bounding_A_norm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Copyright 2024 L3Harris Technologies, Inc.\n",
    "#\n",
    "#    Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "#    you may not use this file except in compliance with the License.\n",
    "#    You may obtain a copy of the License at\n",
    "#\n",
    "#        http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "#    Unless required by applicable law or agreed to in writing, software\n",
    "#    distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "#    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "#    See the License for the specific language governing permissions and\n",
    "#    limitations under the License.\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import sympy\n",
    "from copy import deepcopy\n",
    "import time\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# only one grid point for this analysis.\n",
    "n = 1\n",
    "x = 0 # index of the one and only grid node x is zero.\n",
    "Q = 27\n",
    "nQ = n*Q\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "# Define lexicographical index sort functions per Appendix on variable indexing.\n",
    "def lexi_x(x_alpha):\n",
    "    # This one is simple because we only have one grid point in this analysis.\n",
    "    return x_alpha\n",
    "\n",
    "def lexi_1(i, x_alpha):\n",
    "    # using global Q\n",
    "    return Q*lexi_x(x_alpha) + i\n",
    "\n",
    "def lexi_2(j,k,x_beta,x_gamma):\n",
    "    # using global Q\n",
    "    # using global n\n",
    "    return Q**2*(n*lexi_x(x_beta) + lexi_x(x_gamma)) + Q*j + k\n",
    "\n",
    "def lexi_3(j,k,ell,x_beta,x_gamma,x_delta):\n",
    "    # using global Q\n",
    "    # using global n\n",
    "    return Q**3*(n**2*lexi_x(x_beta) + n*lexi_x(x_gamma) + lexi_x(x_delta)) + Q**2*j + Q*k + ell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Lattice Boltzmann Method: Principles and Practice (Book), Page 90\n",
    "D3Q27_weights = np.zeros(Q, dtype=float)\n",
    "D3Q27_weights[0] = 8.0/27\n",
    "D3Q27_weights[1:7] = 2.0/27\n",
    "D3Q27_weights[7:19] = 1.0/54\n",
    "D3Q27_weights[19:] = 1.0/216\n",
    "\n",
    "\n",
    "# Lattice Boltzmann Method: Principles and Practice (Book), Page 90\n",
    "D3Q27_vectors = np.zeros((Q,3), dtype=int)\n",
    "D3Q27_vectors[0:] = [ 0,  0,  0] # 0\n",
    "D3Q27_vectors[1:] = [ 1,  0,  0] # 1\n",
    "D3Q27_vectors[2:] = [-1,  0,  0]\n",
    "D3Q27_vectors[3:] = [ 0,  1,  0]\n",
    "D3Q27_vectors[4:] = [ 0, -1,  0]\n",
    "D3Q27_vectors[5:] = [ 0,  0,  1]\n",
    "D3Q27_vectors[6:] = [ 0,  0, -1] # 6\n",
    "D3Q27_vectors[7:] = [ 1,  1,  0] # 7\n",
    "D3Q27_vectors[8:] = [-1, -1,  0]\n",
    "D3Q27_vectors[9:] = [ 1,  0,  1]\n",
    "D3Q27_vectors[10:] = [-1,  0, -1]\n",
    "D3Q27_vectors[11:] = [ 0,  1,  1]\n",
    "D3Q27_vectors[12:] = [ 0, -1, -1]\n",
    "D3Q27_vectors[13:] = [ 1, -1,  0]\n",
    "D3Q27_vectors[14:] = [-1,  1,  0]\n",
    "D3Q27_vectors[15:] = [ 1,  0, -1]\n",
    "D3Q27_vectors[16:] = [-1,  0,  1]\n",
    "D3Q27_vectors[17:] = [ 0,  1, -1]\n",
    "D3Q27_vectors[18:] = [ 0, -1,  1] # 18\n",
    "D3Q27_vectors[19:] = [ 1,  1,  1] # 19\n",
    "D3Q27_vectors[20:] = [-1, -1, -1]\n",
    "D3Q27_vectors[21:] = [ 1,  1, -1]\n",
    "D3Q27_vectors[22:] = [-1, -1,  1]\n",
    "D3Q27_vectors[23:] = [ 1, -1,  1]\n",
    "D3Q27_vectors[24:] = [-1,  1, -1]\n",
    "D3Q27_vectors[25:] = [-1,  1,  1]\n",
    "D3Q27_vectors[26:] = [ 1, -1, -1]\n",
    "\n",
    "\n",
    "c = deepcopy(D3Q27_vectors)\n",
    "w = deepcopy(D3Q27_weights)\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done.\n",
      "Elapsed time: 5.10 seconds\n",
      "WARNING!!!  These matrices have not been scaled by the tau parameter yet!\n"
     ]
    }
   ],
   "source": [
    "F_1_matrix = np.zeros((Q,Q))\n",
    "F_2_matrix = np.zeros((Q,Q*Q))\n",
    "F_3_matrix = np.zeros((Q,Q*Q*Q))\n",
    "\n",
    "\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "for i in range(Q):\n",
    "\n",
    "    # Formulas for T_ per Section \"Appendix: Derivation of Functions to Compute S- and F-Matrix Elements\"\n",
    "    T_0_1 = 0.0\n",
    "    T_1_1 = 0.0\n",
    "    T_2_1 = 0.0\n",
    "    T_3_2_dense = 0.0\n",
    "    T_4_2_dense = 0.0\n",
    "    T_3_3_dense = 0.0\n",
    "    T_4_3_dense = 0.0\n",
    "\n",
    "    for j in range(Q):\n",
    "\n",
    "        T_0_1 = -1.0*float(i == j)\n",
    "        T_1_1 = w[i]\n",
    "        T_2_1 = 3*w[i]*np.inner(c[i],c[j])\n",
    "        \n",
    "        F_1_matrix[i,j] = T_0_1 + T_1_1 + T_2_1\n",
    "\n",
    "\n",
    "        for k in range(Q):\n",
    "            \n",
    "            T_3_2_dense = 9*w[i]*np.inner(c[i],c[j])*np.inner(c[i],c[k])\n",
    "            T_4_2_dense = -3*w[i]*np.inner(c[j],c[k])\n",
    "\n",
    "            F_2_matrix[i,lexi_2(k,j,x,x)] = T_3_2_dense + T_4_2_dense\n",
    "\n",
    "            for ell in range(Q):\n",
    "                \n",
    "                T_3_3_dense = (-9.0*w[i]/2.0)*np.inner(c[i],c[k])*np.inner(c[i],c[ell])\n",
    "                \n",
    "                # The original manuscript had a (-1) sign error in (86), the formula \n",
    "                # for the T_4_3_dense term.  This has been corrected in the manuscript.\n",
    "                # This Python script was corrected by JohnP on 16-Sep 2024.\n",
    "                # T_4_3_dense = (-3.0*w[i]/2.0)*np.inner(c[k],c[ell]) # <---- incorrect/old.\n",
    "                T_4_3_dense = (3.0*w[i]/2.0)*np.inner(c[k],c[ell]) # <---- fixed.\n",
    "\n",
    "                F_3_matrix[i,lexi_3(j,k,ell,x,x,x)] = T_3_3_dense + T_4_3_dense\n",
    "\n",
    "\n",
    "\n",
    "end_time = time.time()\n",
    "elapsed_time = end_time - start_time\n",
    "print(\"done.\")\n",
    "print(f\"Elapsed time: {elapsed_time:.2f} seconds\")\n",
    "\n",
    "\n",
    "print(\"WARNING!!!  These matrices have not been scaled by the tau parameter yet!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING!!!  These matrices have not been scaled by the tau parameter yet!\n"
     ]
    }
   ],
   "source": [
    "# write out matrices for posterity (or to skip previous cells).\n",
    "\n",
    "np.savez_compressed(\"F_1_matrix.npz\", F_1_matrix=F_1_matrix)\n",
    "np.savez_compressed(\"F_2_matrix.npz\", F_2_matrix=F_2_matrix)\n",
    "np.savez_compressed(\"F_3_matrix.npz\", F_3_matrix=F_3_matrix)\n",
    "\n",
    "\n",
    "print(\"WARNING!!!  These matrices have not been scaled by the tau parameter yet!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read in matrices.\n",
    "\n",
    "F_1_matrix = np.load(\"F_1_matrix.npz\")[\"F_1_matrix\"]\n",
    "F_2_matrix = np.load(\"F_2_matrix.npz\")[\"F_2_matrix\"]\n",
    "F_3_matrix = np.load(\"F_3_matrix.npz\")[\"F_3_matrix\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rank of F_1 matrix: 23\n"
     ]
    }
   ],
   "source": [
    "plt.imshow(F_1_matrix)\n",
    "plt.title(f\"F_1 matrix ({Q}x{Q})\")\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "print(f\"rank of F_1 matrix: {np.linalg.matrix_rank(F_1_matrix)}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F_1_matrix is size 27x27, rank 1\n",
      "F_2_matrix is size 27x729, rank 1\n",
      "F_3_matrix is size 27x19683, rank 1\n",
      "\n",
      "\n",
      "\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": [
      "F_1_matrix 1-norm (max abs col sum): 3.481481481481482\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": [
      "F_1_matrix inf-norm (max abs row sum): 8.407407407407407\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": [
      "F_2_matrix 1-norm (max abs col sum): 7.333333333333334\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": [
      "F_2_matrix inf-norm (max abs row sum): 565.3333333333334\n"
     ]
    },
    {
     "data": {
      "image/png": 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jjz90dQpLHPPOa3uWMZ9pqviY9JAsPHz4EEIIvUMXZe23337DCy+8gKVLl+LNN99E165dERISku9qnpL8t19SGRkZGDhwIPz8/PDOO+9gxowZOHr0aLHtatWqBVtbW70TsZ92+fJldOvWDa6urtiyZUu+K7yetXHjRty/f7/QQ1sAsHXrVixZsgQfffSR7gRsYw8lWFpaIiAgAO3atYO9vT127twJAHp7DFu2bAkA+Pfff/Xa5h1Cyduzl3fy77MbTyEEcnNzSxRrYfMu731u1KhRke1/++031KlTB+vWrcPbb7+N0NBQhISEFHpjw3/++Sdf2cWLF+Hj46NXVrduXYwbNw7bt29HXFwcsrOzMWvWrELjyDtc9eyVYE9zcXGBnZ0dLly4kG/Z+fPnYWFhkW9vSkl4eHjgvffeQ3R0NOLj41GtWjW9vYxVq1Yt8Aq5a9eulfq1qPJj0kOVSt4ejqelpqbi999/h5eXV6kO9RjL0tIy33+Jv/76a76NbZUqVXRxGmvChAlISEjAypUrMXv2bPj4+KB///7FXnprbW2N5557DseOHcu3LCkpCV27doWFhQW2bduW73BfQdasWQM7Ozvdpe3PSk1NxZAhQ9C6dWt8/fXXWLJkCU6cOIGvv/66ZAMtgdu3b2P69Olo1qyZXtKTd7ht6dKlujKtVovly5fD2dlZlxTl7R1au3atXr8bN25ERkYGmjdvrisr7bw7fvw4FAoFgoKCihxD3t6Hp+fR4cOHERsbW2D96Ohovfl15MgRHD58GGFhYQCABw8e5EuY6tatCwcHhyLniIuLC4KDg7Fs2bJ8V3nlxWZpaYmuXbtiw4YNepe/JycnY82aNXj++efh6OhY5Hiflpubm+/QkqurK2rUqKEXa926dXHo0CFkZ2fryjZt2lTqQ2kkD7wjM1UqYWFh8PT0RGBgIFxdXZGQkIDly5fj5s2b+X5ioKx1794dU6dOxcCBA9G2bVucOXMGP/74o95JnsDjL20nJycsWrQIDg4OqFKlCgIDA/Pdmbo4u3fvxoIFCzB58mTdpefLly9Hx44dMWnSJMyYMaPI9r169cInn3wCjUajt3Hq1q0brly5go8++ggHDhzAgQMHdMvc3NzQpUsXvX5SUlLwxx9/4NVXXy10j9CoUaNw9+5d7Ny5E5aWlujWrRuGDBmCL7/8Er169YK/vz+Ax+fV5J2Xk3c4ad68eXBycoKTkxNGjhyp67NDhw4ICgpCvXr1kJSUhO+//x7p6enYtGmT7oTyvHF27twZUVFRuHPnDvz9/REdHY0DBw5g8eLFUCqVAIAePXqgcePGmDp1Kq5du4Y2bdrg0qVLmDdvHjw8PDB48GBdn6Wddzt27EC7du10hxUL0717d6xbtw4vv/wyXnrpJcTHx2PRokXw8/NDenp6vvr16tXD888/j3fffRdZWVn49ttvUa1aNXz00UcAHu/16dy5M9544w34+fnBysoK69evR3JycoGX4D/tu+++w/PPP48WLVrgnXfeQe3atXH16lVs3rxZd/n8l19+iR07duD555/He++9BysrKyxevBhZWVnFzr9n3b9/H56ennjttdfg7++v23N39OhRvb1SQ4YMwW+//YZu3brhjTfewOXLl7F69WrUrVu3VK9HMmGiq8aI9Eh1R+Z58+aJ559/XlSvXl1YWVkJFxcX0aNHD7Fv375S99W/f39RpUqVfOUdOnQQjRs3zlfu7e0tXnrpJd3zzMxMMW7cOOHh4SFsbW1Fu3btRGxsbIGXmm/YsEH4+fkJKysrvcvXC3utvGV5/Wg0GuHt7S1atGghHj16pFdvzJgxwsLCQsTGxhY53uTkZGFlZSVWrVqlV45CbiUAIN84hBBi0aJFAoDYuHFjga+zYcMGAUDMmjVLrzxvDP7+/rpLivMuxS7o8ezlxGPGjBF16tQRSqVSuLi4iL59++pdOv20+/fvi1GjRgl3d3dhY2MjmjZtKlavXp2vXkpKihgzZoxo0KCBUCqVonr16uLNN98UV65c0atXmnmXmpoqbGxsxJIlSwqM7WlarVZ8/fXXwtvbWyiVStG8eXOxadMm0b9/f73xP31H5lmzZgkvLy+hVCpF+/btxV9//aWrd+fOHTFixAjRsGFDUaVKFaFWq0VgYKD45Zdfio1FCCHi4uLEyy+/LJycnIRKpRK+vr5i0qRJenVOnDghQkNDhb29vbCzsxMvvPCCOHjwoF6dklyynpWVJcaPHy/8/f2Fg4ODqFKlivD39xcLFizIV3fWrFmiZs2aQqlUinbt2oljx44Vesn6r7/+qte2sO+eyZMnCwDi9u3bJXpvqGJQCMGztIjoscGDB+PixYu6OxyT9L799lvMmDEDly9fLvVJ6kRkHCY9RKSTkJCABg0aYNeuXXq/tE7SePToEerWrYuJEyfivffeM3U4RLLDpIcqhLS0tGIvN3d3dy/3voiIqOJg0kMVwoABA7By5coi65R0KkvZFxERVRxMeqhCOHv2bLG3oi/p3Zul7IuIiCoOJj1EREQkC7w5IREREcmC7G5OqNVqcfPmTTg4OEh6+38iIiIqO+L/f9KlRo0aejccLQ3ZJT03b9406PdfiIiIyPSuX78OT09Pg9rKLulxcHAA8PhNK83vwBAREZHpaDQaeHl56bbjhpBd0pN3SMvR0ZFJDxERUQVjzKkpPJGZiIiIZIFJDxEREckCkx4iIiKSBSY9REREJAtMeoiIiEgWmPQQERGRLDDpISIiIllg0kNERESywKSHiIiIZEF2d2Q2F9k5Wvyw/xJ+PHQNd+9nI1cLWFgASmtLNKmpxvAOdfF8fRdYWhR+58n0zByM+uk4TlxLQXqWFgoACgsFHFTWCPBS49s3W8BeVfgqzs7RYvmfV/DH6Zu4dDsdjx4JaAFYW1nAuYoN+gZ6Y0j7OrCxKjw3fnYcWgFYWgA21pao6+KAsCbuGNCudpF9GDuOvD7e//EoDl1JQWYuYKUo/Tjy3ouLyfeRlfO4vIqq5OPIey9Wx17FnfuPkCsAS0sF7Gws0bJWVXzXp2TjyHsvNJlaAICFhQKujkr0K+U4pFqnnJucm8++F/fz5qalAs5VbPCCrys+69EYtjaWJRpHRV6nlWUceX2Yem6WN4UQQpg6iPKk0WigVquRlpZmsp+hiNpyFov3xRdbT2llgf+8GYBuTTzyLes5bz9O39AU20czT0dsHNne4BgAYFhwbUS+6GdwHwoA7xTSh7HjKE0fZTmOkvZhDuOQog/OzSfMYZ2ay9zs4ueKHyJaGRwDYN7rtLKMozR9lOU4SkuK7bf5pF8yUZoPTVaOFsNXn8DWuES98pJOVgA4fUODnvP2GxwDACzeF4+oLWcN7kMU0oex4yhtH2U1jtL0YQ7jkKIPzs0nzGGdmsvc3HH2Fob+96jBMQDmu04ryzhK20dZjcNUmPSUo+wcbak+NHmmbDyLXO3jHXLpmTklnqx5Tt/QID0zx6gYftgfj+wcrWR9GDsOQ/uQehyG9FFZxgFwbuapLOtUinHsOHsLD7NzDY4BML91WlnGYWgfUo/DlJj0lKNVsVcNapekycSR+BQAwJifTxrUR147Q2PQiidtpejD2HEY2ofU4zC0j8oyDs7NJyrLOjV2HADw9f//V19Z1mllGYehfUg9DlNi0lOOrqU8MLjtrfuZAICEew8Nap/XzpgY8tpK0Yex4zCmDynHYWgflWUcAOdmnsqyTqUYx9W7ph/H0205N81rbpoSk55y5O1sZ3BbVwcVAKBWVVuD2ue1MyaGvLZS9GHsOIzpQ8pxGNpHZRkHwLmZp7KsUynG4VPN9ON4ui3npnnNTVNi0lOO3g7yMaidu6MKrWs7AwDm9G5uUB957QyNwULxpK0UfRg7DkP7kHochvZRWcbBuflEZVmnxo4DAD7+/yt1Kss6rSzjMLQPqcdhSkx6ypGNlQWGBdcudbspPf1090SxV1mhmWfpLtVr5umou1+DoTEMbf/kXgtS9GHsOAztQ+pxGNJHZRkHwLmZp7KsUynG0cXPVXe/nsqyTivLOAztQ+pxmJLpI5CZyBf9SjxhlFYWWPRWi3z3Qtk4sn2JJ21B92koTQxAwfdpKE0fikL6MHYcpe2jrMZRmj7MYRxS9MG5+YQ5rFNzmZsF3aensqzTyjKO0vZRVuMwFd6c0ERupj5A22l7Cl2++K0WCPFzL/KutyeupuCVRbEFLgv0qYqlA1oXeUfO4mIY0bEuRoU0KDI7L66PDzrVxchORfdh7DiK66O8xlFUH619qmKZGYxDij44Nx/j3HyiRzN3zHgtoMg7MleWdVpZxlFcH+U1jtLgzQkrsOImQfsGRd/mH0CRE/qL8CbFTvjiYhj4vE+xdYpbHtG2+D6MHUdxfZTXOIpa/qWZjEOKPjg3H+PcfOKjbg2LTHiKiwGoOOu0soyjuD7KaxzlzbyiISIiIiojTHqIiIhIFpj0EBERkSww6SEiIiJZMGnSs3DhQjRr1gyOjo5wdHREUFAQ/vjjj0Lrr1ixAgqFQu+hUqnKMWIiIiKqqIo/vbsMeXp6Ytq0aahfvz6EEFi5ciV69eqFkydPonHjxgW2cXR0xIULF3TPFYqiryIhIiIiAkyc9PTo0UPv+VdffYWFCxfi0KFDhSY9CoUC7u7u5REeERERVSJmc05Pbm4u1q5di4yMDAQFBRVaLz09Hd7e3vDy8kKvXr3w999/F9lvVlYWNBqN3oOIiIjkx+R3ZD5z5gyCgoKQmZkJe3t7rFmzBi+++GKBdWNjY/HPP/+gWbNmSEtLwzfffIN9+/bh77//hqenZ4FtpkyZgs8//zxfeXnckTkpNRNdZ+2C5lHp2y581R/tm7rj/R+PYt8/Kcg14PW3jGyPWtXt8O7KWOyPL32yZ6kAto3qAHuVFbrN2Y3UrNJPleA6zpj1Zgt89OsJg8fxy5Ag+Hk6GjwOCwDbRxs3jhqOSmwY2R4nLt/F6F9P4qG21F1gdURrBNSpihGrDmPv5dRSt88bh7uTyuD3QmmpwI4xHWFjZWHSufm/955HbdcqJp2bzTwc8X3/Voj8/WSFn5ubPghGdo4WITN3Id2Agfz3rVZoUc/ZpHPT2gLYProjbG0sDZ6b34Y3RkiAJ+cmpJubajtrdP/PHiRnlD6KanbW2Dq6A1wclaVuWxAp7shs8qQnOzsbCQkJSEtLw2+//YYlS5Zg79698PMr/nc6Hj16hEaNGqFPnz744osvCqyTlZWFrKws3XONRgMvL68yT3oaTfoDDx8ZsGUkIiKqRBxVVjg9JdTofipF0vOskJAQ1K1bF4sXLy5R/ddffx1WVlb46aefSlS/PH57iwkPERHRE1IkPpXyt7e0Wq3enpmi5Obm4syZM/Dw8Ci+cjlJSs1kwkNERPQUTWYObmtKtm0vSyZNeiIjI7Fv3z5cvXoVZ86cQWRkJGJiYtCvXz8AQEREBCIjI3X1p06diu3bt+PKlSs4ceIE3nrrLVy7dg1Dhgwx1RDy6T53n6lDICIiMjsvLzhg6hBMe8n6rVu3EBERgcTERKjVajRr1gzbtm1Dly5dAAAJCQmwsHiSl927dw9Dhw5FUlISqlatipYtW+LgwYMlOv+nvGgyc0wdAhERkdlJyTDg7HSJmd05PWWtrM/pee6L7bhjBiuWiIjInHg6qXBgYmeD21fKc3oquk3vB5s6BCIiIrOz/r3nTR0Ckx6puTupYGvNt5WIiCiPo8pKsvv1GINb5zJw7oswJj5ERESQ7j49UuCWuYyc+yIMM8IbGdx+4av+WDe88J/jKIktI9sb3cfO0R2MGkfrWo5YM6i1UTH8MiTI5OOoZmeJvR92NCqG1RGtJRmHMX1YKoB9H75g8rn5v/eeN/k69XWxw+oBrYyKwVzm5olPuxjVx3/famXyuWkBYM/YjkaN49vwxpyb/0+quTn3taYGt3dQWuDoxyFmk/AATHrKlJO9yuC2HfzdYa8y/OK6/m084efpaFQf40LqoZ67vVHj+KRHE1Q3YpdmzyYuaF3P2eTjiHqlmVG7Zjs1cMbzfi6SjMOYPj59qSFqVbcz6dzs26oGmtZSm3ydTn25KVydDG9vTnPT2d7G4D461KuK4CauRo3jgxfqGD03J3RrgNquVYx6L55vwrkJSDs3HR0M/977+uUmZnFI62lMeoiIiEgWmPQQERGRLDDpISIiIllg0kNERESywKSHiIiIZIFJDxEREckCkx4iIiKSBSY9REREJAtMeoiIiEgWmPQQERGRLDDpISIiIllg0kNERESywKSHiIiIZIFJDxEREckCkx4iIiKSBSY9REREJAtMeoiIiEgWmPQQERGRLDDpISIiIllg0kNERESywKSHiIiIZIFJDxEREckCkx4iIiKSBSY9REREJAtMeoiIiEgWmPQQERGRLDDpISIiIllg0kNERESywKSHiIiIZIFJTxnJztFiW1yi0X0YKz0zx+gYKsM4ACBTgvfCWObwXlSWdVpZxgFIMzcrw3vBcej3YSxzmJvmRiGEEKZ68YULF2LhwoW4evUqAKBx48b47LPPEBYWVmibX3/9FZMmTcLVq1dRv359TJ8+HS+++GKJX1Oj0UCtViMtLQ2Ojo7GDqFAUVvOYvG+eKP6GNTOB8v+vGpw+/5tPHHyhganb2gM7uM5byccu5ZqcHsAeDmgBtafumlw+55NXHA1NcuocYwLqYcd528Z1UdXP1dsP3vL4PadGjijvrvaqHkhxTja1nHGwSspBrcHjJ+bfVvVQFxiusnnZo9mHvjfacM3TJVlbnaoVxUNazgZNTc/eKEOYv65Y9Q4An2ccPhqqsHtAeDtoFpYFZtgcHvOzSekmJtz32yGHgFeBrd/lhTbb5MmPf/73/9gaWmJ+vXrQwiBlStXYubMmTh58iQaN26cr/7BgwcRHByMqKgodO/eHWvWrMH06dNx4sQJNGnSpESvWdZJjxQJjxSq2Vnj7oNHpg7DaGqVFdKM/E/DzdEGyZpsiSIyjJeTCtdTM43qwxzGIQVnOyukPKj4/z1Wlrnp6aTEjdQso/pwtbfBrXTOTXNhLnOTSU8JODs7Y+bMmRg8eHC+Zb1790ZGRgY2bdqkK2vTpg0CAgKwaNGiEvVflklPdo4WDT79Q9I+iYiIKiJzTHrM5pye3NxcrF27FhkZGQgKCiqwTmxsLEJCQvTKQkNDERsbW2i/WVlZ0Gg0eo+ysir2apn1TURERMYxedJz5swZ2NvbQ6lUYvjw4Vi/fj38/PwKrJuUlAQ3Nze9Mjc3NyQlJRXaf1RUFNRqte7h5SVd1vmsaykPyqxvIiIiMo7Jkx5fX1+cOnUKhw8fxrvvvov+/fvj7NmzkvUfGRmJtLQ03eP69euS9f0sb2e7MuubiIiIjGPypMfGxgb16tVDy5YtERUVBX9/f/znP/8psK67uzuSk5P1ypKTk+Hu7l5o/0qlEo6OjnqPsvJ2kE+Z9U1ERETGMXnS8yytVousrIKvJAgKCsKuXbv0ynbs2FHoOUDlzcbKAsOCa5s6DACPr96qDNQqK6P7cHO0kSAS43g5qYzuwxzGIQVnO+PXqTmoLHPT00lpdB+u9qYfhxQ4N58wh7lZFkya9ERGRmLfvn24evUqzpw5g8jISMTExKBfv34AgIiICERGRurqjxo1Clu3bsWsWbNw/vx5TJkyBceOHcPIkSNNNYR8Il/0kyTxGdTOx6j23Zu5oZmncXu1nvN2Mqo98Pg+PcboUK+q0eN4q3Uto/vo6udqVPv6rnZGzwspxtG2jrNR7QHj52a3xq5mMTd7NPMwqn1lmZt1qxs/N99s5Wn0OAJ9nIxqDzy+T48xODefkGJumiOTJj23bt1CREQEfH190blzZxw9ehTbtm1Dly5dAAAJCQlITHxyg6a2bdtizZo1+P777+Hv74/ffvsN0dHRJb5HT3mJfNEPBye+YFQfH4b64sdBrYzqY+PI9vjutaYGt+9Qv7rR4xjQzsfk48jrY0K3ega3f61FTewaG2xUDJEv+pn8veji58q5+f/ealPL5OPI68PYuWnse2EOc7NTQ+Pn5qjO9U0+jso2Nyd1b2BUH+bGpPvyli5dWuTymJiYfGWvv/46Xn/99TKKSDo2Vsbnk1YS9KEycjdnZRkHAKis+F4AHMfTzGEcAOdmHo7jCXMYB2D83DQ3ZndODxEREVFZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0lJG0B4+M7iM1NdPoPpJS041qn52jNToGKcaRcv+h0X1cTU01qn2SBOOQ4r24eifVqPbpmTlGx8C5+QTn5hMJd9OMal9Z5mauVhgdgxTjSE2X4PvGyLlpbhRCCOPXTgWi0WigVquRlpYGR0fHMnmNDjN349pd474IVdYWyHxk+Jd6/zae+O+hGzBm5T7n7YRj11KN6AGwsVIgO8fwKHo2ccHWc3eQnWt4H+NC6mHWzksGtwcAG0uFUTF0auCM2PhUPDRinUoxjhpqFW6mGfdFaOzc7NuqBn46epNzE+YxNzvUq4oj19KMmpsfvFAH3+25YnB7APBwtEGiJtuoPlRWFsg0IhmWYm72bOaOjaeTjOhBmrm548Jdk3/fzH2zGXoEeBnVx9Ok2H4z6ZGYFAkPPaEAjPoCMhcWAIzfL0HmhHOTzJWFApBgZ5PRzDHp4eEtCaU9eMSER2Jm8LmVBDcqlQ/nJpkrc0h4zJVJk56oqCi0atUKDg4OcHV1RXh4OC5cuFBkmxUrVkChUOg9VCpVOUVctEErjpg6BCIiIiqESZOevXv3YsSIETh06BB27NiBR48eoWvXrsjIyCiynaOjIxITE3WPa9eulVPERTP2XAkiIiIqO1amfPGtW7fqPV+xYgVcXV1x/PhxBAcHF9pOoVDA3d29rMMrtRpqFRKZ+BAREZklszqnJy3t8eWOzs7ORdZLT0+Ht7c3vLy80KtXL/z999+F1s3KyoJGo9F7lJVlA1qXWd9ERERkHLNJerRaLUaPHo127dqhSZMmhdbz9fXFsmXLsGHDBqxevRparRZt27bFjRs3CqwfFRUFtVqte3h5SXcm+bPUdtbwrmZbZv3LkcLUAUjEbD5oJBnOTTJXFpVlcpYBs5nvI0aMQFxcHNauXVtkvaCgIERERCAgIAAdOnTAunXr4OLigsWLFxdYPzIyEmlpabrH9evXyyJ8nb3jO0mS+KisjVs1/dt4Gv2l/Jy3k5E9PL7fhDF6NHGBjaVxfYwLqWdUewBGx9CxgTNsjVynUoyjhtr4k/6NnZt9W9Xg3Px/5jA329eravTc/OCFOka1Bx7fp8dYKivTz82ezYw/9cLYudm9sYtZfN+YI7NIekaOHIlNmzZhz5498PT0LFVba2trNG/eHJcuFXwTJaVSCUdHR71HWds7vhMW9vY3qo8Tk7pg8POley+eFT/tJYQ1sDe4fYf61bFpZDujYvh1WJDR47j41Yt4tYWLUX1cnfYSGjkZ3n5enwCM72bcF/u5L8KMfi+uTnsJrd0tDW4/tL0PVka0NCqGyjI3Vw1qXWnm5qfdjdtASTU329W0Nrj9gLbGz80DE18w+dys72qPmA87GBWDFHPz3Bdh6NPauATs6rSX0KTos00qHJMmPUIIjBw5EuvXr8fu3btRu3btUveRm5uLM2fOwMPDowwiNJydneEf/jxOElyK72Bv+IcXAGyM/M8JkGYcVW2N33vm5KQ2rr0E45CkDycno9qrVMZfv8C5+QTn5hNqtXHjqCxz01KC40vmsk6N/b4xNya9emvEiBFYs2YNNmzYAAcHByQlPb51t1qthu3/f5FERESgZs2aiIqKAgBMnToVbdq0Qb169ZCamoqZM2fi2rVrGDJkiMnGQURERObPpEnPwoULAQAdO3bUK1++fDkGDBgAAEhISICFxZP/6O7du4ehQ4ciKSkJVatWRcuWLXHw4EH4+fmVV9hERERUAZk06SnJz37FxMToPZ8zZw7mzJlTRhERERFRZWUWJzITERERlTUmPURERCQLTHqIiIhIFhSiJCfWVCIajQZqtRppaWmS37Pn35SHaDdjt6R9EhERVUSfvFgHQ4MbSdafFNtvJj0SafDJFmTnyuqtJCIiKpICj2/4KAUptt88vCUBJjxERET5CQC1J242dRg6THqM9G/KQyY8REREhRAALiWlmzoMAEx6jBb23V5Th0BERGTWzGVbyaTHSBlZuaYOgYiIyKw90po6gseY9BipitLwX7wmIiKSA2szyTbMJIyK648POpg6BCIiIrNmLttKJj1GqulsCxtLhanDICIiMksKAPXc7U0dBgAmPZK4+NWLTHyIiIieIeV9eqTApEciF796EZ/3qG/qMIiIiMzCJy/WMauEB2DSIynnKramDoGIiMgsuDuaxyGtpzHpISIiIllg0kNERESywKSHiIiIZIFJj4SupqSaOgQiIiKzsOmvf5GdYya3Yv5/CiGErH4tU4qfpi+Ijxn9iiwREZG5GBZcG5Ev+hndjxTbb4P39KSmpmLJkiWIjIxESkoKAODEiRP4999/De2ywmLCQ0REVLDF++IRteWsqcMAYGDSc/r0aTRo0ADTp0/HN998g9TUVADAunXrEBkZKWV8Zu/U1VRTh0BERGTWftgfbxaHugxKesaOHYsBAwbgn3/+gUql0pW/+OKL2Ldvn2TBVQThi/40dQhERERmTSuAVbFXTR2GYUnP0aNHMWzYsHzlNWvWRFJSktFBERERUeVyLeWBqUMwLOlRKpXQaDT5yi9evAgXFxejgyIiIqLKxdvZztQhGJb09OzZE1OnTsWjR48AAAqFAgkJCZgwYQJeffVVSQM0d9HD25k6BCIiIrNmoQDeDvIxdRiGJT2zZs1Ceno6XF1d8fDhQ3To0AH16tWDg4MDvvrqK6ljNGsBPk6mDoGIiMisDW1fGzZWpr81oFH36Tlw4ABOnz6N9PR0tGjRAiEhIVLGViZ4nx4iIqLyY0736eHNCSX0yuw/cOKW6S/JIyIiMrXgBlWxJKKNZHt4pNh+W5W04nfffVfiTj/44AODgqnonJycgFsppg6DiIjI5EL9PMzikNbTSpz0zJkzR+/57du38eDBg8cbejy+Q7OdnR1cXV1lm/QQERGR+SpxChYfH697fPXVVwgICMC5c+eQkpKClJQUnDt3Di1atMAXX3xRlvESERERGcSg/U6TJk3C3Llz4evrqyvz9fXFnDlz8Omnn0oWHBEREZFUDEp6EhMTkZOTk688NzcXycnJRgdFREREJDWDkp7OnTtj2LBhOHHihK7s+PHjePfdd0t12XpUVBRatWoFBwcHuLq6Ijw8HBcuXCi23a+//oqGDRtCpVKhadOm2LJliyHDkFR2jhZX72SYOgwiIiIqhEFJz7Jly+Du7o7nnnsOSqUSSqUSrVu3hpubG5YsWVLifvbu3YsRI0bg0KFD2LFjBx49eoSuXbsiI6Pw5OHgwYPo06cPBg8ejJMnTyI8PBzh4eGIi4szZCiSiNpyFg0+/QNXUrJMFgMREREVzaj79Fy8eBHnz58HADRs2BANGjQwKpjbt2/D1dUVe/fuRXBwcIF1evfujYyMDGzatElX1qZNGwQEBGDRokXFvobU9+mJ2nIWi/fFG90PERFRZfJVuB/6taktWX/lep+egjRo0MDoROdpaWlpAABnZ+dC68TGxmLs2LF6ZaGhoYiOjpYsjpLKztEy4SEiIqogDEp6Bg0aVOTyZcuWlbpPrVaL0aNHo127dmjSpEmh9ZKSkuDm5qZX5ubmhqSkpALrZ2VlISvryWGngn4d3lCrYq9K1hcRERGVLYOSnnv37uk9f/ToEeLi4pCamopOnToZFMiIESMQFxeHAwcOGNS+MFFRUfj8888l7TPPtZQHZdIvERERSc+gpGf9+vX5yrRaLd59913UrVu31P2NHDkSmzZtwr59++Dp6VlkXXd393yXxScnJ8Pd3b3A+pGRkXqHwzQaDby8vEodY0G8ne0k6YeIiIjKnmQ/imFhYYGxY8fm+7mKogghMHLkSKxfvx67d+9G7drFn/AUFBSEXbt26ZXt2LEDQUFBBdZXKpVwdHTUe0jl7SAfyfoiIiKisiXpL4Fdvny5wJsWFmbEiBFYvXo11qxZAwcHByQlJSEpKQkPHz7U1YmIiEBkZKTu+ahRo7B161bMmjUL58+fx5QpU3Ds2DGMHDlSyqGUiI2VBYYFS3dmOhEREZUdgw5vPXv1lBACiYmJ2Lx5M/r371/ifhYuXAgA6Nixo1758uXLMWDAAABAQkICLCye5GZt27bFmjVr8Omnn+Ljjz9G/fr1ER0dXeTJz2Up8kU/AOBVXERERGbOoPv0vPDCC3rPLSws4OLigk6dOmHQoEGwsjLqSvgyJfV9evLcTH2AttP2SNYfERFRRVZp7tOzZw837s+ysZL0SCERERFJzKAtdadOnZCampqvXKPRGHzJOhEREVFZMijpiYmJQXZ2dr7yzMxM7N+/3+igiIiIiKRWqsNbp0+f1v199uxZvbsg5+bmYuvWrahZs6Z00RERERFJpFRJT0BAABQKBRQKRYGHsWxtbTF37lzJgiMiIiKSSqmSnvj4eAghUKdOHRw5cgQuLi66ZTY2NnB1dYWlpaXkQRIREREZq1RJj7e3N4DHPzlBREREVJGUOOnZuHEjwsLCYG1tjY0bNxZZt2fPnkYHRkRERCSlEic94eHhSEpKgqurK8LDwwutp1AokJubK0VsRERERJIpcdLz9CEtHt4iIiKiioa3ESYiIiJZMPhHsnbt2oVdu3bh1q1b+fb8LFu2zOjAiIiIiKRkUNLz+eefY+rUqXjuuefg4eEBhUIhdVxEREREkjIo6Vm0aBFWrFiBt99+W+p4iIiIiMqEQef0ZGdno23btlLHQkRERFRmDEp6hgwZgjVr1kgdCxEREVGZMejwVmZmJr7//nvs3LkTzZo1g7W1td7y2bNnSxIcERERkVQMSnpOnz6NgIAAAEBcXJzeMp7UTERERObIoKRnz549UsdBREREVKZ4c0IiIiKSBYP29Lz88ssFHsZSKBRQqVSoV68e+vbtC19fX6MDJCIiIpKCQXt61Go1du/ejRMnTkChUEChUODkyZPYvXs3cnJy8PPPP8Pf3x9//vmn1PESERERGcSgPT3u7u7o27cv5s2bBwuLx3mTVqvFqFGj4ODggLVr12L48OGYMGECDhw4IGnARERERIYwaE/P0qVLMXr0aF3CAwAWFhZ4//338f3330OhUGDkyJH5ruwiIiIiMhWDkp6cnBycP38+X/n58+eRm5sLAFCpVLx8nYiIiMyGQYe33n77bQwePBgff/wxWrVqBQA4evQovv76a0RERAAA9u7di8aNG0sXKREREZERDEp65syZAzc3N8yYMQPJyckAADc3N4wZMwYTJkwAAHTt2hXdunWTLlIiIiIiIxiU9FhaWuKTTz7BJ598Ao1GAwBwdHTUq1OrVi3joyMiIiKSiEFJz9OeTXaIiIiIzJHBSc9vv/2GX375BQkJCcjOztZbduLECaMDIyIiIpKSQVdvfffddxg4cCDc3Nxw8uRJtG7dGtWqVcOVK1cQFhYmdYxERERERjMo6VmwYAG+//57zJ07FzY2Nvjoo4+wY8cOfPDBB0hLS5M6RiIiIiKjGZT0JCQkoG3btgAAW1tb3L9/H8DjS9l/+ukn6aIjIiIikohBSY+7uztSUlIAPL5K69ChQwCA+Ph4CCGki46IiIhIIgYlPZ06dcLGjRsBAAMHDsSYMWPQpUsX9O7dGy+//LKkARIRERFJwaCk5/vvv8cnn3wCABgxYgSWL1+ORo0aYerUqVi0aFGJ+9m3bx969OiBGjVqQKFQIDo6usj6MTExul91f/qRlJRkyDCIiIhIRgxKeiwsLJCTk4MjR45g06ZNsLW1RUhICLy9vbF169YS95ORkQF/f3/Mnz+/VK9/4cIFJCYm6h6urq6lHQIRERHJjEH36dm6dSvefvtt3L17N98yhUKh+9HR4oSFhRl0iburqyucnJxK3Y6IiIjky6A9Pe+//z7eeOMNJCYmQqvV6j1KmvAYIyAgAB4eHujSpQv+/PPPIutmZWVBo9HoPYiIiEh+DEp6kpOTMXbsWLi5uUkdT5E8PDywaNEi/P777/j999/h5eWFjh07FnkH6KioKKjVat3Dy8urHCMmIiIic2HQ4a3XXnsNMTExqFu3rtTxFMnX1xe+vr66523btsXly5cxZ84crFq1qsA2kZGRGDt2rO65RqNh4kNERCRDBiU98+bNw+uvv479+/ejadOmsLa21lv+wQcfSBJcSbRu3RoHDhwodLlSqYRSqSy3eIiIiMg8GZT0/PTTT9i+fTtUKpXuMvI8CoWiXJOeU6dOwcPDo9xej4iIiComg5KeTz75BJ9//jkmTpwICwuDTgsCAKSnp+PSpUu65/Hx8Th16hScnZ1Rq1YtREZG4t9//8V///tfAMC3336L2rVro3HjxsjMzMSSJUuwe/dubN++3eAYiIiISB4MSnqys7PRu3dvoxIeADh27BheeOEF3fO8c2/69++PFStWIDExEQkJCXqvO27cOPz777+ws7NDs2bNsHPnTr0+iIiIiAqiEAb8WNaYMWPg4uKCjz/+uCxiKlMajQZqtRppaWlwdHSUrN876Zl47stdkvVHRERUkX0V7od+bWpL1p8U22+D9vTk5uZixowZ2LZtG5o1a5bvRObZs2cbFAwRERFRWTEo6Tlz5gyaN28OAIiLi9Nb9vRJzURERETmwqCkZ8+ePVLHQURERFSmjDsTmYiIiKiCYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSyYNOnZt28fevTogRo1akChUCA6OrrYNjExMWjRogWUSiXq1auHFStWlHmcREREVPGZNOnJyMiAv78/5s+fX6L68fHxeOmll/DCCy/g1KlTGD16NIYMGYJt27aVcaRERERU0VmZ8sXDwsIQFhZW4vqLFi1C7dq1MWvWLABAo0aNcODAAcyZMwehoaFlFSYRERFVAhXqnJ7Y2FiEhITolYWGhiI2NrbQNllZWdBoNHoPIiIikp8KlfQkJSXBzc1Nr8zNzQ0ajQYPHz4ssE1UVBTUarXu4eXlVR6hEhERkZmpUEmPISIjI5GWlqZ7XL9+3dQhERERkQmY9Jye0nJ3d0dycrJeWXJyMhwdHWFra1tgG6VSCaVSWR7hERERkRmrUHt6goKCsGvXLr2yHTt2ICgoyEQRERERUUVh0qQnPT0dp06dwqlTpwA8viT91KlTSEhIAPD40FRERISu/vDhw3HlyhV89NFHOH/+PBYsWIBffvkFY8aMMUX4REREVIGYNOk5duwYmjdvjubNmwMAxo4di+bNm+Ozzz4DACQmJuoSIACoXbs2Nm/ejB07dsDf3x+zZs3CkiVLeLk6ERERFcuk5/R07NgRQohClxd0t+WOHTvi5MmTZRgVERERVUYV6pweIiIiIkMx6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeiTw/bY+pQyAiIqIiMOmRQKNJfyAzR2vqMIiIiKgITHqMlJSaiYePmPAQERGZOyY9Ruo+d5+pQyAiIqISYNJjJE1mjqlDICIiohJg0mMkR5VJf8mDiIiISohJj5E2vR9s6hCIiIioBJj0GMndSQVba76NRERE5o5bawmc+yIMKiu+lUREROaMW2qJHJj4gqlDICIioiIw6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJglkkPfPnz4ePjw9UKhUCAwNx5MiRQuuuWLECCoVC76FSqcox2oI9P22PqUMgIiKiIpg86fn5558xduxYTJ48GSdOnIC/vz9CQ0Nx69atQts4OjoiMTFR97h27Vo5Rpxfo0l/IDNHa9IYiIiIqGgmT3pmz56NoUOHYuDAgfDz88OiRYtgZ2eHZcuWFdpGoVDA3d1d93BzcyvHiPUlpWbi4SMmPERERObOpElPdnY2jh8/jpCQEF2ZhYUFQkJCEBsbW2i79PR0eHt7w8vLC7169cLff/9daN2srCxoNBq9h5S6z90naX9ERERUNkya9Ny5cwe5ubn59tS4ubkhKSmpwDa+vr5YtmwZNmzYgNWrV0Or1aJt27a4ceNGgfWjoqKgVqt1Dy8vL0nHoMnMkbQ/IiIiKhsmP7xVWkFBQYiIiEBAQAA6dOiAdevWwcXFBYsXLy6wfmRkJNLS0nSP69evSxqPo8pK0v6IiIiobJg06alevTosLS2RnJysV56cnAx3d/cS9WFtbY3mzZvj0qVLBS5XKpVwdHTUe0hp0/vBkvZHREREZcOkSY+NjQ1atmyJXbt26cq0Wi127dqFoKCgEvWRm5uLM2fOwMPDo6zCLJK7kwq21hVuhxkREZHsmHxrPXbsWPzwww9YuXIlzp07h3fffRcZGRkYOHAgACAiIgKRkZG6+lOnTsX27dtx5coVnDhxAm+99RauXbuGIUOGmGoIOPdFGFRWJn8riYiIqAgmPyGld+/euH37Nj777DMkJSUhICAAW7du1Z3cnJCQAAuLJwnFvXv3MHToUCQlJaFq1apo2bIlDh48CD8/P1MNAQBwYOILeO7LXcVXJCIiIpNQCCGEqYMoTxqNBmq1GmlpaZKe33MnPZNJDxER0f/7KtwP/drUlqw/KbbfPCZDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSY9Edp66YeoQiIiIzEaOVmvqEPIxi6Rn/vz58PHxgUqlQmBgII4cOVJk/V9//RUNGzaESqVC06ZNsWXLlnKKtGA+Ezdj4qYLJo2BiIjInEzZeB5RW86aOgw9Jk96fv75Z4wdOxaTJ0/GiRMn4O/vj9DQUNy6davA+gcPHkSfPn0wePBgnDx5EuHh4QgPD0dcXFw5R/6Yz8TNJnldIiIicyYALN4Xb1aJj0IIIUwZQGBgIFq1aoV58+YBALRaLby8vPD+++9j4sSJ+er37t0bGRkZ2LRpk66sTZs2CAgIwKJFi4p9PY1GA7VajbS0NDg6OhoV+5YjN/Deur8ePxECytxso/ojIiKqLLIsbQCFAhYK4PwXYbCxMm4/ixTbbyujIjBSdnY2jh8/jsjISF2ZhYUFQkJCEBsbW2Cb2NhYjB07Vq8sNDQU0dHRBdbPyspCVlaW7rlGozE+8P+nS3gAKHOzEb3pE8n6JiIiqsjCu3+FLCsltAJYFXsVg9vXMXVIpj28defOHeTm5sLNzU2v3M3NDUlJSQW2SUpKKlX9qKgoqNVq3cPLy0ua4ImIiKhErqU8MHUIAEy8p6c8REZG6u0Z0mg0ZZL4ZFnaILz7V5L3S0REVBFlWdro/vZ2tjNhJE+YNOmpXr06LC0tkZycrFeenJwMd3f3Atu4u7uXqr5SqYRSqZQm4GcseMX/ySEuhQJZVmXzOkRERBWVhQJ4O8jH1GEAMPHhLRsbG7Rs2RK7du3SlWm1WuzatQtBQUEFtgkKCtKrDwA7duwotH5ZerG1Z7m/JhERUUUytH1to09ilorJoxg7dix++OEHrFy5EufOncO7776LjIwMDBw4EAAQERGhd6LzqFGjsHXrVsyaNQvnz5/HlClTcOzYMYwcOdIk8V+d9pJJXpeIiMicKRTAsODaiHzRz9Sh6Jj8nJ7evXvj9u3b+Oyzz5CUlISAgABs3bpVd7JyQkICLCye5GZt27bFmjVr8Omnn+Ljjz9G/fr1ER0djSZNmphqCLg67SX9y9cB+DipYKeywqNcLQQEbCwtdX8rraxgY6lAVo5Wr+xO8n0kP3UDy5oONrBTWRXZ5umy9IwHSHzmXLEGLlVgZako8rWfji3l9kOkPNW+qsoS7moVcrSixHH8e/sBng7D01EJF0dlkW2ejiMzKxPXNfp38qzhaIOqVZRFxv50n4nJ6bj31M0YLAD4VLOFhQWKXRd5y58dh7u9DextLYt9D/OWP8zOwflb+ivE09EGtkqrEs+Jh+n3ceW+/jqtVVUFGytFidaFgMCd2w+R+lT7ijo37915iLtPrVN7awU8q1WBrZVFieaEFHMzKzsLCWm5+nPTwQZV7Us+N5NupSPlmRvV+lSzhVUJ5mZeWfwNjd46raxzsyTjMXZuZjx4gJsZ+uOo72IHa0uLEseRevch7jwVg8oS8KleBbbWlgbPzbx1WtLvK3OZm4+0gIdahda1q6F/Wx+z2cOTx+T36SlvUt6nh4iIiMqHFNtv80rBiIiIiMoIkx4iIiKSBSY9REREJAtMeoiIiEgWmPQQERGRLDDpISIiIllg0kNERESywKSHiIiIZIFJDxEREcmCyX+Gorzl3YBao9GYOBIiIiIqqbzttjE/JCG7pOf+/cc/FuPl5WXiSIiIiKi07t+/D7VabVBb2f32llarxc2bN+Hg4ACFQiFp3xqNBl5eXrh+/Xql/V0vjrHykMM4OcbKQQ5jBOQxTmPGKITA/fv3UaNGDb0fIi8N2e3psbCwgKenZ5m+hqOjY6WdsHk4xspDDuPkGCsHOYwRkMc4DR2joXt48vBEZiIiIpIFJj1EREQkC0x6JKRUKjF58mQolUpTh1JmOMbKQw7j5BgrBzmMEZDHOE09RtmdyExERETyxD09REREJAtMeoiIiEgWmPQQERGRLDDpISIiIllg0iOR+fPnw8fHByqVCoGBgThy5IipQypUVFQUWrVqBQcHB7i6uiI8PBwXLlzQq9OxY0coFAq9x/Dhw/XqJCQk4KWXXoKdnR1cXV0xfvx45OTk6NWJiYlBixYtoFQqUa9ePaxYsaKshwcAmDJlSr74GzZsqFuemZmJESNGoFq1arC3t8err76K5ORkvT7MeXwA4OPjk2+MCoUCI0aMAFBx1+G+ffvQo0cP1KhRAwqFAtHR0XrLhRD47LPP4OHhAVtbW4SEhOCff/7Rq5OSkoJ+/frB0dERTk5OGDx4MNLT0/XqnD59Gu3bt4dKpYKXlxdmzJiRL5Zff/0VDRs2hEqlQtOmTbFly5YyH+OjR48wYcIENG3aFFWqVEGNGjUQERGBmzdv6vVR0PqfNm1ahRgjAAwYMCBf/N26ddOrU5HXI4ACP58KhQIzZ87U1TH39ViS7UV5fp8ava0VZLS1a9cKGxsbsWzZMvH333+LoUOHCicnJ5GcnGzq0AoUGhoqli9fLuLi4sSpU6fEiy++KGrVqiXS09N1dTp06CCGDh0qEhMTdY+0tDTd8pycHNGkSRMREhIiTp48KbZs2SKqV68uIiMjdXWuXLki7OzsxNixY8XZs2fF3LlzhaWlpdi6dWuZj3Hy5MmicePGevHfvn1bt3z48OHCy8tL7Nq1Sxw7dky0adNGtG3btsKMTwghbt26pTe+HTt2CABiz549QoiKuw63bNkiPvnkE7Fu3ToBQKxfv15v+bRp04RarRbR0dHir7/+Ej179hS1a9cWDx8+1NXp1q2b8Pf3F4cOHRL79+8X9erVE3369NEtT0tLE25ubqJfv34iLi5O/PTTT8LW1lYsXrxYV+fPP/8UlpaWYsaMGeLs2bPi008/FdbW1uLMmTNlOsbU1FQREhIifv75Z3H+/HkRGxsrWrduLVq2bKnXh7e3t5g6dare+n36M2zOYxRCiP79+4tu3brpxZ+SkqJXpyKvRyGE3tgSExPFsmXLhEKhEJcvX9bVMff1WJLtRXl9n0qxrWXSI4HWrVuLESNG6J7n5uaKGjVqiKioKBNGVXK3bt0SAMTevXt1ZR06dBCjRo0qtM2WLVuEhYWFSEpK0pUtXLhQODo6iqysLCGEEB999JFo3LixXrvevXuL0NBQaQdQgMmTJwt/f/8Cl6Wmpgpra2vx66+/6srOnTsnAIjY2FghhPmPryCjRo0SdevWFVqtVghR8dehECLfhkSr1Qp3d3cxc+ZMXVlqaqpQKpXip59+EkIIcfbsWQFAHD16VFfnjz/+EAqFQvz7779CCCEWLFggqlatqhunEEJMmDBB+Pr66p6/8cYb4qWXXtKLJzAwUAwbNqxMx1iQI0eOCADi2rVrujJvb28xZ86cQtuY+xj79+8vevXqVWibyrgee/XqJTp16qRXVpHWoxD5txfl+X0qxbaWh7eMlJ2djePHjyMkJERXZmFhgZCQEMTGxpowspJLS0sDADg7O+uV//jjj6hevTqaNGmCyMhIPHjwQLcsNjYWTZs2hZubm64sNDQUGo0Gf//9t67O0+9LXp3yel/++ecf1KhRA3Xq1EG/fv2QkJAAADh+/DgePXqkF1vDhg1Rq1YtXWwVYXxPy87OxurVqzFo0CC9H9Kt6OvwWfHx8UhKStKLSa1WIzAwUG/dOTk54bnnntPVCQkJgYWFBQ4fPqyrExwcDBsbG12d0NBQXLhwAffu3dPVMZexp6WlQaFQwMnJSa982rRpqFatGpo3b46ZM2fqHS6oCGOMiYmBq6srfH198e677+Lu3bt68Vem9ZicnIzNmzdj8ODB+ZZVpPX47PaivL5PpdrWyu4HR6V2584d5Obm6q1MAHBzc8P58+dNFFXJabVajB49Gu3atUOTJk105X379oW3tzdq1KiB06dPY8KECbhw4QLWrVsHAEhKSipwzHnLiqqj0Wjw8OFD2Nraltm4AgMDsWLFCvj6+iIxMRGff/452rdvj7i4OCQlJcHGxibfBsTNza3Y2POWFVWnPMb3rOjoaKSmpmLAgAG6soq+DguSF1dBMT0ds6urq95yKysrODs769WpXbt2vj7yllWtWrXQsef1UV4yMzMxYcIE9OnTR+8HGj/44AO0aNECzs7OOHjwICIjI5GYmIjZs2frxmHOY+zWrRteeeUV1K5dG5cvX8bHH3+MsLAwxMbGwtLSstKtx5UrV8LBwQGvvPKKXnlFWo8FbS/K6/v03r17kmxrmfTI3IgRIxAXF4cDBw7olb/zzju6v5s2bQoPDw907twZly9fRt26dcs7zFILCwvT/d2sWTMEBgbC29sbv/zyS7lvqMvD0qVLERYWhho1aujKKvo6pMcnNb/xxhsQQmDhwoV6y8aOHav7u1mzZrCxscGwYcMQFRVVIX7G4M0339T93bRpUzRr1gx169ZFTEwMOnfubMLIysayZcvQr18/qFQqvfKKtB4L215UJDy8ZaTq1avD0tIy35nqycnJcHd3N1FUJTNy5Ehs2rQJe/bsgaenZ5F1AwMDAQCXLl0CALi7uxc45rxlRdVxdHQs98TDyckJDRo0wKVLl+Du7o7s7Gykpqbmi6242POWFVWnvMd37do17Ny5E0OGDCmyXkVfh0/HVdTnzd3dHbdu3dJbnpOTg5SUFEnWb3l9rvMSnmvXrmHHjh16e3kKEhgYiJycHFy9ehVAxRjj0+rUqYPq1avrzc/KsB4BYP/+/bhw4UKxn1HAfNdjYduL8vo+lWpby6THSDY2NmjZsiV27dqlK9Nqtdi1axeCgoJMGFnhhBAYOXIk1q9fj927d+fbdVqQU6dOAQA8PDwAAEFBQThz5ozel1LeF7Ofn5+uztPvS14dU7wv6enpuHz5Mjw8PNCyZUtYW1vrxXbhwgUkJCToYqtI41u+fDlcXV3x0ksvFVmvoq9DAKhduzbc3d31YtJoNDh8+LDeuktNTcXx48d1dXbv3g2tVqtL/IKCgrBv3z48evRIV2fHjh3w9fVF1apVdXVMNfa8hOeff/7Bzp07Ua1atWLbnDp1ChYWFrpDQuY+xmfduHEDd+/e1ZufFX095lm6dClatmwJf3//Yuua23osbntRXt+nkm1rS3zKMxVq7dq1QqlUihUrVoizZ8+Kd955Rzg5OemdqW5O3n33XaFWq0VMTIzeZZIPHjwQQghx6dIlMXXqVHHs2DERHx8vNmzYIOrUqSOCg4N1feRdgti1a1dx6tQpsXXrVuHi4lLgJYjjx48X586dE/Pnzy+3S7rHjRsnYmJiRHx8vPjzzz9FSEiIqF69urh165YQ4vEllrVq1RK7d+8Wx44dE0FBQSIoKKjCjC9Pbm6uqFWrlpgwYYJeeUVeh/fv3xcnT54UJ0+eFADE7NmzxcmTJ3VXLk2bNk04OTmJDRs2iNOnT4tevXoVeMl68+bNxeHDh8WBAwdE/fr19S51Tk1NFW5ubuLtt98WcXFxYu3atcLOzi7fZcBWVlbim2++EefOnROTJ0+W7DLgosaYnZ0tevbsKTw9PcWpU6f0PqN5V7ocPHhQzJkzR5w6dUpcvnxZrF69Wri4uIiIiIgKMcb79++LDz/8UMTGxor4+Hixc+dO0aJFC1G/fn2RmZmp66Mir8c8aWlpws7OTixcuDBf+4qwHovbXghRft+nUmxrmfRIZO7cuaJWrVrCxsZGtG7dWhw6dMjUIRUKQIGP5cuXCyGESEhIEMHBwcLZ2VkolUpRr149MX78eL17vAghxNWrV0VYWJiwtbUV1atXF+PGjROPHj3Sq7Nnzx4REBAgbGxsRJ06dXSvUdZ69+4tPDw8hI2NjahZs6bo3bu3uHTpkm75w4cPxXvvvSeqVq0q7OzsxMsvvywSExP1+jDn8eXZtm2bACAuXLigV16R1+GePXsKnJ/9+/cXQjy+bH3SpEnCzc1NKJVK0blz53zjv3v3rujTp4+wt7cXjo6OYuDAgeL+/ft6df766y/x/PPPC6VSKWrWrCmmTZuWL5ZffvlFNGjQQNjY2IjGjRuLzZs3l/kY4+PjC/2M5t2D6fjx4yIwMFCo1WqhUqlEo0aNxNdff62XMJjzGB88eCC6du0qXFxchLW1tfD29hZDhw7Nt/GqyOsxz+LFi4Wtra1ITU3N174irMfithdClO/3qbHbWsX/D4qIiIioUuM5PURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiozAwYMQHh4uKnDKNCKFSvy/TK0ITp27IjRo0cb3Q8RlT0mPUQkS71798bFixdNHQYRlSMrUwdARGQKtra2JvmleCIyHe7pIaJCabVazJgxA/Xq1YNSqUStWrXw1Vdf6ZafOXMGnTp1gq2tLapVq4Z33nkH6enphfbn4+ODb7/9Vq8sICAAU6ZM0T1XKBRYvHgxunfvDjs7OzRq1AixsbG4dOkSOnbsiCpVqqBt27a4fPmyrs2UKVMQEBCAVatWwcfHB2q1Gm+++Sbu379faCzPHt4qSR8ZGRmIiIiAvb09PDw8MGvWrHz9ZmVl4cMPP0TNmjVRpUoVBAYGIiYmBgCQmZmJxo0b45133tHVv3z5MhwcHLBs2bJCYyUiaTDpIaJCRUZGYtq0aZg0aRLOnj2LNWvWwM3NDcDjBCA0NBRVq1bF0aNH8euvv2Lnzp0YOXKk0a/7xRdfICIiAqdOnULDhg3Rt29fDBs2DJGRkTh27BiEEPle5/Lly4iOjsamTZuwadMm7N27F9OmTSvV6xbXx/jx47F3715s2LAB27dvR0xMDE6cOKHXx8iRIxEbG4u1a9fi9OnTeP3119GtWzf8888/UKlU+PHHH7Fy5Ups2LABubm5eOutt9ClSxcMGjTI8DeMiEqmVD9PSkSyodFohFKpFD/88EOBy7///ntRtWpVkZ6erivbvHmzsLCw0P1adv/+/UWvXr10y729vcWcOXP0+vH39xeTJ0/WPQcgPv30U93z2NhYAUAsXbpUV/bTTz8JlUqlez558mRhZ2cnNBqNrmz8+PEiMDCw0PEtX75cqNXqEvdx//59YWNjI3755Rfd8rt37wpbW1sxatQoIYQQ165dE5aWluLff//Ve63OnTuLyMhI3fMZM2aI6tWri5EjRwoPDw9x586dQuMkIunwnB4iKtC5c+eQlZWFzp07F7rc398fVapU0ZW1a9cOWq0WFy5c0O0RMkSzZs10f+f107RpU72yzMxMaDQaODo6Anh86MzBwUFXx8PDA7du3SrV6xbVx+XLl5GdnY3AwEDdcmdnZ/j6+uqenzlzBrm5uWjQoIFev1lZWahWrZru+bhx4xAdHY158+bhjz/+0FtGRGWHSQ8RFagsTvK1sLCAEEKv7NGjR/nqWVtb6/5WKBSFlmm12gLb5NV5enlJGNtHeno6LC0tcfz4cVhaWuots7e31/1969YtXLx4EZaWlvjnn3/QrVu3UsVJRIbhOT1EVKD69evD1tYWu3btKnB5o0aN8NdffyEjI0NX9ueff8LCwkJv78fTXFxckJiYqHuu0WgQHx8vbeBlpG7durC2tsbhw4d1Zffu3dO77L158+bIzc3FrVu3UK9ePb2Hu7u7rt6gQYPQtGlTrFy5EhMmTMC5c+fKdSxEcsWkh4gKpFKpMGHCBHz00Uf473//i8uXL+PQoUNYunQpAKBfv35QqVTo378/4uLisGfPHrz//vt4++23Cz201alTJ6xatQr79+/HmTNn0L9//3x7RMyVvb09Bg8ejPHjx2P37t2Ii4vDgAEDYGHx5Gu0QYMG6NevHyIiIrBu3TrEx8fjyJEjiIqKwubNmwEA8+fPR2xsLFauXIl+/fohPDwc/fr1Q3Z2tqmGRiQbPLxFRIWaNGkSrKys8Nlnn+HmzZvw8PDA8OHDAQB2dnbYtm0bRo0ahVatWsHOzg6vvvoqZs+eXWh/kZGRiI+PR/fu3aFWq/HFF19UmD09ADBz5kykp6ejR48ecHBwwLhx45CWlqZXZ/ny5fjyyy8xbtw4/Pvvv6hevTratGmD7t274/z58xg/fjyWLl0KLy8vAMCCBQvQrFkzTJo0CdOnTzfFsIhkQyGePcBOREREVAnx8BYRERHJApMeIiIikgUmPURERCQLTHqIiIhIFpj0EBERkSww6SEiIiJZYNJDREREssCkh4iIiGSBSQ8RERHJApMeIiIikgUmPURERCQLTHqIiIhIFv4PM/ZntwkLsGIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F_3_matrix 1-norm (max abs col sum): 3.666666666666667\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": [
      "F_3_matrix inf-norm (max abs row sum): 7632.000000000001\n"
     ]
    }
   ],
   "source": [
    "# A.sum(axis=0) # numpy column sum\n",
    "# A.sum(axis=1) # numpy row sum\n",
    "\n",
    "\n",
    "F_matrix_var_names = [\"F_1_matrix\", \"F_2_matrix\", \"F_3_matrix\"]\n",
    "\n",
    "for F_matrix_name in F_matrix_var_names:\n",
    "    F_matrix = locals()[F_matrix_name]\n",
    "    (num_rows, num_cols) = F_matrix.shape\n",
    "    print(f\"{F_matrix_name} is size {num_rows}x{num_cols}, rank {np.linalg.matrix_rank(F_matrix_name)}\")\n",
    "\n",
    "\n",
    "\n",
    "print(\"\\n\\n\")\n",
    "for F_matrix_name in F_matrix_var_names:\n",
    "    F_matrix = locals()[F_matrix_name]\n",
    "\n",
    "    (num_rows, num_cols) = F_matrix.shape\n",
    "\n",
    "    # column sum\n",
    "    F_abs_col_sum = np.abs(F_matrix).sum(axis=0)\n",
    "    plt.stem(F_abs_col_sum)\n",
    "    plt.title(f\"{F_matrix_name} ({num_rows}x{num_cols}) abs col sum\")\n",
    "    plt.xlabel(\"column index\")\n",
    "    plt.ylabel(\"magnitude\")\n",
    "    plt.show()\n",
    "    print(f\"{F_matrix_name} 1-norm (max abs col sum): {np.max(F_abs_col_sum)}\")\n",
    "\n",
    "    # row sum\n",
    "    F_abs_row_sum = np.abs(F_matrix).sum(axis=1)\n",
    "    plt.stem(F_abs_row_sum)\n",
    "    plt.title(f\"{F_matrix_name} ({num_rows}x{num_cols}) abs row sum\")\n",
    "    plt.xlabel(\"row index\")\n",
    "    plt.ylabel(\"magnitude\")\n",
    "    plt.show()\n",
    "    print(f\"{F_matrix_name} inf-norm (max abs row sum): {np.max(F_abs_row_sum)}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A is 20439x20439\n"
     ]
    }
   ],
   "source": [
    "# Construct the A matrix\n",
    "\n",
    "A_dim = nQ + (nQ)**2 + (nQ)**3\n",
    "\n",
    "print(f\"A is {A_dim}x{A_dim}\")\n",
    "\n",
    "A = np.zeros((A_dim,A_dim))\n",
    "I = np.zeros((nQ,nQ))\n",
    "\n",
    "\n",
    "#S matrix in this case (only one node) is zero.\n",
    "\n",
    "\n",
    "\n",
    "rows = slice(0,nQ)\n",
    "cols = slice(0,nQ)\n",
    "A[rows, cols] = F_1_matrix\n",
    "\n",
    "rows = slice(0,nQ)\n",
    "cols = slice(nQ, nQ + (nQ)**2)\n",
    "A[rows, cols] = F_2_matrix\n",
    "\n",
    "rows = slice(0,nQ)\n",
    "cols = slice(nQ + (nQ)**2, nQ + (nQ)**2 + (nQ)**3)\n",
    "A[rows, cols] = F_3_matrix\n",
    "\n",
    "\n",
    "# F_1^[2]\n",
    "F_1_2 = np.kron(I,F_1_matrix) + np.kron(F_1_matrix,I)\n",
    "rows = slice(nQ, nQ + (nQ)**2)\n",
    "cols = slice(nQ, nQ + (nQ)**2)\n",
    "A[rows, cols] = F_1_2\n",
    "\n",
    "\n",
    "# F_2^[2]\n",
    "F_2_2 = np.kron(I,F_2_matrix) + np.kron(F_2_matrix,I)\n",
    "rows = slice(nQ, nQ + (nQ)**2)\n",
    "cols = slice(nQ + (nQ)**2, nQ + (nQ)**2 + (nQ)**3)\n",
    "A[rows, cols] = F_2_2\n",
    "\n",
    "\n",
    "# F_1^[3]\n",
    "F_1_3 = np.kron(I,np.kron(I,F_1_matrix))\n",
    "F_1_3 += np.kron(I,np.kron(I,F_1_matrix))\n",
    "F_1_3 += np.kron(I,np.kron(F_1_matrix,I))\n",
    "rows = slice(nQ + (nQ)**2, nQ + (nQ)**2 + (nQ)**3)\n",
    "cols = slice(nQ + (nQ)**2, nQ + (nQ)**2 + (nQ)**3)\n",
    "A[rows, cols] = F_1_3\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after writing the A matrix to the `A_matrix.npz` file, you may run the `example_A_norm.py` script for some empirical results.\n",
      "running some norm calculations directly in a default-sized Jupyter notebook instance crashes.\n"
     ]
    }
   ],
   "source": [
    "\n",
    "np.savez_compressed(\"F_2_2_matrix.npz\",F_2_2=F_2_2)\n",
    "np.savez_compressed(\"F_1_2_matrix.npz\",F_1_2=F_1_2)\n",
    "np.savez_compressed(\"F_1_3_matrix.npz\",F_1_3=F_1_3)\n",
    "\n",
    "np.savez_compressed(\"A_matrix.npz\", A=A)\n",
    "\n",
    "print(\"after writing the A matrix to the `A_matrix.npz` file, you may run the `example_A_norm.py` script for some empirical results.\")\n",
    "print(\"running some norm calculations directly in a default-sized Jupyter notebook instance crashes.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F_1_inf_norm: 9.0/tau\n",
      "F_1_1norm: 4.0/tau\n",
      "\n",
      "F_2_inf_norm: 566.0/tau\n",
      "F_2_1norm: 8.0/tau\n",
      "\n",
      "F_3_inf_norm: 7633.0/tau\n",
      "F_3_1norm: 4.0/tau\n",
      "\n",
      "A 1-norm bound: 6 + 32.0/tau\n",
      "\n",
      "A inf-norm bound: 2 + 8208.0/tau\n",
      "\n",
      "A spectral norm bound: ((2 + 8208.0/tau)*(6 + 32.0/tau))**0.5\n",
      "\n",
      "\n",
      "Recall that 0.5 < tau <= 1.0.\n",
      "if tau=0.5, then the upper bound on ||A||_2 is: 1072.03544717514\n",
      "if tau=1.0, then the upper bound on ||A||_2 is: 558.551698591992\n"
     ]
    }
   ],
   "source": [
    "# Establishing an upper bound on the spectral norm of A per \"Appendix: Bounding the spectral norm of A\" \n",
    "\n",
    "tau = sympy.Symbol(\"tau\")\n",
    "\n",
    "\n",
    "F_1_1norm =  (1/tau)*np.ceil(np.linalg.norm(F_1_matrix, ord=1))\n",
    "F_2_1norm =  (1/tau)*np.ceil(np.linalg.norm(F_2_matrix, ord=1))\n",
    "F_3_1norm =  (1/tau)*np.ceil(np.linalg.norm(F_3_matrix, ord=1))\n",
    "\n",
    "F_1_inf_norm = (1/tau)*np.ceil(np.linalg.norm(F_1_matrix, ord=np.inf))\n",
    "F_2_inf_norm =  (1/tau)*np.ceil(np.linalg.norm(F_2_matrix, ord=np.inf))\n",
    "F_3_inf_norm =  (1/tau)*np.ceil(np.linalg.norm(F_3_matrix, ord=np.inf))\n",
    "\n",
    "\n",
    "\n",
    "print(f\"F_1_inf_norm: {F_1_inf_norm}\")\n",
    "print(f\"F_1_1norm: {F_1_1norm}\\n\")\n",
    "\n",
    "print(f\"F_2_inf_norm: {F_2_inf_norm}\")\n",
    "print(f\"F_2_1norm: {F_2_1norm}\\n\")\n",
    "\n",
    "print(f\"F_3_inf_norm: {F_3_inf_norm}\")\n",
    "print(f\"F_3_1norm: {F_3_1norm}\\n\")\n",
    "\n",
    "\n",
    "A_1norm_bound = F_3_1norm + 2*(F_2_1norm) + (6+3*(F_1_1norm))\n",
    "print(f\"A 1-norm bound: {A_1norm_bound}\\n\")\n",
    "\n",
    "\n",
    "A_inf_norm_bound = 2 + F_1_inf_norm + F_2_inf_norm + F_3_inf_norm\n",
    "# 2 is from the inf norm of the S matrix\n",
    "print(f\"A inf-norm bound: {A_inf_norm_bound}\\n\")\n",
    "\n",
    "\n",
    "A_spec_norm_bound = (A_1norm_bound*A_inf_norm_bound)**(1/2)\n",
    "print(f\"A spectral norm bound: {A_spec_norm_bound}\\n\\n\")\n",
    "\n",
    "print(\"Recall that 0.5 < tau <= 1.0.\")\n",
    "tau_vals = [0.5, 1.0]\n",
    "for tau_val in tau_vals:\n",
    "    print(f\"if tau={tau_val}, then the upper bound on ||A||_2 is: {A_spec_norm_bound.evalf(subs={tau: tau_val})}\")\n",
    "\n"
   ]
  }
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