1v3, group_1_list_V)\n",
    "combine_arrays(group_list_v1v3, group_3_list_V)\n",
    "\n",
    "# Combine group_2_list_V and group_3_list_V\n",
    "combine_arrays(group_list_v2v3, group_2_list_V)\n",
    "combine_arrays(group_list_v2v3, group_3_list_V)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84fb560a",
   "metadata": {},
   "source": [
    "## III. Numerical results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "69c474ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_I3(det_v1, det_v2, det_v3, det_x1v1, det_x2v2, det_x3v3, \n",
    "               det_v1v2, det_v1v3, det_v2v3, len_group_1, len_group_2, len_group_3):\n",
    "    \n",
    "    # 2 groups are empty\n",
    "    if len_group_1 == 0 and len_group_2 == 0:\n",
    "        I_3 = round(0.5 * np.log(det_v3/det_x3v3), 8)\n",
    "    elif len_group_1 == 0 and len_group_3 == 0:\n",
    "        I_3 = round(0.5 * np.log(det_v2/det_x2v2), 8)\n",
    "    elif len_group_2 == 0 and len_group_3 == 0:\n",
    "        I_3 = round(0.5 * np.log(det_v1/det_x1v1), 8)\n",
    "    \n",
    "    # 1 group is empty\n",
    "    elif len_group_1 == 0:\n",
    "        I_3 = round(0.5 * (np.log(det_v2/det_x2v2) + \\\n",
    "                           np.log(det_v3/det_x3v3) - \\\n",
    "                           np.log(det_v2*det_v3/det_v2v3)), 8)\n",
    "    elif len_group_2 == 0:\n",
    "        I_3 = round(0.5 * (np.log(det_v1/det_x1v1) + \\\n",
    "                           np.log(det_v3/det_x3v3) - \\\n",
    "                           np.log(det_v1*det_v3/det_v1v3)), 8)\n",
    "    elif len_group_3 == 0:\n",
    "        I_3 = round(0.5 * (np.log(det_v1/det_x1v1) + \\\n",
    "                           np.log(det_v2/det_x2v2) - \\\n",
    "                           np.log(det_v1*det_v2/det_v1v2)), 8)\n",
    "        \n",
    "    # None of the groups are empty\n",
    "    else:\n",
    "        I_3 = round(0.5 * (np.log(det_v1/det_x1v1) + \\\n",
    "                           np.log(det_v2/det_x2v2) + \\\n",
    "                           np.log(det_v3/det_x3v3) - \\\n",
    "                           np.log(det_v1*det_v2/det_v1v2) - \\\n",
    "                           np.log(det_v1*det_v3/det_v1v3) - \\\n",
    "                           np.log(det_v2*det_v3/det_v2v3)), 8)\n",
    "    return I_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6f5b846d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_two_largest_values(a, b, c):\n",
    "    values = {\"1\": a, \"2\": b, \"3\": c}\n",
    "    sorted_values = sorted(values.items(), key=lambda x: x[1], reverse=True)\n",
    "    (name1, value1), (name2, value2) = sorted_values[:2]\n",
    "    return (name1, value1), (name2, value2)\n",
    "\n",
    "def compute_SAP(Cov_x1v1, Cov_x2v1, Cov_x3v1,\n",
    "                Cov_x1v2, Cov_x2v2, Cov_x3v2,\n",
    "                Cov_x1v3, Cov_x2v3, Cov_x3v3,\n",
    "                Cov_x1v4, Cov_x2v4, Cov_x3v4,\n",
    "                Cov_x1v5, Cov_x2v5, Cov_x3v5, SAP_flag):   \n",
    "\n",
    "    S_11 = (Cov_x1v1/std_dev_v1) ** 2 \n",
    "    S_21 = (Cov_x2v1/std_dev_v1) ** 2 \n",
    "    S_31 = (Cov_x3v1/std_dev_v1) ** 2 \n",
    "    \n",
    "    S_12 = (Cov_x1v2/std_dev_v2) ** 2 \n",
    "    S_22 = (Cov_x2v2/std_dev_v2) ** 2 \n",
    "    S_32 = (Cov_x3v2/std_dev_v2) ** 2 \n",
    "    \n",
    "    S_13 = (Cov_x1v3/std_dev_v3) ** 2 \n",
    "    S_23 = (Cov_x2v3/std_dev_v3) ** 2 \n",
    "    S_33 = (Cov_x3v3/std_dev_v3) ** 2\n",
    "\n",
    "    S_14 = (Cov_x1v4/std_dev_v4) ** 2 \n",
    "    S_24 = (Cov_x2v4/std_dev_v4) ** 2 \n",
    "    S_34 = (Cov_x3v4/std_dev_v4) ** 2\n",
    "\n",
    "    S_15 = (Cov_x1v5/std_dev_v5) ** 2 \n",
    "    S_25 = (Cov_x2v5/std_dev_v5) ** 2 \n",
    "    S_35 = (Cov_x3v5/std_dev_v5) ** 2\n",
    "    \n",
    "    result1_v1, result2_v1 = find_two_largest_values(S_11, S_21, S_31)\n",
    "    result1_v2, result2_v2 = find_two_largest_values(S_12, S_22, S_32)\n",
    "    result1_v3, result2_v3 = find_two_largest_values(S_13, S_23, S_33)\n",
    "    result1_v4, result2_v4 = find_two_largest_values(S_14, S_24, S_34)\n",
    "    result1_v5, result2_v5 = find_two_largest_values(S_15, S_25, S_35)\n",
    "          \n",
    "    diff_1 = result1_v1[1] - result2_v1[1]\n",
    "    diff_2 = result1_v2[1] - result2_v2[1]\n",
    "    diff_3 = result1_v3[1] - result2_v3[1]\n",
    "    diff_4 = result1_v4[1] - result2_v4[1]\n",
    "    diff_5 = result1_v5[1] - result2_v5[1]\n",
    "    \n",
    "    SAP = 1/s * (diff_1 + diff_2 + diff_3 + diff_4 + diff_5)\n",
    "    print(colored(f'\\nSAP = {round(SAP, 4)}', 'red', attrs=['bold']))\n",
    "    \n",
    "    r = 0\n",
    "    \n",
    "    # 5 - 0\n",
    "    if result1_v1[0] == result1_v2[0] == result1_v3[0] == result1_v4[0] == result1_v5[0]:\n",
    "        print('(v1, v2, v3, v4, v5) can be captured by a single latent variable.')\n",
    "        r = 3\n",
    "\n",
    "    # 4 - 1\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v3[0] == result1_v4[0]:\n",
    "        print('(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v3[0] == result1_v5[0]:\n",
    "        print('(v1, v2, v3, v5) can be captured by a single latent variable and v4 by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v4[0] == result1_v5[0]:\n",
    "        print('(v1, v2, v4, v5) can be captured by a single latent variable and v3 by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] == result1_v4[0] == result1_v5[0]:\n",
    "        print('(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.')\n",
    "    elif result1_v2[0] == result1_v3[0] == result1_v4[0] == result1_v5[0]:\n",
    "        print('(v2, v3, v4, v5) can be captured by a single latent variable and v1 by a second latent variable.')\n",
    "\n",
    "    # 3 - 2\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v3[0] and result1_v4[0] == result1_v5[0]:\n",
    "        print('(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.')\n",
    "        r = 2\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v4[0] and result1_v3[0] == result1_v5[0]:\n",
    "        print('(v1, v2, v4) can be captured by a single latent variable and (v3, v5) by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v5[0] and result1_v3[0] == result1_v4[0]:\n",
    "        print('(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] == result1_v4[0] and result1_v2[0] == result1_v5[0]:\n",
    "        print('(v1, v3, v4) can be captured by a single latent variable and (v2, v5) by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] == result1_v5[0] and result1_v2[0] == result1_v4[0]:\n",
    "        print('(v1, v3, v5) can be captured by a single latent variable and (v2, v4) by a second latent variable.')\n",
    "    elif result1_v1[0] == result1_v4[0] == result1_v5[0] and result1_v2[0] == result1_v3[0]:\n",
    "        print('(v1, v4, v5) can be captured by a single latent variable and (v2, v3) by a second latent variable.')\n",
    "        \n",
    "    elif result1_v2[0] == result1_v3[0] == result1_v4[0] and result1_v1[0] == result1_v5[0]:\n",
    "        print('(v2, v3, v4) can be captured by a single latent variable and (v1, v5) by a second latent variable.')\n",
    "    elif result1_v2[0] == result1_v3[0] == result1_v5[0] and result1_v1[0] == result1_v4[0]:\n",
    "        print('(v2, v3, v5) can be captured by a single latent variable and (v1, v4) by a second latent variable.')\n",
    "    elif result1_v2[0] == result1_v4[0] == result1_v5[0] and result1_v1[0] == result1_v3[0]:\n",
    "        print('(v2, v4, v5) can be captured by a single latent variable and (v1, v3) by a second latent variable.')\n",
    "        \n",
    "    elif result1_v3[0] == result1_v4[0] == result1_v5[0] and result1_v1[0] == result1_v2[0]:\n",
    "        print('(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.')\n",
    "\n",
    "    # 3 - 1 - 1\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v3[0] and result1_v4[0] != result1_v5[0]:\n",
    "        print('(v1, v2, v3) can be captured by a single latent variable, v4 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v4[0] and result1_v3[0] != result1_v5[0]:\n",
    "        print('(v1, v2, v4) can be captured by a single latent variable, v3 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v2[0] == result1_v5[0] and result1_v3[0] != result1_v4[0]:\n",
    "        print('(v1, v2, v5) can be captured by a single latent variable, v3 by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] == result1_v4[0] and result1_v2[0] != result1_v5[0]:\n",
    "        print('(v1, v3, v4) can be captured by a single latent variable, v2 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] == result1_v5[0] and result1_v2[0] != result1_v4[0]:\n",
    "        print('(v1, v3, v5) can be captured by a single latent variable, v2 by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v4[0] == result1_v5[0] and result1_v2[0] != result1_v3[0]:\n",
    "        print('(v1, v4, v5) can be captured by a single latent variable, v2 by a second latent variable, and v3 by a third latent variable.')\n",
    "        \n",
    "    elif result1_v2[0] == result1_v3[0] == result1_v4[0] and result1_v1[0] != result1_v5[0]:\n",
    "        print('(v2, v3, v4) can be captured by a single latent variable, v1 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif result1_v2[0] == result1_v3[0] == result1_v5[0] and result1_v1[0] != result1_v4[0]:\n",
    "        print('(v2, v3, v5) can be captured by a single latent variable, v1 by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif result1_v2[0] == result1_v4[0] == result1_v5[0] and result1_v1[0] != result1_v3[0]:\n",
    "        print('(v2, v4, v5) can be captured by a single latent variable, v1 by a second latent variable, and v3 by a third latent variable.')\n",
    "        \n",
    "    elif result1_v3[0] == result1_v4[0] == result1_v5[0] and result1_v1[0] != result1_v2[0]:\n",
    "        print('(v3, v4, v5) can be captured by a single latent variable, v1 by a second latent variable, and v2 by a third latent variable.')\n",
    "\n",
    "    # 2 - 2 - 1\n",
    "    elif result1_v1[0] == result1_v2[0] and result1_v3[0] == result1_v4[0]:\n",
    "        print('(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.')\n",
    "        r = 1\n",
    "    elif result1_v1[0] == result1_v2[0] and result1_v3[0] == result1_v5[0]:\n",
    "        print('(v1, v2) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v2[0] and result1_v4[0] == result1_v5[0]:\n",
    "        print('(v1, v2) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v3 by a third latent variable.')\n",
    "\n",
    "    elif result1_v1[0] == result1_v3[0] and result1_v2[0] == result1_v4[0]:\n",
    "        print('(v1, v3) can be captured by a single latent variable, (v2, v4) by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] and result1_v2[0] == result1_v5[0]:\n",
    "        print('(v1, v3) can be captured by a single latent variable, (v2, v5) by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v3[0] and result1_v4[0] == result1_v5[0]:\n",
    "        print('(v1, v3) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v2 by a third latent variable.')\n",
    "\n",
    "    elif result1_v1[0] == result1_v4[0] and result1_v2[0] == result1_v3[0]:\n",
    "        print('(v1, v4) can be captured by a single latent variable, (v2, v3) by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v4[0] and result1_v2[0] == result1_v5[0]:\n",
    "        print('(v1, v4) can be captured by a single latent variable, (v2, v5) by a second latent variable, and v3 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v4[0] and result1_v3[0] == result1_v5[0]:\n",
    "        print('(v1, v4) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v2 by a third latent variable.')\n",
    "    \n",
    "    elif result1_v1[0] == result1_v5[0] and result1_v2[0] == result1_v3[0]:\n",
    "        print('(v1, v5) can be captured by a single latent variable, (v2, v3) by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v5[0] and result1_v2[0] == result1_v4[0]:\n",
    "        print('(v1, v5) can be captured by a single latent variable, (v2, v4) by a second latent variable, and v3 by a third latent variable.')\n",
    "    elif result1_v1[0] == result1_v5[0] and result1_v3[0] == result1_v4[0]:\n",
    "        print('(v1, v5) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v2 by a third latent variable.')\n",
    "\n",
    "    elif result1_v2[0] == result1_v3[0] and result1_v4[0] == result1_v5[0]:\n",
    "        print('(v2, v3) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v1 by a third latent variable.')\n",
    "    elif result1_v2[0] == result1_v4[0] and result1_v3[0] == result1_v5[0]:\n",
    "        print('(v2, v4) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v1 by a third latent variable.')\n",
    "    elif result1_v2[0] == result1_v5[0] and result1_v3[0] == result1_v4[0]:\n",
    "        print('(v2, v5) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v1 by a third latent variable.')\n",
    "        \n",
    "    else:\n",
    "        print('Error!') \n",
    "        \n",
    "    count = 0\n",
    "    \n",
    "    if SAP_flag == 0 and r == 1:\n",
    "        count = 1\n",
    "        \n",
    "    if SAP_flag == 1 and r == 2:\n",
    "        count = 1\n",
    "        \n",
    "    if SAP_flag == 2 and r == 3:\n",
    "        count = 1        \n",
    "    \n",
    "    return SAP, count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "28a52ed2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def max_I3(cov_XV, I3_flag):\n",
    "    max_MI = -100000\n",
    "    max_idx = 0\n",
    "    \n",
    "    det_x1v1_arr = []\n",
    "    det_x2v2_arr = []\n",
    "    det_x3v3_arr = []\n",
    "\n",
    "    # Generate an array of indices\n",
    "    for i, (group_1_idx_V, group_2_idx_V, group_3_idx_V,\n",
    "            group_1_idx_XV, group_2_idx_XV, group_3_idx_XV,\n",
    "            group_idx_v1v2, group_idx_v1v3, group_idx_v2v3) in enumerate(zip(group_1_list_V, group_2_list_V, group_3_list_V,\n",
    "                                                                             group_1_list_XV, group_2_list_XV, group_3_list_XV,\n",
    "                                                                             group_list_v1v2, group_list_v1v3, group_list_v2v3)):\n",
    "        \n",
    "        # Generate two-digit numbers with repetition from the array and in increasing order\n",
    "        group_1_two_digit_numbers_V = [int(str(a) + str(b)) for a, b in product(group_1_idx_V, repeat=2)]\n",
    "        group_2_two_digit_numbers_V = [int(str(a) + str(b)) for a, b in product(group_2_idx_V, repeat=2)]\n",
    "        group_3_two_digit_numbers_V = [int(str(a) + str(b)) for a, b in product(group_3_idx_V, repeat=2)]\n",
    "        \n",
    "        group_1_two_digit_numbers_XV = [int(str(a) + str(b)) for a, b in product(group_1_idx_XV, repeat=2)]\n",
    "        group_2_two_digit_numbers_XV = [int(str(a) + str(b)) for a, b in product(group_2_idx_XV, repeat=2)]\n",
    "        group_3_two_digit_numbers_XV = [int(str(a) + str(b)) for a, b in product(group_3_idx_XV, repeat=2)]\n",
    "        \n",
    "        group_two_digit_numbers_v1v2 = [int(str(a) + str(b)) for a, b in product(group_idx_v1v2, repeat=2)]\n",
    "        group_two_digit_numbers_v1v3 = [int(str(a) + str(b)) for a, b in product(group_idx_v1v3, repeat=2)]\n",
    "        group_two_digit_numbers_v2v3 = [int(str(a) + str(b)) for a, b in product(group_idx_v2v3, repeat=2)]\n",
    "    \n",
    "        # Specify the positions to extract\n",
    "        tuple_list_1_V = [(number // 10 - 1, number % 10 - 1) for number in group_1_two_digit_numbers_V]\n",
    "        tuple_list_2_V = [(number // 10 - 1, number % 10 - 1) for number in group_2_two_digit_numbers_V]\n",
    "        tuple_list_3_V = [(number // 10 - 1, number % 10 - 1) for number in group_3_two_digit_numbers_V]\n",
    "        \n",
    "        tuple_list_1_XV = [(number // 10 - 1, number % 10 - 1) for number in group_1_two_digit_numbers_XV]\n",
    "        tuple_list_2_XV = [(number // 10 - 1, number % 10 - 1) for number in group_2_two_digit_numbers_XV]\n",
    "        tuple_list_3_XV = [(number // 10 - 1, number % 10 - 1) for number in group_3_two_digit_numbers_XV]\n",
    "        \n",
    "        tuple_list_v1v2 = [(number // 10 - 1, number % 10 - 1) for number in group_two_digit_numbers_v1v2]\n",
    "        tuple_list_v1v3 = [(number // 10 - 1, number % 10 - 1) for number in group_two_digit_numbers_v1v3]\n",
    "        tuple_list_v2v3 = [(number // 10 - 1, number % 10 - 1) for number in group_two_digit_numbers_v2v3]\n",
    "    \n",
    "        # Get the new matrix from specified positions\n",
    "        dim_v1 = len(group_1_idx_V)\n",
    "        dim_v2 = len(group_2_idx_V)\n",
    "        dim_v3 = len(group_3_idx_V)\n",
    "        \n",
    "        dim_x1v1 = len(group_1_idx_XV)\n",
    "        dim_x2v2 = len(group_2_idx_XV)\n",
    "        dim_x3v3 = len(group_3_idx_XV)\n",
    "        \n",
    "        dim_v1v2 = len(group_idx_v1v2)\n",
    "        dim_v1v3 = len(group_idx_v1v3)\n",
    "        dim_v2v3 = len(group_idx_v2v3)\n",
    "    \n",
    "        cov_v1 = np.array([cov_XV[i, j] for i, j in tuple_list_1_V]).reshape(dim_v1, dim_v1)\n",
    "        if len(cov_v1) == 1:\n",
    "            cov_v1 = cov_v1[0]\n",
    "        cov_v2 = np.array([cov_XV[i, j] for i, j in tuple_list_2_V]).reshape(dim_v2, dim_v2)\n",
    "        if len(cov_v2) == 1:\n",
    "            cov_v2 = cov_v2[0]\n",
    "        cov_v3 = np.array([cov_XV[i, j] for i, j in tuple_list_3_V]).reshape(dim_v3, dim_v3)\n",
    "        if len(cov_v3) == 1:\n",
    "            cov_v3 = cov_v3[0]\n",
    "    \n",
    "        cov_x1v1 = np.array([cov_XV[i, j] for i, j in tuple_list_1_XV]).reshape(dim_x1v1, dim_x1v1)\n",
    "        cov_x2v2 = np.array([cov_XV[i, j] for i, j in tuple_list_2_XV]).reshape(dim_x2v2, dim_x2v2)\n",
    "        cov_x3v3 = np.array([cov_XV[i, j] for i, j in tuple_list_3_XV]).reshape(dim_x3v3, dim_x3v3)\n",
    "        \n",
    "        cov_v1v2 = np.array([cov_XV[i, j] for i, j in tuple_list_v1v2]).reshape(dim_v1v2, dim_v1v2)\n",
    "        cov_v1v3 = np.array([cov_XV[i, j] for i, j in tuple_list_v1v3]).reshape(dim_v1v3, dim_v1v3)\n",
    "        cov_v2v3 = np.array([cov_XV[i, j] for i, j in tuple_list_v2v3]).reshape(dim_v2v3, dim_v2v3)\n",
    "    \n",
    "        # Compute the determinant of each covariance matrix\n",
    "        det_x1v1 = det(cov_x1v1)\n",
    "        det_x2v2 = det(cov_x2v2)\n",
    "        det_x3v3 = det(cov_x3v3)\n",
    "        \n",
    "        det_v1v2 = det(cov_v1v2)\n",
    "        det_v1v3 = det(cov_v1v3)\n",
    "        det_v2v3 = det(cov_v2v3)\n",
    "        \n",
    "        if len(cov_v1) == 1:\n",
    "            det_v1 = cov_v1[0]\n",
    "            det_x1v1_arr.append(det_x1v1) \n",
    "        else:    \n",
    "            det_v1 = det(cov_v1)\n",
    "            \n",
    "        if len(cov_v2) == 1:\n",
    "            det_v2 = cov_v2[0]\n",
    "            det_x2v2_arr.append(det_x2v2) \n",
    "        else:    \n",
    "            det_v2 = det(cov_v2)\n",
    "            \n",
    "        if len(cov_v3) == 1:\n",
    "            det_v3 = cov_v3[0]\n",
    "            det_x3v3_arr.append(det_x3v3) \n",
    "        else:    \n",
    "            det_v3 = det(cov_v3)\n",
    "        \n",
    "        # Compute I_3\n",
    "        I_3 = compute_I3(det_v1, det_v2, det_v3, \n",
    "                         det_x1v1, det_x2v2, det_x3v3, \n",
    "                         det_v1v2, det_v1v3, det_v2v3,\n",
    "                         len(group_1_idx_V), len(group_2_idx_V), len(group_3_idx_V))\n",
    "    \n",
    "        if I_3 > max_MI:\n",
    "            max_MI = I_3\n",
    "            max_idx = i+1\n",
    "        \n",
    "    print(colored(f'\\nThe maximum value of I_3 is {round(max_MI, 4)} at Partition {max_idx}.', 'red', attrs=['bold']))\n",
    "    \n",
    "    partition = max_idx\n",
    "    r = 0\n",
    "    \n",
    "    # 5 - 0 - 0\n",
    "    if partition in [1, 32, 243]:\n",
    "        print('(v1, v2, v3, v4, v5) can be captured by a single latent variable.')\n",
    "        r = 3\n",
    "\n",
    "    # 4 - 1 - 0\n",
    "    elif partition in [6, 27, 37, 112, 233, 238]:\n",
    "        print('(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.')\n",
    "    elif partition in [5, 28, 36, 111, 234, 239]:\n",
    "        print('(v1, v2, v3, v5) can be captured by a single latent variable and v4 by a second latent variable.')\n",
    "    elif partition in [4, 29, 35, 110, 235, 240]:\n",
    "        print('(v1, v2, v4, v5) can be captured by a single latent variable and v3 by a second latent variable.')\n",
    "    elif partition in [3, 30, 34, 109, 236, 241]:\n",
    "        print('(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.')\n",
    "    elif partition in [2, 31, 33, 108, 237, 242]:\n",
    "        print('(v2, v3, v4, v5) can be captured by a single latent variable and v1 by a second latent variable.')\n",
    "\n",
    "    # 3 - 2 - 0\n",
    "    elif partition in [16, 17, 122, 192, 193, 223]:\n",
    "        print('(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.')\n",
    "        r = 2\n",
    "    elif partition in [15, 18, 121, 191, 194, 224]:\n",
    "        print('(v1, v2, v4) can be captured by a single latent variable and (v3, v5) by a second latent variable.')\n",
    "    elif partition in [14, 19, 120, 190, 195, 225]:\n",
    "        print('(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.')\n",
    "    elif partition in [13, 20, 119, 189, 196, 226]:\n",
    "        print('(v1, v3, v4) can be captured by a single latent variable and (v2, v5) by a second latent variable.')\n",
    "    elif partition in [12, 21, 118, 188, 197, 227]:\n",
    "        print('(v1, v3, v5) can be captured by a single latent variable and (v2, v4) by a second latent variable.')\n",
    "    elif partition in [11, 22, 117, 187, 198, 228]:\n",
    "        print('(v1, v4, v5) can be captured by a single latent variable and (v2, v3) by a second latent variable.')\n",
    "        \n",
    "    elif partition in [10, 23, 116, 186, 199, 229]:\n",
    "        print('(v2, v3, v4) can be captured by a single latent variable and (v1, v5) by a second latent variable.')\n",
    "    elif partition in [9, 24, 115, 185, 200, 230]:\n",
    "        print('(v2, v3, v5) can be captured by a single latent variable and (v1, v4) by a second latent variable.')\n",
    "    elif partition in [8, 25, 114, 184, 201, 231]:\n",
    "        print('(v2, v4, v5) can be captured by a single latent variable and (v1, v3) by a second latent variable.')\n",
    "        \n",
    "    elif partition in [7, 26, 113, 183, 202, 232]:\n",
    "        print('(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.')\n",
    "\n",
    "    # 3 - 1 - 1\n",
    "    elif partition in [50, 57, 103, 104, 203, 204]:\n",
    "        print('(v1, v2, v3) can be captured by a single latent variable, v4 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif partition in [46, 56, 99, 105, 205, 206]:\n",
    "        print('(v1, v2, v4) can be captured by a single latent variable, v3 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif partition in [49, 53, 96, 100, 207, 208]:\n",
    "        print('(v1, v2, v5) can be captured by a single latent variable, v3 by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif partition in [42, 55, 95, 106, 209, 210]:\n",
    "        print('(v1, v3, v4) can be captured by a single latent variable, v2 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif partition in [45, 52, 92, 101, 211, 212]:\n",
    "        print('(v1, v3, v5) can be captured by a single latent variable, v2 by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif partition in [44, 48, 93, 97, 213, 214]:\n",
    "        print('(v1, v4, v5) can be captured by a single latent variable, v2 by a second latent variable, and v3 by a third latent variable.')\n",
    "        \n",
    "    elif partition in [38, 54, 91, 107, 215, 216]:\n",
    "        print('(v2, v3, v4) can be captured by a single latent variable, v1 by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif partition in [41, 51, 88, 102, 217, 218]:\n",
    "        print('(v2, v3, v5) can be captured by a single latent variable, v1 by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif partition in [40, 47, 89, 98, 219, 220]:\n",
    "        print('(v2, v4, v5) can be captured by a single latent variable, v1 by a second latent variable, and v3 by a third latent variable.')\n",
    "        \n",
    "    elif partition in [39, 43, 90, 94, 221, 222]:\n",
    "        print('(v3, v4, v5) can be captured by a single latent variable, v1 by a second latent variable, and v2 by a third latent variable.')\n",
    "\n",
    "    # 2 - 2 - 1\n",
    "    elif partition in [82, 87, 123, 144, 155, 176]:\n",
    "        print('(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.')\n",
    "        r = 1\n",
    "    elif partition in [78, 79, 125, 149, 153, 177]:\n",
    "        print('(v1, v2) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif partition in [72, 73, 124, 152, 154, 180]:\n",
    "        print('(v1, v2) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v3 by a third latent variable.')\n",
    "\n",
    "    elif partition in [83, 86, 126, 138, 158, 170]:\n",
    "        print('(v1, v3) can be captured by a single latent variable, (v2, v4) by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif partition in [77, 80, 128, 143, 156, 171]:\n",
    "        print('(v1, v3) can be captured by a single latent variable, (v2, v5) by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif partition in [66, 67, 127, 151, 157, 181]:\n",
    "        print('(v1, v3) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v2 by a third latent variable.')\n",
    "\n",
    "    elif partition in [84, 85, 129, 135, 161, 167]:\n",
    "        print('(v1, v4) can be captured by a single latent variable, (v2, v3) by a second latent variable, and v5 by a third latent variable.')\n",
    "    elif partition in [71, 74, 131, 142, 159, 172]:\n",
    "        print('(v1, v4) can be captured by a single latent variable, (v2, v5) by a second latent variable, and v3 by a third latent variable.')\n",
    "    elif partition in [65, 68, 130, 148, 160, 178]:\n",
    "        print('(v1, v4) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v2 by a third latent variable.')\n",
    "    \n",
    "    elif partition in [76, 81, 134, 137, 162, 165]:\n",
    "        print('(v1, v5) can be captured by a single latent variable, (v2, v3) by a second latent variable, and v4 by a third latent variable.')\n",
    "    elif partition in [70, 75, 133, 140, 163, 168]:\n",
    "        print('(v1, v5) can be captured by a single latent variable, (v2, v4) by a second latent variable, and v3 by a third latent variable.')\n",
    "    elif partition in [64, 69, 132, 146, 164, 174]:\n",
    "        print('(v1, v5) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v2 by a third latent variable.')\n",
    "\n",
    "    elif partition in [60, 61, 136, 150, 166, 182]:\n",
    "        print('(v2, v3) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v1 by a third latent variable.')\n",
    "    elif partition in [59, 62, 139, 147, 169, 179]:\n",
    "        print('(v2, v4) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v1 by a third latent variable.')\n",
    "    elif partition in [58, 63, 141, 145, 173, 175]:\n",
    "        print('(v2, v5) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v1 by a third latent variable.')\n",
    "\n",
    "    else:\n",
    "        print('Error!')\n",
    "        \n",
    "    count = 0\n",
    "    \n",
    "    if I3_flag == 0 and r == 1:\n",
    "        count = 1\n",
    "        \n",
    "    if I3_flag == 1 and r == 2:\n",
    "        count = 1\n",
    "        \n",
    "    if I3_flag == 2 and r == 3:\n",
    "        count = 1    \n",
    "    \n",
    "    return max_MI, count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0a1d0a9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_comparison(I3_scores, SAP_scores):\n",
    "    \"\"\"\n",
    "    Plot the comparison of I3 and SAP scores.\n",
    "    \"\"\"\n",
    "\n",
    "    # Define indices for (gamma, lambda) pairs\n",
    "    pair_indices = range(1, 26)\n",
    "\n",
    "    # Plot I3 and SAP scores\n",
    "    plt.plot(pair_indices, I3_scores, label='$I_3$', marker='o', linestyle='-', color='blue')\n",
    "    plt.plot(pair_indices, SAP_scores, label='SAP', marker='s', linestyle='--', color='green')\n",
    "\n",
    "    # Set axis labels and legend with LaTeX code\n",
    "    plt.xlabel(r'$(\\gamma, \\lambda)$ Pair Index')\n",
    "    plt.ylabel('Scores')\n",
    "\n",
    "    # Configure legend placement\n",
    "    plt.legend(loc='best')\n",
    "\n",
    "    # Enable LaTeX rendering\n",
    "    plt.rc('text', usetex=True)\n",
    "\n",
    "    # Display the plot\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "971ff2a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_score_across_scenarios(score_1, score_2, score_3, flag):\n",
    "    \"\"\"\n",
    "    Plot of Score Distribution Across Scenarios\n",
    "    \"\"\"\n",
    "    \n",
    "    scenarios = ['Scenario 1', 'Scenario 2', 'Scenario 3']\n",
    "    scores = [score_1, score_2, score_3]\n",
    "\n",
    "    # Create a boxplot with colored boxes\n",
    "    boxplot = plt.boxplot(scores, labels=scenarios, patch_artist=True, medianprops=dict(color='black'))\n",
    "\n",
    "    # Set box colors\n",
    "    colors = ['lightblue', 'lightgreen', 'lightcoral']\n",
    "    for box, color in zip(boxplot['boxes'], colors):\n",
    "        box.set_facecolor(color)\n",
    "\n",
    "    # Add statistics (mean, median, std) labels to legend\n",
    "    legend_labels = []\n",
    "    for i, data in enumerate(scores, start=1):\n",
    "        mean, median, std = np.mean(data), np.median(data), np.std(data)\n",
    "        label = f'Mean = {mean:.2f}\\nMedian = {median:.2f}\\nStd = {std:.2f}'\n",
    "        legend_labels.append(label)\n",
    "\n",
    "    if flag == 0:\n",
    "        plt.ylabel('$I_3$ Scores')\n",
    "    else: \n",
    "        plt.ylabel('SAP Scores')\n",
    "\n",
    "    plt.grid(True, linestyle='-', alpha=0.7)\n",
    "    plt.tight_layout()\n",
    "\n",
    "    # Move the legend outside and below the figure\n",
    "    plt.legend(handles=[boxplot[\"boxes\"][0], boxplot[\"boxes\"][1], boxplot[\"boxes\"][2]],\n",
    "               labels=legend_labels, loc='upper center', bbox_to_anchor=(0.5, -0.2), fancybox=True, shadow=True, ncol=3)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0559a89e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 1:\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of generative variable V:\u001b[0m\n",
      "[[ 0.0025  0.0003 -0.     -0.      0.    ]\n",
      " [ 0.0003  0.0004  0.      0.      0.    ]\n",
      " [-0.      0.      0.0004  0.0001 -0.    ]\n",
      " [-0.      0.      0.0001  0.0009 -0.    ]\n",
      " [ 0.      0.     -0.     -0.      0.0009]]\n",
      "\u001b[1m\u001b[31mThe matrix is not singular.\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of input data Y:\u001b[0m\n",
      "[[0.0026 0.     0.     0.     0.0003]\n",
      " [0.     0.001  0.     0.0001 0.    ]\n",
      " [0.     0.     0.001  0.     0.    ]\n",
      " [0.     0.0001 0.     0.0005 0.    ]\n",
      " [0.0003 0.     0.     0.     0.0005]]\n",
      "\u001b[1m\u001b[31mThe matrix is positive definite.\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Case 1:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,-0.02), the reconstruction error SATISFIES the tolerance error = 0.0066412.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3709\n",
      "\n",
      "Reconstruction error:\n",
      "0.0066412\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3235\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1552 at Partition 14.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0475\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 2:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00663316.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.371\n",
      "\n",
      "Reconstruction error:\n",
      "0.00663316\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3235\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.209 at Partition 155.\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1273\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 3:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.0), the reconstruction error SATISFIES the tolerance error = 0.00662511.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.371\n",
      "\n",
      "Reconstruction error:\n",
      "0.00662511\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3236\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1634 at Partition 233.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0344\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 4:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.01), the reconstruction error SATISFIES the tolerance error = 0.00661706.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.371\n",
      "\n",
      "Reconstruction error:\n",
      "0.00661706\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3237\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.2467 at Partition 14.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1664\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 5:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.02), the reconstruction error SATISFIES the tolerance error = 0.00660901.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3711\n",
      "\n",
      "Reconstruction error:\n",
      "0.00660901\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3237\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1866 at Partition 120.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0795\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 6:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00326023.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3916\n",
      "\n",
      "Reconstruction error:\n",
      "0.00326023\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3409\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.2967 at Partition 120.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2157\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 7:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00325259.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3916\n",
      "\n",
      "Reconstruction error:\n",
      "0.00325259\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3409\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.2395 at Partition 120.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1647\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 8:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.0), the reconstruction error SATISFIES the tolerance error = 0.00324495.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3916\n",
      "\n",
      "Reconstruction error:\n",
      "0.00324495\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.341\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1601 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0089\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 9:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.01), the reconstruction error SATISFIES the tolerance error = 0.00323731.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3917\n",
      "\n",
      "Reconstruction error:\n",
      "0.00323731\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3411\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1495 at Partition 14.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0243\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 10:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.02), the reconstruction error SATISFIES the tolerance error = 0.00322966.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.3917\n",
      "\n",
      "Reconstruction error:\n",
      "0.00322966\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3412\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1684 at Partition 233.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0443\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 11:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,-0.02), the reconstruction error SATISFIES the tolerance error = 1.574e-05.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.4178\n",
      "\n",
      "Reconstruction error:\n",
      "1.574e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3567\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.2736 at Partition 87.\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1793\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 12:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,-0.01), the reconstruction error SATISFIES the tolerance error = 7.44e-06.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.4121\n",
      "\n",
      "Reconstruction error:\n",
      "7.44e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.357\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1971 at Partition 123.\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.067\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34m\n",
      "Case 13:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.0), the reconstruction error SATISFIES the tolerance error = 2e-07.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.4118\n",
      "\n",
      "Reconstruction error:\n",
      "2e-07\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3581\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1782 at Partition 112.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0307\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 14:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.01), the reconstruction error SATISFIES the tolerance error = 6.74e-06.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.4143\n",
      "\n",
      "Reconstruction error:\n",
      "6.74e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.364\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.2272 at Partition 123.\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1211\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 15:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.02), the reconstruction error SATISFIES the tolerance error = 1.181e-05.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "0.4241\n",
      "\n",
      "Reconstruction error:\n",
      "1.181e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3769\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3015 at Partition 87.\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1863\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 16:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,-0.02), the reconstruction error SATISFIES the tolerance error = 0.0049449.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "69.3532\n",
      "\n",
      "Reconstruction error:\n",
      "0.0049449\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.9316\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 2.7473 at Partition 87.\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4482\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 17:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00494502.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "66.0894\n",
      "\n",
      "Reconstruction error:\n",
      "0.00494502\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5851\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.5249 at Partition 26.\u001b[0m\n",
      "(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2575\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 18:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.0), the reconstruction error SATISFIES the tolerance error = 0.00494515.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "67.8722\n",
      "\n",
      "Reconstruction error:\n",
      "0.00494515\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.9316\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.5756 at Partition 183.\u001b[0m\n",
      "(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1438\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 19:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.01), the reconstruction error SATISFIES the tolerance error = 0.00494527.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "69.5126\n",
      "\n",
      "Reconstruction error:\n",
      "0.00494527\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.9316\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.7964 at Partition 26.\u001b[0m\n",
      "(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1868\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 20:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.02), the reconstruction error SATISFIES the tolerance error = 0.0049454.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "68.213\n",
      "\n",
      "Reconstruction error:\n",
      "0.0049454\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.9316\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 2.2187 at Partition 195.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3086\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 21:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00980911.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "142.7111\n",
      "\n",
      "Reconstruction error:\n",
      "0.00980911\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.575\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 2.0541 at Partition 49.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable, v3 by a second latent variable, and v4 by a third latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3492\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v5) by a second latent variable, and v4 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 22:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00980935.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "140.2112\n",
      "\n",
      "Reconstruction error:\n",
      "0.00980935\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.9316\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.6524 at Partition 232.\u001b[0m\n",
      "(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2729\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 23:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.0), the reconstruction error SATISFIES the tolerance error = 0.00376483.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "140.8119\n",
      "\n",
      "Reconstruction error:\n",
      "0.00376483\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.1073\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.8609 at Partition 195.\u001b[0m\n",
      "(v1, v2, v5) can be captured by a single latent variable and (v3, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3315\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 24:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.01), the reconstruction error SATISFIES the tolerance error = 0.00980984.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "143.343\n",
      "\n",
      "Reconstruction error:\n",
      "0.00980984\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5851\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.8051 at Partition 202.\u001b[0m\n",
      "(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2954\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34m\n",
      "Case 25:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.02), the reconstruction error SATISFIES the tolerance error = 0.00981008.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "141.1517\n",
      "\n",
      "Reconstruction error:\n",
      "0.00981008\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5851\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.6813 at Partition 183.\u001b[0m\n",
      "(v3, v4, v5) can be captured by a single latent variable and (v1, v2) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1868\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v3, v4) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\n",
      "The disentanglement success rate using I_3 and SAP metrics are 24.0% and 72.0%, respectively.\n",
      "\u001b[0m\n",
      "\u001b[4m\u001b[1m\n",
      "Scenario 2:\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of generative variable V:\u001b[0m\n",
      "[[ 0.0025  0.0003  0.0007  0.      0.    ]\n",
      " [ 0.0003  0.0004  0.0001  0.      0.    ]\n",
      " [ 0.0007  0.0001  0.0003 -0.      0.    ]\n",
      " [ 0.      0.     -0.      0.0016  0.0006]\n",
      " [ 0.      0.      0.      0.0006  0.0019]]\n",
      "\u001b[1m\u001b[31mThe matrix is not singular.\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of input data Y:\u001b[0m\n",
      "[[0.0026 0.     0.     0.0007 0.0003]\n",
      " [0.     0.0017 0.0006 0.     0.    ]\n",
      " [0.     0.0006 0.002  0.     0.    ]\n",
      " [0.0007 0.     0.     0.0004 0.0001]\n",
      " [0.0003 0.     0.     0.0001 0.0005]]\n",
      "\u001b[1m\u001b[31mThe matrix is positive definite.\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Case 1:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00912858.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.1638\n",
      "\n",
      "Reconstruction error:\n",
      "0.00912858\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0209\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.5296 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1987\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 2:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00911649.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.1642\n",
      "\n",
      "Reconstruction error:\n",
      "0.00911649\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.021\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4666 at Partition 192.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.109\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 3:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.0), the reconstruction error SATISFIES the tolerance error = 0.00910441.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.1642\n",
      "\n",
      "Reconstruction error:\n",
      "0.00910441\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0211\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6053 at Partition 16.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2723\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 4:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.01), the reconstruction error SATISFIES the tolerance error = 0.00909233.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.164\n",
      "\n",
      "Reconstruction error:\n",
      "0.00909233\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0212\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6432 at Partition 122.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2629\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 5:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.02), the reconstruction error SATISFIES the tolerance error = 0.00908025.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.1631\n",
      "\n",
      "Reconstruction error:\n",
      "0.00908025\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0212\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6664 at Partition 223.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2642\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 6:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00448225.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2059\n",
      "\n",
      "Reconstruction error:\n",
      "0.00448225\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0524\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.8141 at Partition 193.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4336\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 7:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00447078.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.206\n",
      "\n",
      "Reconstruction error:\n",
      "0.00447078\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0526\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.7549 at Partition 16.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4127\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 8:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.0), the reconstruction error SATISFIES the tolerance error = 0.0044593.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.206\n",
      "\n",
      "Reconstruction error:\n",
      "0.0044593\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0527\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4234 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1123\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 9:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.01), the reconstruction error SATISFIES the tolerance error = 0.00444783.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2061\n",
      "\n",
      "Reconstruction error:\n",
      "0.00444783\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0528\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.5611 at Partition 223.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2268\u001b[0m\n",
      "(v1, v3) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v2 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 10:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.02), the reconstruction error SATISFIES the tolerance error = 0.00443636.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2061\n",
      "\n",
      "Reconstruction error:\n",
      "0.00443636\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.0529\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.7641 at Partition 17.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2873\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 11:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,-0.02), the reconstruction error SATISFIES the tolerance error = 2.186e-05.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2678\n",
      "\n",
      "Reconstruction error:\n",
      "2.186e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1296\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6882 at Partition 122.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2819\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34m\n",
      "Case 12:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,-0.01), the reconstruction error SATISFIES the tolerance error = 1.092e-05.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2862\n",
      "\n",
      "Reconstruction error:\n",
      "1.092e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1532\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6522 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2478\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 13:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.0), the reconstruction error SATISFIES the tolerance error = 6.2e-07.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2742\n",
      "\n",
      "Reconstruction error:\n",
      "6.2e-07\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1384\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.74 at Partition 193.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3622\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 14:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.01), the reconstruction error SATISFIES the tolerance error = 1.089e-05.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2883\n",
      "\n",
      "Reconstruction error:\n",
      "1.089e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1557\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.623 at Partition 193.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2469\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 15:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.02), the reconstruction error SATISFIES the tolerance error = 2.173e-05.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.2885\n",
      "\n",
      "Reconstruction error:\n",
      "2.173e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1559\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4582 at Partition 192.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1114\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 16:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00491656.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "69.0694\n",
      "\n",
      "Reconstruction error:\n",
      "0.00491656\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.4203\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.3745 at Partition 193.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2141\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 17:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00491707.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "69.7538\n",
      "\n",
      "Reconstruction error:\n",
      "0.00491707\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.4203\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.4148 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0584\u001b[0m\n",
      "(v2, v3, v4, v5) can be captured by a single latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 18:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.0), the reconstruction error SATISFIES the tolerance error = 0.00491754.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "69.5293\n",
      "\n",
      "Reconstruction error:\n",
      "0.00491754\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5015\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.6856 at Partition 122.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.527\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 19:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.01), the reconstruction error SATISFIES the tolerance error = 0.00491624.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "69.328\n",
      "\n",
      "Reconstruction error:\n",
      "0.00491624\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5015\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 2.0586 at Partition 223.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4926\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 20:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.02), the reconstruction error SATISFIES the tolerance error = 0.00491952.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "70.6094\n",
      "\n",
      "Reconstruction error:\n",
      "0.00491952\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5015\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.5317 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1017\u001b[0m\n",
      "(v2, v3, v4, v5) can be captured by a single latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 21:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00969184.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "143.5471\n",
      "\n",
      "Reconstruction error:\n",
      "0.00969184\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.4203\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.2674 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1417\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 22:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00967157.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "143.4224\n",
      "\n",
      "Reconstruction error:\n",
      "0.00967157\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5015\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.7219 at Partition 122.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3381\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 23:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.0), the reconstruction error SATISFIES the tolerance error = 0.00967589.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "142.4598\n",
      "\n",
      "Reconstruction error:\n",
      "0.00967589\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.4203\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.3042 at Partition 122.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2153\u001b[0m\n",
      "(v1, v2) can be captured by a single latent variable, (v4, v5) by a second latent variable, and v3 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 24:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.01), the reconstruction error SATISFIES the tolerance error = 0.00968375.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "143.5097\n",
      "\n",
      "Reconstruction error:\n",
      "0.00968375\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.4203\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.4169 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1284\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34m\n",
      "Case 25:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.02), the reconstruction error SATISFIES the tolerance error = 0.00965585.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "142.8941\n",
      "\n",
      "Reconstruction error:\n",
      "0.00965585\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.5015\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.5897 at Partition 122.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4436\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\n",
      "The disentanglement success rate using I_3 and SAP metrics are 72.0% and 84.0%, respectively.\n",
      "\u001b[0m\n",
      "\u001b[4m\u001b[1m\n",
      "Scenario 3:\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of generative variable V:\u001b[0m\n",
      "[[0.0025 0.0003 0.0008 0.001  0.0005]\n",
      " [0.0003 0.0004 0.0001 0.0001 0.    ]\n",
      " [0.0008 0.0001 0.0003 0.0003 0.0002]\n",
      " [0.001  0.0001 0.0003 0.0013 0.0002]\n",
      " [0.0005 0.     0.0002 0.0002 0.0017]]\n",
      "\u001b[1m\u001b[31mThe matrix is not singular.\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of input data Y:\u001b[0m\n",
      "[[0.0026 0.001  0.0005 0.0008 0.0003]\n",
      " [0.001  0.0014 0.0002 0.0003 0.0001]\n",
      " [0.0005 0.0002 0.0018 0.0002 0.    ]\n",
      " [0.0008 0.0003 0.0002 0.0004 0.0001]\n",
      " [0.0003 0.0001 0.     0.0001 0.0005]]\n",
      "\u001b[1m\u001b[31mThe matrix is positive definite.\u001b[0m\n",
      "\u001b[1m\u001b[34m\n",
      "Case 1:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00604977.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.3861\n",
      "\n",
      "Reconstruction error:\n",
      "0.00604977\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1574\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4133 at Partition 37.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2474\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable, v4 by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 2:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00604578.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.3861\n",
      "\n",
      "Reconstruction error:\n",
      "0.00604578\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1574\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.9675 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3439\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 3:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.0), the reconstruction error SATISFIES the tolerance error = 0.00604178.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.3862\n",
      "\n",
      "Reconstruction error:\n",
      "0.00604178\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1575\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4147 at Partition 3.\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2061\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 4:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.01), the reconstruction error SATISFIES the tolerance error = 0.00603779.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.3862\n",
      "\n",
      "Reconstruction error:\n",
      "0.00603779\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1575\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.8315 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3214\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 5:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.98,0.02), the reconstruction error SATISFIES the tolerance error = 0.00603379.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.3863\n",
      "\n",
      "Reconstruction error:\n",
      "0.00603379\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1576\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.8574 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3134\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 6:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00326798.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.4334\n",
      "\n",
      "Reconstruction error:\n",
      "0.00326798\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1941\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3498 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1259\u001b[0m\n",
      "(v1, v3, v5) can be captured by a single latent variable and (v2, v4) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 7:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00326375.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.4334\n",
      "\n",
      "Reconstruction error:\n",
      "0.00326375\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1942\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.5132 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2045\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 8:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.0), the reconstruction error SATISFIES the tolerance error = 0.00325951.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.4335\n",
      "\n",
      "Reconstruction error:\n",
      "0.00325951\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1943\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.7067 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2933\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 9:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.01), the reconstruction error SATISFIES the tolerance error = 0.00325528.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.4335\n",
      "\n",
      "Reconstruction error:\n",
      "0.00325528\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1943\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4215 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2294\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 10:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (0.99,0.02), the reconstruction error SATISFIES the tolerance error = 0.00325105.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.4335\n",
      "\n",
      "Reconstruction error:\n",
      "0.00325105\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.1944\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.7211 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3397\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 11:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,-0.02), the reconstruction error SATISFIES the tolerance error = 8.38e-06.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.5485\n",
      "\n",
      "Reconstruction error:\n",
      "8.38e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.2793\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4848 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1492\u001b[0m\n",
      "(v1, v2, v3, v5) can be captured by a single latent variable and v4 by a second latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34m\n",
      "Case 12:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,-0.01), the reconstruction error SATISFIES the tolerance error = 4.3e-06.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.6295\n",
      "\n",
      "Reconstruction error:\n",
      "4.3e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.3272\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6243 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2068\u001b[0m\n",
      "(v1, v3, v4) can be captured by a single latent variable, v2 by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 13:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.0), the reconstruction error SATISFIES the tolerance error = 5.6e-07.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.5677\n",
      "\n",
      "Reconstruction error:\n",
      "5.6e-07\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.3061\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.848 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3104\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 14:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.01), the reconstruction error SATISFIES the tolerance error = 4.27e-06.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.547\n",
      "\n",
      "Reconstruction error:\n",
      "4.27e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.2892\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.6133 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2672\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable and (v4, v5) by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 15:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.0,0.02), the reconstruction error SATISFIES the tolerance error = 7.31e-06.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "1.6408\n",
      "\n",
      "Reconstruction error:\n",
      "7.31e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "1.3746\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3482 at Partition 233.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1531\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable, v4 by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 16:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,-0.02), the reconstruction error SATISFIES the tolerance error = 0.0050178.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "73.5626\n",
      "\n",
      "Reconstruction error:\n",
      "0.0050178\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "2.6129\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.7286 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1416\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 17:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00501844.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "73.6059\n",
      "\n",
      "Reconstruction error:\n",
      "0.00501844\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "2.6129\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.9082 at Partition 34.\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3172\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 18:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.0), the reconstruction error SATISFIES the tolerance error = 0.00501651.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "72.981\n",
      "\n",
      "Reconstruction error:\n",
      "0.00501651\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "2.6129\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.3224 at Partition 34.\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.7572\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 19:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.01), the reconstruction error SATISFIES the tolerance error = 0.00501669.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "73.2224\n",
      "\n",
      "Reconstruction error:\n",
      "0.00501669\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "2.6129\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.9974 at Partition 3.\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4652\u001b[0m\n",
      "(v1, v3, v5) can be captured by a single latent variable, v2 by a second latent variable, and v4 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 20:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.01,0.02), the reconstruction error SATISFIES the tolerance error = 0.00501819.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "73.5456\n",
      "\n",
      "Reconstruction error:\n",
      "0.00501819\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "2.6129\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.1968 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.5387\u001b[0m\n",
      "(v1, v3, v4, v5) can be captured by a single latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 21:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,-0.02), the reconstruction error SATISFIES the tolerance error = 0.00906181.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "146.4454\n",
      "\n",
      "Reconstruction error:\n",
      "0.00906181\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.2581\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.3883 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2468\u001b[0m\n",
      "(v1, v4) can be captured by a single latent variable, (v2, v3) by a second latent variable, and v5 by a third latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 22:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,-0.01), the reconstruction error SATISFIES the tolerance error = 0.00906592.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "146.8912\n",
      "\n",
      "Reconstruction error:\n",
      "0.00906592\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.2581\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.3493 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.203\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 23:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.0), the reconstruction error SATISFIES the tolerance error = 0.00908991.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "146.8257\n",
      "\n",
      "Reconstruction error:\n",
      "0.00908991\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.2581\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.5458 at Partition 6.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4263\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[34m\n",
      "Case 24:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.01), the reconstruction error SATISFIES the tolerance error = 0.00906299.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "146.5353\n",
      "\n",
      "Reconstruction error:\n",
      "0.00906299\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.2581\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.3109 at Partition 233.\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3639\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable, v4 by a second latent variable, and v5 by a third latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34m\n",
      "Case 25:\u001b[0m\n",
      "\n",
      "Given (gamma,lambda) = (1.02,0.02), the reconstruction error SATISFIES the tolerance error = 0.00900565.\n",
      "\n",
      "\u001b[1m\u001b[31mThe optimal solution is NOT unique!\n",
      "\u001b[0m\n",
      "\u001b[1mAt optimal solution:\u001b[0m\n",
      "\n",
      "Mutual information of the encoder:\n",
      "146.8039\n",
      "\n",
      "Reconstruction error:\n",
      "0.00900565\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "3.2581\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 1.4803 at Partition 243.\u001b[0m\n",
      "(v1, v2, v3, v4, v5) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3708\u001b[0m\n",
      "(v1, v2, v3, v4) can be captured by a single latent variable and v5 by a second latent variable.\n",
      "\u001b[1m\n",
      "The disentanglement success rate using I_3 and SAP metrics are 68.0% and 12.0%, respectively.\n",
      "\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# Numerical Simulation\n",
    "all_I3_score_arr = []\n",
    "all_SAP_score_arr = []\n",
    "\n",
    "for case in range(num_cases):\n",
    "    # Compute Sigma_Y given Sigma_V\n",
    "    Sigma_V = generate_Sigma_V(case)\n",
    "    \n",
    "    Sigma_Y = eigenvectors @ Sigma_V @ eigenvectors.T + Sigma_Z_tilde\n",
    "    print(colored('\\nCovariance matrix of input data Y:', 'blue', attrs=['bold']))\n",
    "    print(np.round(Sigma_Y, 4))\n",
    "    is_positive_definite(Sigma_Y)\n",
    "    \n",
    "    # Compute the determiant of each generative variable\n",
    "    diagonal_elements = [Sigma_V[i, i] for i in range(s)]\n",
    "    det_v_1, det_v_2, det_v_3 = diagonal_elements[0], diagonal_elements[1], diagonal_elements[2]\n",
    "    \n",
    "    # Constants\n",
    "    MAX_SOLS = 1\n",
    "    is_array = 1\n",
    "    flag = 0\n",
    "    case_num = 1\n",
    "\n",
    "    # Initiate arrays\n",
    "    min_recon_err_arr = []\n",
    "    min_en_mi_arr = []\n",
    "    min_de_mi_arr = []\n",
    "    all_recon_mi_arr = []\n",
    "    satisfied_recon_mi_arr = []\n",
    "    satisfied_gamma_lambda_arr = []\n",
    "    \n",
    "    I3_count_all = 0\n",
    "    SAP_count_all = 0\n",
    "    \n",
    "    # Iteration step\n",
    "    for i in range(0, len(gamma_arr)):\n",
    "        gamma = gamma_arr[i]\n",
    "        for j in range(0, len(lambda_arr)):\n",
    "            lamda = lambda_arr[j]\n",
    "        \n",
    "            min_recon_err, min_en_mi, min_de_mi, min_opt_sol = print_comprehensive_results(gamma, lamda, flag, m, n, is_array)\n",
    "        \n",
    "            first_iter = 1\n",
    "            for num_sols in range(0, MAX_SOLS):\n",
    "                current_recon_err, current_en_mi, current_de_mi, current_opt_sol = print_comprehensive_results(gamma, lamda, flag, m, n, is_array)\n",
    "    \n",
    "                # Check for unique optimal solutions for each (gamma, lambda) pair\n",
    "                if first_iter == 1:\n",
    "                    if is_close_to_zero(current_opt_sol[:2*n*m+n*n+m*m] - min_opt_sol[:2*n*m+n*n+m*m], 1e-6):\n",
    "                        is_unique = 1\n",
    "                        unique_opt_sol = current_opt_sol[:2*n*m+n*n+m*m]\n",
    "                    else:\n",
    "                        is_unique = 0\n",
    "                    first_iter = 0\n",
    "                else:\n",
    "                    if is_unique == 1:\n",
    "                        if is_close_to_zero(current_opt_sol[:2*n*m+n*n+m*m] - unique_opt_sol, 1e-6):\n",
    "                            unique_opt_sol = current_opt_sol[:2*n*m+n*n+m*m]\n",
    "                        else:\n",
    "                            is_unique = 0\n",
    "    \n",
    "                # Return the solution with smallest reconstruction error\n",
    "                if current_recon_err < min_recon_err:\n",
    "                    min_recon_err = current_recon_err\n",
    "                    min_en_mi = current_en_mi\n",
    "                    min_de_mi = current_de_mi\n",
    "                    min_opt_sol = current_opt_sol\n",
    "                \n",
    "            min_recon_err_arr = np.concatenate((min_recon_err_arr, [min_recon_err]))\n",
    "            min_en_mi_arr = np.concatenate((min_en_mi_arr, [min_en_mi]))\n",
    "            min_de_mi_arr = np.concatenate((min_de_mi_arr, [min_de_mi]))\n",
    "            all_recon_mi_arr = np.concatenate((all_recon_mi_arr, [min_recon_err, min_en_mi, min_de_mi]))\n",
    "        \n",
    "            print(colored('\\nCase {}:'.format(case_num), 'blue', attrs=['bold']))\n",
    "            case_num += 1\n",
    "        \n",
    "            if min_recon_err > MAX_RECON_ERR:\n",
    "                print('\\nGiven (gamma,lambda) = ({},{}), the reconstruction error EXCEEDS the tolerance error = {}.\\n'.format(gamma, lamda, min_recon_err, MAX_RECON_ERR))\n",
    "            else:\n",
    "                print('\\nGiven (gamma,lambda) = ({},{}), the reconstruction error SATISFIES the tolerance error = {}.\\n'.format(gamma, lamda, min_recon_err, MAX_RECON_ERR))\n",
    "            \n",
    "                satisfied_gamma_lambda_arr = np.concatenate((satisfied_gamma_lambda_arr, [gamma, lamda]))\n",
    "                satisfied_recon_mi_arr = np.concatenate((satisfied_recon_mi_arr, [min_recon_err, min_en_mi, min_de_mi]))\n",
    "        \n",
    "            if is_unique == 1:\n",
    "                print(colored('The optimal solution is unique!\\n', 'blue', attrs=['bold']))\n",
    "            else:\n",
    "                print(colored('The optimal solution is NOT unique!\\n', 'red', attrs=['bold']))\n",
    "        \n",
    "            print_optimal_solution(min_opt_sol, m)\n",
    "        \n",
    "            # Compute mutual information I(V;X) and I_3\n",
    "            B_opt = min_opt_sol[n*m:2*n*m].reshape((m, n))\n",
    "            Sigma_W_opt = min_opt_sol[2*n*m+n*n:2*n*m+n*n+m*m].reshape((m, m))\n",
    "        \n",
    "            mutual_info_VX = mi_VX(B_opt, Sigma_W_opt)\n",
    "            print('\\nMutual information between generative variable and latent variable:')\n",
    "            print(round(mutual_info_VX, 4))\n",
    "        \n",
    "            cov_XV = covariance_matrix_XV(B_opt)\n",
    "            \n",
    "            I3_flag = case\n",
    "            I3_max, I3_count = max_I3(cov_XV, I3_flag)\n",
    "            \n",
    "            I3_count_all = I3_count_all + I3_count\n",
    "            \n",
    "            # Extract elements from covariance matrix (X,V)\n",
    "            Cov_x1v1 = cov_XV[0, 3]\n",
    "            Cov_x2v1 = cov_XV[1, 3]\n",
    "            Cov_x3v1 = cov_XV[2, 3]\n",
    "\n",
    "            Cov_x1v2 = cov_XV[0, 4]\n",
    "            Cov_x2v2 = cov_XV[1, 4]\n",
    "            Cov_x3v2 = cov_XV[2, 4]\n",
    "\n",
    "            Cov_x1v3 = cov_XV[0, 5]\n",
    "            Cov_x2v3 = cov_XV[1, 5]\n",
    "            Cov_x3v3 = cov_XV[2, 5]\n",
    "\n",
    "            Cov_x1v4 = cov_XV[0, 6]\n",
    "            Cov_x2v4 = cov_XV[1, 6]\n",
    "            Cov_x3v4 = cov_XV[2, 6]\n",
    "\n",
    "            Cov_x1v5 = cov_XV[0, 7]\n",
    "            Cov_x2v5 = cov_XV[1, 7]\n",
    "            Cov_x3v5 = cov_XV[2, 7]\n",
    "            \n",
    "            # Compute SAP\n",
    "            SAP_flag = case\n",
    "            SAP_score, SAP_count = compute_SAP(Cov_x1v1, Cov_x2v1, Cov_x3v1,\n",
    "                                               Cov_x1v2, Cov_x2v2, Cov_x3v2,\n",
    "                                               Cov_x1v3, Cov_x2v3, Cov_x3v3,\n",
    "                                               Cov_x1v4, Cov_x2v4, Cov_x3v4,\n",
    "                                               Cov_x1v5, Cov_x2v5, Cov_x3v5, SAP_flag)\n",
    "            \n",
    "            SAP_count_all = SAP_count_all + SAP_count\n",
    "            \n",
    "            all_I3_score_arr.append(I3_max)\n",
    "            all_SAP_score_arr.append(SAP_score)\n",
    "            \n",
    "    # Compute disentanglement success rate\n",
    "    I3_rate = round(I3_count_all / 25 * 100, 2)\n",
    "    SAP_rate = round(SAP_count_all / 25 * 100, 2)\n",
    "    \n",
    "    print(colored('\\nThe disentanglement success rate using I_3 and SAP metrics are {}% and {}%, respectively.\\n'.format(I3_rate, SAP_rate), attrs=['bold']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e835507f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 1:\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 2:\u001b[0m\n"
     ]
    },
    {
     "data": {
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Hjh6V77wUWBjgEBGRR7SsXnz22fKdt39/cU5JEvk9RPYwwCEiIo9oWdxP7q2XWA+HOsIAh4iIZCdn9WJ7GOBQRxQJcAwGAxISEjo8TqfTwWQywWQy2T2HwWAAABiNRuttIiJS3qZNQHm5PNWL7bGspGKiMbXH6wGOTqcDAKcCkvT0dERFRSEqKgoqlQoqlQp5eXkAgPz8fCQkJEClUiEzMxNardaj7SYiIudZVk+lpna+erE9CQmiJs6ePaLWDlFrXg9w0tLSEB8f3+FxJpMJhYWFkCTJ+pWbm4usrCwAQEJCAiorK1FZWYmioiJoNBoPt5yIiJzlyekpAOjZEzj9dHG7uNgz70H+zadzcNLS0qy3dTqdzX0A0Gg0DGyIiHzM3r1ix29AnurF7eE0FTniswFOy8DFZDKhoqLCZhrKZDJBp9NBp9MhOzsbRqNRgVYSEVFrnqhebA8TjcmREKUb4Izs7Gzk5ubaPJaRkWENgrRaLVJTU1FaWmr39XV1dairq7Per66uBgCYzWbrl+U+eQ/7XRnsd2V0pX7/6qtgAEGYPLkRZnOTx95n5EgAUKO4WEJdXQOC7PzJ7mv93tgIrFunwr59op7P2LESgoOVbpX8PNXvrpxPJUmSJOu7O/vGKhWceWuTyYSEhIQ2wYvBYLDm8phMJkRFRaG0tNRusvHTTz+NOXPmtHn8k08+QXh4uJs/ARERtVZXF4QbbpiE+voQvPLKKgwZUu2x92psVOHaayejvj4Er7++ArGxxzz2XnL46af+eOeds3DkSHfrY717n8Dtt/+G88/fp2DL/EdNTQ1mzpyJqqoqREREODzW5wMcvV6P7OxslLQoV2kwGJCcnIzKykoAzQFOZWWl3ZwceyM4sbGxOHz4MCIiImA2m1FUVITU1FSo1erO/3DkFPa7Mtjvyugq/b5kiQpXXRWC2FgJ27c3yF7gr7WLLgrGDz8E4Z13GnDjjW0/U3yl3xctUuGaa4IhPvaaO0WlEm3+7LNGXH21Ih/HHuGpfq+urkZMTIxTAY6iU1Qmk8kmIDEYDNBoNDajMAaDAdHR0Tav02q1NlNWer0eaWlp7SYch4aGIjQ0tM3jarXapuNb3yfvYL8rg/2ujEDv96VLxffLL1ehWzfP/5yjRwM//AAYDCG47bb2j1Oy3xsbgYcfBuz9TS9JKqhUwCOPhGDaNATcdJXc/e7KubyeZGwZkQGAnJwca10ce/ctWk87aTQaJCYmIi8vDwUFBSguLkZhYaFnG05ERA55unqxPf6ws/jataJeT3skCdi9WxxH8vH6CE5KSgpSUlLaJA0DsBukWOretBYfH+9UPR0iIvKOX35prl580UXeeU9LgPPrr0BtrWeKCnbWPifTa5w9jpzjs8vEiYjIPzQ2AqtXA//+t7ifkuK9QOPkk4G+fYGGBrE9hC/q31/e48g5DHCIiMhtCxcCgweLERtLhsGaNeJxb1CpfL8ezrhxwKBB7e+orlIBsbHiOJIPAxwiInLLwoVAWlrb/BKTSTzurSDH1wOc4GDg1VftP2cJeubODbwEY6UxwCEiIpc1NgL339/eyiDx/YEHxHGe5g9bNkydKka4QlplvkZEiMenTlWmXYGMAQ4REbnMl1YGJSaK76WlwJEjnn8/d40bJ3KFAOCqq8T3pCQGN57CAIeIiFzmSyuDoqOB4cPFbV/eWXzNGvH9zDOB554Tt9etE6u/SH4McIiIyGW+tjLIH6apvv9efB8/Hjj9dGDAABHc/PCDsu0KVAxwiIjIZb62MsjXE40B2wBHpRLL6QGgqEi5NgUyBjhEROQyy8oge0nGSqwMahngKLPDomMVFcBvv4nbF14ovlsCHL1emTYFOgY4RETklqlTmxN8Wxo0yPsrg849F1CrgcOHgbIy772vs9auFYHXqacCJ50kHrMEOAaDbydH+ysGOERE5JZdu8SHMwB8+CHwySfAqlUiwPD2yqDQUBHkAL45TdVyesqif3/gjDNE4LNypTLtCmQMcIiIyC0FBUBTEzBxInDjjcC11wITJihXsM6X83DsBTgAkJoqvjMPR34McIiIyGX19cC8eeL2XXcp2xYLX11JVVUlNiIF2gY4zMPxHAY4RETksoULgYMHxVLnK69UujWCZQTHYADMZmXb0tK6dWKka9gw0V8tjR8vcofKykShQpIPAxwiInLZf/8rvs+aJT6gfcHw4UBkpKgtY1mx5Avam54CgJ49gfPPF7c5TSUvBjhEROSSLVtEVd7gYBHg+IqgIN/Mw3EU4ACcpvIUBjhEROQSy+jNVVcBAwcq2pQ2fC3AOXoUKCkRt9sLcCyJxitXemdz0q6CAQ4RETnt6FHgo4/EbV9JLm7JEuD4SqLxjz+KoGXwYCAuzv4xiYliaq2ysnnZvT9rbAS+/16FNWsG4vvvVYoFbQxwiIjIafPnA8eOASNGABddpHRr2rIEOH/+CVRXK9sWoOPpKQAICWnuS3/Pw1m4UARzqakhePnlRKSmhmDwYPG4tzHAISIip0gS8NZb4vadd7a/D5WS+vUTIyWS1Dw1pCRnAhwgMPJwFi4E0tKAPXtsHy8vF497O8hhgENERE754QexOql7d+Cmm5RuTft8pR5OTQ1QXCxudxTgWPJwfvhBvM7fNDYC999vfx8wy2MPPODdHCMGOERE5BTL6M111wEajaJNcchXEo1/+knU4xk0CBgyxPGxw4eLkaf6erFvlb9Zu7btyE1LkgTs3u3dn40BDhERdejgQbGBJiCmp3yZrwQ4LaenOprOU6map6n8MQ9n3z55j5MDAxwiIurQu++K0YjzzgPi45VujWMJCaImTnm5+FKKs/k3Fv68L1X//vIeJwcGOERE5FBjI/D22+K2Ly4Nb61HD+DMM8Xt4mJlMqFra5tzgJwNcCZOFN83bwYOHPBMuzxl3DigV6/2n1epgNhYcZy3MMAhIiKHliwBdu0CoqOB6dOVbo1zLNNUSgU469cDdXViVdfw4c69pm9f4Nxzxe0VKzzWNI/YvBk4ftz+c5bpublzvbvTPAMcIiJyyFK5+LbbgLAwZdviLMtKquXLlSk450r+TUv+uFy8oUFcG01NYl+tQYNsnx80SORvTZ3q3XYxwCEionaVlgLffSduZ2Yq2xZXWIr8/fprkCIF51zNv7FomYdjb8m1L3rpJWDTJiAqCli0CNixAygqasBDD21EUVEDysq8H9wADHCIiMiB/HzxQXvppcDQoUq3xjkLFwKPPNL2cW8VnKuvF0vEAdcDnHHjgNBQseR62zb52ya3bduAp54St195BTjpJDENNX68hAsvLMf48ZJXp6VaYoBDRER21dYC770nbvtDcjHgGwXniouBEyeAPn2A005z7bXduwNjxojbvr6aqqlJ7CZfVwdcfDFw441Kt8gWAxwiIrKrsBA4ckQUoJs8WenWOMcXCs5ZpqcuvNC97Sz8Zbl4QQGwZo1YtZaf73tbdygS4BgMBiQkJDh1nOGfrVWNRqP1tuV+Xl4edDod8vLyYDKZPNVcIqIuyVK5ODPTu6tfOsMXCs65m39jYUk0XrVKJPD6oj17gKwscfvf/xYbbPoarwc4un9KYRqc2BM+Pz8fCQkJUKlUyMzMhFartT6Xnp6OrKwspKWlIS0tDbNmzfJYm4mIuhqDAfj5Z0CtFitk/IXSBefMZrGfFOB+gDNypFiSf/So8tWY7ZEk4I47RPvOPx+4+26lW2RfiLffMC0tzeljExISUFlZCQDQtNj4xGg02hyn1Wqh96c1dUREPs6yNDwtTSSO+otx48Sy5PJy+3k4KpV43lMF5wwGUQ8mOrq52KCrgoNF0T+dTiwXv+ACedvYWZ99Bnz7LdCtG/DOO747uufzOTgajcYmuAEAvV6P6Ohom8eio6OdGhUiIiLHTCbgk0/EbX9JLrYIDgZefVXcbp0T4o2Cc5bpqXHjxHYR7vLVPJxDh4D77hO3//Uv4PTTlW2PIz4d4JhMJuh0Ouh0OmRnZ1tHbtrLt6moqPBi64iIAtNHHwE1NcBZZzWv6PEnU6eK0Y+BA20fDw/3fMG5zubfWFjycH7+WUwF+YoHHgAOHxbXRna20q1xzOtTVK7IyMiwjt5otVqkpqaitLS03ePbC3zq6upQV1dnvV/9TwUos9ls/bLcJ+9hvyuD/a4Mf+l3SQLefDMEgAoZGY1oaGhSukluueIKsfJr9epGfPDBDnz++aloaJAwZkwDPPUraGwE1q0TfTdmjLlT7xMbC2i1ITAaVVixogGXXaZ81b8lS1T45JMQBAVJyM9vhEoltfszeup6d+V8Ph3gGI1GxP+zba1Wq4XRaITRaIRGo2kzWlNRUdFmKssiJycHc+bMafP48uXLER4ebr1f5GtjgV0E+10Z7Hdl+Hq/b94cg23bxiAsrAExMcuwZImPLuNxwTXXAOvX98eOHZF47LGtuOqq9v9Q7ozt2yNRXT0B4eFm7NmzpNMrtYYPPxtG4xC8++5OqFRb5Gmkm2pqQnDvvRMBhOCKK0px8ODvWLKk49fJfb3X1NQ4faxKkpQpBq1SqeDorQ0GA5KTk61JxiaTCVFRUaisrERFRQXS09NRUlJiPT4qKgplZWV2gxx7IzixsbE4fPgwIiIiYDabUVRUhNTUVKjVavl+SHKI/a4M9rsy/KXfZ8wIxqJFQbjjjka89pp/jt60ZOn38vJLcffdoRgyRMIffzR4JAdn7twgZGUFY/LkJnz5ZecrCX7xhQrXXhuC006T8Ouvygaa994bhPz8YGi1EgyGBrQYG7DLU9d7dXU1YmJiUFVVhYiICIfHKjqCYzKZbAISg8EAjUYDrVYLrVaL3Nxc63N6vR5paWl2k46NRiMSExPbHcEJDQ1FaGhom8fVarVNx7e+T97BflcG+10Zvtzve/cCixeL23ffHQy12keXx7jhuuuC8K9/AWVlKhQVqXHFFfK/x7p14vuECUFQqzuf4nrxxSIx+s8/VTh4UN0mp8hb1q4VhfwA4J13VIiMdP76lft6d+VcXk8y1uv1yP4nMyknJ8daF6f1fY1Gg8TEROTl5aGgoADFxcUoLCy0HltYWIjs7GzodDrk5+fbPEdERK6bN0/kkYwb5/4SZ18VHt5cz+eNN+Q/f1NTc3XkziYYW0RHA5aauCtWyHNOV5040dxvt98OXHSRMu1wh9dHcFJSUpCSkmIzOmPROkiJj4+35uC01nKEx5XaOkRE1JbZLErvA/63NNxZd94pdr5evhzYuhUYMUK+c//2G1BZCfTsCbTzseWW1FRg40axXFyJvZ6eeQb4+29RGPE///H++3eGTy8TJyIi71i8WExR9e3r2WXUStJqgcsvF7fffFPec1uWh48ZA4TIOHRgWS6u19svXOhJmzY1BzX//S/QThaIz2KAQ0RE1srFs2aJCrWB6p57xPcPPpC3voxc9W9aGzNG7DC+fz/w++/yntsRsxm49VYxZZmeDkyZ4r33lgsDHCKiLu6vv0SOR1AQkJGhdGs8KyUFOOUUEdx8/LE855Qksas2IH+AExoqdiUHxCiOt7z0EvDLL0BUFPD66957XzkxwCEi6uLeflt8v/xyIC5O2bZ4WlBQ8yjOG2/IM+3zxx+ium/37kBiYufP15plmspbJZS2bgWeflrcnjvXv/Yia4kBDhFRF9TYCKxeDbz/vtgwEQjc5OLWbrpJJAP/+SewcmXnz2eZnrrgAs9M71n2pfr+e6C+Xv7zA83Xw/z5Ykqqrg645BLghhs8837ewACHiKiLWbgQGDxYLPm99Vax+3VwsG/teeRJERHNK5LkWDLuqfwbi7POAvr0Eb+nn3+W//wtr4frrxcrwlQq4Oqr225Y6k8Y4BARdSELFwJpacCePbaPNzYC06eL57sCyzTV4sXAzp3un0eSPB/gBAV5bpqqvetBksSyen++HhjgEBF1EY2NwP33O847eeABcVygO+00IDlZFOizrCBzx7ZtwIEDIhl41Cj52tday+Xicgn064EBDhFRF7F2bdu/1FuSJGD37uaKvIHOMorzzjuiYq87LKM3o0cDYWHytMseSx7Ohg2AySTPOQP9emCAQ0TUBZSXi60YnNHZXbD9xRVXiFVjR44An33m3jk8PT1lERsrKi83NYlkYDk4+3v21+uBAQ4RUYA6ehT48EPx139sLPDJJ869rn9/z7bLVwQHN68ce/1115eMeyP/piW583D69XPuOH+9HhjgEBH5Ecty3k8/Fd9b50eYzcC33wLXXivql9x8c3OZ/zFjRLn99lbGqFQiEBo3zrM/gy+57TaRP7Npk+srlIxGMTKmVospKk+zTFPJkYcjScCSJY6P8ffrgQEOEZGfaLmcd+ZM8X3wYOCLL0Ruxn33AQMHioJ9n30m8kpOOQV49lmgtBRYtw54911xrtZBjuX+3LliZKOriIkRfQm4XrHXMnozapTYrdzTJkwQv5tt24Bdu9w/jyQBjz8OvPhi82OBeD0wwCEi8gPtLefds0c8ft554gP60CFRM+W++0TQ89dfwL/+JTaaBMRGmjqdCIRaGjRIPB6oG206Ykk2Lix0Ld/Em9NTABAZ2bxSy91RHEkS18MLL4j7r78uAuRAvB5k3POUiIg8wZnlvAAwY4ao0puSIqZN2jN1qtg8ce1a8YHev7+YhvDXv9Q7Kz4eOP984KefRCL2k0869zpvBziA+N3+9JPIw7n1VtdeK0niZ/v3v8X9V19tDu4C8XpggENE5OM6Ws5rcccdYhrDGcHBzh/bFdx7rwgc3n4beOyxjrdc2LlTfAUHiy0avCU1VUw56vViRVWQC/Mwc+YAzz0nbr/yihjlswjE64FTVEREPi7Ql/P6gmnTRFL2vn3AokUdH28ZvUlMFPtaecvo0eL9Dh8GNm92/nVz5ogvAHj5ZVHAL9AxwCEi8nHOLtP11+W8vqBbNyAzU9x2Zn8qJaanADH1aHlPZ5eLP/ts8+7gL74IPPigR5rmcxjgEBH5uHHjRNInl3d7VmYmEBIiVpv98ovjY5UKcADXlos/91xzTlFeHvDww55rl69hgENE5OOCg0VCqD2BsJzXVwwYIKaqAMejOOXlYtl9UBAwdqx32taSpeDfmjVAbW37x/3738ATT4jbubnAo496vm2+hAEOEZEfmDrV/lYLgbCc15dYVhXNnw9UVNg/xjJ6M3IkEBHhnXa1dPrpYjqythb48Uf7x7zwAvB//ydu5+QAWVnea5+vYIBDROQnzjhDfO/bV2y7sGoVUFbG4EZOY8YA554rggdLUcTWlJyeAsSonaNtG/LygNmzxe3nnxerwroiBjhERH5ixw7xfcQIsRWDpbItyUelah7FeeuttlthAMoHOEBzHs7Chbbbdrz4IpCdLZ579llRsbirYoBDROQndu4U308+Wdl2BLprrwWiokRA2Xq/pv37ga1bRSCkZFJ3XZ34vm1b87YdvXs359nMmSMqFndlDHCIiPyEJcAZPFjRZgS88HCxCSfQdn+qNWvE97PPFkGQEhYuBDIy2j5eVSW+T5/ufDXmQMYAh4jIT3AEx3vuukuM0hQVif28LJSennJm246ffrI/tdbVMMAhIvITlhwcBjieN2SI2JUdELk4FkoHOM5s27F7tziuq2OAQ0TkBySJIzjeZkk2/uAD4OhRsT3C77+Lxy68UJk2cdsO53GzTSIiP1BRARw/Lm7HxSnblq4iJUWsWNu6Ffjoo+atMM44A4iJUaZN3LbDeRzBISLyA5bRm379gLAwZdvSVQQFAXffLW7n5gIFBeK2kqunuG2H8xjgEBH5AebfKCMqSgQNu3cDy5aJxxYsECuZlNBy247WQQ637bClSIBjMBiQkJDg1HF5eXnIy8tDeno6TCaTzXMGgwEAYDQarbeJiAIR82+8b+FC4MYb265YqqwE0tKUC3KmThXbcwwcaPs4t+2w5fUAR6fTAYBTAYler0dWVhaysrKQlJSE5ORk63P5+flISEiASqVCZmYmtFqtx9pMRKQ01sDxLkfLsS2PPfCAcsuxp04Vo3qrVnHbjvZ4PcBJS0tDfHx8h8cZDAbk5OTYvM5gMMBoNAIAEhISUFlZicrKShQVFUGj0XiqyUREiuMIjnd1tBxbkpRfjh0cLLbr4LYd9vnsKqr4+HjMa7F1rmV6Kjo62voYgxoi6iqYg+NdXI7t/3w2wAHEqI3F559/jpSUFGtQYzKZrNNdxcXFnKYiooDGERzv4nJs/+fTAY6FJZgpKSmxPpaRkWENdrRaLVJTU1FaWmr39XV1daiz7EwGoLq6GgBgNputX5b75D3sd2Ww35XRmX4/ehSorFQDAAYMMIO/Oue52++jRwMDB4Zg715AktquyVapJAwcCIwe3cDfhx2e+n/GlfOpJMnRjhaeo1Kp4OxbZ2ZmIjs722aExmAwWHN5TCYToqKiUFpaancU5+mnn8acOXPaPP7JJ58gPDzczZ+AiMg7du7shfvvn4heverx8cdLlW5Ol/HTT/2Rm5v0z72WQY747MrOLsb553OOyptqamowc+ZMVFVVISIiwuGxPh/g5OXlIS0tDVqt1pqHYzQakZycjMrKSgDNAU5lZaXdvBx7IzixsbE4fPgwIiIiYDabUVRUhNTUVKjVall+PuoY+10Z7HdldKbfv/1WhauvDsG550rYsKHBQy0MTJ293hctUuGhh4JRXt4c4AwaJOGllxpx9dWKfHz6BU/9P1NdXY2YmBinAhxFp6hMJpNNQGIwGKDRaKyjMDqdDvHx8dbgZsGCBcjIyIBWq0Vubq71dXq9Hmlpae0mHYeGhiI0NLTN42q12qbjW98n72C/K4P9rgx3+r28XHwfPFjF35mb3L3ep08Hpk0Tq6X27RM5N+PGqRAc7BcZHoqT+/8ZV87l9d+QXq9HUVERACAnJwdJSUnWZGLL/aysLBiNRqSnp9u8VqPRWHNvEhMTkZeXB41Gg9LSUhQWFnr7RyEi8grWwFGWZTk2+RevBzgpKSlISUmxGYGxaBmkaLVah1NY8fHxTtXTISLyd1xBReQ67kVFROTjWAOHyHUMcIiIfBxHcIhcxwCHiMiH1dYCBw6I28zBIXIeAxwiIh+2a5f43rMnEBWlbFuI/AkDHCIiH9Yy/0bVtqAuEbWDAQ4RkQ9j/g2RexjgEBH5MNbAIXIPAxwiIh/GERwi9zDAISLyYayBQ+QetwKcF198ETv++Ve3cuVKDBs2DMOHD8eqVavkbBsRUZfHERwi97gV4OTn52PwPxPC6enpeOyxx7Bs2TJkZGTI2TYioi7NbG650aaiTSHyO27tRWXZI2rFihWorKzE7bffDgA4cuSIfC0jIuriysuBpiYgNBTo21fp1hD5F7cCHK1Wi9mzZ6OwsNA6alNWVgatVitr44iIujJL/k1cHBDEjEkil7j1T6awsBBarRaPPfYY3n77bQCAyWTC7NmzZW0cEVFXxvwbIve5FeBERkZCq9Vi48aNePzxxwEAFRUViGIdcSIi2bAGDpH73ApwZs+ejYKCAmRmZqKoqAgAkJiYiOzsbFkbR0TUlXEEh8h9buXg6HQ6/P333wCaE44jIyNhMplkaxgRUVfHGjhE7nN7iurXX38FAKj+2f1t06ZNiIyMlK9lRERdHEdwiNzn1gjOggULkJiYiKSkJFRWVuLOO++EXq9HYWGh3O0jIuqSmpqA3bvFbebgELnO7WXiFRUV+OKLL2A0GqHRaPDCCy9wBIeISCb79wP19UBwMDBggNKtIfI/bgU4L774Ih555BFMmzZN7vYQERGa828GDQJC3PqfmqhrcysHZ8OGDVi0aJHcbSEion8w/4aoc9z6u2D27NmYPn06jEYjkpOTodForM8N5mQxEVGnsQYOUee4FeDMmjULkiThv//9r7WSsSRJUKlU1uXjRETkPo7gEHWOWwHOxo0bAYjNNo1GI4YOHYqJEyfK2jAioq6MNXCIOsetAKe6uhrx8fGIiorCkCFDkJ+fj6qqKuj1epzMf41ERJ3GERyiznErwElPT0d+fj6Sk5Otj+l0OmRkZGDZsmWyNY6IqCuSJAY4RJ3l1iqq0tJSm+AGANLS0qxTV0RE5L4jR4CaGnE7Lk7ZthD5K7cCHK1Wa92qweKXX37BkCFDZGkUEVFXZsm/6d8fCA1VtClEfsutKaq3334biYmJSE1NhVarRWlpKVasWIEVK1bI3T4ioi6H01NEnef2CE5FRQVSUlIgSRJSU1NhNBpx7rnnytw8IqKuhwEOUee5NYKzcOFCaLVazJo1y/rYF198AZVKhalTp3b4eoPBgFmzZqGkpMThcUajETqdDlqtFkajERkZGdaigo6eIyLyZyzyR9R5bgU42dnZbYKT5ORkJCUldRjgWIISg8HQ4fukp6db38doNGLWrFnWHcsdPUdE5M9YA4eo89wKcI4cOYKIiAibxzQaDY4cOdLha9PS0px6D6PRaHNfq9VCr9d3+BwRkb/jFBVR57mVg5OYmNhms82VK1dCq9XK0igA0Ov1iI6OtnksOjoaBoPB4XNERP6OAQ5R53VqFVVWVhZSUlJQWlqKkpKSDnNqXGEymew+XlFR4fA5IiJ/VlUFWP6LY4BD5D63AhzLKiqdToeysjKkpKRg2rRpcrfNrvaCG0fP1dXVoa6uznq/uroaAGA2m61flvvkPex3ZbDfleFsv2/fDgBq9O4tITS0Afw1dQ6vd2V4qt9dOZ9bAY6Fs/k07tBoNG1GZCoqKqDRaBw+Z09OTg7mzJnT5vHly5cjPDzcer+oqKjzDSeXsd+VwX5XRkf9vmHDSQBGIzKyCkuWfO+dRnUBvN6VIXe/11hKfDtBJUmS5MyBO3bsgMlksql1s3LlSuTm5qKiogLXXHMNHn74YeffWKWCo7c2Go02K6UAICoqCmVlZaioqGj3OXtBjr0RnNjYWBw+fBgREREwm80oKipCamoq1Gq10z8DdQ77XRnsd2U42+9vvRWEBx4IxpQpTSgsbPRiCwMTr3dleKrfq6urERMTg6qqqjaLnVpzegQnMzMTmZmZ1gBn06ZNSE1NRW5uLkaOHIns7GwAcCnIMZlMNgGJwWCARqOBVqttk7BsNBqRmJhoHcFp7zl7QkNDEWqn3rlarbbp+Nb3yTvY78pgvyujo37fs0d812qDoFa7tQ6E7OD1rgy5+92Vczkd4GzcuNFmp/D8/HxMmzYNjzzyCACx6ikpKanDAEev11uHrHJycpCUlGSd6rLcz8rKAgAUFhYiOzsbSUlJKC4utqlz4+g5IiJ/xRo4RPJwOsBpPZ1UWFiIefPmWe9rNJo29WnsSUlJQUpKCnJzc9s81zpI0Wq11uNa5/s4eo6IyF9xiTiRPJwe/0xJScG7774LQGzLUFlZiZSUFOvzZWVl3E2ciKiTGOAQycPpEZx58+YhISEBWVlZMJlMKCwstEnwyc3NRWZmpkcaSUTUFZw4ARw8KG5zHyqiznE6wImMjMT27dtRVlaG6OhoREZG2jyfnp6O5ORk2RtIRNRVWEZvevUCuHcwUee4XAenvWkoBjdERJ3TcnpKpVK2LUT+jmsQiYh8BPNviOTDAIeIyEdYAhzm3xB1HgMcIiIfwRo4RPJhgENE5CM4RUUkHwY4REQ+ggEOkXwY4BAR+YD6emDvXnGbOThEnccAh4jIB+zZAzQ1AWFhQN++SreGyP8xwCEi8gGW6am4ONbAIZIDAxwiIh/A/BsieTHAISLyAayBQyQvBjhERD6ANXCI5MUAh4jIB3CKikheDHCIiHwAAxwieTHAISJSWGMjsHu3uM0cHCJ5MMAhIlLYvn2A2QyEhAADBijdGqLAwACHiEhhlumpQYOA4GBl20IUKBjgEBEpjPk3RPILUboBRJ3V2AisXSuG+fv3B8aN41/B5F9YA4dIfgxwyK8tXAjcf7/Yx8di0CDg1VeBqVOVaxeRK1gDh0h+nKIiv7VwIZCWZhvcAEB5uXh84UJl2kXkKk5REcmPAQ75pcZGMXIjSW2fszz2wAPiOCJfxwCHSH4McMgvrV3bduSmJUkSdUXWrvVem4jcIUnMwSHyBAY45Jf27ZP3OCKlHDoEnDgBqFRAbKzSrSEKHAxwyC/17+/ccfv3e7YdRJ1lGb3p3x/o1k3ZthAFEgY45JfGjgW6d+/4uIceAi6+GNi40fNtInIH82+IPIMBDvml//5XDOvbo1KJr0mTALUaKCoCkpKA9HRg61bvttPXNDYC33+vwpo1A/H99yomYfsA5t8QeQYDHPI7GzYADz8sbt96q6h709KgQYBOByxZIgKaG24QAY9OB5xxBnD77c0bG3YlCxeKD9HU1BC8/HIiUlNDMHgwl9MrjTVwiDxDkQDHaDQiLy8POp0OeXl5MJlM7R6r0+lgMpnsHmMwGGAwGKzntNymwFVRAUyfLjYmnDYNeOcd8QGxahXwySfie1lZc5G/IUOAjz4CNm8GrrxSjGC8+y4wfLgIkg4fbj53YyOwejXw6afieyCNbrBmkO/iFBWRZygS4KSnpyMrKwtpaWlIS0vDrFmzHB4bFRWFqKgoqFQqqFQq5OXlAQDy8/ORkJAAlUqFzMxMaLVab/0IpABJAm6+WXwgDB0qAhWVSmzLMGECcO214ru9bRrOPBP46ivgxx+B8eOBujrg5ZcBrRZ45hlg/nwxunHRRcDMmeJ7oIxusGaQb2OAQ+QZXg9wjEajzX2tVgu9Xm/3WJPJhMLCQkiSZP3Kzc1FVlYWACAhIQGVlZWorKxEUVERNBqNp5tPCnrpJeDrr4HQUGDBAiAy0vVznH++GOX57jtg5Ejg6FHgqaeA668P3NGNrlQzyB9H4ZiDQ+QZXg9w9Ho9oqOjbR6Ljo5ud3opLS3Nelun09ncBwCNRsPApgv44QfgscfE7VdfBeLj3T+XSgVccolYWfXpp0BIOzuyBcroRlepGWTJMfKnUTiTCaiqErfj4hRtClHA8XqA016+TUVFRZvHWgYuJpMJFRUVNtNQJpMJOp0OOp0O2dnZbUaHKDAcOgTMmCGCjJkzgYwMec4bFAT06wc0NLR/TCCMbjhbM8jZ43yRv+YYWUZvYmKAHj2UbQtRoPGZ3cQdJRoDQHZ2NnJzc20ey8jIsAZBWq0WqampKC0tbfPauro61NXVWe9XV1cDAMxms/XLcp+8x5l+b2oCrrsuGOXlQRgxQsIbbzQ4DEhctXu3Cs78M9i9uwFms50kFj8wejQwcGAIyssBQGX3mJAQCaGhDfDHfwKNjcB994X8M+Jm+/NJEqBSSbj/fmDy5Aa7+VneYu96Ly0V119cXBPMZj8eJvRh/P9dGZ7qd1fO5/UAR6PRtBmtqaiocDjNZDKZoNfr2xxjNBoR/89chVarhdFohNFobJNsnJOTgzlz5rQ57/LlyxEeHm69X1RU5OJPQ3Jw1O8LFpyCoqLT0K1bA+66aw3WrDkq63vv3NkbwFgnjvsZS5YckfW9vSk1dSg++OAMO8+IoK2hQYVx44KRnr4NaWnbEBLiP8Hcb7/1Rnl5+79DSVJhzx7gxRfX46yzlP8dtrzely4dAuBshIbux5Ilxco1qgvg/+/KkLvfa2pqnD7W6wFOSkoK8vPz2zyemJjY7ms2btzYJrgxGAxITk5GZWWlzeOt83sAYPbs2XjooYes96urqxEbG4uLL74YERERMJvNKCoqQmpqKtRqtYs/Ebmro35ftUqFzz4Tf3K/9RZw443jZG/DJZcAb78tYe9e8UHYmkolYeBA4JFHzlP0r//OkCTgtdeCAajQvbuEEyeaf85Bg4CnnmrEkiVBWLQoCJ99diq2bh2B995rwBn24iEfVF1tf1SqtZNPHo3Jk5UL3Oxd76tXiyyB8847CZMnT1asbYGM/78rw1P9bpmBcYbXA5zWoytGoxGJiYnWAMZgMECj0dgcZzAY2gQuWq3WZspKr9cjLS3N7khQaGgoQkND2zyuVqttOr71ffIOe/2+bx9w441iiurWW4HbbvPMpapWA6+9JvI0VCp7S6lVePVVICzMf6+LpUuBlSvFPke//aZCWVkDli79BZMmnYuLLgpBcHAIbrsN+Owz4O67gU2bVDjvPDWee05sdeHrgZ2zG1TGxobAF/55t7zeLQUnhwwJhlrt4x3t5/j/uzLk7ndXzqVIHZzCwkJkZ2dDp9MhPz8fhYWF1udycnKg0+navKZ1YKTRaJCYmIi8vDwUFBSguLjY5jzkvxoaRE2bAweAs84CXn/ds+83daqocjxwYNvnXnutuWigP2psBP6pqoD77hP1g8aPl3DhheUYP16yBi8qlejzLVuAyy4D6uvF6y68EPj7b+Xa74yyso6PGTQIGCf/AGCnsQYOkecokmTccvSl9bJve0GKpe5Na/Hx8dYcHAocTz8NfP890LMnUFgItEiT8pipU4EpU8RqqX37RBHAjRubl/D6qw8+EEFLVBTw+OMdHz9ggKg19P77Ynn8jz8C55wD5OUBd90lVp75iro60ca3325+zP4onPi57D2uNNbAIfIcH/rvikgU4Hv+eXH7nXeAESO8994tKyLfcYd4bMEC772/3I4fB554Qtx+4gkR5DhDpRLTgr/9BkycKDY1vfdeIDW1+QMZULao3p49oiL122+L9s6ZI4Lh1qNwffqIOkcbNogq2L5Uz+j4cVECAeAIDpEnMMAhn7F7t6goDIjRghkzlGvL1VeLD8bNm4G//lKuHZ3x8stiNGrIENGfrjr5ZLET+xtviFG0lSvFlOF77wFffKFcUb3Vq4GEBGD9ekCjAb75BnjySZFH1Xpfsn37RJtCQsR2HHfe6TsjObt2ie8REeLnICJ5McAhn2A2A9dcAxw5IqoUv/yysu2JjhYjFoB/juIcOCCmlQAgJ0dsb+GOoCCRePzLL8AFF4itLW67TZmiepIktutISQEOHhRTZxs3Ai0XH9nbl+yKK4D//U/8LPPmicRpXwhymH9D5FkMcMgnPP64yPeIjBRTDe5+IMtp+nTx3R8DnKefBo4dA0aNav45OmP4cGDNGqBVrU0bntza4tgxEQA/8og49/XXi+tl6FDnXj9jhticFQDmzm2eulMS82+IPIsBDimisRH4/nsV1qwZiH//Owgvvigef/99scO3L7jqKrGM/PffxZe/+OsvMVIBAC++KHJU5BAcLAImRzyxtcXWrcB554lAMyRETJl99JHryec33wy8+aa4/fzzYmRLSTt2iO8cwSHyDAY45HWWTRFTU0Pw8suJePppsVb58stF7ouv0GhEIUDAv0ZxsrNFADllivxLo53dkHPtWlHDqLMWLQKSkoA//hB7ZX3/vZgyczdou+uu5qm7xx8XZQCUwikqIs9igENe1d6miADw7be+tyliy2kqX8jb6MiaNcDixWK0xdF0kruc3ZDzySfF7tj33dfxCit7q7EaG0UAMnWqyPsZNw4wGEQeUGc9+qhoHwDcf3/z1JW3McAh8iwGOOQ1jY3iA8VRoOCJ/I3OmDJF5AP99ZdYNu3LmppEjgogdlz3xBL7ceNE0TxHIyjh4aKGUXm5KNJ40UUiMJo1S5QBqK9vPtYymtdyNVZcnEg0t0whPfAAsGKF2PldLk8/DTz8sLg9a5YIrryNOThEnsUAh5zmbt2TvXuBL78EbrrJ/siNhSfyNzorIgK49FJx29enqRYsAIqLRXDx1FOeeY/gYODVV8Xt1kGOSiW+Pv5Y1Hf55hvgllvEirRDh0Rdo0mTgL59gRtuEFNp9kbz9u4Vy/O7dRPLvV95BbJvsaBSAf/5j6h3JEmiPV9+Ke97OFJfL35OgCM4RJ7CAIecYu8vbXt1TyorRe2U558XSboDB4qvq68WdUic4Wyeh7dY6vH48jRVXR0we7a4nZ0NnHSS596rva0tBg0Sj0+dCoSFiS0f3ntPLFnX60X+S//+ojr0//4ncmEc9Wd0tDwrwNqjUomk4xtvFMH6jBnAsmWee7+Wdu8WP3v37qIYIRHJT5GtGsi/WPJmWn8YlZcD06aJv9Jra8XowfbtbV8fFASccYb4AFy6tOP3czbPw1suv1x8YP/9t6gHM3Kk0i1q6803xaqcAQNEnRdPa721Rf/+YvrK3sacISFAcrL4ev114OefxVLtjraO279fnH/CBE/8BEJQkMjBOXFCtOeqq8Q02vjxnntPoHl6Ki5OvlVuRGSLAQ455ChvxvLY++/bPj50qFj5YvmKjwd69BDnGjxYBEb2zqdS+eamiL16iWJyCxeKURxfC3AqK4HnnhO3n33WO3t3Ac1F9VwRFCQShXfu7DjAAbwzmhcSIkaUampEovvll4sRp8RE5wI4dzD/hsjzOEVFDi1f7jhvxuLWW8VfvocPi1GcTz8VIwnjxongBug4fwMQf9nL9SEiJ1+epnr+eRHknHWWyHPyB86O0nlrNK9bNzG9NnGiKCo4caKYgvPUVhSsgUPkeQxwqI2aGvHXdXq6mIZwRkqKqBnTu7fj45zJ3/BFl10m8iWMRqCkROnWNCsrE9M+gMhp8cXg0J6OVmOpVEBsrHdH88LCgK++EqvPampE7lBLcm5FwSXiRJ7HACfAObvyqbZWFFW75hqR9Dh9ugg4zGbn3seVv7SnThV/wRYVNeChhzaiqKgBZWW+G9wAYhTq8svFbV9aTfV//ydW5FgCTH/hq6N53buLujv2yLkVBQMcIs9jgBPAOlr5VFcHfP212Nenb18RYHz+ufjrdfBgICsL2LDBM39pBwcD48dLuPDCcowfL/nFyIOvTVNt3CgCV8uSZ39LVvXF0by1a5uXb9sjVykD5uAQeR6TjANURyufJkwANm0SS3YtYmPFyM306SI52PKB+eqr4lwqle35fD1vRm6TJomRnJ07ReB33nnKtUWSmov63XADcO65yrWlM1xZjeUNziY1dyb5ubFRBEkAR3CIPIkBTgByZuXT6tXi+4ABItdmxgzxgR1kZ0zP8pf2/ffbJhwPGiSCG1+eWpJTeDhw5ZVi1GTBAmUDnG++EfsyhYU1r6DyV+6sxvIUbyQ/790LNDSI1Vu+VhKBKJBwiioArV3r3MqnV18Vf0nOnQucf7794MbCkjezapWoLrtqFXw+b8YTWu5NJcdmku5oaBDTh4DIB4mNVaYdgcgbyc+7domTx8Z2jZFPIqVwBCcAOTt83qeP46CmNV/6S1spl14q6uLs2SMK1smx+aOr3nlH7I0VEwM89pj33z+QWZKf7U3JAuJ+Z6dkmX9D5B0cwQlAvlZjJJCEhTUvnVdiNdXRo837TD35JBAZ6f02BLr2kp/lsnOnGMFh/g2RZzHACUDjxjnei0iJGiOBxDJNVVjonWmqlkv9774bOHgQGDYMyMz0/Ht3VfamZLOzxXN33CF+B+6yTFExwCHyLE5RBSCTqf0P3q628skTLr5YjJzs3Qv88INnA8WFC9smdwNiz6Ru3Tz3vtR2Svb884ElS4DffgPuvFOM8rizNH/XLvGdAQ6RZ3EEJ8A0NIgRhkOHxCjOgAG2z/t6xWB/EBoqAgxA1A3yFMtSf3sJ4y+9JN+2AeSc0FDgo4/E6qeFC8XIjjssU1TMwSHyLAY4ASYrC1i5UtRr0evFX4tdfeWTJ1imqXS6zle1tcfRUn8LOSrqkmvOPbc5B+qee0RdKVdIEkdwiLyFAU4A+fhj4JVXxO2PPgLOPLN5mP3aa8V3TkvJIyUFiIoS+xV1tqqtPR0t9Zeroi657rHHRCFMkwm4/XbXqlpXVYWitlYFlUqMphKR5zDACRAbNwKzZonbTzzBURpP69YNuPpqcdsT01TeqKhL7gkJAT78UExZffcd8O67zr/24MHuAMTUMXOoiDyLScYyamxUpuT8gQPiw7auTmwI+fTTnn9PEtNU770HfPGF2NE7RMZ/TVzq79tOOw14/nmxXcaDD4oRPWdyag4dCgcQOPk3u6p24XDN4XafjwmPQVxknBdbRNSMAY5M7K12GTRIFA3z5GhKfX1zIuqIEcD//uda8T5y38SJQO/eIqH7+++B5GT5zj1uHNCvH7B/v/3nLVMcXOqvnAceAL78Eli3DrjlFmDFio7/7R08KAKcQMi/2VW1CyPeGIHahtp2jwkLCcPWe7YyyCFF8KNQBu2tdikvF497crXLAw+I/2AjIoCvvmLhN29Sq5uDV7mnqY4fb3/0j0v9fUNwMPDBB2KPstWrgTfe6Pg1hw6JKapACHAO1xx2GNwAQG1DrcMRHiJPYoDTSc5sbOmp1S7z5gH//a/4wPvkEzGCQ941Y4b4vnAhYDbLc86mJuC660SAHB3ddhqKS/19x9ChwIsvituPPQZs2+b4+EAawSHydYpMURmNRuh0Omi1WhiNRmRkZECj0dg91mAwAADi4+NhNBphMpkQHx/v8nk8xZXVLnLu4/Tjj6KqLQA8+yxw2WXynZucN3682NPr0CGxPP+SSzp/ziefFLuFh4UBy5YBI0cqk9tFzrnjDhHg6vXATTeJEdX2fj+WEZxAycEh8mWKBDjp6ekoKSkBIIKUWbNmobCw0O6x+fn5KCgoAACkpKTYHOfKeTxFidUu5eXAtGlixCAtDXj8cfnOTa4JCRG/i7ffFntTdTbAWbBAJK8CYoQuMVHc7uqbnPoylUqspDrrLLEB64svNm/r0JIkdc0RnIamBqWbQF2U1wMco9Foc1+r1UKv17d7fEJCAiorKwHAZnTG1fN4irOrWLZvF//BuVPavaXaWjE1sX+/qHPz/vudPyd1zowZIsBZtEhMGbq7/PeXX0SyKiBW51x/vWxNJA+LixMLCm65RYzATZ4sAp6WTCbgxAm19fiuIiSo+WPm8y2fY2T/kTil9yltjuOKLJKb1wMcvV6P6Ohom8eio6NhMBisU0+t2Zt2cuc8njBunMiJKC93XPDrySfFEPbLLwMJCe69lySJaakNG0SRuS+/BHr2dO9cJB/L5qYHDojf8eTJrp/j0CGx/UNNjdjr6oUXZG8medhNN4mpqq+/Frd//tk22N25U3zv00dCeHjX+6vEVGvC9YuuR0NTA06NORVTRkzBlSOuxHkDz0P50XKuyCLZeT3J2GQy2X28oqKi3eN1Oh10Oh2ys7OtIzeunsdTgoPFX25A25EUlUp8paWJfIo1a8SUw003uV7iHQDeekvUXQkKEqt2hg7tfPup84KDxe8YEFNMrjKbgfR08QE4bBjw2WfMsfFHKhVQUCASwzdtap5qtGjeRdyF0scB5NDxQ5gweAJCgkLw1+G/kPtDLsa8NwYDXh6Ae5fcyxVZJDufqYPTXsDSMnFYq9UiNTUVpaWlLp2nrq4OdXV11vvV1dUAALPZbP2y3HfHFVcAn32mwkMPBaO8vDnKGThQwksvNeLqqyXs3g088UQwPvkkCB99BBQWSnj44SY8/HATevTo+D3WrFHhgQeCAaiQk9OICROaZFu1o5TO9rsvmTZNhTffDMGXX0o4dqwBoaHOv/b++4Pw/ffB6NlTgk7XgJ495VuRZU8g9buv6d0beO01Fa6/PgTPPy9h8uQGWAaUjUYR2MTGNsFs9v9NxCLVkQgLDkNto4NRl+AwRKojYTabMThiMJZcswRVtVX4rvQ7fPP3N/iu9DscPH4Qi7ctduo9GxoaXL5ueb0rw1P97sr5vB7gaDSaNqMsFRUV7a5+MhqN1ikny2opo9Ho0nlycnIwZ86cNo8vX74c4eHh1vtFRUUu/jTNQkOB114D/vijNyorwxAVVYvTTz+C4GBgyRJxzPTpwLnnavD++2fizz9747nngvHWW/W4/vo/MWHCbpsiYY2NzecKCpKQn382GhpCcOGFu3HKKQbrOQNBZ/rdVzQ1AdHRF6OiojtyckowatQBp163fPnJ+O9/zwUA3HffBuzYsR87dniunS0FQr/7op49gTFjEvHDDwORnn4CL730Pbp1a8K6dWcAGIamph1YsuR3pZspi9dHvI6D9QcRghCbXBuLiJAIbPlhC7Zgi83jvdAL13a7Fmkj0vDH8T9QdKQI60zrOny/devWYV+4eys2eL0rQ+5+r6mpcfpYlSS5slVc5xmNRpvVTwAQFRWFsrKyNsGJwWBAcnKyNcnYZDIhKioKlZWVqKiocPo89kZwYmNjcfjwYURERMBsNqOoqAipqalQq9Xy/9CtSBKwcKEKjz8ejLIyMeIzcqSEvLxGjB8vYdGitqNBADB4sIRffmlAi5jMr3m73z3t4YeD8PrrwZg5swkffNDxX+g//qhCamowzGYVnn66EY8/3uSFVgZev/uiw4eBkSNDcOCACg891IgXXmhCeroKX30VghdfrMd99wVODs6za5/Ff376D7LOz8K/xv3LrXNs2r8J5713XofHrb91PUb2G+nSuXm9K8NT/V5dXY2YmBhUVVUhIiLC4bFeH8HRarU2941GIxITE61BicFggEajgVarhVarRW5urvVYvV6PtLQ0aDSaNkFM6/O0FBoailA7cwZqtdqm41vf96RrrhFJpa+/Djz3HLBpkwqpqSEYNQooLrafsLxzpworVqgDrsCbN/vdk665Rvw+v/46CI2NQQgLa//YPXvE6ivLUv8nnwyGSuXdxJtA6Xdf1L+/yMeZMgV45ZVgTJkSjD/+EAFsTU0wgoKCAybP6sc9P6K2oRb9evVz+3oKcXIjt5CQELffg9e7MuTud1fOpUgl48LCQmRnZ0On0yE/P9+mdk1OTg50Oh0AMZ2VmJiIvLw8FBQUoLi42OZYR+fxB2FhwKOPiiXkd90lkoc3bHC8GstTVZGp80aPFivqjh4Vu0y358QJsTnqgQPA2WdzqX+guvJKsaBAksS+ZX//Lf67ffLJYAwe7NktXLzF3GjGT3t+AgCMO5kbo5FvUSTJuOXITJpl+ck/Wgcp8fHx7S77dnQef9KnD/Dmm0BSUnMdFHs8VRWZ5BEUJPKsXn5ZrKa66qq2x0gSkJEBbNwoElK51D+wJScDH37Y9o8Syz51/r7lxqb9m1BjrkFUWBRO73O60s0hhbWsZdTQ0IDSmlJs2r/JOkLn7VpGPrOKiuD0yhs5qyKTvCwBzuLFoqZN63ypl18WO74HBwOFhcCQIcq0kzyvsbH9KuOWop8PPCCmsfx1umrtzrUAgLFxYxGkcn9CICY8BmEhYR3WwYkJj3H7Pciz2t1dvsX+bN6uZcQAx4c4WxXZ2eMCnS9WPh01SpTh37kTWLpUbONgsWwZkJUlbs+dC1x0kVebRl6m1D513rR2lwhwxsV1bnoqLjIOW+/ZavPv+cUfX8SnWz7FlBFT8OT4J1nJ2Me5srs8A5wuqKOqyCqVeH4cp7rb/2uhBSUqn6pUYhTnP/8B3ngDqK8XAWm/fiIJuakJuO225o1SKXApsU+dNzVJTVi3SyztliP/Ji4yzubf6s3n3oyvtn6Fvj36Ir6/96rTU+BggONDLFWR09LEB2XLIMeShDp3rv8OZ8vJF/9asIj5ZxR99WrxBYhNORsagPPPF/lWTCoOfIE+ImtuNCN7TDZ+2vOTRwKQiUMmoiKrAqEhLlTNJGqBAY6PmTpVJB7ef7/t8PagQSK48eeERF8l51TXwoXAY4+1fbzhnw2Vb7vN+Vwr8m+BPiIbGhKKR8c86rHzhwTZLx5I5CxePT5o6lSReLh2rRi+7t9f/CfIkRvXbd6/Gaf0PgU9u9lfqiTnVFdjowhMHS3znzMHuPlm/i67Ao7Iymf/sf3o17Of0s0gP6NIHRzqWHCwSDy89lrxnf8JuueWxbcgIicCI94YgemF0/Hvtf/Gmp1rrM+7MtXVkY6SSoHmpFLqGiwjsgMH2j4+aJD/LxHX/aHDrqpdHn2P6rpqnPbmaYh9JRZVtVUefS8KPAxwKKDFhMdAgoRtR7ah8I9C/N/K/8ObxW9an2+S5NseIdCTSsk9U6cCO3YARUUNeOihjSgqakBZmX8HNztNO5FemA7tq1ocrz/usfeJCI2AJEloaGqA3qj32PtQYOIUFQW0Zdcvw6CIQfh1/6/4Zf8v+OXAL5g4eKL1+fLqctneK9CTSsl9wcHA+PESjh8vx/jx5/j9iKxleXh8/3j06NbDo+81adgkbD2yFUu3L8W006d1/AJShC/WMmKAQ35p31Hnh0H69uiL1KGpSB2a2ua54CD5PmkCPamUyMJS4O/Cky/0+HtNGj4Jc9fPxdLtSyFJElRcguiT4iLj8N/L/otdVbswYfAEhAWFYd26dRg7dqxilYw5RUV+R5IkvPDDCx0e58xfCwN6DZCrWdakUqDtMnAmlVIgkavAnzMuPPlChKvDsffoXmw+sNnj70fue3fTu3hq9VNYv0fs+j40fChG9huJ+P7xiO8f7/WSHRzBIb+z5eAWFJcXIzQ4FJ9N+wxxGvv/aJSofMpl/hToDtccxp+H/wQgtmjwtLCQMFw0+CJ8+/e3WLp9Kc7pd47H35Nct9O0E+t2rYMKKlx71rVKNwcAAxzyQ2eddBZ+ueMX/Lr/V1x12lVKN6cNLvOnQGapXnx6n9PRO7y3V95z8vDJ1gDnsbF2Ck2R4j7d8ikAYPzg8RgUMQhms1nhFjHAIT91asypODXm1E6fx1OJcZZl/uQdvrgvWaCy5N94Y3rKYvLwybh95O24/JTLvfae5Jr5v80HAFx31nUKt6QZAxzyG4u3LkbfHn0xetBo2c5pb5O/lhoaG9CvVz9+OPowX92XLFBljcnC6EGjMVgz2GvvOVgzGPOunOe19yPXbD6wGVsObkG34G5IOz1N6eZYMcAhv7Dv6D7c9OVNqK6rRtENRZg4ZGLHL3JS603+ALF8/J6l9+D3g7/jr3v+ku29SH6+vC9ZIDqp50lIPyNd6WaQD5m/WYzeXDb8MmjCNMo2pgWuoiKfJ0kS7vz2TphqTRjZb6RXlqZGd4/GqrJV+Lvib3y/43uPvx8ROdYkNWFD+Qa8sO4FSI72QyGvKz8q6on50vQUwBEc8gOfbfkMX239CuogNd6f8r5XNuDrru6OGWfMQIGhAB/8+gEuGnKRx9+TyNf9b/P/sMO0A1NPm4rT+5zu1fc2N5px0YcXocZcg0uHXYpz+53r1ffvrEDOE/vf1P8hJzkHfXr0UbopNhjgkE87cOwA7l16LwDgXxf+C2eddJbX3vumc29CgaEAX/zxBd6c/Ga7G3YSdRXvbnoXq3esRp/wPl4PcEJDQjFxyER8s+0bLP17qV8FOF0hTyw2MlbpJrTBKSryafcsvQdHThzBOSedg9ljZ3v1vc8fdD6GRw/HcfNx6P7QefW9iXxNfWM9ft7zMwBg3MnKlOOeNGwSAGDp9qWKvL+75NzU15fUN9bj4PGDSjejXQxwyGetKlsF3R86hASF4P0p70MdrPbq+6tUKtx0zk0AgA9//dCr703OO3DsgNJN6BJK9pagtqEWvbv3xmkxpynSBkuA8+PuH2GqNSnSBmq29O+lGPDSANz61a1KN8UuBjjksyYMnoCCywvw7EXPYmT/kYq04YZzboAKKqzesRo7TDsUaQO1r0lqwoPLHnTq2DU713i4NYHNsj3D2Lixiu0HNSRqCE6NORWNUiOKSosUaQM1m//bfDRKjYjuHq10U+xigEM+S6VSYVbCLEUrl8ZFxuGupLvw6qWv+tTyRxKCVEF4fuLzUKHjD9ysoiwsL13uhVYFJkuA441VjI746zRVoKmuq8bX274GAMw8a6bCrbGPScbkcwz7DBgWPQwRoRFKNwUA8MbkN5RuAjkw7fRpMN5vRMWJCrvPNzQ24MnVT2JZ6TJM+WwKll63FBMGT/BuI/1ck9SEH3b9AMC7FYztmTRsEl75+RVrPhApY9Gfi1DbUItTY07FyH7KjLB3hAEO+ZSKExW47JPLoA5SY9n1y3BaH2Xm+sl3Hak5ghm6GXjp4pesGy8O1gx2WFl38bWLMfXzqfj2729x+SeXY9n1yzAmboyXWuz/dlXtQn1jPXqoeyg2XWxx4ckXYu0ta2WtaE6ua7k1g1JTlh3hFBX5lAeXPYj9x/ajR7ceGBI1ROnmWFXXVeMdwzt46ceXlG6KW3ZV7YJhnwGGfQZs2r8JpTWl2LR/k/WxXVW7lG6iUypPVCL141SsKFuB6xZehyapyanXdQvuBt10HVK0KThuPo5J8ydh075NHm5t4BisGQzTYyYYMg1eqUPlSGhIKMbGjVW8HZ6wy+Qf/w73H9uPFWUrAADXnukbO4fbE3hXCPmtb7d9i49+/QgqqPDele8hLCRM6SZZbdq3CbO+noWI0AjcmXQnwtXhSjfJae3W4NjWfNOVGhxKFSyrqq3CJf+7BJv2b0Kf8D5YkL4AQSrn/0YLCwnDV9d8hcnzJ6O+sR7aKK3sbQxkIUEhOKX3KUo3wy85s6kvANz73b04b9B56N+rv5da5p7PtnyGJqkJoweNxtDooUo3p10McMgnVNVWIfObTADAg6MfxPmx5yvcIlvjTh6HwZrB2GHagS//+tJnk+rskXOvJqUKlh2tO4pJ8yeheG8xenfvjRU3rnCr0Fy4OhzfzPwGkiShV2gv2dpH3mVuNOP+7+7H8tLl2Jix0ecXAHS0qe+RmiO4/evbsatqFy6dfym+v/l7n/6Zbjj7BnQP6Y6Tep6kdFMcYoAToPytLPjDyx9G+dFyDIsehmcnPqt0c9oIUgXhxrNvxDNrnsGHv37oVwGOnJTY2PJ4/XFc9sll+GnPT4gKi4L+Rn2nKlq3rkj9VvFbmDhkIk6NObWzTQ1IZZVluHT+pUgekow3J7/pE/kW6mA1Vu9YjdLKUhSVFvn05p+SJMFYacTQ6KEO/02sumkVxrw3BpsPbMaUz6bgu+u+Q3d1dy+21Hm9w3sjMzFT6WZ0iAFOAJL7r2w5g6WW52poaEBpTSneLnkb7256FwCQMzHHZ6d/bjxHBDh6ox7l1eUYGDFQ6SbJ6uNfP8bGvRvRs1tPm68z+pyBHt16AIAimxw+tfoprN21FpGhkSi6oUjWEv3vGt7F3UvuxoBeA/D9zd9jWPQw2c4dKNbsXINtR7ahd/fePhHcWEwaNgl/Hv4TS7cv9ekAZ+GfCzFDNwMPnf8Q8lLz2j1OG6XFd9d9hws/uBBrdq7BzIUzUZheGJC5Rt7CngtAvjol4UwuyA1f3oBRg0b51OiSxdDooRgXNw5rd63Fx5s/VrQ+jyfMXT/X7uMlGSWI7x8PAPjglw+816B/PD3haWw7sg2Pj3scCQMSZD33lFOnYO76udhycAuSP0rGmpvX4GTNybK+h7+z1L9Renl4a5OGT8LLP7+MpduXQpIknwq+LGobavFo0aNolBqdyik8p985WHzNYlzyv0vw5V9f4s5v7kTBFQU+87NJkoRrv7gWY+PG4pZzb7H+4eOrFFlFZTQakZeXB51Oh7y8PJhMpnaPNRgMyMvLQ15eHtLT022ONRgMMBgM1nNabpN85NxDJRD2Y2m5dYMSoxmuMtWa8Nr615w6dtKwSZgyYgqShyRj1MBROL3P6YiLjENkaKT1mJqGGk811UZjU6P1ds9uPbH42sUeWRYcEx4D/Q16jOg9AruqduGiDy/Cnuo9sr+PP7MGOArtP9WecXHj0EPdA/uP7ccv+39Rujl2vfrzqygzlWFArwHIGpPl1GvGDx6PT6d9iiBVEMpMZR3+n+lNxXuL8fnvnyNbnw0Jvv//nyIjOOnp6SgpKQEgApNZs2ahsLDQ7rF6vR5ZWeLCyMvLQ3JysvW1+fn5KCgoAACkpKS0ew6y794l9+KH236w3v/qr69QY65B3x590adHH/Tt0RcNTQ0KttD3pJ+RjgeWPYC4yDhU1VX5bCJgfWM9Xl//Op5f+zwqayudes1zE5+zjtS055Zzb8F7m95z6nzvGN6BqdaEK0dcaXf1TXtTn+ZGMx4tehRJA5Lw0iWeX5Z/Us+TsOLGFRj/wXiUVpZi3Hvj8Pblb6NPjz52j/e1/DVPOnDsALYd2QYVVBgT61t1g0JDQpGsTcbirYuxdPtSxevztHbg2AE8v/Z5AEBOck6b3C9Hrj7tajFddfKFCA0J9VQTXTZ/s6h9c9WpV7n08yjF6wGO0Wi0ua/VaqHX6+0eazAYkJOTYw1w0tLSkJ2dDaPRCK1Wi4SEBFRWiv+8NRqNR9sdiHZV29ZceGbNMzDsc28U7OHlD6NXt15olBqhCdNg/tT51ufu+vYubNq/CUfrjnaqvb4gIjQCex7cg8iwyI4PVlCQKgjvbHoHlbWV0Gq0MJqMHb/ICa7kR73y8yv449AfeLToUYzoPQJXjrgSV464EucPOh/lR8s7nPpcu2strjr1Kq+MHAyMGIiVN63EBe9egB1VO3Dp/EvbPdYTq8R81bpd6wAAZ/Y9E1HdoxRuTVuThk2yBjiPj3tc6ebYeGLVEzhafxSJAxJx/dnXu/z61KGp1tuSJOGvw38pWvi0oakBn/3+GQBg5pn+scjC61NUer0e0dG2G3NFR0fbnV6Kj4/HvHnzrPct01MtX6/RaBjcuOn/xv2fzf3RA0djwuAJOKPPGegT3selGiOrd6zG19u+xpK/l2CFcYXNc1sObsHPe37G74d+l6XdSvPF4EaSJCwvXW4NGEKCQjD3krl478r3oL9R3+H8f1hIGGLCY2RrT5PUhLsS78LFQy+GOkiNrUe24j8//gfj3h+Hk148CY+veNypoXdvzvHHRcbhrcve6vA4X59GlZOv5t9YTBo2CUOjhiKxf6JPTRn/sv8XvGN4BwAw95K5Lv1f2lqT1ISHlz+Mc94+R9ENRleWrcTB4wcREx6Di4derFg7XOH1EZz28m0qKuzvI5OWlma9/fnnnyMlJcUa0JhMJuh0OgBAcXExMjMzodWyeJezRg0cZXP/zcvetLnf2NSI1TtWI+XjlA7P9fjYxzEkagiCVcFtPpSen/g8Kk5UoMxU5vTOz/6gvLoc1XXVHvurytnVa8XlxcjSZ2H1jtV4+eKX8eD5oo8vGXaJ9diWNTgaGhqwbt06jB07FiEhITbn6ogzBcvCQsLQt0df3D3qbtw96m5U11Vj2fZlWLxtMb7d9i2OnDiC6rpqp/rA2wZFDFK6CT7lpB4nYUTvEYpvsNmekzUnY/t925VuRhvGSiMiQiNw6bBLZdkSZN+xfTA3mXH151dj1U2rkDQwSYZWusayNcP006dDHaz2+vu7w2dWUTlKNLY8r9PprPk3AJCRkWENdrRaLVJTU1FaWtrmtXV1dairq7Per64W/7mazWbrl+V+IGhocC5vpqGhocOfuZfauWJoU06ZYrPhWsvzjh4gkkM37XeuNL4z7VLa+7+8jzuW3IFJwybhy+lfyn7+XVW7cObbZ6K2sf1AoltwNyQPTsbSUrGrcmhwKKprq+32Xf/w/ugfLqqjms1m7AvfhzN7nwm1uvk/Kmf6vH94f2zJ3IIjJ460e0zv7r3RP7y/9Xzdg7rjqlOuwlWnXIWGpgb8uPtH7D++37oTsSPevhbk/LfTmj/+P/PI6EfwyOhHIEmSX7W7JSX6/YphV+CPO/5AgyTP9fvOZe/g8PHD0JfpMXn+ZKy6cRVG9B4hQ0udU2OuwcI/FwIAZpw+w6mfyVP97sr5vB7gaDSaNqM1FRUVHU4zZWdno6ioyOY4o9GI+HiRFKnVamE0Gq35OS3l5ORgzpw5bc65fPlyhIc35xQUFSk3/CcnQ3XHeTRqlRqbf96Mfd32OTyutKZtwGjPunXrsC/ce+dSWkNtAyRI+G77d/jkq0+gUWtkPX9pTanD4AYQicRLS5dCBRUmRE3AzP4z0ae6D5YsWeLUe3jqet+HfdiCLQ6POVBzwKlzefta8MY1Gij/z/iSBqkBW49vxWk9Tmt3Okipft8EefY8u63nbdjRfQe2n9iO8e+Ox71x9yIiJMLusREhEejTzX6SvDsO1R/CaWGnoVxVjopfK7Bks3P/xwDy93tNjfMrOVWSlycujUajzSoqAIiKikJZWVm7QU5eXh7S0tKg1WqtIz1GoxHJycnWJGOTyYSoqChUVla2OY+9EZzY2FgcPnwYERERMJvNKCoqQmpqqs1ftP6orqEOF3xwAX47+BvGxY7Df1L+Y7eGQu/uvZ0u8tfRSEJYcBi23LHFqTo4cp3LF4z9YCw27N2AvOQ8PHDeA7Kee9P+TTjvvfM6PO6CQRfgtUtfw9l9z3b63L5wvTv7862/db3NyKCnebJdne33XVW7Ohw5k/Pfzb5j+xDTPcbnpyOapCYMfWMoyo+W2/29ePN6/99v/0Pv7r0xadgkj5z/0PFDGPPBGOyo2uHwOE/9P2puNDt9PXiq36urqxETE4OqqipERNgP8Cy8PoLTenTFaDQiMTHRGpQYDAZoNBrrcTqdDvHx8dbgZsGCBcjIyIBWq0Vubq71PHq9HmlpaXaDpNDQUISGtl1qp1arbTq+9X1/9NSap/Dbwd8QEx6DwumFnd4rZGjMUGy9t/09VADn8zdan6szuSC+4JaRt2DD3g34+LeP8ciYR2QtxmXpj468Pvn1Dpd2t0fJ693Zny8kJMSrbfRGu9zp911Vu3Bm/ple3QPshq9uQMneEixIX4DJwyfLck5PSRiQgPKt5SgqK8Ko2FF2j/H09X7o+CE8uPxBVNVV4duZ33qkzwZoBuD1ya/jik+vcHhcbWMtqsxVsv+87pxP7n535VyK5OAUFhYiOzsbSUlJKC4utqlfk5OTg6SkJGRlZVlHe1rSaDTW3JvExETk5eVBo9GgtLRUsTo4vrLv04+7f0TuDyLoy788X7aN0OIi42Rrf8tzWXJBRvYb6ZeB5YwzZuCB7x7Abwd/wy/7f/G5OhwUOLy9B1hdQx3W71mPusY6v9i+ouVy8f+78P86foEHPLX6KVTVVWFkv5G4dFj7ZQY6a0CvAR47tz2GfQZEd4/GYM1gr76vHBQJcFqOvrRcJQXAJkjRarUOl/7Fx8dbc3CUotTuyq0drz+Om768CU1SE64/+3pMPW2qx96LhKjuUbhyxJUo/KMQH/76IQMcFzi7GkvOpevOcKZdKqg6tezXHxTvLUZdYx369uiL4dHDlW5OhyxTQj/t+QkVJyoQ3T26g1fIa8vBLcgvyQcAvHLJKwF1fdz/3f1Yt2sdPr76Y7fq+SjJZ1ZR+Ssldle2J1ufje0V2zGw10C8Pul1j70P2brpnJtQ+EchvvzrS7xyySs+s2eMr4uLjLNZum6PEtOVjtpVWVuJGxfeiCY0QR3kfyOOrli7s7n+jT9c0ydrTsbpfU7HH4f+QFFpEWacOcNr7y1JEh5c9iCapCZMO20axg8e77X39rSdpp1Yt2udWMgweILSzXEZA5wAMUQzBKHBoXh/yvs+u31AILpk2CV4f8r7mHraVFk/CL766yvZzuWr5Jz6lJOjdq28aSUiwyLRr2c/L7fKu3y9wJ89k4ZNwh+H/sDS7Uu9GuB8+/e30Bv16BbczeFu4f7o0y2fAhD7Y/ljjajAGUfr4h6+4GHseGCHTXlv8ryQoBDcfO7NiAh1nM3vio9+/QjPrHmmw+OUmMLp6kbEjLAJbo7UtL+qSU5llWVeeR9AFPj8YbfYo87XNth0xJLU+93279AkNXnlPc2NZjy8/GEAwAPnPQBtlO8UmpVjgbSluN91Z13X6XMpgSM4fq6+sR7dgrsBQMD/VekPmqSmTs2//33kb9z61a0AgBvPvhH3nXdfuyND/rTiLBDN3zwfd3x7B76c8SWStckee5/1e9bj1sW3euz8rW0+sBnVddXo1a0XzjnpHK+9b2eNjRuL5y56DpcOuxQqeGdaLSQoBP9J/Q/yfshTLLm5PbNXzMYX079Ar1DnirW2tvnAZmw5uAXdgrsh7fS0jl/ggxjg+LEv/vgC/1r1L3x01UeKlO6mZgt+X4AX1r2AW869Bfeed6/b5xneezhen/Q6fj3wK9667K2ASlYMNMtKl+FY/TGkF6Zjw6wNHllttLx0OaZ+PhXHzcdlP3d7+vTog+cnPo8T5hMIDgr22vt2Vrfgbl4PMlQqlXUTWW9xJhEeAIqMRXhM/1ibLXic9clvnwAALht+md+mPTDA8VMHjh1A5jeZOHLiCBb9tYgBjsL2H9uPTfs3IejXILcCnJYjP3cm3QlJkvwiubMrK7iiANuObMP68vW48tMr8dNtP8m6EevnWz7HDYtugLnJjHFx47ChfAPqGuvaPV4dpJZlynJQxCCf25nbF9U11CE0pG19NU9zJkF/p2knXvrpJTxzUcdT3e2xbKXir9NTAHNwvKagpEC2eWFJkpDxTQaOnDiCc046B09PeFqW85L7Zp41E+ogNUr2leD3g67tmr7k7yUY894Ym3wOBje+LywkDItmLMLAXgPx5+E/MXPhTDQ2Ncpy7reK38K1X1wLc5MZM86YAf2Nemy7dxtKMkrafN1y7i1QB6nx7EXPdvkpS0mSsOD3Bbjlq1tQccL+Bs5y+OPQH4h9JRavrX9NkV3M4yLjEN8/vt2vq0+7GmtvWYve4b0BiH75bMtnMDc6v4/Thts3YP7U+bjslMs89WN4HAOcTrIMF3bkg18+wPYKeXa9/fDXD7F462Kog9T46OqPrDk4pJyY8BjrfwQf/vqh068rKi3C1M+n4uc9P+PFH1/0VPPIQ/r36o+vrvkK3UO6Y8nfS/CY/rFOn/PvI3/jvqX3QYKEOxPvxPyp89EtuFu7H2r5l+fj1zt+RfbY7E6/976j+7Dg9wXYd9S394Jrj0qlwjPfP4MPfvkARaWe23vqkeWP4FDNIazascpn/xhp2a53DO/g2i+uxcSPJjr9u+3RrQdmnjXTqc83X8Upqk5yZrhwVdkq9OvZD6f0PqXT77fTtBP3Lb0PAPDMRc/g7JOc34OIPOumc27Cl399iY83f4x/J/8bIUGO/3mtKluFKz+7EnWNdbjq1Ks6NZxMykkYkID3p7yPa764Bi/+9CIuGXYJUrQpbp9veO/heG/KeyitKMXTE57u8ANUHazGaX1Os95vbGp0O3dm6faluG3xbRgbNxZrb1nr1jmUNmnYJPx+6HdZlovbq1L/w64fsHT7UoSoQvDg6Ac7dX5v6dujLyJCI7Bu1zqMzB+JBekLcOHJF9o9NpCmxxngyKCjeh6t9wrauHcj9h/bj8tPudyl92mSmnDLV7fgaP1RXBB7AR694FG32kueMXn4ZMSEx2D/sf0oKi3CpOHtb7i3dudaXP7p5ahtqMVlwy/D52mf+/ymhtS+GWfOwO+HfkeT1ISJQya6/Pr6xnocOn4IAyMGAgBuPOdGt9qxoXwDbvryJnww5QOcN6jjTUNb88f6N61NGj4JL/70YqeXi3dUpb5BasAl/7vE41Xq5TDl1CnYOGsjpi2Yht8O/oaJH07ECykv4OHzH24TzCzeuhj/WvUv3JN0DzITMxVqsTw4ReVlh44fwtWfX40rP70Sz615zqV/gEfrjiI4KBjh6nB8eNWHfrXCoSvoFtwNM8+cCcDxNNVPu3/C5E8mo8Zcg0uGXgLddB2nGQPAnAlz8NzE51xe+Xa8/jiu/PRKjP9gPPYf29+pNry2/jX8dfgvzFw4E9V11S6/vmUFY381Nm4senbriQPHD2DTvk1un8eVKvX+YHjv4fj59p9x/dnXo1FqxKNFjyK9MB2/H/wdhn0G69cbG97AloNbsHbXWhj2GbCrapfSTXcbAxwviwyLxBWnXAEJEp5Y9QTSFqThaN1Rp1+77PplWH/7er/YAK8ruvncm3HVqVfhhrNvsPt8Y1Mjbv/6dhyrP4aJQyZi0YxFfj3HTc1a/iVc21CLp1Y9heP1jpd3H6k5guSPkrGsdBn2HduHrYe3dqoNb0x+AydHngxjpRH3LLnHpdfuPboXpZWlUEGFC2Iv6FQ7lNQtuBuSh4i6REu3L1W4Nb4lXB2Oj676CG9NfgvqIDW++PMLxOfHI6EgwfqlL9MDEEX+EgoSMOKNEX4b5DDA8bJuwd3w1mVvYd4V89AtuBsW/bUIo98djb+P/N3ua1pm6QepgnBm3zO90VRyw8j+I7FoxqJ2Vx4EBwVj8TWLcd1Z12HxNYvRXd3dyy0kb5heOB3PrHkGt3x1S7urbPZU78G498dhffl6RHePxoobV3R6HyNNmAbzp85HkCoIH2/+GPM3z3f6tZbRm3P6nSPrcnclWKoaM8BpS6VS4c6kO7H2lrV49PxHUd9U7/B4fxqlao05OAq5Pf52nNn3TEz9fCr+OPQHkuYl4ZNpn+DMvme2uZjeMbyD/cf248HRD+Jkzck+P9/bldlLSgSaa2bEhMdgaPRQ/G/q/xRoHXlL1pgsfLf9OxT+UYjob6ORkZCBhoYGlNaUYtP+TdhzbA/uXnI39h/bj4G9BmL5Dctxep/TZXnvMXFj8MSFT2DO93Nw57d34vzY853aQiAQ8m8sLLuLH68/7tLSaED8QfnrgV8x96e5HmiZ7zhv0HlQB6vxn5/+o3RTPIYBjoJGDxqNkowSpBWm4cfdP2Luz3Oxdtfadud9F/0lpjP8IamtK+ooKREAf39dhGXbgOwV2cgvyUd+SX7zk9uab6qgwoK0BbIFNxb/uvBfKDIW4cfdP+L6hddjzS1rOlzVF0gBTmxkLMofKseAXgNgNjsX4Ow07cQnv32C+b/Nx++HXKtlRb6JAY7C+vfqj1U3rcLza57HxCETMeHDCQ6PtwwX8gPS97iSlMjfX+BLGZoCrHB8jAQJYWr5c7BCgkIwf+p8nPP2OdCEaXC8/niH005fX/s11u5ci4uGXCR7e7zNMpK6/9h+m5GzkBDxkddyH7fvd3yPJ1Y9YQ3wACA0OBRjYsdg5Y6VirSf5MEAxwd0C+6GORfNgWGfQemmEFGAGKwZjOJZxRgePdypuiZxkXG47mz/Lctv0e5IaouRs9DgUGy7dxviIuPQ0NSAtbvWQgUVJgyegOvPvh5TT5sKY6URCQUJ3m08yYoBDhFRgGpdXNTcaA74ekvOjKTWNdZZR1InDJ6AuZfMxbTTp2FQxCDrMc5sahkWEibL/l/kGQxwiIgC3NG6o7h36b040XACn037rM2ITlZRFmLCY3DTOTfhpJ4nKdRKZQQHBeP+0fe3edyZKvUtp7rI9zDAISIKcFuPbMX83+ajoakBk4ZNws3n3mx97oT5BOb+PBfmJjOmnTYNJ6FrBTiOdFSl3t8F+igVAxwiogCXOCARz0x4Bo+vfBz3LLkHY2LHYHjv4QDE9g7mJjP69+zv1HJyChyBPkrFAIeIqAvIGpOF5cblWL1jNWYunIkfbv0B3YK7NS8PP3lcwGyySM4L5FEqVjL2IZbhQkf8ebgw0PH3Ry352vUQHBSMj6/+GJGhkdi4dyMyvs6AYZ8B3/79LQBgcORgv997iKgljuD4kEAfLgx0/P1RS62vh4aGBqxbtw5jx461W4/FG5qkJtSYawCIDWFbbgqb92Me8n7MYzFKChgMcHxMIA8XdgX8/VFLLa8Hs9mMfeH7MLLfSKjVyizVPlxzGOYmx5V9/b0YZaAnzpLzGOAQEVHA8MWRM1IGAxwiIgoovjZyRspgkjEREREFHAY4REREFHAY4BAREVHAYYBDREREAUeRJGOj0QidTgetVguj0YiMjAxoNBqXj3XlPEREXR2XUFNXokiAk56ejpKSEgAiSJk1axYKCwtdPtaV8xARdXUsRkldidcDHKPRaHNfq9VCr9e7fKwr5yEiIoHFKKmr8HoOjl6vR3R0tM1j0dHRMBgMLh3rynmIiIioa/F6gGMymew+XlFR4dKxrpyHiIiIuhafqWTcXsDi6rH2nqurq0NdXZ31fnV1NQBR4dLyZblP3sN+Vwb7XRnsd2Ww35XhqX535XxeD3A0Gk2bUZaKigq7q58cHevKeXJycjBnzpw2jy9fvhzh4eHW+0VFRS78JCQX9rsy2O/KYL8rg/2uDLn7vaamxuljVZIkSbK+eweMRqPN6icAiIqKQllZWZvgxNGxFRUVTp/H3ghObGwsDh8+jIiICJjNZhQVFSE1NZV7lXgR+10Z7HdlsN+VwX5Xhqf6vbq6GjExMaiqqkJERITDY70+gqPVam3uG41GJCYmWoMSg8EAjUYDrVbr8Fh7wVDL87QUGhqK0NDQNo+r1Wqbjm99n7yD/a4M9rsy2O/KYL8rQ+5+d+VciuTgFBYWIjs7G0lJSSguLrapXZOTk4OkpCRkZWV1eKyj54iIiKjrUiTA0Wq1yM3NBQCkpaXZPNc6SHF0rKPniIiIqOviXlREREQUcHxmmbg3WfKqWy4Xr6mpQXV1NedovYj9rgz2uzLY78pgvyvDU/1u+dx2Zn1Ulwxwjh49CgCIjY1VuCVERETkqqNHjyIyMtLhMV5fJu4LmpqasHfvXvTq1Qsqlcq6bHz37t0dLjsj+bDflcF+Vwb7XRnsd2V4qt8lScLRo0cxYMAABAU5zrLpkiM4QUFBGDRoUJvHIyIi+A9AAex3ZbDflcF+Vwb7XRme6PeORm4smGRMREREAYcBDhEREQUcBjgQlY6feuopu9WOyXPY78pgvyuD/a4M9rsyfKHfu2SSMREREQU2juAQERFRwGGAQ0RERAGnSy4TtzAajdDpdNBqtTAajcjIyLC7GznJy2AwAADi4+NhNBphMpkQHx+vcKsCk8FgwKxZs1BSUmLzOK99z2qv33nte5bBYIBerwcAFBcXY968edbrmte85zjqd0WveakLi4+Pt94uLS2V0tLSFGxN15GRkSEBkABIKSkpUmVlpdJNCkiFhYVSSUmJZO+fOa99z3HU77z2PSs3N9fmdsvrnNe85zjqdyWv+S6bZGw0GpGenm7zF1ZUVBQqKysVbFXXUFBQgOnTpwMA/4LyApVKZbNvC69972jd7wCvfU8yGAxITk62XsdGoxFDhw5FaWkpAPCa9xBH/a7VahW95rtsDo5er0d0dLTNY9HR0dbhNPIsjUbD/+AVwmtfWbz2PSM+Ph7z5s2z3jeZTADEtc1r3nMc9buFUtd8l83BsfwSWquoqPBuQ7ogk8kEnU4HQMzXZmZmQqvVKtyqroPXvnJ47XtWWlqa9fbnn3+OlJQUaDQaXvMe1l6/A8pe8102wGlPe/8QSD4tk/u0Wi1SU1Otw8ikHF77nsdr3zssH6qtk7ztHUfysdfvSl7zXXaKSqPRtIneKyoqOHTsBUaj0XrbsqKh5WPkWbz2lcNr3zuys7NRVFRkvaZ5zXtH634HlL3mu2yAk5KSYvfxxMREL7eka7EkpLXWen6cPIfXvjJ47XtHXl4esrOzodVqYTKZYDKZeM17gb1+V/qa77IBTus5QKPRiMTEREb0HqbVapGbm2u9r9frkZaWxn73sJZD8bz2vad1v/Pa9yydTof4+Hjrh+yCBQug0Wh4zXuYo35X8prvssvEAXGR5+fnIykpCcXFxZg9ezYveC+wFIXSaDQoLS21+QdA8tHr9SgqKkJeXh6ysrKQlJRkTQbkte85jvqd177nWJYnt6TRaGyWL/Oal19H/a7kNd+lAxwiIiIKTF12ioqIiIgCFwMcIiIiCjgMcIiIiCjgMMAhIiKigMMAh4iIiAIOAxwiIiIKOAxwiMihQNmvhztHE3UtDHCIqF0FBQWy7LhsNBqRmppqN1jKy8tz6hzp6emIiopCQkICEhISMHToUGRnZzvdhoSEBJeCnNTUVJfO35JKpXLrdUQkHwY4RGSXwWBAdHR0mzL37tBqtYiPj0dOTk6b5zIyMpwOJDIyMlBSUoKSkhKUlpbCaDQiMzPTqddKkoT4+HiX2k1E/osBDhHZlZOTY91iQA6ZmZkoKCho87ilXL47Owzn5uZiwYIFnW0aEQUgBjhE1IbJZJJl5KYlrVaL6Ohou9NEM2bMgE6nc/mcrae8srOzMXToULvTV1FRUdYgyjJdlZ6e7vQU2dChQ1FQUIDU1FRERUXZtFev12Po0KFISEho875Go7HNlFp2drbNyJPlvEQkHwY4RNTGggULkJSUZPNYQUGB9UO85WiLK3ktmZmZyM/Pb/N4fHw8ioqKXGqjJUCZPXu29bGkpCSUlpaitLQUBQUF0Ov1dl9rMpmQnp6OGTNmICsry6n3q6ioQFFREYqKijBv3jxrsGIymZCamor8/HyUlJS06beEhATMmzfPOqWm1+uRm5uLjRs3QqfTwWg0Ijc3F4WFhS79/ETkGAMcImqjtLTUZgTHEiiUlpZi3rx51h2B9Xq9S3ktGo2m3SklZ5KZCwoKrEnG2dnZyM3NtQlQWk6pTZ8+3WHwlZmZ6fIU3IwZMwAAKSkp1iBvwYIFSElJQUpKivU5C51Oh8TERGsfzZ492xrIrFixAtnZ2UhPT0d+fj53tiaSWYjSDSAi32Mymdp84GZkZAAQoy3trYhypKCgAFqtFlqtFnq93iYQcFZGRoY1uLLHZDKhoKAApaWl0Ov1DoMGd97f3rSdo+k8o9FonaJq/b4ajQZpaWlu9wUROcYRHCJqQ6PR2AQwrT+AU1JSkJOTg8TERKfOZ0kuTklJwYwZM+xOU3WWJZDQarXIzc3tMGhwZ8TE3ms0Gk27CdIajQYpKSnWlV8lJSXWAM0yXZWYmGg3+ZqIOocBDhG1MXToUIermiwf6i0/8A0Gg93XFBQUoKSkxDoClJGRYTehODo6ulNttrQnLS0NGo0GGzdu7NT5nDV9+nTo9XrrdFjLYKX1cyaTyTrdl5qaisLCQuTn5yM/P5+FCIlkxgCHiNpISUlBcXFxu8+bTCZrPopFTk5OmxVEJpPJ+iFuYQlCWgY5BoOh06uILCM2UVFRSE9Ph1arRe/evTt1TmdoNBoUFhYiOTnZOhVlmbKyPDdr1iwMHToUycnJAETRwszMTOtxhYWFSE9PD5iq0US+QCVJkqR0I4jI96Snp7e7sken0yE+Pr5N7olOp3Ordo5l2bTcS9OJqOviCA4R2ZWZmdlubZri4mLZghHLqAWDGyKSEwMcIrIrJSUFFRUVdqdNhg4d2uYxd1cD5eTkOFwZRUTkDk5REZFD9paMExH5OgY4REREFHA4RUVEREQBhwEOERERBRwGOERERBRwGOAQERFRwGGAQ0RERAGHAQ4REREFHAY4REREFHAY4BAREVHAYYBDREREAef/AQ/+XYfh1rXwAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 3:\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Divide into three arrays, each with 25 values for each scenario\n",
    "SAP_1, SAP_2, SAP_3 = np.array_split(all_SAP_score_arr, 3)\n",
    "I3_1, I3_2, I3_3 = np.array_split(all_I3_score_arr, 3)\n",
    "\n",
    "# Plot Comparison of I3 and SAP Scores for each scenario\n",
    "print(colored('Scenario 1:', attrs=['bold', 'underline']))\n",
    "plot_comparison(I3_1, SAP_1)\n",
    "\n",
    "print(colored('Scenario 2:', attrs=['bold', 'underline']))\n",
    "plot_comparison(I3_2, SAP_2)\n",
    "\n",
    "print(colored('Scenario 3:', attrs=['bold', 'underline']))\n",
    "plot_comparison(I3_3, SAP_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "27097c95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vZwAAANiWjoKdbduanp5WPp9XMpmUJN24cUO2be9q5wAAANC+ji53ks/nZdu2/uEf/kHf+c53JEm1Wk3T09O72jkAAAC0r6Ngd+zYMdm2rfn5eX3ta1+TJFWrVQ0ODu5q5wAAANC+joLd9PS0crmcUqmU5ubmJEmRSETpdHpXOwcAAID2dXSOXaFQ8Ga/1idSHDt2TLVabdc6BgAAgO3p+FDsf/7nf0qSAoGAJOnq1as6duzY7vUMAAAA29LRiN3FixcViUQ0Pj6upaUl/e3f/q2KxaLy+fxu9w8AAABt6vhyJ9VqVd///vflOI4sy9JLL73EiB0AAICPOr6l2Isvvqjnnntut/sDAACADnV0jt1//Md/6Ac/+MFu9wUAAAA70NGI3fT0tE6fPi3HcTQxMSHLsrznTpw4sUtdAwAAwHZ0FOwmJyfluq6+/e1ve3eecF1XgUDAuwwKAAAAuqujYDc/Py9Junz5shzH0ejoqD772c/uascAAACwPR0Fu+XlZYVCIQ0ODuqJJ55QNpvVb3/7WxWLRX3sYx/b7T4CAACgDR0Fu0QioWw2q4mJCW9ZoVBQMpnUj3/8413rHAAAANrX0azYSqXSEOokKR6Pe4doAQAA0H0dBTvbtr1bitX97Gc/0xNPPNHW+o7jaHZ2VoVCQbOzs23fYzadTnM/WgAAgE10dCj2O9/5jiKRiGKxmGzbVqVS0eXLl3X58uW21k8kEiqVSpLuhrzJycktb0dWLpc1Ozur6enpTroMAABgvI5H7KrVqqLRqFzXVSwWk+M4+tSnPrXluo7jNL1WsVhsaz3btjvpLgAAQE/oaMTu0qVLsm1bk5OT3rLvf//7CgQCevbZZx+4brFYVDAYbFgWDAZVLpcVCoVarlMoFBSPx5VOpzvpLgAAQE/oKNil02nvUGrdxMSExsfHtwx2m50jV61WN21/750tNrO6uqrV1VXv8fLysiRpbW1Na2trW66P3bGxseH95HNHL6Dm0Uuod39s57PuKNi98847Onr0aMMyy7L0zjvvdPJykjYPfBcvXlQymdxy/ZmZGZ07d65p+dWrV3X48OGO+4XtWVhYaPgJmI6aRy+h3v1x586dttt2FOwikYh+8IMf6Itf/KK37LXXXmvrHDjLsppG56rVastRuWKxqNOnT7fVp+npaZ09e9Z7vLy8rOHhYZ06daophGLvjY2NKRKJ+N0NoGuoefQS6r276kch27GjWbFTU1OKRqOqVCoqlUpNh2dbiUajymazTcs3K5CLFy96f3ccRzMzM3r++eebzsfr7+9Xf39/0/p9fX3q6+vobaIDBw4c8H7yuaMXUPPoJdS7P7bzWXf0r1KfFVsoFHTjxg1Fo1E999xzba97L8dxFIlEvBG7crksy7Jk27ai0WhD21QqpVQqxexYAACAFnYUt+PxeEfr5fN5pdNpjY+P68qVKw3XsJuZmdH4+Limpqa8ZbVaTblcTpKUyWSUSqU2nUELAADQq9oOdjdv3lStVmu4Vt1rr72mTCajarWqL33pS3rhhRfaei3btpXJZCQ1h8NWFyq2LEtTU1MNYQ8AAACN2r5AcSqVari48NWrVxWLxRSLxfTSSy/pe9/7nl5++eU96SQAAAC21vaI3fz8vH784x97j7PZrJ577jm9+OKLku7OYB0fH2971A4AAAC7q+0RO9d1Gx7n83l96Utf8h5bltV0uzAAAAB0T9vBLhqN6rvf/a6ku7cPW1paapi1euPGDT3xxBO730MAAAC0pe1DsefPn1c4HNbU1JRqtZry+XzDhX/rs1UBAADgj7aD3bFjx/TLX/5SN27cUDAY1LFjxxqeTyQSmpiY2PUOAgAAoD3bvo7dZodbCXUAAAD+avscOwAAAOxvBDsAAABDEOwAAAAMQbADAAAwxLaC3Ve+8hUFg0EdP36c24cBAADsM23Pip2enla1WlWpVNLS0pJOnz4t27b1xS9+cS/7BwAAgDa1HewKhYJ+8YtfSLp7yZOLFy9qenqaYAcAALBPtH0o9v4LEodCIb3zzju73iEAAAB0pu1gFwgE2loGAAAAf7R9KLZSqWh6erphmeM4TctmZmZ2p2cAAADYlraD3cTEhCqVypbLAAAA4I+2g10+n9/LfgAAAGCHdu0Cxa+99pqef/753Xo5AAAAbNOOgt3Nmzc1PT2tYDCoaDS6W30CAABAB9o+FFu3vLysXC6nbDarSqWiQCCgixcv6rnnntuL/gEAAKBNbQe7f/7nf1Y+n9fc3JxCoZCmpqaUSCQUjUYJdQAA+OTWrVtaXFzsyrYWFha8n3192x4b6sjQ0JBGRka6si0TtP2vkkwmFYvF5DiOTpw44S3nWnYAAPjj1q1bOjk2ppX33uvqds+cOdO1bQ0cOqRrCwuEuza1HexKpZIuXLigUCik8fFxfeUrX+F2YgAA+GhxcVEr772n3LPP6smhoT3f3u/W1nSrVtOIZenDXRixu764qOSlS1pcXCTYtantf5VTp07p1KlTeumll3T58mVls1n99V//tX7729/q9ddf1zPPPLOX/QSAtnTzsJTEoSnsD08ODelTjz3WlW19mtrb1zraC01MTGhiYkKSVCgUNDMzo3g8rtOnT+vb3/72rnYQANp169YtjZ0c03sr3T0sJXX30NShgUNauMahKQDNdvz1Mh6PKx6Pq1ar6fz587vRJwDoyOLiot5beU9fzn5Zjz75aFe2+cHvPlD1VlXBkaA+9OEP7fn23r7+tl5NvcqhKQAt7dpxA8uy9NWvfnW3Xg4AOvbok49q+E+Hu7Y9+/+1u7YtAHiQti9QfPPmTf3sZz9rWPbaa6/pc5/7nMbHx/Xyyy/vdt8AAACwDW0Hu1QqJcdxvMdXr15VLBZTLBbTSy+9pO9973uEOwAAAB+1fSh2fn5eP/7xj73H2WxWzz33nF588UVJUrFY1Pj4uF544YXd7yUAAAC21PaIneu6DY/z+by+9KUveY8ty2oY0QMAAEB3tR3sotGovvvd70qSvv/972tpaUnRaNR7/saNG3riiSd2v4cAAABoS9uHYs+fP69wOKypqSnVajXl83kdPXrUez6TySiVSu1JJwEAALC1toPdsWPH9Mtf/lI3btxQMBjUsWPHGp5PJBLeRYsBAADQfdu+jt1mh1sJdQAAAP5q+xw7AAAA7G8EOwAAAEMQ7AAAAAxBsAMAADDEtidP7AbHcVQoFGTbthzHUTKZlGVZLdsWi0VJUq1W05UrV/T8888rFAp1sbcAAAAPB1+CXSKRUKlUknQ35E1OTiqfz2/a9vLly4pGo6pWq0okEqpUKt3sLgAAwEOh64di77/tmG3b3qhcK/l8vmGEbrORPQAAgF7X9WBXLBYVDAYblgWDQZXL5Zbt771tWT6f5+4WAAAAm+j6odhardZyebVa3XSdcrmsCxcuKBaLKZlMtmyzurqq1dVV7/Hy8rIkaW1tTWtra513GNuysbHh/eRzR7f1Us2xb4PUOzXf6/W+nffuyzl2rWwW+CQpFArJtm2l02kVCgXF4/GmNjMzMzp37lzT8qtXr+rw4cO72VU8wMLCQsNPoJt+/vOf+92Frrl27Zr3RQq9q1dqvtfr/c6dO2237XqwsyyraXSuWq1uee6cZVlKJBKKxWJaWlpqaj89Pa2zZ896j5eXlzU8PKxTp07p6NGju9V9tGlsbEyRSMTvbqDHHDjQO1dwOnnyJFcIQM/UfK/Xe/0oZDu6Huyi0aiy2WzT8lYhoFgsKpFIaGlpSdLdiRbS3QkY9/8D9/f3q7+/v+k1+vr61Ne3bwYmjVffyRw4cIDPHV3XSzXHvg2S9MEHH0iSri8u+tyTvVF/Xx988EFP1/t23nvXP6V6OKtzHEeRSMQbgSuXy7IsS7ZtKxgMNkyeqD/Xy6kdAIC6mzdvSpKSly7525E9dvPmTT399NN+d+Oh4Ev8zefzSqfTGh8f15UrVxquYTczM6Px8XFNTU0pFArp+eefVy6XkyTNzc15178DAKDXnThxQpKUe/ZZPTk05G9n9sD1xUUlL13y3ie25kuws21bmUxGkpomQtx/oeJ7n99sRiwAAL3o0KFDkqQnh4b0qcce87k3e6f+PrG13jjrEgAAoAcQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADEGwAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADBEn98dwN67deuWFhcXu7KthYUF72dfX/fKa2hoSCMjI13bHgAA+xHBznC3bt3SyZMntbKy0tXtnjlzpqvbGxgY0LVr1wh3AICeRrAz3OLiolZWVvT3//R/9Lj9x3u+vfdXf6f/futX+l9/NKxH+j+859uTpF87v9S3vvp3WlxcJNgBAHoawa5HPG7/sew/+WRXtjUW+n+6sh0AANCIyRMAAACGYMQOgDHee+89SdLb19/2uSd7p/7e6u8VAO5FsANgjJs3b0qSXk296m9HuuDmzZt6+umn/e4GgH2GYAfAGCdOnJAkfTn7ZT365KP+dmaPvH39bb2aetV7rwBwL4IdAGMcOnRIkvTok49q+E+Hfe7N3qq/VwC4F5MnAAAADEGwAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADEGwAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAzR58dGHcdRoVCQbdtyHEfJZFKWZbVsWy6XVSwWJUlXrlzR+fPnN20LAADQy3wJdolEQqVSSdLdkDc5Oal8Pt+ybbFY1NTUlCRpdnZWExMT3roAAEC6vrjYle38bm1Nt2o1jViWPty39xGiW+/LJF0Pdo7jNDy2bdsbkbtfuVzWzMyMF+zi8bjS6bQcx5Ft23veVwAA9rOhoSENHDqk5KVLfndlzwwcOqShoSG/u/HQ6HqwKxaLCgaDDcuCwaDK5bJCoVDD8lAopPPnz3uPa7Wa1x4AgF43MjKiawsLWuzSyNabb76pM2fO6JVXXtFTTz3VlW0ODQ1pZGSkK9syQdeDXT2c3a9arbZcHo/Hvb9fuHBB0Wi05Tl2q6urWl1d9R4vLy9LktbW1rS2ttZ5hx9yvfTee/3fGtQ7etNjjz2mxx57rCvbev/99yVJTz75pD75yU92ZZtSb/3fbmU779+Xc+xa2Szw3ft8oVDY9Py6mZkZnTt3rmn51atXdfjw4d3o4kPp5z//ud9d6Jpr165pY2PD727AR9Q7sLcWFhYafqI77ty503bbrgc7y7KaRueq1eqWM13T6bTm5uY2bTc9Pa2zZ896j5eXlzU8PKxTp07p6NGjO+32Q+vAgd65os3JkyebDuejt1DvQHeMjY0pEon43Y2eUT8K2Y6uB7toNKpsNtu0/EEFMjs7q3Q6Ldu2vZG9+wNef3+/+vv7m9bt6+tTXxdm7uxXvfTee/3fGtQ7sNfqX54OHDhA/XXRdj7rrn+9vX82q+M4ikQiXlArl8sNM2cLhYJCoZAX6i5evMh17AAAAFrwJW7n83ml02mNj4/rypUrDdewm5mZ0fj4uKampuQ4jhKJRMO6lmUpmUx2u8sAAAD7ni/BzrZtZTIZSY2zXiU1hDzbtuW6blf7BgAA8LDqnTONAQAADEewAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwhC+3FEP3vPfee5KkXzu/8Lkne6f+3urvFQCAXkWwM9zNmzclSd/66v/2tyNdcPPmTT399NN+dwMAAN8Q7Ax34sQJSdLf/9P/p8ftj/vbmT3ya+cX+tZX/7f3XgEA6FUEO8MdOnRIkvS4/XHZf/JJn3uzt+rvFQCAXsXkCQAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQ3DnCQDGefv6213b1ge/+0DVW1UFR4L60Ic/tOfb6+Z7A/DwIdgBMMbQ0JAODRzSq6lX/e7Knjo0cEhDQ0N+dwPAPkSwA2CMkZERLVxb0OLiYte2+eabb+rMmTN65ZVX9NRTT3Vlm0NDQxoZGenKtgA8XAh2AIwyMjLS1dCztrYmSRobG1MoFOradgGgFSZPAAAAGIJgBwAAYAiCHQAAgCEIdgAAAIZg8gQAAD1mZWVFCwsL216vvs7CwoL6+rYfIcbGxjQwMLDt9dA+gh0AAD1mYWFB4XC44/XPnDnT0XqlUonZ43uMYAcAQI8ZGxtTqVTa9nq3b9/W66+/rmeeeUZHjhzpaLvYWwQ7AAB6zMDAQEcjZ2tra3rkkUcUiUQ6OhSLvcfkCQAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAM4UuwcxxHs7OzKhQKmp2dVa1We2D7crm8owspAgAA9AJfLkKTSCS8CyM6jqPJyUnl8/mWbQuFgmzbVrlc7mYXAQAAHjpdD3aO4zQ8tm1bxWJx0/bxeHyvuwQAAGCErh+KLRaLCgaDDcuCwSAjcgAAADvU9RG7zc6nq1arO3rd1dVVra6ueo+Xl5cl3b39ydra2o5e+2HWS++91/+t4Y+NjQ3vJ/UH062vr8t1Xa2vr/vdlZ6ynX3LvrnR21YTKLYyMzOjc+fONS2/evWqDh8+vKPXfpj9/Oc/97sLXXPt2jXvlyzQLQsLCw0/AZO5rqtaraZyuaxAIOB3d3rGnTt32m7b9WBnWVbT6Fy1WpVlWTt63enpaZ09e9Z7vLy8rOHhYZ06dUpHjx7d0Ws/zA4c6J0r2pw8ebKjm1oDu2FsbEyRSMTvbgB7an19XeVyWaFQSAcPHvS7Oz2jfhSyHV0PdtFoVNlstmn5TneI/f396u/vb1re19envr59MzDZdb303nv93xr+qH95OnDgAPWHnhAIBHTw4EHqvYu281l3fTjHtu2Gx47jKBKJeCN25XK5aeZs3U4P1wIAAJjMl+N0+Xxe6XRahUJB2Wy24Rp2MzMzKhQK3uNisah0Ot3yOQAAAPyeL+Ootm0rk8lIar5O3f0XKo5Go4pGo157AAAAtNY7Z9YDAAAYjmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIX24phu77tfPLrmzn/dXf6b/f+pX+1x8N65H+D3dlm916bwAA7HcEO8MNDQ1pYGBA3/rq3/ndlT01MDCgoaEhv7sBAICvCHaGGxkZ0bVr17S4uNiV7b355ps6c+aMXnnlFT311FNd2aZ0N8COjIx0bXsAAOxHBLseMDIy0rXQs7a2JkkaGxtTKBTqyjYBAMBdBDsAkLSysqKFhYVtr1dfZ2FhQX1929+ljo2NaWBgYNvrAUArBDsA0N1gFg6HO17/zJkzHa1XKpUY3Qawawh2AKC7I2elUmnb692+fVuvv/66nnnmGR05cqSj7QLAbiHYAYDuzqzuZORsbW1NjzzyiCKRSEeHYgFgN3GBYgAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADEGwAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADNHndwewP62srGhhYWHb69XXWVhYUF9fZ+U1NjamgYGBjtYFAKCX+RLsHMdRoVCQbdtyHEfJZFKWZe24LXbPwsKCwuFwx+ufOXOm43VLpZJCoVDH6wMA0Kt8CXaJREKlUknS3eA2OTmpfD6/47bYPWNjY97nvh23b9/W66+/rmeeeUZHjhzpeNsAAGD7uh7sHMdpeGzbtorF4o7bYncNDAx0NGq2tramRx55RJFIpONDsQAAoDNdnzxRLBYVDAYblgWDQZXL5R21BQAA6HVdH1Kp1Wotl1er1R21XV1d1erqqvd4eXlZ0t0RpLW1te13FB1ZX1+X67paX1/3uytAV1Dz6CXUuz+2k2P2zbGyzUJcu21nZmZ07ty5puVXr17V4cOHd9AzbIfruqrVaiqXywoEAn53B9hz1Dx6CfXujzt37rTdtuvBzrKsphG3arXacqbrdtpOT0/r7Nmz3uPl5WUNDw/r1KlTOnr06K70HVtbX19XuVxWKBTSwYMH/e4OsOeoefQS6t0f9aOQ7eh6sItGo8pms03LI5HIjtr29/erv7+/aXlfXx8n8XdZIBDQwYMH+dzRM6h59BLqvfu281l3ffKEbdsNjx3HUSQS8UbhyuWyNxt2q7YAAAD4PV/idj6fVzqd1vj4uK5cudJwXbqZmRmNj49rampqy7YAAAD4vYDruq7fndgLy8vLOnbsmH77299yjl0Xra2taX5+nuvYoWdQ8+gl1Ls/tpNpun4oFgAAAHuDYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhjD26oL16y5v58a52Lm1tTXduXNHy8vLXLwSPYGaRy+h3v1RzzLt3FPC2H+Vd999V5I0PDzsc08AAAB27t1339WxY8ce2MbYW4ptbGzoN7/5jT7ykY8oEAj43Z2esby8rOHhYf3qV7/iVm7oCdQ8egn17g/XdfXuu+/qscce04EDDz6LztgRuwMHDujxxx/3uxs96+jRo/ynR0+h5tFLqPfu22qkro7JEwAAAIYg2AEAABiCYIdd1d/fr3/8x39Uf3+/310BuoKaRy+h3vc/YydPAAAA9BpG7AAAAAxBsIMvyuWy310AuoqaRy+h3v1DsDNcrVZTIpHQ4OCgBgcHFYvF5DiO391SOBzmPz72BDWPXkK9434EO8OFw2HFYjEtLS1paWlJqVRKtVrN727JdV2FQqGO1y+Xy4rFYvvivWB/MbHmi8WiRkdHvV/c++H9YH8wsd7r+/fR0dF9E1QfJkyeMJjjOAqHw1paWvK7K7sqlUqpWq2qUChoaWlJlmX53SXsEybWfH1EZm5uTpKUTqdVLBZVKpV87hn8Zmq9T0xM6PLly7IsS7Ozs7pw4QL1vg2M2BksGAyqVqupUChs2sZxHMViMQ0ODmp0dNRrW99hjI6OKp1Oe+1HR0eVy+W8de597XQ6rdHR0aZ16kPyiURCs7OzkqTBwUHvW1i9D/VvZ1t928xms8rn89v+PGA+E2vecZyG185kMiqXy4xiwMh6tyzLC3WSZNv2vhiBfKi4MFo+n3cluZZluclk0i2VSg3PW5bl5vN513Vdd2lpyXvesizv7/F43J2bm/OWx+Nx77Vt227Y1r2vW1/Htm3Xtu2m5yuVStO25ubmGl7zQSS5S0tL7X0Q6Bkm17zrum6lUnHZdaPO5HqvVCpuKBRys9lsm58GXNd12Tv0gKWlJTefz7vxeNyV5P1nvP8/bV0+n3ej0aj3uFQquclk0nXd5p3EZr9gksmkm8lkXNe9+5++/ve6+n/6bDbr7UTqQqGQ18cHIdhhM6bWfH07U1NTbbVFbzCx3pPJpCupoZ9oT58vw4ToKsuyFI/HFY/HNTs7q0wmo2g0KsdxFI1Gm9o7juMN09fd28627ZbbqdVqyuVyqlQqKhaLDee+tdqOJFUqlabXs22bw0zYEVNrfnZ2VpZlKZPJbNkWvcPEes9ms8pms8rlcgqHw5xjtw2cY9djQqGQqtWqpM3/c1mWpWg0qlKp5P259xdJq8kK9Z2EbdveTuX+12xldHS0qQ+O42y6YwG2y5SaT6VShDpsyZR6r0smkyqXyyoWi221B8HOaMViUalUyvtPVavVlE6n9fzzz0uS4vG45ufnvf8w9ZNwT58+rWKx6F2DqFarbfmfynEc71ujZVman59vq4/3b6tQKKhWq2367Q94EFNrPpVKKRaLKZlMtrUN9AYT671YLCqXy3mPc7mcLMtSJBJpa3sg2BktGo16s5ACgYDC4bCef/55TU1NeW1KpZLS6bQGBwe9YXnLspTP5zU5OanR0VFNTEy0tS3p7kyoRCIh27Z1/PjxLderz4CanJzU4OCgstmsd1mHzaTTaa+v4XBYiURiy+2gN5hY8/VfdIlEQoFAwPvDxV9hYr3Xt1OffZvNZhtmyWJrXMcOAADAEIzYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIfr87gB239ramt5//32/uwEAwK575JFH1NdHfNkMn4xBXNfVrVu3tLi46HdXAADYM0NDQxoZGVEgEPC7K/sOwc4g9VD3R3/0Rzpy5IgOHOBIOwDAHBsbG7p9+7beeustSdLHPvYxn3u0/xDsDLG2tuaFuj/4gz/wuzsAAOyJI0eOSJLeeustraysaGxsjJG7ezCkY4j6OXX1ggcAwFT133X/9m//pp/97GdyXdfnHu0fBDvDcPgVAGC6+u+6vr4+vfHGG/qf//kfn3u0f5ACAADAQ+nYsWNaWVnRu+++63dX9g2CHXyVSqUUCATkOE7Tc7VaTYFAQIlEwoeewSTUGfYaNeaPQCAg13W1sbHhd1f2DYIdfGfbtgqFQtPyXC4n27Z96FHnHMdRLBbT6OhoWzvxcrmsWCymWq3mLcvlcgoEAk1/isXiHvbcfL1aZ8ViUaOjoxocHGyqNUmanZ1VOBzW6Oio0un0HvbafL1aY/X92OjoqGKxWEO43e4+ETtHsIPv4vG4stls0/ILFy4oHo/70KPOxWIxpdNpVSoVxWIxxWKxTdumUinNzMw0BbZkMinXdb0/S0tLikajikaje919o/VindVqNWUyGVUqFS0tLSkUCmliYsJ7PpVK6Z133lGpVFKlUlEmk+nWWzBSr9bY5OSk8vm81/beALedfSJ2B8EOvjt+/Lhs21a5XPaW1b/xjY6ONrR1HKfl6EI6ndbo6GjLUYfR0VHlcjnFYjENDg62/Ea9G+r9rwewZDKp+fn5phGSumw2q3w+v+XrTkxMtPxlge3pxTpzHKehn5lMRuVyWY7jyHEcXbx4UcePH/fe672fDbavF2vMsixdvnxZlmVJujtqWW+33X0idgfBDvtCIpFoCC/ZbFapVKqpXTgc1vnz51WpVOQ4jjfaNT4+rkqlokqlolwu1zAKVq1WNTc3p7m5OZ0/f37PDjc5jtN0uMW27Zbn3LQrl8spEok8dIdx9qteq7NQKNQw0ltvUw8ftVpNtm2rVCopnU5zqGwX9FqNSfJCneM4mpmZ8fq1F/tEbI0LFGNfSCaTGhwc9HaIuVxON27c0MWLF702hUJBkUhEoVBIkjQ9Pa1sNqtoNNpwmOP06dMql8sNv9Cef/55SXe/OW62U6nVapqZmXlgP48fP66pqamWz1WrVW8Hd//yTqXTaZVKpY7XR6Ner7NMJuO9bv116u8pmUwqnU63/GWM9vVqjaVSKeVyOUWjUSWTyY5fBztHsMO+EY1GvW+n0Wi0aYdQP3wUDocb1pHu7shyuZwqlYqKxWLTuu38orIsa0fnGAWDwaZDDI7jKBgMdvR6xWJRwWCQX7K7rFfrbHZ2tmHbrWorGAwS7HZBL9ZYNptVNptVLpdTOBxWqVTa9X0i2kOww76RSqWUzWYVDAa9b6X3sixL0Wi06Xyz+qyrTCbjjTq0WncrO/2W2+oQQ/1QVyfy+fxDd8L1w6AX6yyVSikcDje8ZigUanqdarVKqNsFvVhjdclkUqlUSsVicdf3iWgPwQ77RjQa9c5FaTVZ4PTp097J36FQSLVaTfPz85LUcEhpfn6+oxmkO/2WWz+sUigUFI/HvcMS9R1x/ZtrOztm6e77aHVuDnam1+oslUopFos1fUmwbVuRSES5XE7JZNK7JAe/dHeul2qsWCzKcRzv8Gsul5NlWYpEIl77zV4He4PJE9hX0un0pmHGsizl83lNTk5qdHTUu2xDfcc3ODioRCIh27Z1/PjxrvX5XnNzc8pmsxodHdXc3FzDrNfJyUnlcjnvcTqd9g7FhMPhphPX+Wa7d3qlzorFonK5nBKJRMM1EeuzFfP5vPL5vEZHR5XP53X58mVf3o+JeqXG6n2uz+TNZrMNs2Qf9DrYGwGXO+caYWVlRdeuXdPJkyc1MDDgd3cAANgz9d95N2/e1PXr1xWPx/Xxj3/c727tC4zYAQAAGIJgBwAAYAiCHYzH1fTRDdQZ9ho1hnYwK7YH3Lp1S4uLi13b3tDQkEZGRtpqW7+oZaVSaZooUKvVNDg4qHg8vu0TbgOBgOqnj9avqVSf6YW90c06206NSdSZKdiXUWPYGsHOcLdu3dLJkye1srLStW0ODAzo2rVrbe8QbdtWoVBouqZS/fILO7Uf5wc5jqNUKiXHcRQKhbbc2ZfLZaXTaeXzeW+2WS6Xaznrbm5urqNLJOzErVu3NHZyTO+tvNeV7R0aOKSFawvbCnfU2YPrrFgsKpVKqVqtKhKJNNTa4OBgQ9toNNr12Y23bt3SybExrbzXnRqTpIFDh3Rtof06o8Y6r7F7X8e27YbnsD0EO8MtLi5qZWVFf/9P/0eP23+859v7tfNLfeurf6fFxcW2d4bxeFzZbLZpZ3jhwgXF43Ej7ysYi8W8WwjVb+o9NzfXsm19R3jvPSOluxcCrV87Sro7KpBIJLoe6qS7dfbeynv6cvbLevTJR/d0W29ff1uvpl7dVo1J1NmD6qxWqymTyahSqUi6e6mOiYmJhtvZ3bhxw9dftIuLi1p57z3lnn1WTw4N7fn2ri8uKnnpEvuyLexGjdVqNYXDYV2+fFmhUEi5XE6Tk5NcGqVDBLse8bj9x7L/5JN+d6Ol48ePezclrx9iqO8AR0dHG3aGjuMokUioVqspHo97F+GsfxOsX9H9XoODgyqVSrJtW+l0WoVCQZIa1q9vqz4qNj8/r/Pnz+/JnR/q58nU+1m/wnytVmv5i7N+gdNAIPDA152YmPB9R/jok49q+E+Hfe3DZqizzevMcZyGuxxkMhkFAoF9eXuxJ4eG9KnHHvO7Gy1RY53VWLlclm3b3mdWv3vFZvtEPBiTJ7AvJBKJhiu0Z7PZlocZw+Gwzp8/r0qlIsdxVCwWVavVvG+NpVJJ4+Pjm25nfHxclUpFlUpFuVyuYRSsWq1qbm5Oc3NzOn/+fMvb+eyGVr8sW916ZztyuZwikci++yW831BnressFAo1hIh6m3vXTyQSGh0dVSwWa7r/J36PGuusxlrdP9bEEc5uYMQO+0IymdTg4KC3Q8zlcrpx44YuXrzotSkUCopEIt63uunpaWWzWTmOo2g06u00HnQo8t5vradPn1a5XG5oX7+vYzQafeBOZSf3YqxWqy2/hVar1Qe+3oOk0+mGw2ZojTprr84ymUzDa9q2rVQq5d0W6v7DtPg9amz7NRaNRpVIJLygWL+rxU72ib2MYId9IxqNet86W91P0HEcOY7j3Yar3m47t96q1WrezLVisdi0jXZfZyf3YgwGg00jHo7jtPzG2o5isahgMMhoXZuoswfX2ezsbNN27w1xp0+f5jDZFqix7dWYZVnKZrMKh8OKRCLe7RUjkUhH/ep1BDvsG6lUStlsVsFg0Pu2ea/6OSf331Q7l8u1NWTvOI5isZgymYx3LkirbbRjJ99yWx2q2Ml9YfP5/J6cP2Mq6mzzOkulUgqHwy1fr45RlK1RY9uvsXsng9XPueOLQ2cIdtg3otGody7K/Ts86e5IQSaT8U5MrtVqmp+f90YQ6svrw/j3cxxHlmV5IWh+fr7jGaQ7+ZZbP/xSKBS8Q1v3fquvfwNud6c2Pz+/6c3G0Yw6syQ111kqlVIsFmv6klAsFjU3N+f1oz4Dkl+6m6PGLEnt15j0+/P1arWaJicnO+4TmDyBfSadTm8aUizLUj6f1+TkpEZHRzUxMdGwfGJiwju00eobY33HNzg4qEQiIdu2dfz48T16Jw82NzenbDar0dFRzc3NNcxmnZycbNihp9Np732Fw2HvMEXdTkb7ehV11lhnxWJRuVxOiURCgUDA+1M/b+v48eMKh8PezE6/Z18/DKix9mtMunvOXf2zmJ6e5ijEDgTc/XjFQ2zbysqKrl27ppMnT2pgYMBbXi6XFQ6Hu34dO66O3lvqddbN69hRY72lXmPdvo4ddbY/1X/n3bx5U9evX1c8HtfHP/5xv7u1L3Ao1nBDQ0MaGBjQt776d13b5sDAgIa6sOPF/jE0NKRDA4f0aurVrmzv0MAhaqzHDA0NaeDQISUvXeraNgcOUWd4+BDsDDcyMqJr167t2/srwgwjIyNauLawb+8Vi4ffyMiIri10r8Yk6gwPJ4JdDxgZGWHnhD1HnWGvUWPA1pg8Ad/V73E6ODiowcFBxWKxbV9xfKvbbQHUGfYaNYb9gGAH34XDYcViMS0tLWlpacm7+GldOp3edNp/N9SvGTU6Oto0I7WVcrnc8rZLxWJRo6Oj3g6f2zJ1V6/UWX15/fZf3Jape3qlxupyuZx3v1fsHwQ7+MpxHFWrVe/ClNLdW+Xsp1losVhM6XRalUpFsVhMsVhs07apVEozMzMN922U7n6Tz2QyqlQqWlpaUigU8i5xgL3XS3U2OTmpfD7vvU47v8Cxc71SY3W1Wk3ZbJbrGe5HLoxw584dd35+3r1z547fXdmWpaUlV5Kbz+dbPp9MJl3LslzLstxQKOTOzc25ruu6c3Nzrm3bbigUcqempty9KuVSqeTatt2wzLIsd2lp6YHrSWpoUyqVvL7f26ZSqexWV/EAvVJnrus2PM7n802vi73RSzXmunffTzabdW3b9mU/Vv+dVygU3G984xvu9evXu96H/YpgZ4iHNdi57t1fPpJcy7LcZDLplkqlhufrO5C6+g60vmOsr79XfYtGow3LQqFQUx/vt9nOsK5SqexZn9Far9VZpVJxQ6FQw3vC3uqVGqtUKl5IJNjtP8yKhe/i8biWlpZULBZ14cIFhcNhzc3NbXqLnIsXLyoajXrPP+hWOju5D6J0976YrQ417PR+mZlM5oH348Tu66U6S6VS3u2d7j00iL3VKzWWSqW45dc+RrDDvlC/72E8Htfs7KwymcymO7nt3EJrJ/dBlKRgMNh04rDjOAoGgx2/5uzs7I77hc70Sp1ls1lls1nlcjmFw2GVSqWO+4btMb3GCoWCJHHLr32MYId9JxQK6cKFC5s+b1lW27Owdvot17btpm3t5N6sqVRK4XCY0bp9wOQ6q0smk0qlUioWix3fJB6dM7HGrly5IsdxNDo6Kun3M23T6TSjw/uF38eCsTse1nPs5ubm3GQy6Z2jsbS05IZCITeTyXhtpqam3KmpKe/5+nkp9XNDMpnMnp6vZtu2d0J0NpttOE+l3p/7qcV5KclkctMTq7G3eqXO5ubmGs7hymazbZ0gj53rlRpr9Tzn2O0vBDtDPKzBznXv7sxs23YlubZtN+wIXffubC5JbigU8nZK+Xzem11WX3+vVCoVNxqNurZtu/F4vGEnF4/Hm3bcoVDIey/xeNx13bs7fUlNf7Y6cRm7pxfqzHVdb6ZifaYlNdY9vVJj9yLY7T8B13Xdrg0PYs+srKzo2rVrOnnypAYGBvzuDgAAe6b+O+/mzZu6fv264vG4Pv7xj/vdrX2BCxQDAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYGWZjY8PvLgAAsKf4Xbc5gp0hHnnkEUnS7du3fe4JAAB7q/677oMPPvC5J/sPd54wRF9fn4aGhvTWW29Jko4cOaIDB8jtAABzbGxs6Pbt23rrrbdUq9UYuWuBYGeQkZERSfLCHQAAJqrVanr77be1vr6uAwcO6EMf+pDfXdo3CHYGCQQC+tjHPqZAIKC5uTmtr68rGAwqEAj43TUAAHbFBx98oI2NDW1sbOitt97SRz/6UQWDQb+7tW9w5wlDLSwsqFgs6t133yXYAQCM47quPvrRj+ov//Iv9dhjj/ndnX2DYGew//7v/9bS0pLW1tb87goAALuqv79fx48f1+DgoN9d2VcIdgAAAIZg2iQAAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIf4v91Ltf4NUxtwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plots of Distribution of I3 and SAP Scores Across Scenarios\n",
    "plot_score_across_scenarios(I3_1, I3_2, I3_3, 0)\n",
    "plot_score_across_scenarios(SAP_1, SAP_2, SAP_3, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bbaba389",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 1:\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 2:\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 3:\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Comparison of Disentaglement Success Rate using I3 and SAP Metrics for each scenario\n",
    "def plot_success_rate(y1, y2):\n",
    "    x = np.arange(1, 6)\n",
    "    \n",
    "    plt.plot(x, y1, marker='o', linestyle='-', color='b', label='$I_3$')\n",
    "    plt.plot(x, y2, marker='s', linestyle='--', color='g', label='SAP')\n",
    "    \n",
    "    plt.xlabel('Iteration')\n",
    "    plt.ylabel('Disentanglement Success Rate (\\%)')\n",
    "    \n",
    "    plt.xticks(x)\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "# Scenario 1\n",
    "print(colored('Scenario 1:', attrs=['bold', 'underline']))\n",
    "plot_success_rate([20, 28, 32, 32, 44], [80, 76, 84, 80, 80])\n",
    "\n",
    "# Scenario 2\n",
    "print(colored('Scenario 2:', attrs=['bold', 'underline']))\n",
    "plot_success_rate([80, 80, 64, 68, 64], [52, 72, 28, 56, 36])\n",
    "\n",
    "# Scenario 3\n",
    "print(colored('Scenario 3:', attrs=['bold', 'underline']))\n",
    "plot_success_rate([64, 56, 60, 48, 48], [4, 12, 28, 4, 4])\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}