Part2-2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d644d434",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2023-02-11 18:54:19.137732: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  SSE4.1 SSE4.2\n",
      "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import torch\n",
    "import torchvision as tv\n",
    "from torchvision import transforms, datasets\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "695c2eb6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create random data between (-10, 10) and determine groundtruth\n",
    "sim_ip = 20 * torch.rand((1000, 1)) - 10\n",
    "ground_Truth = np.cos(sim_ip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9ebd0c55",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the number of parameters in a neural network\n",
    "def calcParams(inputModel):\n",
    "    val = sum(params.numel() for params in inputModel.parameters() if params.requires_grad)\n",
    "    return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "961a7cc4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up NN for cos(x) training - 2 Hidden Layers, 32 parameters - Shallow Network\n",
    "class Forward_nn(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(1, 3)\n",
    "        self.fc2 = nn.Linear(3, 5)\n",
    "        self.fc3 = nn.Linear(5, 1)\n",
    "\n",
    "    def forward(self, val):\n",
    "        val = F.relu(self.fc1(val))\n",
    "        val = F.relu(self.fc2(val))\n",
    "        val = self.fc3(val)\n",
    "        return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f8fef520",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up necessary auxilaries for neural net training\n",
    "optimal_network = Forward_nn()\n",
    "Cost_func = nn.MSELoss()\n",
    "opt = optim.Adam(optimal_network.parameters(), lr=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f7dbe074",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training of network to visualize optimization\n",
    "training_num = 8\n",
    "EPOCHS = 30 # Must be divisible by 3 for how epoch_num is used in training\n",
    "epoch_num = round(EPOCHS / 3)\n",
    "layer1_connections = 3\n",
    "layer2_connections = 15\n",
    "layer3_Connections = 5\n",
    "tot_Model_Connections = layer1_connections + layer2_connections + layer3_Connections\n",
    "\n",
    "# Number of training iterations for visualization\n",
    "cost_List = []\n",
    "counter = 0\n",
    "layer2_weights_tensor = torch.zeros((training_num * epoch_num, layer2_connections))\n",
    "whole_Model_Weights_Tensor = torch.zeros((training_num * epoch_num, tot_Model_Connections))\n",
    "costTensor = torch.zeros((training_num * epoch_num, 1))\n",
    "for trainingIndex in range(training_num): \n",
    "    \n",
    "    # Training of individual series, reset model on every series\n",
    "    optimal_network = Forward_nn()\n",
    "    Cost_func = nn.MSELoss()\n",
    "    opt = optim.Adam(optimal_network.parameters(), lr=0.001)\n",
    "    for epoch_Index in range(EPOCHS):\n",
    "        optimal_network.zero_grad()\n",
    "        output = optimal_network(sim_ip)\n",
    "        cost = Cost_func(output, ground_Truth)\n",
    "        cost.backward()\n",
    "        opt.step()\n",
    "\n",
    "        # Every 3 epochs, collect weights and cost\n",
    "        if epoch_Index % 3 == 0:\n",
    "            # Gather weights of the model\n",
    "            layer1Weights = torch.reshape(torch.flatten(optimal_network.fc1.weight), (1, layer1_connections))\n",
    "            layer2Weights = torch.reshape(torch.flatten(optimal_network.fc2.weight), (1, layer2_connections))\n",
    "            layer3Weights = torch.reshape(torch.flatten(optimal_network.fc3.weight), (1, layer3_Connections))\n",
    "            # Combine weights for whole model\n",
    "            temp = torch.cat((layer2Weights, layer1Weights), dim=1)\n",
    "            whole_Model_Weights = torch.cat((temp, layer3Weights), dim=1)\n",
    "            # Save weights and cost for later\n",
    "            whole_Model_Weights_Tensor[counter] = whole_Model_Weights\n",
    "            layer2_weights_tensor[counter] = layer2Weights\n",
    "            costTensor[counter] = cost\n",
    "            counter += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2c42fb4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implementation of PCA for dimention reduction of weights\n",
    "def pca1(input_arr, dim):\n",
    "    m, n = input_arr.shape\n",
    "    \n",
    "    # Calculate means and Normalize by subtracting mean from each column\n",
    "    means_of_Inputs = np.array([np.mean(input_arr[:, index]) for index in range(n)])\n",
    "    input_Normalized = input_arr - means_of_Inputs\n",
    "    \n",
    "    # Calculate egn_val and egn_vec\n",
    "    # X'X \n",
    "    mtr = np.dot(np.transpose(input_Normalized),input_Normalized)\n",
    "    egn_val, egn_vec = np.linalg.eig(mtr)\n",
    "    pairs = [(np.abs(egn_val[index]), egn_vec[:, index]) for index in range(n)]\n",
    "\n",
    "    # Sort pairs and return dimensions requested\n",
    "    pairs.sort(key=lambda x: x[0], reverse=True)\n",
    "    feat_From_Data = np.array([value[1] for value in pairs[:dim]])\n",
    "    reduced_dim_data = np.dot(input_Normalized, np.transpose(feat_From_Data))\n",
    "    return reduced_dim_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "635f522b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(80, 15)\n"
     ]
    }
   ],
   "source": [
    "# Reduce dimensions using PCA\n",
    "layer2_reduced = layer2_weights_tensor.detach().cpu().numpy()\n",
    "print(layer2_reduced.shape)\n",
    "whole_Model_Reduced = whole_Model_Weights_Tensor.detach().cpu().numpy()\n",
    "cost_Vector = costTensor.detach().cpu().numpy()\n",
    "layer2_reduced = pca1(layer2_reduced, 2)\n",
    "whole_Model_Reduced = pca1(whole_Model_Reduced, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5548c828",
   "metadata": {},
   "outputs": [
    {
     "data": {
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BQkICzz33HBEREYWe/qhfvz7dunVj4cKFXH/99VxzzTUe2/v378/MmTPp0aMHf//732nZsiX+/v78+eefLF26lFtuuYVbb731nI7jjjvuYOHChTz99NNUqVKFVatWubeFhIRw9dVXF7pfSkoKnTp14u6776ZBgwZUqFCBtWvXsmjRIm677bazvm5ISAjNmzfniy++wMfHxz3/J0+HDh3cN+vLH4Datm3L/fffzz333MO6deto37495cqVIzExkR9//JEmTZrw0EMPFfqa3bp1o23btjz++OOkpqYSHR1NXFwc06dPB6w5Weci7349X3/9NREREVSoUIGoqChatWpFr169aNq0KZUqVWLr1q18/PHHxMTEEBwcXGR7devW5eOPP2bAgAFcd911PPbYY0RFRbF//34+/PBDFi5cyKhRo+jXr1+BfdetW8d9993HnXfeSUJCAk8//TRXXHEFDz/8sEd/P//8c95++22io6Px8fGhRYsW53TspZWamkqPHj0ICgpi1KhRBe6ofvXVVxMSEkKvXr2YNm0aDRo0oGnTpqxfv55XXnmlwMhN3bp1CQoKYubMmTRs2JDy5csTGRlJZGRkgdeOiori/vvv580338THx4fu3bu7rwKrUaMGjz76qFePXWzmEk/CFrng8q6KKWrZuXOnMcaYl156ydSuXds4nU7TsGFD89577xW4KiW/adOmGcDMnj270O1ZWVnmn//8p7nmmmtMYGCgKV++vGnQoIF54IEHzPbt2931atWqZXr27Fni4ynuWDp06FDkfunp6ebBBx80TZs2NSEhISYoKMhERUWZcePGmePHj5fotZ944gkDmBYtWhTY9sUXXxjABAQEFNrehx9+aFq1amXKlStngoKCTN26dc2gQYPMunXr3HXOvArMGOsKtHvuucdUrFjRBAcHm86dO5tVq1YZwPz73/9218v7rA4ePOixf97nn/c5G2PMxo0bTdu2bU1wcLDH+zZ69GjTokULU6lSJeN0Os2VV15pHn30UXPo0KESvT9btmwxgwcPNtWrVzf+/v6mcuXKplu3bmb+/PkF6ub169tvvzWxsbGmYsWKJigoyPTo0cPj5yPvPbjjjjtMxYoVjcPh8PiZpIirwM686rGo92fw4MGmXLlyHmX529y5c2exP3NLly41xhhz9OhRM3ToUFOtWjUTHBxsrr/+erNixQrToUOHAj+Xs2bNMg0aNDD+/v4er1XY71tOTo6ZNGmSqV+/vvH39zehoaFm4MCBJiEhwaNehw4dTKNGjQq8z4X9TIkUxmHMGTcOEZFC3X777axatYpdu3bh7+9/qbtjK5988gkDBgzgp59+ok2bNpe6O+dk2rRp3HPPPaxdu/aijeaISNF0CkykGBkZGWzYsIE1a9Ywb948XnvtNYUfL5s1axZ79+6lSZMm+Pj4sGrVKl555RXat2//lw0/InL5UQASKUZiYiJt2rQhJCSEBx54gEceeeRSd6nMq1ChArNnz+b555/n+PHjREREMGTIEJ5//vlL3TURKUN0CkxERERsR5fBi4iIiO0oAImIiIjtKACJiIiI7dhyEnRubi779u2jQoUKpX4kgYiIiFwaxhjS0tKIjIw85xuj5rFlANq3b1+BBxSKiIjIX0NCQkKBu46Xli0DUN6DKRMSEggJCbnEvREREZGSSE1NpUaNGgUeMH0ubBmA8k57hYSEKACJiIj8xVyI6SuaBC0iIiK2owAkIiIitqMAJCIiIrajACQiIiK2Y8tJ0CLy17F2ylpWvrKStMQ0qjWqRtfXu1KrXa0i6/8y8xdWvrySw9sPE+gKpF63enT+Z2eCqwQDkJOVw48Tf+Tnj34mdW8qoVGh3DTpJup1q3exDklELgMaARKRy9bmOZtZ+MhCMtIywEDKnyl83OVjUvakFFp/z497mBc7jxOHToCBnMwctn6xlS8GfeGu8/0z37Pu7XWENgzFGeLk4K8HmdljJqvfXH2RjkpELgcKQCJSqClrpxD6ciiOCQ58JvgQNTmKFbtXFFk/IzuDJxc/ieslF44JDhwTHFR9pSofxn8IwHvr36Pd1HZUmlSJSpMq0WRKExwTHPSZ3afINr9/+nuMMR5lOek5/PjSj4XW3zRrE3hWJycjhz+++8O9/vP0n/EN8AUD1/3tOnKzcwmqFMT/Fv3vLO+IiJQlOgUmIh6mrJ3Ck0ue5FjmMQCqBFUhOjKapTuX0nVGV34b/hs1XTXd9TOyM/jH0n/w2qrXyM7NBqBCQAUGXTOIa8OvpUFoA7Yc2MJzPzzH8azjJKcn81CLh/ho40f4Onw5mXWy0H7kZOZwdMfRQrf99sVv9JzSs0D5sUSrz9npVj+MMdb3+W4Zkn4kHZNrSE9OZ/vC7TgrOnH4Oji45WDp3ywR+ctSABIRpqydwj+W/oPDJw97lFevUJ39x/ezYvcKarpqcjT9KKOXjGbW5llFtjXppkl8EP8Bb619q8A2X4cvFZ0VWfS/Rbze7XX+tuBvHDxRePBI25dW5GscO3Cs2OM5ecQKVXlBKH8Acvg4rLFvH/AP8ifzWCYm2+Dw03MBRexEp8BEbGzK2ikEPh/I3xb8zR1+fPL9s3DwxEFqumoS5B+Er8OXIyePFBl+KgdW5oryV/Dkkif5/fDvhdYJ8A0gOSMZH4cP/Rv3J9fkEuAb4FEndV0qG2/YSNKyJHdZva71CK4azMnDp0aLcgo/noy0jMI35MKURlMACKkeQk56DhnJGWSdyMJkW+fMTLY5HZhEpMxTABKxqTmb5/DIwkfIyMnA38efAB8riOSS667j9HNSMbAigX6BpGQUPvG4cmBlAnwCOJJ+hL3H9gIQ4gzBz2ENMNeoYD142M/hR4+regBQLqAco5eMJtg/mKrBVT3aS3glgeSlySRNtwJQYJVANs/eTHZ6Nj6+p//JKmwi9JHtR4o83mP7rVGjrPQscICPvw8129XE1+nrrvNZ/8+K3F9EyhYFIBGbem3Va/g4rH8CcnJz3PN38gvwDeDwycNk5mQWOVfnSPoRMnMzAXDgwMfhQ3ZONlFVogBISEsAoGu9rny17St8Hb5sP7ydWZtn0bF2R3x9fEnfnU7a+jTSNqRx6MtDACT/kAxAxtGMAhOhgUInQhc5AgTkZuWSkZbBiYMnCKwUiF+gH84KTgLKnx6BSt6dXOT+XjdlCtSpA4GBEB0NK4qecA7AW29Bw4YQFARRUTB9uuf2zz+HFi2gYkUoVw6uvRY+/thbvRf5y9EcIBEbyszJZP2+9eQY61xS/lGf/DKyrcvPcUCuKbxOfgZDk2pN+GX/L2w5tMVj2/zt893fn8w+SUZ2Bt/8/g0A5baWY/qb07ni6BXuOo4ca06OyT11iirHkJt9ug+/ffEbTpeTtL1p3Dr9Vned4hzdcZScjBxyMqzj3r5gu8f2K2+68qzH6BVz5sAjj0ClSmAM/PkndOkC27ZBzZoF67/9NowaBdWqWesHDsDQoeDrCwMGWGWVK0PTpnD4MCQmwu7dMHiwFYh6975ohyZyudIIkIgNHTpxyB1+iuLAQUZOBpm5mQT4BpCdm43T18mVFa9kXIdxdKjVwV3Xl9OnkTbt31Roez744Dg1G9nX4cvPD/3MzVE306lOJ95/532qpVbzqB+A59yg9OR0dxgCayL09m+2s+PbHSU7aCC0QSid/9m5yO3F3WDRa6ZMgbvvhtxcK6xERED79pCRAS+9VLD+zJkwYgSkp8OePVZgio6GChWs8jx798Inn0CvXlZbDRtaAen55y/esYlcxhSARGxk3b51XPfudbR6r9VZ6xoMmTmZpGakcviEdRrMx+HD94O/JyM7g0MnDlExsCIAOeS4w40580Y8WJfFj75+tPuUW6XASoQGh+L0dRLkF0SdA3Xwz/H32MeJ02Pd4esgqHLQ6YJC8lveHKHgqsH4BPjgE3j6n7irel6FX6AfbR5vg1+Q5+C3w9fq+8IRC8/6vlxQQ4fC3/5mhR+n0xr12bcP5s+HkBD45pvTdYcMAYcDBg6E7HynK3NzYc0a8PODI0esOnn1MjJg8mRrZMlx6iq3Eycu6iGKXK50CkzERt5a8xbrEteVer+MnAxqu2rTtmZben7Sk5PZJzmeeRyX00VKegoGg6+Pb6HziADSMtP4MP5D96jToZOHiHg1AoCoKlE0nNGQrQO3euzjgw9++JHNqXv65Bh8/HysS9qLONNVsU5FTh456Q5CuemnT5m1HtkagJ9e/onsk1abD/7yIB+0/gCArJNZpOxOweQa61J5b2vTBuLiTq9HRsJPP1mnvI4eteYCHbLmQ1GvHuwoYqTrxhut+UIHT91OICLCOuWV39Gj1muFh58+RSZicxoBEinjdifv5ptt3/CP7//BtJ+nlXp/l9NFnYp1KBdQjrg/49idspsTmSe4vub1BPmdHpHJH36GXzeca8KuAayrxCoFViLpeFKBtjvU6sBvw38jbEBYoa8dSWSBMr9AP4/7+uTXcnhLd3jJf7rML9CPK1pa84vWTF7jLn+n6Ttkncgi60QW/sHWCFR2hpcvhZ8yxZq4nD/8AOzcCVWqWHN0AgOtkZrsbGsUp3NnKF++8PYWLYLjx0+v54UfX19rVCmPMdYpttatL+jhiPxVKQCJlHG1/12b3rN789yK50q9b3n/8uSYHE5knWB3ym4OHj/I1aFXk5qRytytc/nt8G/uU15XV72aabdMo3yA9Yc6715AR9KPcDT9KD4OH+pXqc+vD/+KGWcw4wzLhiwr9vUrU9ljPahKEPV71XePAEVER+Ab4Mu8QfMAuHbItXR9vStBlYM8JkTf9MpN7u/v+uqu0w3mC1JZx7OA4m/AeN7mzIHhw635O2fy8YHMTCukZGZadfz84PbbYdq00+suV8leKyfHCk/t2sHNN0PLluDvD/fdd0EPSeSvSgFIpIybcesM99yb0nD6OsnKzcLX4UvSqCTGth9Ljslhzb41nMi25pEE+QUxvsN4zDjDloe3MPjawXw78FuW/LGEk9knqRxUmRdueIHssdnk/COHbcO30bBqwxL3If9EaD/8OPK/I+xevhuw5u30mdaHQFegx0ToVo+04t6V97rXfZ2+tLi/hXs9tEEoAxYOwMfPxz3qkzcHqMIVFXDVKGHAOBdPP22NxBTG19c6VXXs1F2uMzOty9cXLbK+nzMHFiw4PZcHrDlEVapY3wedGo278owr2f75T2sOUESENVl6505r3pCIzWkOkEgZN6DpABpWbUj0u9Elqu/n8KNSYCXi7oujbuW67vIn2j7BE22fOOv+MTVi2Dp861nrlcSZE6HzK1etXInaaHRnI+vhp6f4BfpRr1s9hvwwhP8++l/2rt6Lj68PfuX9qFy3skfdCyozs+h5PABZWVa4ycy0Rm9ycyE42BoRKl8e+vWzyvN79FHrNNlHH8HJk6fbya9Nm9OBxxhrFKmoECZiIwpAIgJYl6ZXDqzMyqErqeGqgdOv6PBxsfjgQyCBpHPGKSMHNOjToPidT02Wbvtk2wKbVkxcQWSLSG7/5HamtpuKw9dB6p+pNI1teuE6f6Znnz17HWMgNdUKQn5+VpgxBtJOnZYLCLACUp5mzTz39/GBhARr5ChvXpDDYY0uBQRYo0QdO1rrIjanACRiA9XKVaNqcFWOnDzivhLLgQODwYGD5UOWc13kdTgcjssi+ORXhzpsxXNEyS/Qr9Bgk5/D4cBVx0W1xtUKbMtIzeCroV9xfP9xcrJyKB9enhsn3kjtjrUvZNctu3dbd2V+4YXS7TdzpnXjwjxNm0KnTvDvf58uq1rVumw+T95IT/5J0dnZVggyxhpFKm0/RMooBSARG6geUp2ERxMwxpCRnUH5gPJk5WZhjCErN4uQwJBL3UXrUvhBWznzptTVqEaWI4ukKkmcTD1JSPUQuv6rKxVrVQSsidDJu5ILtOcb4Mv1Y64v9LVaPNCCn176yb1+LPEY343+jv8t/B9Dlg25QEeEdVn79YX3oUi1a1untBYuPH06y+mEn3+G11/3rLtvn3XFWJcucP/9VsAZNMi6U7SPjzXis2oVTJpkjSK99daFOCqRMsFhCnvIThmXmpqKy+UiJSWFkJBL/w+/iFj+fPNP/jfifwXK671Rj+qPVL8EPToPu3dbYaY0Jk+2bowYEwObN1sjN2lpVsg5eBAaN7bazXPixOnJz++/b+37/vtWCHI4oEYN+O476z5CImXAhfz7ravAROSyEVQvqFTll62ffip9+Bk2zHoGWOPGVvjJe2xF3lVfPXpY4Sfg1JVxQ4acDj+rV1uPzcjMtMIPWKe89uzRZe9SYtFYU+fylkCs00QOIBiYnK/u8DPqFrVUL0GdgiepL46LEoCmTJlCnTp1CAwMJDo6mhXFPOV42bJlOByOAstvv/3mUW/u3LlcffXVOJ1Orr76aubNm+ftwxARLyvXpBz+Yf5UaFGB+u/Up0KLCviH+VOuScmu+LpslPa012uvwbvvWo++2LHDulw9ORnuvRfCwqyrwX780aqblQVXX23dUBFgwgSYO9faz8/POl3mcFhtGQPLll3II5MyqjuwASuQ5D0RLwPriTM+QGXgESCu0L0LFwnsLUG9m0vR5oXk9QA0Z84cRo4cydNPP018fDzt2rWje/fu7Nmzp9j9tm3bRmJionu56qqr3Nvi4uLo168fsbGx/Pzzz8TGxtK3b19Wr17t7cMRES8KrB5IzO4Ymq9pTuQDkTRf05yY3TEEVg+81F0rnYceKlk9Pz/rgaWPPmqtR0dDq1anQ0v58rB0KTRvbp0Gq17dqrtu3enRn+Rk6x5BAQHW/X46dLBGoHr2vNBHJWXYt4Av0AjYfca2XKwg4wc8dpZ23gI+BdYCSafabA18c6q8sN/kF8+51+fH63OAWrVqRfPmzXn77bfdZQ0bNqRPnz5MnDixQP1ly5bRqVMnjh49SsWKFQtts1+/fqSmprJw4ekHF3br1o1KlSoxa9ass/ZJc4BExOtmzrQeSFoYhwOWL7fuzuy8vK66E/s5AlTBGv0JwBr5ASusZOSrFwT4A8lYp8AKm1Lvi3WjdheQijWCFAQsA04AN+D5KL96wPZS9PUvMwcoMzOT9evX06VLF4/yLl26sHLlymL3bdasGREREdx4440sXbrUY1tcXFyBNrt27VpkmxkZGaSmpnosIiKXREgIbNliPaJC4UcuA2tPfTV4Bp7yp8r8scJRBlaIAbjm1NL4jLZyOB2kck59PQm0AjpR8DnGT12QIzg3Xg1Ahw4dIicnh7AwzwcdhoWFkZRU8MGIABEREbz77rvMnTuXzz//nKioKG688UZ++OEHd52kpKRStTlx4kRcLpd7qVGjxnkemYjIWdSvb12KHhwMd99tffXxgfnzoWHJHwci4i3TExOptGIFiw8fLraeH1ZwyeX04/OGARuBl7FGddrm25YD7McKP/lu28mZ4zV+wD3n3v3zdlHuA+TI/+wawBhToCxPVFQUUVFR7vWYmBgSEhL45z//Sfv27c+pzTFjxvDYY6fPXKampioEiYh3XXed9Wyv8uWt4JObaz3nS6fd5TLx6p9/kpyTw6u//np64n6+v6PHOD2acxIrBJ15PWb3UwtYp7N2YJ0Gy+V0+BkJjMKaFB3E6VGmXhfyYM6BVwNQaGgovr6+BUZmDhw4UGAEpzitW7dmxowZ7vXw8PBStel0OnFqqFlELrb8YcfHR+FHLrmfUlLYefIkDoeDTXl3DM97xly+KcF+QDpWmAlwOPKeLENxY5d7sQJTCNY8oTwBwBVAIp6n2ArOAr64vHoKLCAggOjoaBYvXuxRvnjxYtq0aVPiduLj44mIiHCvx8TEFGjz22+/LVWbIiIidnN9fDyxv/3GwK1bPefjHD7sMfqTfSoM5RjDYU7foN116mswVrAZAYwFnFiByWCN/ORv+1/AEOCqfGWBwFme5ud1Xj8F9thjjxEbG0uLFi2IiYnh3XffZc+ePTz44IOAdXpq7969TJ8+HYDXX3+d2rVr06hRIzIzM5kxYwZz585l7ty57jb//ve/0759eyZNmsQtt9zCl19+yZIlS/gx7z4ZIiIiUsBDkZG8nf/5cXk2b7Zut1ChgrWe9/w4h4OcfNVW4nl12JuFvEbek+gaAruwTp99dEadJ86x/xeS1wNQv379OHz4MM8++yyJiYk0btyYBQsWUKuWdaulxMREj3sCZWZmMmrUKPbu3UtQUBCNGjVi/vz59OjRw12nTZs2zJ49m2eeeYaxY8dSt25d5syZQ6tWrbx9OCIiIn9ZU+rX5/cTJ/guObngxg0brK8NG0K1au4RIX/gVawbIdYD/sAaCUoGegCL8BzxcQJjgHH5yv4LdDv1/URg9AU5mvOjZ4HpnLyIiNjIzP37Gbh161nrPVe7Ns+U9pEuXvaXuQ+QiIiIXF7qB5bszuohfhflQvFLRgFIRETERq5zufj+mmvOWi8mbz5QGVW2452IiIgU0KlSJVKuv57c3FycPj6k5+RgjMHX15cAh4Msyv4IUNk+OhERESlU/oATdEbYOfOGh2WRToGJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtKACJiIiI7SgAiYiIiO0oAImIiIjtXJQANGXKFOrUqUNgYCDR0dGsWLGiyLqff/45nTt3pmrVqoSEhBATE8N///tfjzrTpk3D4XAUWNLT0719KCIiIlIGeD0AzZkzh5EjR/L0008THx9Pu3bt6N69O3v27Cm0/g8//EDnzp1ZsGAB69evp1OnTvTu3Zv4+HiPeiEhISQmJnosgYGB3j4cERERKQMcxhjjzRdo1aoVzZs35+2333aXNWzYkD59+jBx4sQStdGoUSP69evHP/7xD8AaARo5ciTJycnn1KfU1FRcLhcpKSmEhIScUxsiIiJycV3Iv99eHQHKzMxk/fr1dOnSxaO8S5curFy5skRt5ObmkpaWRuXKlT3Kjx07Rq1atahevTq9evUqMEKUX0ZGBqmpqR6LiIiI2JdXA9ChQ4fIyckhLCzMozwsLIykpKQStfHqq69y/Phx+vbt6y5r0KAB06ZN46uvvmLWrFkEBgbStm1btm/fXmgbEydOxOVyuZcaNWqc+0GJiIjIX95FmQTtcDg81o0xBcoKM2vWLMaPH8+cOXOoVq2au7x169YMHDiQa665hnbt2vF///d/1K9fnzfffLPQdsaMGUNKSop7SUhIOL8DEhERkb80P282Hhoaiq+vb4HRngMHDhQYFTrTnDlzGDp0KJ9++ik33XRTsXV9fHy47rrrihwBcjqdOJ3O0nVeREREyiyvjgAFBAQQHR3N4sWLPcoXL15MmzZtitxv1qxZDBkyhE8++YSePXue9XWMMWzcuJGIiIjz7rOIiIiUfV4dAQJ47LHHiI2NpUWLFsTExPDuu++yZ88eHnzwQcA6PbV3716mT58OWOFn0KBB/Pvf/6Z169bu0aOgoCBcLhcAEyZMoHXr1lx11VWkpqbyxhtvsHHjRt566y1vH46IiIiUAV4PQP369ePw4cM8++yzJCYm0rhxYxYsWECtWrUASExM9Lgn0H/+8x+ys7P529/+xt/+9jd3+eDBg5k2bRoAycnJ3H///SQlJeFyuWjWrBk//PADLVu29PbhiIiISBng9fsAXY50HyAREZG/nr/MfYBERERELkcKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsKQCIiImI7CkAiIiJiOwpAIiIiYjsXJQBNmTKFOnXqEBgYSHR0NCtWrCi2/vLly4mOjiYwMJArr7ySd955p0CduXPncvXVV+N0Orn66quZN2+et7ovIiIiZYzXA9CcOXMYOXIkTz/9NPHx8bRr147u3buzZ8+eQuvv3LmTHj160K5dO+Lj43nqqacYMWIEc+fOddeJi4ujX79+xMbG8vPPPxMbG0vfvn1ZvXq1tw9HREREygCHMcZ48wVatWpF8+bNefvtt91lDRs2pE+fPkycOLFA/SeffJKvvvqKrVu3ussefPBBfv75Z+Li4gDo168fqampLFy40F2nW7duVKpUiVmzZp21T6mpqbhcLlJSUggJCTmfwxMREZGL5EL+/fbqCFBmZibr16+nS5cuHuVdunRh5cqVhe4TFxdXoH7Xrl1Zt24dWVlZxdYpqs2MjAxSU1M9FhEREbEvrwagQ4cOkZOTQ1hYmEd5WFgYSUlJhe6TlJRUaP3s7GwOHTpUbJ2i2pw4cSIul8u91KhR41wPSURERMqAizIJ2uFweKwbYwqUna3+meWlaXPMmDGkpKS4l4SEhFL1X0RERMoWP282Hhoaiq+vb4GRmQMHDhQYwckTHh5eaH0/Pz+qVKlSbJ2i2nQ6nTidznM9DBERESljvDoCFBAQQHR0NIsXL/YoX7x4MW3atCl0n5iYmAL1v/32W1q0aIG/v3+xdYpqU0RERCQ/r44AATz22GPExsbSokULYmJiePfdd9mzZw8PPvggYJ2e2rt3L9OnTwesK74mT57MY489xrBhw4iLi+ODDz7wuLrr73//O+3bt2fSpEnccsstfPnllyxZsoQff/zR24cjIiIiZYDXA1C/fv04fPgwzz77LImJiTRu3JgFCxZQq1YtABITEz3uCVSnTh0WLFjAo48+yltvvUVkZCRvvPEGt99+u7tOmzZtmD17Ns888wxjx46lbt26zJkzh1atWnn7cERERKQM8Pp9gC5Hug+QiIjIX89f5j5AIiIiIpcjBSARERGxHQUgERERsR0FIBEREbEdBSARERGxHQUgERERsR0FIBEREbEdBSARERGxHQUgERERsR0FIBEREbEdBSARERGxHQUgERERsR0FIBEREbEdBSARERGxHQUgERERsR0FIBEREbEdBSARERGxHQUgERERsR0FIBEREbEdBSARERGxHQUgERERsR0FIBEREbEdBSAvmzJlCnXq1CEwMJDo6GhWrFhRbP2MjAyefvppatWqhdPppG7dunz44Yfu7dOmTcPhcBRY0tPTvX0oIiIiZYYCkBfNmTOHESNGsG/fPjIyMtiwYQPt27fHz8+PyZMnF7rPHXfcwaRJk9izZw+ZmZn88ccfDB06FIfDQWBgIAC+vr4F9gsKCqJnz55ePR4REZGywmGMMZe6ExdbamoqLpeLlJQUQkJCvPY69erVY8eOHUVur1q1KnPnzqVdu3YALFq0iN69e5OdnX3Wtn19ffH19SUzM7PAtl69evHpp5+6A5OIiEhZcCH/fmsEyEsyMzPZsWMHPj5Fv8UHDx6kc+fO7NmzB4DJkyeTm5sLQOXKlYmMjKR3796FjuwEBQXh7+9foHzAgAGsWrWKMWPGXKAjERERKXsUgLxk3759AO5A43A4CAoKolq1ajgcDnc9h8PB22+/DcAvv/xCbm4uPj4+pKSksG/fPr7++mvmz5/v0bavry/169cnKyvLXeZyuQgICKBOnToMGjSIdevWefsQRURE/rIUgLzkyJEjHuvGGNLT0wkPD/coz83NZeXKlQCcOHHCXRYSEsLIkSM9TmP5+/sTHByMMYY//vjDo62UlBQyMzOJi4tj/vz5mg8kIiJSDAWgC2z69OmUK1eO1q1bF9hmjCE3N9djBCgnJ4ekpCQAAgIC3OUbN27kX//6F1dccYW7LCsrC5fLRUREBO3bt3efOsvvu+++IyAggNGjR1/IwxIRESlTFIAusFdffZUTJ054nJ7Kb/fu3fj6+hY4DQZQq1YtwDrFVbNmTXJzcz0mUZcrV4569erRoEEDvvzyS2rXru3RtsPhoHz58mzatInnnnvuAh+ZiIhI2aEAdAH89NNPjB07loEDB/LLL78UW/fYsWNkZ2eTd/GdMYawsDAA7rrrLsAaFVq+fDkjRozw2Dc2NhZjDJs2beJ///ufe34RWOGnadOmOJ1OAF588UWP7SIiInKaLoO/AJfB5x/NORe+vr7UqlWLn3/+mSuvvJKDBw+6283/8WzatInXX3/d48aIedudTic33HAD3333HQA+Pj4cO3as0HsGiYiI/BXpMvjLzEMPPXRe++fk5PDHH39QvXp1YmJiuPbaawE8wk90dDSNGzfm/fffZ/Lkyfj4+Hhsz8jIYOHChWRmZhIYGMjNN9+s8CMiIlIEBaALYMqUKcyYMaPU+1WvXp3ly5czePBgAgMDOXHiBCkpKcTHx5OcnOxx5+cHHnjAvd/DDz/M6NGjqVixYoE2y5Urx913381//vOfcz4eERGRsk6nwC7QnaBnzpzJwIEDz1pv/fr1NG/e/IK8poiIiJ3oFNhlqH79+uc9F0hEREQuDgWgC+S6664jOTmZTZs2UaFChULrVKxYkWrVql3knomIiMiZ/C51B8qSkJAQGjduzMGDB0lJSaF8+fIEBgaSnp7OsWPHcLlc7svURURE5NJRAPICp9PpMdITHBxMcHDwJeyRiIiI5KdTYCIiImI7Xg1AR48eJTY2FpfLhcvlIjY2luTk5CLrZ2Vl8eSTT9KkSRPKlStHZGQkgwYNcj9ZPU/Hjh1xOBweS//+/b15KCIiIlIKf/87+PmBw3F6GTOm6PobN0KFCp71/f0h311gsJ4ytR6Xq4JHvYgIWLCgdP3zagC6++672bhxI4sWLWLRokVs3LiR2NjYIuufOHGCDRs2MHbsWDZs2MDnn3/O77//zs0331yg7rBhw0hMTHQvuu+NiIjI5ePIESuc5Dd9etH1f/8djh3zLMvOhnffhY4drfUBA4KAZoBnw0lJ8OCDpeuf1+YAbd26lUWLFrFq1SpatWoFwHvvvUdMTAzbtm0jKiqqwD4ul4vFixd7lL355pu0bNmSPXv2ULNmTXd5cHAw4eHh3uq+iIiInIePP4YtW+CXXyAnxyo7ebLo+uvXQ7lycPx4wW0rV1pfV6zwA9KACgQFOcjKskISwIkTpeuf10aA4uLicLlc7vAD0Lp1a1wuFyvzjqQEUlJScDgcBe56PHPmTEJDQ2nUqBGjRo0iLS2tyDYyMjJITU31WERERMS7XngBRo8uWd24OGjc2Pre4YDgYMgb96hfP6/cANatZqpU8RxhKu19Eb0WgJKSkgq95021atVISkoqURvp6emMHj2au+++2+OOjwMGDGDWrFksW7aMsWPHMnfuXG677bYi25k4caJ7HpLL5aJGjRqlPyAREREple7d4fnnS1Y3KQlSUqzvjbFGdPbssdZffNH6et11ue76f/6ZNyfIcuWVpetbqQPQ+PHjC0xAPnNZt24dUPhT0o0xJbpjclZWFv379yc3N5cpU6Z4bBs2bBg33XQTjRs3pn///nz22WcsWbKEDRs2FNrWmDFjSElJcS8JCQmlPWwREREpgQkTrMnPEyaUft8jR6yvPj7gcp0uHzMG0tJg8+aiY0spTi4B5zAHaPjw4We94qp27dr88ssv7N+/v8C2gwcPEhYWVuz+WVlZ9O3bl507d/L999+f9XkfzZs3x9/fn+3btxf6nC2n06kbEIqIiFwEEydac34mToRx40q+X1gYbN9uhR+nE/LPVvn1V2s+0aFDPkDhjzA9eRIyMyEgoGSvV+oAFBoaSmho6FnrxcTEkJKSwpo1a2jZsiUAq1evJiUlhTZt2hS5X1742b59O0uXLqVKlSpnfa0tW7aQlZVFREREyQ9ERERELoi5c62Q4nBARoZVlpEBN9wAnTqVrI1GjeDHHyE3t/DJ0p99BlFROWzbZo0CrVwJ7dtbp8vyJlnn5hbcryhefRp89+7d2bdvn/sS9fvvv59atWrx9ddfu+s0aNCAiRMncuutt5Kdnc3tt9/Ohg0b+OabbzxGiipXrkxAQAA7duxg5syZ9OjRg9DQUH799Vcef/xxgoKCWLt2Lb6+vmftlzeeBi8iImJXJX0WuJ8fjBgBd9xhLUlJULs27Nhhjf5ERVmBxsfH+po/oezaBf/4RybTp/sDcNVVDrZv92z/xAkICiphn70ZgI4cOcKIESP46quvALj55puZPHmyxxVdDoeDqVOnMmTIEHbt2kWdOnUKbWvp0qV07NiRhIQEBg4cyObNmzl27Bg1atSgZ8+ejBs3jsqVK5eoXwpAIiIiF05JA1CeqlUhPd2a1wOng05R7YSHQ2IifP31cW6+ORBrCrNnZV/f05fEl6jP3gxAlysFIBERkQuncWNrjk5J+flZV3CdOdLz8svw1lunr/4Cq86xY9bIjvX3uym+vjvJyXG4t/v4wP/7f6evFisJPQtMREREzsvmzVC+fMnrDxhgfR00CDp0OF3+xBPWjRODgqw7QOfN7/E8rbWbRYtO0KqVNVm6dm3rirPnnitdnzUCpBEgERGR89a9OyxaVPi2556DZ545/9e4kH+/NQIkIiIi561fv0vdg9JRABIREZHzNmQITJ1qfe9wQLNmp7dde+2l6FHxvPYwVBEREbGXIUOgZ0+oXNm6Kisnx7q7c9Wql7pnBSkAiYiIyAWTP+z4+l6e4Qd0CkxERERsSAFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsx6sB6OjRo8TGxuJyuXC5XMTGxpKcnFzsPkOGDMHhcHgsrVu39qiTkZHBI488QmhoKOXKlePmm2/mzz//9OKRiIiISFni1QB09913s3HjRhYtWsSiRYvYuHEjsbGxZ92vW7duJCYmupcFCxZ4bB85ciTz5s1j9uzZ/Pjjjxw7doxevXqRk5PjrUMRERGRMsTPWw1v3bqVRYsWsWrVKlq1agXAe++9R0xMDNu2bSMqKqrIfZ1OJ+Hh4YVuS0lJ4YMPPuDjjz/mpptuAmDGjBnUqFGDJUuW0LVr1wt/MCIiIlKmeG0EKC4uDpfL5Q4/AK1bt8blcrFy5cpi9122bBnVqlWjfv36DBs2jAMHDri3rV+/nqysLLp06eIui4yMpHHjxkW2m5GRQWpqqsciIiIi9uW1AJSUlES1atUKlFerVo2kpKQi9+vevTszZ87k+++/59VXX2Xt2rXccMMNZGRkuNsNCAigUqVKHvuFhYUV2e7EiRPd85BcLhc1atQ4jyMTERGRv7pSB6Dx48cXmKR85rJu3ToAHA5Hgf2NMYWW5+nXrx89e/akcePG9O7dm4ULF/L7778zf/78YvtVXLtjxowhJSXFvSQkJJTiiEVERKSsKfUcoOHDh9O/f/9i69SuXZtffvmF/fv3F9h28OBBwsLCSvx6ERER1KpVi+3btwMQHh5OZmYmR48e9RgFOnDgAG3atCm0DafTidPpLPFrioiISNlW6gAUGhpKaGjoWevFxMSQkpLCmjVraNmyJQCrV68mJSWlyKBSmMOHD5OQkEBERAQA0dHR+Pv7s3jxYvr27QtAYmIimzdv5uWXXy7t4YiIiIgNeW0OUMOGDenWrRvDhg1j1apVrFq1imHDhtGrVy+PK8AaNGjAvHnzADh27BijRo0iLi6OXbt2sWzZMnr37k1oaCi33norAC6Xi6FDh/L444/z3XffER8fz8CBA2nSpIn7qjARkQtnClAHCASigRXF1F0GOApZfstXZwtwO1D71LbXL3B/RaQkvHYZPMDMmTMZMWKE+4qtm2++mcmTJ3vU2bZtGykpKQD4+vqyadMmpk+fTnJyMhEREXTq1Ik5c+ZQoUIF9z7/+te/8PPzo2/fvpw8eZIbb7yRadOm4evr683DERHbGQp8mG/9Z+AmYDtQ84y6y4BORbSzHWiAFX76n/pqTm37ABh5QXorIiXnMMaYs1crW1JTU3G5XKSkpBASEnKpuyMil6U5WGElj4PToSUWmH5G/eHAW4W082/gQSAA+CfwNJCZb3tjYNMF6K9I2Xch/357dQRIROSva8AZ6z5A3t3mvzhjW1HhByAYK/x0AH64UJ0TkfOkACQiUkBXToed2kDyqQWskaDjJWzHD7gfqA9sA5oClU6tv3eqzuHz7ayInAMFIBGRAr7N931fYBJW8AHrNFhJZg74Atmnvv8bcOaNWvMC0NFz7KOInA+vPgxVROSvZufOJ/GcGZn36Jz8t/8o+mauBes4gK1nbMv/ArpHmciloBEgEZFTUlPXkZLyMp43lV916mtF4NCp7wPO2POaU0ttwAXMA9JObTNA7qnvU4ArgIx8+15xAXouIqWlESARsb2DB+eya9dzbN7cx6PcGDBmI2lpD+MZWq4+9XUMMAgYBmwEOgK3Auvx/P9l0KmvFYA1QKN821JO7fu/8z8QESkxjQCJiK2lp+9my5Y73Os5OXDmzUGCg98+Y683scLPv7BOcU3HuqHha1iB5iSn5/+ANQeIU2UDsO4nlGcv0AxrgnT+chHxJgUgEbG1Vatqe6znnLr4yxhwOKyvPh5j5S2AtkAfrFEh16ny94FEPIMPQAiQ95iem7BGewqzu/SdF5FzplNgImJbKSk/FVp++DDueUCe84H8gM+w5u0cAvyxLo9vghVgcilo6qmvURT9GI0KnL7MXkQuBgUgEbGt+PjrCy3fvBnS0k6vWyGoKvAdUAtrgrMDyHuwcxZwDM8AVBWYD9x2an17MT1pXtqui8h50ikwEbGtyMiH2LfvzPk9lg0brK91675OjRp/P2Nr6hnrv3F2hY0OicilohEgEbGt+vWn0LDhjGJqOKla9faL1h8RuXgUgEREitCw4SwCA6tf6m6IiBcoAImIrQUG1sf6p9BJlSr98PEJBqBRo0WEhd16SfsmIt6jOUAiYmsu13Vcf/1RfHzK4+PjQ25uLrm5x/DzC7nUXRMRL1IAEhHbyx92fHx88PFR+BEp63QKTERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbMerAejo0aPExsbicrlwuVzExsaSnJxc7D4Oh6PQ5ZVXXnHX6dixY4Ht/fv39+ahiIiISBni583G7777bv78808WLVoEwP33309sbCxff/11kfskJiZ6rC9cuJChQ4dy++23e5QPGzaMZ5991r0eFBR0AXsuIiIiZZnXAtDWrVtZtGgRq1atolWrVgC89957xMTEsG3bNqKiogrdLzw83GP9yy+/pFOnTlx55ZUe5cHBwQXqFiUjI4OMjAz3empqamkORURERMoYr50Ci4uLw+VyucMPQOvWrXG5XKxcubJEbezfv5/58+czdOjQAttmzpxJaGgojRo1YtSoUaSlpRXZzsSJE92n4VwuFzVq1Cj9AYmIiEiZ4bURoKSkJKpVq1agvFq1aiQlJZWojY8++ogKFSpw2223eZQPGDCAOnXqEB4ezubNmxkzZgw///wzixcvLrSdMWPG8Nhjj7nXU1NTFYJERERsrNQBaPz48UyYMKHYOmvXrgWsCc1nMsYUWl6YDz/8kAEDBhAYGOhRPmzYMPf3jRs35qqrrqJFixZs2LCB5s2bF2jH6XTidDpL9JoiIiJS9pU6AA0fPvysV1zVrl2bX375hf379xfYdvDgQcLCws76OitWrGDbtm3MmTPnrHWbN2+Ov78/27dvLzQAiYiIiORX6gAUGhpKaGjoWevFxMSQkpLCmjVraNmyJQCrV68mJSWFNm3anHX/Dz74gOjoaK655pqz1t2yZQtZWVlERESc/QBERETE9rw2Cbphw4Z069aNYcOGsWrVKlatWsWwYcPo1auXxxVgDRo0YN68eR77pqam8umnn3LfffcVaHfHjh08++yzrFu3jl27drFgwQLuvPNOmjVrRtu2bb11OCIiIlKGePVGiDNnzqRJkyZ06dKFLl260LRpUz7++GOPOtu2bSMlJcWjbPbs2RhjuOuuuwq0GRAQwHfffUfXrl2JiopixIgRdOnShSVLluDr6+vNwxEREZEywmGMMZe6ExdbamoqLpeLlJQUQkJCLnV3REREpAQu5N9vPQtMREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsx6sB6IUXXqBNmzYEBwdTsWLFEu1jjGH8+PFERkYSFBREx44d2bJli0edjIwMHnnkEUJDQylXrhw333wzf/75pxeOQERERMoirwagzMxM7rzzTh566KES7/Pyyy/z2muvMXnyZNauXUt4eDidO3cmLS3NXWfkyJHMmzeP2bNn8+OPP3Ls2DF69epFTk6ONw5DREREyhiHMcZ4+0WmTZvGyJEjSU5OLraeMYbIyEhGjhzJk08+CVijPWFhYUyaNIkHHniAlJQUqlatyscff0y/fv0A2LdvHzVq1GDBggV07dr1rP1JTU3F5XKRkpJCSEjIeR+fiIiIeN+F/Pt9Wc0B2rlzJ0lJSXTp0sVd5nQ66dChAytXrgRg/fr1ZGVledSJjIykcePG7jpnysjIIDU11WMRERER+7qsAlBSUhIAYWFhHuVhYWHubUlJSQQEBFCpUqUi65xp4sSJuFwu91KjRg0v9F5ERET+KkodgMaPH4/D4Sh2Wbdu3Xl1yuFweKwbYwqUnam4OmPGjCElJcW9JCQknFf/RERE5K/Nr7Q7DB8+nP79+xdbp3bt2ufUmfDwcMAa5YmIiHCXHzhwwD0qFB4eTmZmJkePHvUYBTpw4ABt2rQptF2n04nT6TynPomIiEjZU+oAFBoaSmhoqDf6Qp06dQgPD2fx4sU0a9YMsK4kW758OZMmTQIgOjoaf39/Fi9eTN++fQFITExk8+bNvPzyy17pl4iIiJQtXp0DtGfPHjZu3MiePXvIyclh48aNbNy4kWPHjrnrNGjQgHnz5gHWqa+RI0fy4osvMm/ePDZv3syQIUMIDg7m7rvvBsDlcjF06FAef/xxvvvuO+Lj4xk4cCBNmjThpptu8ubhiIhcPFOmQJUq4HBYi48PREXBihUF6w4ZcrpeYUujRjBtWuHbqlaFNWsu9tGJXHrGiwYPHmyAAsvSpUvddQAzdepU93pubq4ZN26cCQ8PN06n07Rv395s2rTJo92TJ0+a4cOHm8qVK5ugoCDTq1cvs2fPnhL3KyUlxQAmJSXlfA9RROTCmz3bGF9fYxwOY6Dg8uyznvWTk43Zts2Y7t0Lrw/GtG1rTEiIMZ06GePnV3idbt0uzfGKlNCF/Pt9Ue4DdLnRfYBE5LLWqhXs2gVpaXDyZOF1pkyBM28ym5IC/frBt99akSY/Pz/w94fbb4cZMwpvMyTEakPkMlVm7wMkImJ7mZmwbh0cPFgw/AQHn/5++HDYs8dze1wcLFt2OvzkXRk7ejR06QIZGTBz5un6DgecuvhExG4UgERELieHDkFurucIjp8ftGwJQUHg62uV5ebC22977vvVV5D/kUB5bXz7LYwYAU8/ba3nXWVrjBW08lSvfmGPReQypgAkInK5WLcO7ryzYHlODtSrd3oydJ4z737/xx+QnV1w/w0boG9f+OgjaN8ejhzxbDtPvXrn13+RvxAFIBGRy8UrrxQMNWCN1GRlQUDA6dNaAGfe/T4313Pd4YAbb7S+T021TpmtWGGdCitMYVeYiZRRCkAiIpfS7t2wfr01SvP110XXW7PGCi75R2zOvPv9met33glvvum5ffVqz1EkgOuus74ePVowRImUUQpAIiKXUu3a0KIFREcXfcUXQEKCdYVW/gCUkACDBp1eP/MKrrFj4fffT68bA//5T8GQs3bt6e8DAmDHjlIfhshfjQKQiMhfwZkTo8EKTDNmQN26VvjZuNFz+2efwbBhnmXvv1/862zcCHpgtNiAApCIyKVU1D15CpN/9CcoyAoqxliTnx95BNLTYcGC03UmTDh9lZe/P9x3H8yaVXT7NWpA48bWKJBIGacAJCJyKQ0YULoQBNbl6osWWfOH6ta1wk3ePYG6d4f588HlOl3f398aCXrjDejfH0aOhLCw03OGgoKgfn049QxGETvQnaB1J2gRudQWLoQePYqvM2OGFZZEbEx3ghYRKUuaNPEcsRERr1MAEhG51KpXh/374eOPT5flv6Td4bBOUYnIBeN3qTsgIiKA0wkDB0LXrtajL1wua4LzoUPWHB2drhe5oBSAREQuJ1Wreq6HhV2afoiUcToFJiIiIrajACQiIiK2owAkIiIitqMAJCIiIrajACQiIiK2owAkIiIitqMAJCIiIrajACQiIiK2owAkIiIitqMAJCIiIrZjy0dhGGMASE1NvcQ9ERERkZLK+7ud93f8fNgyAKWlpQFQo0aNS9wTERERKa20tDRcLtd5teEwFyJG/cXk5uayb98+KlSogMPhuNTduWylpqZSo0YNEhISCNGTqC8b+lwuT/pcLk/6XC5P5/q5GGNIS0sjMjISH5/zm8VjyxEgHx8fqlevfqm78ZcREhKifzguQ/pcLk/6XC5P+lwuT+fyuZzvyE8eTYIWERER21EAEhEREdtRAJIiOZ1Oxo0bh9PpvNRdkXz0uVye9LlcnvS5XJ4uh8/FlpOgRURExN40AiQiIiK2owAkIiIitqMAJCIiIrajACQiIiK2owAkIiIitqMAJB5eeOEF2rRpQ3BwMBUrVizRPsYYxo8fT2RkJEFBQXTs2JEtW7Z4t6M2c/ToUWJjY3G5XLhcLmJjY0lOTi52nyFDhuBwODyW1q1bX5wOl1FTpkyhTp06BAYGEh0dzYoVK4qtv3z5cqKjowkMDOTKK6/knXfeuUg9tZfSfC7Lli0r8HvhcDj47bffLmKPy74ffviB3r17ExkZicPh4IsvvjjrPhf790UBSDxkZmZy55138tBDD5V4n5dffpnXXnuNyZMns3btWsLDw+ncubP7obNy/u6++242btzIokWLWLRoERs3biQ2Nvas+3Xr1o3ExET3smDBgovQ27Jpzpw5jBw5kqeffpr4+HjatWtH9+7d2bNnT6H1d+7cSY8ePWjXrh3x8fE89dRTjBgxgrlz517knpdtpf1c8mzbts3jd+Oqq666SD22h+PHj3PNNdcwefLkEtW/JL8vRqQQU6dONS6X66z1cnNzTXh4uHnppZfcZenp6cblcpl33nnHiz20j19//dUAZtWqVe6yuLg4A5jffvutyP0GDx5sbrnllovQQ3to2bKlefDBBz3KGjRoYEaPHl1o/SeeeMI0aNDAo+yBBx4wrVu39lof7ai0n8vSpUsNYI4ePXoReifGGAOYefPmFVvnUvy+aARIzsvOnTtJSkqiS5cu7jKn00mHDh1YuXLlJexZ2REXF4fL5aJVq1bustatW+Nyuc76Hi9btoxq1apRv359hg0bxoEDB7zd3TIpMzOT9evXe/ycA3Tp0qXIzyAuLq5A/a5du7Ju3TqysrK81lc7OZfPJU+zZs2IiIjgxhtvZOnSpd7sppTApfh9UQCS85KUlARAWFiYR3lYWJh7m5yfpKQkqlWrVqC8WrVqxb7H3bt3Z+bMmXz//fe8+uqrrF27lhtuuIGMjAxvdrdMOnToEDk5OaX6OU9KSiq0fnZ2NocOHfJaX+3kXD6XiIgI3n33XebOncvnn39OVFQUN954Iz/88MPF6LIU4VL8vvh5pVW5rIwfP54JEyYUW2ft2rW0aNHinF/D4XB4rBtjCpSJp5J+LlDw/YWzv8f9+vVzf9+4cWNatGhBrVq1mD9/Prfddts59treSvtzXlj9wsrl/JTmc4mKiiIqKsq9HhMTQ0JCAv/85z9p3769V/spxbvYvy8KQDYwfPhw+vfvX2yd2rVrn1Pb4eHhgJXeIyIi3OUHDhwokObFU0k/l19++YX9+/cX2Hbw4MFSvccRERHUqlWL7du3l7qvdhcaGoqvr2+BUYXifs7Dw8MLre/n50eVKlW81lc7OZfPpTCtW7dmxowZF7p7UgqX4vdFAcgGQkNDCQ0N9UrbderUITw8nMWLF9OsWTPAOi+/fPlyJk2a5JXXLCtK+rnExMSQkpLCmjVraNmyJQCrV68mJSWFNm3alPj1Dh8+TEJCgkdQlZIJCAggOjqaxYsXc+utt7rLFy9ezC233FLoPjExMXz99dceZd9++y0tWrTA39/fq/21i3P5XAoTHx+v34tL7JL8vnhterX8Je3evdvEx8ebCRMmmPLly5v4+HgTHx9v0tLS3HWioqLM559/7l5/6aWXjMvlMp9//rnZtGmTueuuu0xERIRJTU29FIdQJnXr1s00bdrUxMXFmbi4ONOkSRPTq1cvjzr5P5e0tDTz+OOPm5UrV5qdO3eapUuXmpiYGHPFFVfoczlHs2fPNv7+/uaDDz4wv/76qxk5cqQpV66c2bVrlzHGmNGjR5vY2Fh3/T/++MMEBwebRx991Pz666/mgw8+MP7+/uazzz67VIdQJpX2c/nXv/5l5s2bZ37//XezefNmM3r0aAOYuXPnXqpDKJPS0tLcfz8A89prr5n4+Hize/duY8zl8fuiACQeBg8ebIACy9KlS911ADN16lT3em5urhk3bpwJDw83TqfTtG/f3mzatOnid74MO3z4sBkwYICpUKGCqVChghkwYECBy3jzfy4nTpwwXbp0MVWrVjX+/v6mZs2aZvDgwWbPnj0Xv/NlyFtvvWVq1aplAgICTPPmzc3y5cvd2wYPHmw6dOjgUX/ZsmWmWbNmJiAgwNSuXdu8/fbbF7nH9lCaz2XSpEmmbt26JjAw0FSqVMlcf/31Zv78+Zeg12Vb3u0GzlwGDx5sjLk8fl8cxpyaZSQiIiJiE7oMXkRERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERsRwFIREREbEcBSERERGxHAUhERERs5/8DYV8O2ZaW5MYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot optimization of Layer 2 of NN\n",
    "color_List = ['r*', 'b*', 'g*', 'm*', 'c*', 'y*', 'k*']\n",
    "colorNameList = [\"red\", \"blue\", \"green\", \"purple\", \"cyan\", \"yellow\", 'black']\n",
    "counter = 0\n",
    "colorCounter = 0\n",
    "for pair in layer2_reduced:\n",
    "    if (counter % 10) == 0 and counter != 0:\n",
    "        # Change Color\n",
    "        if colorCounter >= len(color_List) - 1:\n",
    "            colorCounter = 0\n",
    "        else:\n",
    "            colorCounter += 1\n",
    "    plt.plot(pair[0], pair[1], color_List[colorCounter])\n",
    "    plt.annotate(str(round(cost_Vector[counter][0], 2)), (pair[0], pair[1]), color=colorNameList[colorCounter])\n",
    "    counter += 1\n",
    "plt.title(\"Layer 2's Weights Optimization\") \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9cb15742",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot optimization of Whole Model of NN\n",
    "counter = 0\n",
    "colorCounter = 0\n",
    "for pair in whole_Model_Reduced:\n",
    "    if (counter % 10) == 0 and counter != 0:\n",
    "        if colorCounter >= len(color_List) - 1:\n",
    "            colorCounter = 0\n",
    "        else:\n",
    "            colorCounter += 1\n",
    "    plt.plot(pair[0], pair[1], color_List[colorCounter])\n",
    "    plt.annotate(str(round(cost_Vector[counter][0], 2)), (pair[0], pair[1]), color=colorNameList[colorCounter])\n",
    "    counter += 1\n",
    "plt.title(\"Whole Model's Weights Optimization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60f49d47",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}