I3_vs_SAP_s3n4m3.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: Independent of generative parameters\n",
    "            std_devs = [std_dev_v1, std_dev_v2, std_dev_v3]\n",
    "            V_1 = [np.random.normal(mean, std_dev, size=num_samples) for std_dev in std_devs]\n",
    "\n",
    "            # Compute covariance matrix of V \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 and v_2, with independence of v_3\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",
    "            \n",
    "            # Calculate v_2 using scaling factor alpha and random noise\n",
    "            random_noise_z2 = np.random.normal(mean, std_dev_z2, num_samples)\n",
    "            v_2 = alpha * v_1 + random_noise_z2\n",
    "            \n",
    "            # Create generative variable V\n",
    "            V_2 = np.array([v_1, v_2, v_3])\n",
    "\n",
    "            # Compute covariance matrix of V \n",
    "            Sigma_V_2 = np.round(np.cov(V_2), 4)  \n",
    "        \n",
    "        else:\n",
    "            # Case 3: Linear dependence of v_2 and v_3, with v_1\n",
    "            v_1 = np.random.normal(mean, std_dev_v1, size=num_samples)\n",
    "            \n",
    "            # Calculate additional generative parameters using scaling factors\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",
    "            v_2 = alpha * v_1 + random_noise_z2\n",
    "            v_3 = beta * v_1 + random_noise_z3\n",
    "\n",
    "            # Create generative variable V\n",
    "            V_3 = np.array([v_1, v_2, v_3])\n",
    "\n",
    "            # Compute covariance matrix of V \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(f'Given (sigma_v1, sigma_v2, sigma_v3) = {std_dev_v1, std_dev_v2, std_dev_v3}:')\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(f'Given (sigma_v1, sigma_v3) = {std_dev_v1, std_dev_v3}, alpha = {alpha}, and sigma_z2 = {std_dev_z2}:')\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(f'Given sigma_v1 = {std_dev_v1}, (alpha, beta) = {alpha, beta}, and (sigma_z2, sigma_z3) = {std_dev_z2, std_dev_z3}:')\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]\n",
      " [0 1 0]\n",
      " [0 0 1]\n",
      " [0 0 0]]\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance of noise Z_tilde:\u001b[0m\n",
      "[[0.0016 0.     0.     0.    ]\n",
      " [0.     0.0016 0.     0.    ]\n",
      " [0.     0.     0.0016 0.    ]\n",
      " [0.     0.     0.     0.0016]]\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Given:\n",
    "1. Maximum number of iterations: MAX_ITERS = 10,000\n",
    "2. Dimensions of the matrix: s = 3, n = 4, 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 = 3, 4, 3\n",
    "TOL_ERR = 1e-8\n",
    "MAX_RECON_ERR = 0.05\n",
    "\n",
    "num_cases = 3\n",
    "num_samples = int(1e7)\n",
    "alpha = 2\n",
    "beta = 4\n",
    "mean = 0\n",
    "std_dev_v1 = 0.01\n",
    "std_dev_v2 = 0.02\n",
    "std_dev_v3 = 0.03\n",
    "std_dev_z2 = 0.02\n",
    "std_dev_z3 = 0.03\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],\n",
    "                         [0, 1, 0],\n",
    "                         [0, 0, 1],\n",
    "                         [0, 0, 0]])\n",
    "print(colored('\\nIndependent eigenvectors:', 'blue', attrs=['bold']))\n",
    "print(eigenvectors)\n",
    "\n",
    "# Covariance of noise Z_tilde\n",
    "sigma_squared = 0.04**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}\n",
      "Partition 2: Group 1: set(), Group 2: {4}, Group 3: {5, 6}\n",
      "Partition 3: Group 1: set(), Group 2: {5}, Group 3: {4, 6}\n",
      "Partition 4: Group 1: set(), Group 2: {6}, Group 3: {4, 5}\n",
      "Partition 5: Group 1: set(), Group 2: {4, 5}, Group 3: {6}\n",
      "Partition 6: Group 1: set(), Group 2: {4, 6}, Group 3: {5}\n",
      "Partition 7: Group 1: set(), Group 2: {5, 6}, Group 3: {4}\n",
      "Partition 8: Group 1: set(), Group 2: {4, 5, 6}, Group 3: set()\n",
      "Partition 9: Group 1: {4}, Group 2: set(), Group 3: {5, 6}\n",
      "Partition 10: Group 1: {5}, Group 2: set(), Group 3: {4, 6}\n",
      "Partition 11: Group 1: {6}, Group 2: set(), Group 3: {4, 5}\n",
      "Partition 12: Group 1: {4}, Group 2: {5}, Group 3: {6}\n",
      "Partition 13: Group 1: {4}, Group 2: {6}, Group 3: {5}\n",
      "Partition 14: Group 1: {5}, Group 2: {4}, Group 3: {6}\n",
      "Partition 15: Group 1: {5}, Group 2: {6}, Group 3: {4}\n",
      "Partition 16: Group 1: {6}, Group 2: {4}, Group 3: {5}\n",
      "Partition 17: Group 1: {6}, Group 2: {5}, Group 3: {4}\n",
      "Partition 18: Group 1: {4}, Group 2: {5, 6}, Group 3: set()\n",
      "Partition 19: Group 1: {5}, Group 2: {4, 6}, Group 3: set()\n",
      "Partition 20: Group 1: {6}, Group 2: {4, 5}, Group 3: set()\n",
      "Partition 21: Group 1: {4, 5}, Group 2: set(), Group 3: {6}\n",
      "Partition 22: Group 1: {4, 6}, Group 2: set(), Group 3: {5}\n",
      "Partition 23: Group 1: {5, 6}, Group 2: set(), Group 3: {4}\n",
      "Partition 24: Group 1: {4, 5}, Group 2: {6}, Group 3: set()\n",
      "Partition 25: Group 1: {4, 6}, Group 2: {5}, Group 3: set()\n",
      "Partition 26: Group 1: {5, 6}, Group 2: {4}, Group 3: set()\n",
      "Partition 27: Group 1: {4, 5, 6}, 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, 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",
    "    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",
    "          \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",
    "    \n",
    "    SAP = 1/s * (diff_1 + diff_2 + diff_3)\n",
    "    print(colored(f'\\nSAP = {round(SAP, 4)}', 'red', attrs=['bold']))\n",
    "    \n",
    "    if result1_v1[0] == result1_v2[0] == result1_v3[0]:\n",
    "        print('(v1, v2, v3) can be captured by a single latent variable.')\n",
    "        r = 1\n",
    "    elif result1_v1[0] == result1_v2[0]:\n",
    "        print('(v1, v2) are captured by one latent variable and v3 by a second latent variable.') \n",
    "        r = 2\n",
    "    elif result1_v2[0] == result1_v3[0]:\n",
    "        print('(v2, v3) are captured by one latent variable and v1 by a second latent variable.')\n",
    "        r = 3\n",
    "    elif result1_v1[0] == result1_v3[0]:\n",
    "        print('(v1, v3) are captured by one latent variable and v2 by a second latent variable.')\n",
    "        r = 4\n",
    "    else:\n",
    "        print('Each factor can be captured by a single latent variable.')\n",
    "        r = 5\n",
    "        \n",
    "    count = 0\n",
    "    \n",
    "    if SAP_flag == 0 and r == 5:\n",
    "        count = 1\n",
    "        \n",
    "    if SAP_flag == 1 and r == 2:\n",
    "        count = 1\n",
    "        \n",
    "    if SAP_flag == 2 and r == 1:\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 = -1000\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",
    "    \n",
    "    if 12 <= partition <= 17:\n",
    "        print('Each factor can be captured by a single latent variable.') \n",
    "    elif partition in [1, 8, 27]:\n",
    "        print('(v1, v2, v3) can be captured by a single latent variable.')\n",
    "    elif partition in [4, 5, 11, 20, 21, 24]:\n",
    "        print('(v1, v2) are captured by one latent variable and v3 by a second latent variable.')\n",
    "    elif partition in [3, 6, 10, 19, 22, 25]:\n",
    "        print('(v1, v3) are captured by one latent variable and v2 by a second latent variable.')\n",
    "    else:\n",
    "        print('(v2, v3) are captured by one latent variable and v1 by a second latent variable.')\n",
    "    \n",
    "    count = 0\n",
    "    \n",
    "    if I3_flag == 0 and 12 <= partition <= 17:\n",
    "        count = 1\n",
    "        \n",
    "    if I3_flag == 1 and partition in [4, 5, 11, 20, 21, 24]:\n",
    "        count = 1\n",
    "        \n",
    "    if I3_flag == 2 and partition in [1, 8, 27]:\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": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[4m\u001b[1mScenario 1:\u001b[0m\n",
      "Given (sigma_v1, sigma_v2, sigma_v3) = (0.01, 0.02, 0.03):\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of generative variable V:\u001b[0m\n",
      "[[0.0001 0.     0.    ]\n",
      " [0.     0.0004 0.    ]\n",
      " [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",
      "[[0.0017 0.     0.     0.    ]\n",
      " [0.     0.002  0.     0.    ]\n",
      " [0.     0.     0.0025 0.    ]\n",
      " [0.     0.     0.     0.0016]]\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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 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 = 0.0.\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",
      "0.0\n",
      "\n",
      "Reconstruction error:\n",
      "0.0\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 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 = 4.5e-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",
      "0.001\n",
      "\n",
      "Reconstruction error:\n",
      "4.5e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0003\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0001 at Partition 17.\u001b[0m\n",
      "Each factor can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "Each factor can be captured by a single 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 = 4.86e-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",
      "0.0015\n",
      "\n",
      "Reconstruction error:\n",
      "4.86e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0004\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0003 at Partition 16.\u001b[0m\n",
      "Each factor can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0001\u001b[0m\n",
      "Each factor can be captured by a single 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 = 1e-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",
      "0.0061\n",
      "\n",
      "Reconstruction error:\n",
      "1e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0019\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0014 at Partition 3.\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0007\u001b[0m\n",
      "Each factor 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 = 2.31e-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",
      "0.0026\n",
      "\n",
      "Reconstruction error:\n",
      "2.31e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0002\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0001 at Partition 10.\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 by a second latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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 = 1.754e-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",
      "0.0058\n",
      "\n",
      "Reconstruction error:\n",
      "1.754e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.001\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0008 at Partition 13.\u001b[0m\n",
      "Each factor can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0005\u001b[0m\n",
      "Each factor can be captured by a single 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 = 0.00397009.\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",
      "69.4224\n",
      "\n",
      "Reconstruction error:\n",
      "0.00397009\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1216 at Partition 2.\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0641\u001b[0m\n",
      "Each factor can be captured by a single 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 = 0.00496269.\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",
      "68.5922\n",
      "\n",
      "Reconstruction error:\n",
      "0.00496269\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3347\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.2928 at Partition 15.\u001b[0m\n",
      "Each factor can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1478\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00397025.\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",
      "68.7889\n",
      "\n",
      "Reconstruction error:\n",
      "0.00397025\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0956 at Partition 2.\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0383\u001b[0m\n",
      "Each factor can be captured by a single 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 = 0.00397033.\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",
      "69.4525\n",
      "\n",
      "Reconstruction error:\n",
      "0.00397033\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1266 at Partition 9.\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0673\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 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 = 0.00496305.\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",
      "68.8759\n",
      "\n",
      "Reconstruction error:\n",
      "0.00496305\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.3347\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1542 at Partition 23.\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.03\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00788166.\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",
      "143.1681\n",
      "\n",
      "Reconstruction error:\n",
      "0.00788166\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1186 at Partition 2.\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0603\u001b[0m\n",
      "Each factor can be captured by a single 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 = 0.00788181.\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",
      "142.8622\n",
      "\n",
      "Reconstruction error:\n",
      "0.00788181\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0742 at Partition 2.\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0156\u001b[0m\n",
      "Each factor 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 = 0.00788197.\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",
      "141.8937\n",
      "\n",
      "Reconstruction error:\n",
      "0.00788197\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0771 at Partition 3.\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0161\u001b[0m\n",
      "Each factor can be captured by a single 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 = 0.00788212.\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",
      "143.6209\n",
      "\n",
      "Reconstruction error:\n",
      "0.00788212\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0882 at Partition 3.\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0321\u001b[0m\n",
      "Each factor can be captured by a single latent variable.\n",
      "\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 = 0.00788227.\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",
      "144.2899\n",
      "\n",
      "Reconstruction error:\n",
      "0.00788227\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1419\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1114 at Partition 10.\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0523\u001b[0m\n",
      "(v2, v3) are captured by one latent variable and v1 by a second latent variable.\n",
      "\u001b[1m\n",
      "The disentanglement success rate using I_3 and SAP metrics are 16.0% and 40.0%, respectively.\n",
      "\u001b[0m\n",
      "\u001b[4m\u001b[1m\n",
      "Scenario 2:\u001b[0m\n",
      "Given (sigma_v1, sigma_v3) = (0.01, 0.03), alpha = 2, and sigma_z2 = 0.02:\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of generative variable V:\u001b[0m\n",
      "[[ 0.0001  0.0002 -0.    ]\n",
      " [ 0.0002  0.0008 -0.    ]\n",
      " [-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",
      "[[0.0017 0.0002 0.     0.    ]\n",
      " [0.0002 0.0024 0.     0.    ]\n",
      " [0.     0.     0.0025 0.    ]\n",
      " [0.     0.     0.     0.0016]]\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 = 0.01522543.\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",
      "0.0789\n",
      "\n",
      "Reconstruction error:\n",
      "0.01522543\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.02\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0096 at Partition 21.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0004\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.01519563.\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",
      "0.0789\n",
      "\n",
      "Reconstruction error:\n",
      "0.01519563\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.02\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0106 at Partition 21.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0059\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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 = 0.01516584.\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",
      "0.0789\n",
      "\n",
      "Reconstruction error:\n",
      "0.01516584\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.02\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0186 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0295\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.01513606.\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",
      "0.079\n",
      "\n",
      "Reconstruction error:\n",
      "0.01513606\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.02\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0165 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0236\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.01510628.\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",
      "0.079\n",
      "\n",
      "Reconstruction error:\n",
      "0.01510628\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.02\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.016 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0209\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00748475.\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",
      "0.0892\n",
      "\n",
      "Reconstruction error:\n",
      "0.00748475\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0224\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0116 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0017\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00745645.\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",
      "0.0892\n",
      "\n",
      "Reconstruction error:\n",
      "0.00745645\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0224\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0114 at Partition 5.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.001\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00742817.\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",
      "0.0892\n",
      "\n",
      "Reconstruction error:\n",
      "0.00742817\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0224\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0171 at Partition 21.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0207\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00739988.\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",
      "0.0893\n",
      "\n",
      "Reconstruction error:\n",
      "0.00739988\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0225\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0218 at Partition 5.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0365\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.0073716.\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",
      "0.0893\n",
      "\n",
      "Reconstruction error:\n",
      "0.0073716\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0225\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0123 at Partition 5.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0078\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 5.375e-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",
      "0.0996\n",
      "\n",
      "Reconstruction error:\n",
      "5.375e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0238\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.023 at Partition 21.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0383\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second 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 = 2.691e-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",
      "0.1014\n",
      "\n",
      "Reconstruction error:\n",
      "2.691e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0249\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0169 at Partition 11.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0155\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 1e-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",
      "0.1025\n",
      "\n",
      "Reconstruction error:\n",
      "1e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0249\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0182 at Partition 4.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0251\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 2.678e-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",
      "0.101\n",
      "\n",
      "Reconstruction error:\n",
      "2.678e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0262\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0155 at Partition 24.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0103\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 4.87e-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",
      "0.1055\n",
      "\n",
      "Reconstruction error:\n",
      "4.87e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.0294\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0157 at Partition 20.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0042\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00486884.\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",
      "69.1992\n",
      "\n",
      "Reconstruction error:\n",
      "0.00486884\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1442 at Partition 21.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1404\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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 = 0.00486918.\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",
      "68.902\n",
      "\n",
      "Reconstruction error:\n",
      "0.00486918\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1236 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1328\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00496281.\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",
      "68.6817\n",
      "\n",
      "Reconstruction error:\n",
      "0.00496281\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4513\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3051 at Partition 20.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2134\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00486911.\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",
      "69.3164\n",
      "\n",
      "Reconstruction error:\n",
      "0.00486911\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.209 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2762\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00486923.\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",
      "68.7568\n",
      "\n",
      "Reconstruction error:\n",
      "0.00486923\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1407 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1267\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00985198.\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",
      "143.3847\n",
      "\n",
      "Reconstruction error:\n",
      "0.00985198\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4259\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3442 at Partition 4.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2943\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00966621.\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",
      "142.6265\n",
      "\n",
      "Reconstruction error:\n",
      "0.00966621\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1359 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1497\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00966619.\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",
      "140.7633\n",
      "\n",
      "Reconstruction error:\n",
      "0.00966619\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1392 at Partition 21.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1285\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00966628.\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",
      "143.0055\n",
      "\n",
      "Reconstruction error:\n",
      "0.00966628\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1268 at Partition 5.\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0722\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\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 = 0.00966646.\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",
      "142.0741\n",
      "\n",
      "Reconstruction error:\n",
      "0.00966646\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.2281\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1362 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1536\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 by a second latent variable.\n",
      "\u001b[1m\n",
      "The disentanglement success rate using I_3 and SAP metrics are 64.0% and 92.0%, respectively.\n",
      "\u001b[0m\n",
      "\u001b[4m\u001b[1m\n",
      "Scenario 3:\u001b[0m\n",
      "Given sigma_v1 = 0.01, (alpha, beta) = (2, 4), and (sigma_z2, sigma_z3) = (0.02, 0.03):\n",
      "\u001b[1m\u001b[34m\n",
      "Covariance matrix of generative variable V:\u001b[0m\n",
      "[[0.0001 0.0002 0.0004]\n",
      " [0.0002 0.0008 0.0008]\n",
      " [0.0004 0.0008 0.0025]]\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",
      "[[0.0017 0.0002 0.0004 0.    ]\n",
      " [0.0002 0.0024 0.0008 0.    ]\n",
      " [0.0004 0.0008 0.0041 0.    ]\n",
      " [0.     0.     0.     0.0016]]\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 = 0.01517876.\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",
      "0.2726\n",
      "\n",
      "Reconstruction error:\n",
      "0.01517876\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1485\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0975 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1865\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.01514335.\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",
      "0.2727\n",
      "\n",
      "Reconstruction error:\n",
      "0.01514335\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1486\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0943 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1336\u001b[0m\n",
      "(v1, v2, v3) 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 = 0.01510793.\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",
      "0.2728\n",
      "\n",
      "Reconstruction error:\n",
      "0.01510793\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1486\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1015 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1667\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.01507249.\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",
      "0.2729\n",
      "\n",
      "Reconstruction error:\n",
      "0.01507249\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1487\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0604 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0241\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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 = 0.01503704.\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",
      "0.273\n",
      "\n",
      "Reconstruction error:\n",
      "0.01503704\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1487\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1233 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2713\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00878012.\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",
      "0.2895\n",
      "\n",
      "Reconstruction error:\n",
      "0.00878012\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1589\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0807 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0509\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00873896.\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",
      "0.2896\n",
      "\n",
      "Reconstruction error:\n",
      "0.00873896\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.159\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.106 at Partition 8.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1652\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00869777.\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",
      "0.2898\n",
      "\n",
      "Reconstruction error:\n",
      "0.00869777\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.159\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1201 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.2421\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00865654.\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",
      "0.2899\n",
      "\n",
      "Reconstruction error:\n",
      "0.00865654\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1591\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1005 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1644\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00861527.\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",
      "0.29\n",
      "\n",
      "Reconstruction error:\n",
      "0.00861527\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1592\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.0927 at Partition 8.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.1194\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 9.197e-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",
      "0.3176\n",
      "\n",
      "Reconstruction error:\n",
      "9.197e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1684\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1221 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.229\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 4.743e-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",
      "0.3178\n",
      "\n",
      "Reconstruction error:\n",
      "4.743e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1699\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.155 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3817\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 1e-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",
      "0.3216\n",
      "\n",
      "Reconstruction error:\n",
      "1e-06\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1777\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1441 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3353\u001b[0m\n",
      "(v1, v2, v3) 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 = 5.893e-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",
      "0.3209\n",
      "\n",
      "Reconstruction error:\n",
      "5.893e-05\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1768\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.1678 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4074\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00012199.\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",
      "0.3216\n",
      "\n",
      "Reconstruction error:\n",
      "0.00012199\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.1777\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.092 at Partition 8.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.0721\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00493006.\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",
      "68.6707\n",
      "\n",
      "Reconstruction error:\n",
      "0.00493006\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.6396\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4226 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.7187\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00493014.\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",
      "69.401\n",
      "\n",
      "Reconstruction error:\n",
      "0.00493014\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.6396\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4356 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.653\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00478051.\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",
      "69.398\n",
      "\n",
      "Reconstruction error:\n",
      "0.00478051\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4892\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.386 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.6847\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00493073.\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",
      "69.5115\n",
      "\n",
      "Reconstruction error:\n",
      "0.00493073\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.6396\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4252 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.7546\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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 = 0.00478055.\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",
      "68.952\n",
      "\n",
      "Reconstruction error:\n",
      "0.00478055\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4892\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4534 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.7508\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00948151.\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",
      "143.7622\n",
      "\n",
      "Reconstruction error:\n",
      "0.00948151\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4892\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.388 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.6238\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single 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 = 0.00978111.\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",
      "144.1148\n",
      "\n",
      "Reconstruction error:\n",
      "0.00978111\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.6396\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3192 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.3794\u001b[0m\n",
      "(v1, v3) are captured by one latent variable and v2 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 = 0.00977889.\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",
      "143.1695\n",
      "\n",
      "Reconstruction error:\n",
      "0.00977889\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.6396\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3045 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4356\u001b[0m\n",
      "(v1, v2) are captured by one latent variable and v3 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 = 0.00948664.\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",
      "142.7783\n",
      "\n",
      "Reconstruction error:\n",
      "0.00948664\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4892\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.4298 at Partition 27.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.7363\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\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 = 0.00948298.\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",
      "143.4011\n",
      "\n",
      "Reconstruction error:\n",
      "0.00948298\n",
      "\n",
      "Mutual information between generative variable and latent variable:\n",
      "0.4892\n",
      "\u001b[1m\u001b[31m\n",
      "The maximum value of I_3 is 0.3033 at Partition 1.\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\u001b[31m\n",
      "SAP = 0.4232\u001b[0m\n",
      "(v1, v2, v3) can be captured by a single latent variable.\n",
      "\u001b[1m\n",
      "The disentanglement success rate using I_3 and SAP metrics are 100.0% and 92.0%, 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 = 5\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",
    "            # 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, 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": {
      "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": [
    "# 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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",
      "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)"
   ]
  }
 ],
 "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
}