EE599_ML_Systems_HW2.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/meghana009/Calculating-the-annual-medical-insurance-cost/blob/main/EE599_ML_Systems_HW2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nc3kdYUUlfGP"
      },
      "source": [
        "# HW2 EE599 Systems for Machine Learning, Fall 2023\n",
        "University of Southern California\n",
        "\n",
        "Instructors: Arash Saifhashemi, Murali Annavaram\n",
        "\n",
        "## Prerequisites:\n",
        "\n",
        "* Set the runtime type to GPU. (Runtime -> Change Runtime Type)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zTvIwDlYvBzC"
      },
      "source": [
        "# Initial Setup\n",
        "\n",
        "This section imports all required packages from PyTorch.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "hbiiMcdNJI--"
      },
      "outputs": [],
      "source": [
        "#%matplotlib inline\n",
        "import scipy.ndimage as ndi\n",
        "import numpy as np\n",
        "np.set_printoptions(suppress=True)\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.cm as cm\n",
        "grays=plt.get_cmap('gray')\n",
        "np.set_printoptions(precision=2)\n",
        "\n",
        "\n",
        "import torch\n",
        "import torchvision\n",
        "import torchvision.transforms as transforms\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim\n",
        "from torch.utils.data import DataLoader\n",
        "from copy import deepcopy\n",
        "\n",
        "\n",
        "import inspect\n",
        "import re\n",
        "import pprint"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "15XifXfwrviU"
      },
      "source": [
        "## Mount Google Drive"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NKd_r1C-rucF",
        "outputId": "63821a02-22cf-455b-800a-e3d3562f811b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ],
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "fNR6HA1gsDT3"
      },
      "outputs": [],
      "source": [
        "import sys, os\n",
        "figures_dir = '/content/drive/MyDrive/UtilFolder/hw2_figures'\n",
        "weights_dir = '/content/drive/MyDrive/UtilFolder/weights'\n",
        "data_dir = '/content/drive/MyDrive/UtilFolder/data'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FG3WW1Owq1Fh"
      },
      "source": [
        "**Reminder:** set the runtime type to \"GPU\", or your code will run much more slowly on a CPU."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "A3RF5VmcoUMG"
      },
      "outputs": [],
      "source": [
        "if torch.cuda.is_available():\n",
        "    device = torch.device('cuda')\n",
        "else:\n",
        "    device = torch.device('cpu')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FjKQYob-hDrw"
      },
      "source": [
        "# Section 1: Convolution\n",
        "\n",
        "**Definition**:\n",
        "Convolution is a mathematical operation where a filter (or kernel) is applied over an input (e.g., image) to produce a modified output known as a feature map.\n",
        "\n",
        "**Key Components**:\n",
        "- **Kernel/Filter**: A small matrix that slides over the input. It captures patterns or features from the input.\n",
        "  \n",
        "- **Stride**: The number of pixels the filter moves at each step.\n",
        "  \n",
        "- **Padding**: Zeros added around the input's border, often used to control the output's spatial dimensions.\n",
        "\n",
        "**Operation**:\n",
        "The filter starts at the top-left corner of the image. For each position, values under the filter are multiplied with its corresponding filter values, then summed to produce a single pixel in the output. This process is repeated across the entire input.\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gOR3xVytYchU"
      },
      "source": [
        "## Create a sample image\n",
        "\n",
        "Create a 2D  `image` of shape `(10,10)` as a numpy-array. The signal values are 1 (white) in the `(4,4)`-center region and 0 (black) elsewhere.\n",
        "\n",
        "**TODO**: Plot the image as a grid with black or white colors and write the 0 or 1 value on each cell."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "lv5aiZYjhVMj"
      },
      "outputs": [],
      "source": [
        "image = np.zeros((10,10))\n",
        "image[3:7,3:7] = 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "HWt-4xoXhqb9",
        "outputId": "6863588f-58d4-4c18-bb66-d7c56acf45ce"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plot_image_with_values(image, title):\n",
        "    \"\"\"\n",
        "    Plots a 2D image with numeric values overlaid on each cell.\n",
        "\n",
        "    Parameters:\n",
        "    - image (2D numpy array): The image to be plotted.\n",
        "    - title (str): The title of the plot.\n",
        "    \"\"\"\n",
        "    plt.figure(figsize=(5,5))\n",
        "\n",
        "    # Plot the image\n",
        "    plt.imshow(image, cmap='gray')\n",
        "\n",
        "    # Looping through all cells to overlay the numeric values\n",
        "    for i in range(image.shape[0]):\n",
        "        for j in range(image.shape[1]):\n",
        "            pixel_value = image[i, j]\n",
        "            text_color = 'white' if pixel_value < 0.5 else 'black'  # Setting text color based on pixel value\n",
        "            plt.text(j, i, f'{pixel_value:.2f}', ha='center', va='center', color=text_color)\n",
        "\n",
        "    plt.title(title)\n",
        "    plt.axis('off')\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "plot_image_with_values(image, 'A sample image')\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xqQLUTPfi0JZ"
      },
      "source": [
        "## Create an Average Filter\n",
        "\n",
        "**TODO**: Create a 2-dimensional average filter of size 3x3.\n",
        "\n",
        "To create a 2-dimensional average filter (also known as a mean filter) of size 3x3, the filter should consist of equal values such that they sum up to 1. For a 3x3 filter, each value in the filter should be $\\frac{1}{9}$\n",
        "  since there are 9 values in total.\n",
        "\n",
        "- Use `conv2d` to colvolve this filter with `image`. Note that to do so, you have to convert the image from a numpy array to a tensor of appropriate size.\n",
        "- Plot the image as a grid with black or white colors and write the 0 or 1 value on each cell.\n",
        "- Explain the output."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "cVgk7qEuizVj"
      },
      "outputs": [],
      "source": [
        "avg_filter = torch.ones(1,1,3,3)/9\n",
        "image_tensor = torch.tensor(image, dtype = torch.float32)\n",
        "image_tensor = image_tensor.unsqueeze(0)\n",
        "image_tensor = image_tensor.unsqueeze(1)\n",
        "conv1 = nn.Conv2d(1,1,kernel_size = 3, padding = 1, bias = False)\n",
        "conv1.weight.data = avg_filter\n",
        "image_conv = conv1(image_tensor)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "image_conv"
      ],
      "metadata": {
        "id": "AWt9LhcuTQBY",
        "outputId": "68e1663d-8f8f-4e43-f017-07e262065c72",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[[0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.1111, 0.2222, 0.3333, 0.3333, 0.2222, 0.1111,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.2222, 0.4444, 0.6667, 0.6667, 0.4444, 0.2222,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.3333, 0.6667, 1.0000, 1.0000, 0.6667, 0.3333,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.3333, 0.6667, 1.0000, 1.0000, 0.6667, 0.3333,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.2222, 0.4444, 0.6667, 0.6667, 0.4444, 0.2222,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.1111, 0.2222, 0.3333, 0.3333, 0.2222, 0.1111,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
              "           0.0000, 0.0000],\n",
              "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
              "           0.0000, 0.0000]]]], grad_fn=<ConvolutionBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Converting the convolved tensor back into numpy array for plotting"
      ],
      "metadata": {
        "id": "eaPulDkPSsg0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "image_array = image_conv.squeeze().detach().numpy()\n",
        "plot_image_with_values(image_array,'Convolved Image')"
      ],
      "metadata": {
        "id": "fUDFmuF_SS9R",
        "outputId": "ab636688-2a98-45b3-aec6-5ce55245049f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a14_iJ0ZnZJi"
      },
      "source": [
        "## Edge Detection\n",
        "\n",
        "In image processing, edge detection refers to the process of identifying abrupt changes or discontinuities in an image. These abrupt changes often correspond to object boundaries, textures, or other significant features.\n",
        "\n",
        "The concept of **central differences** can be applied to images to detect edges by estimating the gradient magnitude at each pixel. In the context of images, the derivative approximations can highlight the areas of rapid intensity change, which are often the edges.\n",
        "\n",
        "\n",
        "Create a 3x2 2-dimensional filter, which calculates the gradient in x-direction (detecting vertical edges).\n",
        "\n",
        "Use of the concept of central differences. One possible filter for this purpose is:\n",
        "\n",
        "\\begin{bmatrix}\n",
        "-1 & 0 & 1 \\\\\n",
        "-1 & 0 & 1 \\\\\n",
        "-1 & 0 & 1 \\\\\n",
        "\\end{bmatrix}\n",
        "\n",
        "\n",
        "**Question** Why is convolving the image with this filter analogous to computing the partial derivatives of the image with respect to x?\n",
        "\n",
        "**TODO**: Create this filter and visualize it. Plot the filter as a grid with black or white colors and write the value of each cell on it.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "yyx3gh-eoErn",
        "outputId": "33138da8-0dc3-432e-f002-14903c95eb6a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "edge_filter = np.zeros((3,3))\n",
        "edge_filter[:,0] = -1\n",
        "edge_filter[:,2] = 1\n",
        "plot_image_with_values(edge_filter, 'Edge Filter to calculate gradient in x-direction')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E89kE08so5QL"
      },
      "source": [
        "**TODO:** Apply this filter on the original image.\n",
        "\n",
        "Plot the image as a grid with black or white colors and write value of each cell on it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "VVflGKC5o7jZ"
      },
      "outputs": [],
      "source": [
        "edge_filter_tensor = torch.tensor(edge_filter, dtype = torch.float32)\n",
        "edge_filter_tensor = edge_filter_tensor.unsqueeze(0)\n",
        "edge_filter_tensor = edge_filter_tensor.unsqueeze(1)\n",
        "\n",
        "conv2 = nn.Conv2d(1,1,kernel_size = 3, padding = 1, bias = False)\n",
        "conv2.weight.data = edge_filter_tensor\n",
        "image_edge_x = conv2(image_tensor)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "image_edge_x"
      ],
      "metadata": {
        "id": "PDo1nE_bYt08",
        "outputId": "6fa27402-806f-4a9d-c687-93deb983b8dd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "          [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "          [ 0.,  0.,  1.,  1.,  0.,  0., -1., -1.,  0.,  0.],\n",
              "          [ 0.,  0.,  2.,  2.,  0.,  0., -2., -2.,  0.,  0.],\n",
              "          [ 0.,  0.,  3.,  3.,  0.,  0., -3., -3.,  0.,  0.],\n",
              "          [ 0.,  0.,  3.,  3.,  0.,  0., -3., -3.,  0.,  0.],\n",
              "          [ 0.,  0.,  2.,  2.,  0.,  0., -2., -2.,  0.,  0.],\n",
              "          [ 0.,  0.,  1.,  1.,  0.,  0., -1., -1.,  0.,  0.],\n",
              "          [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "          [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]]]],\n",
              "       grad_fn=<ConvolutionBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Converting the tensor to numpy array and plotting it"
      ],
      "metadata": {
        "id": "B3u7ahBEYzAN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "image_conv_edge = image_edge_x.squeeze().detach().numpy()\n",
        "plot_image_with_values(image_conv_edge,'Edge Detection for gradient in X-direction')"
      ],
      "metadata": {
        "id": "8rHc2Hd9Y2gD",
        "outputId": "df30269d-69b9-4ce8-8226-5017f8c25404",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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tjY2NmDp1Kry8vPDqq6/CxcUFzzzzDJYuXYrJkycjIiICwcHB2L17t2K5jh07yj9r897btW7mZ9qSP+rnTA1CnEO5kQceeABXrlzBqlWr5GmNjY145513FHVeXl7o1q0b1q1bJx9yAoB9+/bh5MmTitrx48ejsbERr732WrPXu3LlSqvuUv/kk0+wZs0aREREYNCgQQCAnj17okuXLnjzzTcV2czKysrkf5uvbmmaYcyYMbCzs8O8efOabYFIkoSKigoAQFhYGDp37ozly5c3W8e1y7X0Ok3Z2dlhyJAh+M9//qP4UyAlJSX45JNP0L9//2aHXNT05z//GZ6ennjvvfcUh5O2b9+O//73vzd9lVRTdnZ2uP/++7FlyxYUFhbK07OzsxXn8G5mPTY2NmhsbJSn5eXlYcuWLYo683mZt99+WzF9+fLlN3yNoUOHon379li4cCEaGhqazb/2/XOzzOcs2vJP27z99ttIS0vD22+/LR8enjdvHgwGAx5//HFcuXIFHTp0wP3336/4cnZ2RqdOnRASEoKPPvoIFy9elNe5e/dunD59+rYz/VE/Z2oQYg9l+/btyMzMbDa9b9++8PX1RUxMDPr164cXXngBeXl5CAwMxObNmxVvIrOFCxdi1KhR6NevHyZPnowLFy5g5cqV6Natm+IX+cCBAzFt2jQsWrQI6enpGDJkCBwcHHD27Fls2rQJK1aswIMPPnjD7F988QV0Oh3q6+vlO+UPHDiA4OBgbNq0Sa6ztbXFmjVrMHz4cAQFBWHy5Mm488478fPPPyM5ORnt27fHN998A+Bq8wGuHleOi4uDg4MDYmJi0KVLF8yfPx9z5sxBXl4eYmNj4eLignPnzuGrr77C1KlT8Y9//AO2trZYtWoVYmJiEBISgsmTJ6NTp07IzMxERkYGdu7cqXidp59+GkOHDoWdnR3i4uIsfp/z58/H7t270b9/fzz55JOwt7dHYmIi6urqsGTJkhv+nFrDwcEBixcvxuTJkzFw4EBMmDBBvmz47rvvxnPPPXfb6547dy527dqFfv364YknnkBjY6P8fklPT7+pdYwYMQJLly7FsGHD8NBDD6G0tBTvvvsu/Pz8FOcRQkJCMGHCBPzrX//CxYsX0bdvX+zdu/em9obat2+PVatW4eGHH0ZYWBji4uLg4eGB8+fPIykpCf369cPKlStv6Xtv164dAgMD8dlnn8Hf3x933HEHunXrpto5gRvJz8/HK6+8gpiYGIwePVqertVqsWLFCowZMwYrVqzA3//+9xbXsWjRIowYMQL9+/fHo48+isrKSrzzzjsICgqyuOF2M/6onzNVtMm1Zf/f9S4bRpPLgSsqKqSHH35YvrHx4YcfbvHGxo0bN0oBAQGSk5OT1K1bN+nrr7+Wxo4dKwUEBDTL8P7770s9e/aU2rVrJ7m4uEjdu3eXZs+eLRUWFl43e9MbEJ2dnSWDwSCNHDlS+ve//y1dvnzZ4nJpaWnSmDFjJHd3d8nJyUny8fGRxo8fL+3du1dR99prr0l33nmnZGtr2+wS4i+//FLq37+/pNVqJa1WKwUEBEjTp0+XsrKyFOv44YcfpMGDB8s3SPXo0UN655135PlXrlyRnnrqKcnDw0OysbG5qRuuhg4dKul0Okmj0UhRUVFSSkqKoqalm1UtXXJqyfVudv3ss8+k0NBQycnJSbrjjjuue2Pjrdi7d68UGhoqOTo6Sl26dJHWrFkj/f3vf5ecnZ0Vdfj/NzZa8sEHH0hdu3aVnJycpICAAGnt2rUWb468dOmS9PTTT0vu7u6SVqu95Rsbk5OTpaFDh0qurq6Ss7Oz1KVLF+mRRx6Rjh49esOfgaU8KSkpUs+ePSVHR8dW3djYlKUbC5sy33T5008/WZw/cuRISafTWbyZ8FpffvmlfCNzYGDgLd/Y2NKl/7/nz9mvxUaS2ujszW8sJCQEHh4ezY7FElkSGxuLjIwMi8fnicgyqziHcisaGhpw5coVxbTvvvsOx48fv6k/gEd/PJcuXVI8P3v2LLZt28b3C9Et+t3toeTl5eH+++9HfHw8vLy8kJmZiffeew+urq44deqU/OdciMw6deqERx55BL6+vvjpp5+watUq1NXVIS0trcV7EYioOSFOyqupQ4cO6NmzJ9asWYOysjJotVqMGDECr7/+OpsJWTRs2DB8+umnKC4uhpOTEyIiIrBw4UI2E6Jb9LvbQyEiorbxuzuHQkREbYMNhYiIVMGGQkREqrjpk/Lm/3uaiIj+eBISEm5Ywz0UIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWo8l8A9+rVC3379oVOp0NxcTG2b9+OwsLCFusDAwMRFRUFNzc3VFRUYM+ePcjOzlbUREZGIiwsDM7OzsjPz0dSUhIqKyt/F7lEziZqLpGziZpL5Gyi5hI5m6i5rtXqPZSgoCAMGTIE+/btQ2JiIkpKShAfHw+NRmOx3mAwYOzYsUhLS0NiYiKysrIQFxcHDw8PuaZfv34IDw9HUlIS1qxZg/r6esTHx8POzs7qc4mcTdRcImcTNZfI2UTNJXI2UXM11eqG0qdPHxw7dgzp6ekoLy/H1q1b0dDQgNDQUIv14eHhyM7ORkpKCsrLy5GcnIyioiL07t1bUbN//35kZWWhtLQUW7ZsgYuLCwICAqw+l8jZRM0lcjZRc4mcTdRcImcTNVdTrWootra28PLyQm5urmJ6bm4uDAaDxWW8vb2b1efk5Mj1bm5ucHFxUdTU1dWhoKAA3t7eVp1L5Gyi5hI5m6i5RM4mai6Rs4may2LW214SgEajga2tLWpqahTTa2pqoNPpLC6j0+ma1RuNRrne/GhpnVqt1qpziZxN1FwiZxM1l8jZRM0lcjZRc1nCq7yIiEgVrWootbW1MJlMzTqaVquF0Wi0uIzRaGxWr9Pp5Hrzo6V1Nu2m1pZL5Gyi5hI5m6i5RM4mai6Rs4may5JWNRSTyYTCwkL4+voqpvv6+qKgoMDiMvn5+ejcuXOL9VVVVaiurlas09HREQaDAfn5+VadS+RsouYSOZuouUTOJmoukbOJmsuSVh/yOnToEMLCwhAcHAy9Xo+RI0fCwcEB6enpAIDY2FgMGjRIrk9NTYWfnx8iIiLg7u6OgQMHwsvLC4cPH1bUDBgwAP7+/vD09MTo0aNRXV2NzMxMq88lcjZRc4mcTdRcImcTNZfI2UTN1VSrb2zMyMiARqNBZGSkfMPNhg0b5N0mV1dXSJIk1xcUFGDz5s2IiopCdHQ0KisrsXHjRpSVlck1Bw4cgIODA2JiYuDs7Izz589j/fr1aGxstPpcImcTNZfI2UTNJXI2UXOJnE3UXE3ZSNemuI558+bd9osQEZF1S0hIuGENr/IiIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgV9mqspFevXujbty90Oh2Ki4uxfft2FBYWtlgfGBiIqKgouLm5oaKiAnv27EF2draiJjIyEmFhYXB2dkZ+fj6SkpJQWVn5u8glcjZRc4mcTdRcImcTNZfI2UTNda1W76EEBQVhyJAh2LdvHxITE1FSUoL4+HhoNBqL9QaDAWPHjkVaWhoSExORlZWFuLg4eHh4yDX9+vVDeHg4kpKSsGbNGtTX1yM+Ph52dnZWn0vkbKLmEjmbqLlEziZqLpGziZqrqVY3lD59+uDYsWNIT09HeXk5tm7dioaGBoSGhlqsDw8PR3Z2NlJSUlBeXo7k5GQUFRWhd+/eipr9+/cjKysLpaWl2LJlC1xcXBAQEGD1uUTOJmoukbOJmkvkbKLmEjmbqLmaalVDsbW1hZeXF3JzcxXTc3NzYTAYLC7j7e3drD4nJ0eud3Nzg4uLi6Kmrq4OBQUF8Pb2tupcImcTNZfI2UTNJXI2UXOJnE3UXBaz3vaSADQaDWxtbVFTU6OYXlNTA51OZ3EZnU7XrN5oNMr15kdL69RqtVadS+RsouYSOZuouUTOJmoukbOJmssSXuVFRESqaFVDqa2thclkatbRtFotjEajxWWMRmOzep1OJ9ebHy2ts2k3tbZcImcTNZfI2UTNJXI2UXOJnE3UXJa0qqGYTCYUFhbC19dXMd3X1xcFBQUWl8nPz0fnzp1brK+qqkJ1dbVinY6OjjAYDMjPz7fqXCJnEzWXyNlEzSVyNlFziZxN1FyWtPqQ16FDhxAWFobg4GDo9XqMHDkSDg4OSE9PBwDExsZi0KBBcn1qair8/PwQEREBd3d3DBw4EF5eXjh8+LCiZsCAAfD394enpydGjx6N6upqZGZmWn0ukbOJmkvkbKLmEjmbqLlEziZqrqZafWNjRkYGNBoNIiMj5RtuNmzYIO82ubq6QpIkub6goACbN29GVFQUoqOjUVlZiY0bN6KsrEyuOXDgABwcHBATEwNnZ2ecP38e69evR2Njo9XnEjmbqLlEziZqLpGziZpL5Gyi5mrKRro2xXXMmzfvtl+EiIisW0JCwg1reJUXERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBWt/v9QqGWBgYFtHcHqnD59uq0jWJ2MjIy2jmB1goKC2jrC7xL3UIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgg2FiIhUocpfG+7Vqxf69u0LnU6H4uJibN++HYWFhS3WBwYGIioqCm5ubqioqMCePXuQnZ2tqImMjERYWBicnZ2Rn5+PpKQkVFZWWn2u06dP4+uvv8a5c+dw4cIF/OMf/0Dv3r2vu0xGRgbWrVuH/Px8uLu7Y+zYsYiMjFTU7NixA9988w2qqqrg4+ODRx99FH5+fjedS/RsgJjjKXIuAOjduzcGDx4MX19fuLi4YNasWfjpp59uuFyfPn3wl7/8BR4eHiguLsaGDRuQlpamqBk/fjwGDRoErVaLzMxMrFmzBsXFxVafTdTxFDXXtVq9hxIUFIQhQ4Zg3759SExMRElJCeLj46HRaCzWGwwGjB07FmlpaUhMTERWVhbi4uLg4eEh1/Tr1w/h4eFISkrCmjVrUF9fj/j4eNjZ2Vl9rrq6Otx9992YMmXKTdWXlpbi9ddfR1BQEJYsWYIRI0bgvffeQ3p6ulyTkpKCdevW4cEHH8TixYvh4+ODBQsW4OLFizedS/Rsoo6nqLnMnJyckJmZiQ0bNtz0Mv7+/njmmWfw7bff4vnnn8eRI0cwa9YseHt7yzWjRo3C8OHDsXr1arz44ouoq6vDSy+9BAcHB6vOJup4ipqrqVY3lD59+uDYsWNIT09HeXk5tm7dioaGBoSGhlqsDw8PR3Z2NlJSUlBeXo7k5GQUFRUptoTDw8Oxf/9+ZGVlobS0FFu2bIGLiwsCAgKsPldoaCji4uJuuOVvtmvXLnh6emLixIkwGAwYNmwY+vTpg6SkJLlm69atGDRoEKKiomAwGPDYY4/B0dERycnJN51L9Gyijqeoucy+//57fPnllzh58uRNL/PAAw8gPT0d33zzDX7++Wd89tlnyM3NxbBhwxQ1mzdvxtGjR3H+/HmsXLkSHTp0QK9evaw6m6jjKWquplrVUGxtbeHl5YXc3FzF9NzcXBgMBovLeHt7N6vPycmR693c3ODi4qKoqaurQ0FBgWIrxBpz3Y6zZ8+ie/fuimnBwcE4c+YMAODKlSvIzc1V1Nja2qJ79+5yjbVnE3U8Rc3VWv7+/s1+yR8/fhxdu3YFAHh6eqJDhw44ceKEPP/SpUvIzs6Gv7+/1WYTdTxFzWUx620vCUCj0cDW1hY1NTWK6TU1NdDpdBaX0el0zeqNRqNcb360tE6tVmvVuW5HVVUVXF1dFdNcXV1x6dIl1NfX45dffoHJZIKbm5uixs3NDVVVVb9art8ym6jjKWqu1nJzc2t2SPLixYvyOJofr1djjdlEHU9Rc1nC/wKY6Heif//+mDp1qvx84cKFyMzMbMNE/yNyNlJPqxpKbW0tTCZTs46m1WphNBotLmM0GpvV63Q6ud782HQdWq0WJSUlVp3rdrS0RdauXTs4Ojqiffv2sLW1bbbFX1VV1WZbi2pnE3U8Rct19OhRnD17Vn5+u1frtLTnaR5H8+O108zP8/LyrC6bmWjjKXouS1p1yMtkMqGwsBC+vr6K6b6+vigoKLC4TH5+Pjp37txifVVVFaqrqxXrdHR0hMFgQH5+vlXnuh1du3Ztdsz4xIkT8vFge3t7+Pr64tSpU/J8k8mEU6dO/erHs3+rbKKOp2i5Ll++jJKSEvmroaHhpr6Pps6cOdPs3FiPHj3khlBaWooLFy4oatq1awc/P78Wz42JnM1MtPEUPZclrb7K69ChQwgLC0NwcDD0ej1GjhwJBwcH+dLR2NhYDBo0SK5PTU2Fn58fIiIi4O7ujoEDB8LLywuHDx9W1AwYMAD+/v7w9PTE6NGjUV1dfUu7yKLmunz5MvLy8uStpdLSUuTl5aG8vBwA8Mknn2DlypVy/ZAhQ1BaWor169fj559/xs6dO3Hw4EGMGDFCrhk5ciT27t2L7777DgUFBVizZg3q6uqa3Q9izdlEHU9Rc5lptVr4+PjIJ2O9vLzg4+Oj2MqfPn06JkyYID/ftm0bgoODMXLkSHh5eWHcuHHo0qULduzYoagZM2YMevbsCW9vb8yYMQMXLlzAkSNHrDqbqOMpaq6mWn0OJSMjAxqNBpGRkfINNxs2bJBP9ri6ukKSJLm+oKAAmzdvRlRUFKKjo1FZWYmNGzeirKxMrjlw4AAcHBwQExMDZ2dnnD9/HuvXr0djY6PV58rJycG8efPk5+vWrQMADBw4ENOnT8eFCxfkX+DA1atWXnjhBXz00UfYtm0b3N3d8fjjjyMkJESu6du3L3755Rd8/vnnqKqqwt13340XX3zxlg95iZxN1PEUNZfZn//8Z0yfPl1+/txzzwEANm3ahE2bNgEA9Hq9IuOZM2fw9ttvIy4uDhMmTEBRURHeeOMNxZbrf/7zHzg5OWHatGnQaDTIzMzEwoULb2nPQ8Rsoo6nqLmaspGuTXEd1/6ioZsTGBjY1hGszunTp9s6gtXJyMho6whWJygoqK0jWJ2EhIQb1vBveRERkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgv8F8K+If9H01vGvDd86/rXhW8fP5q+DeyhERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqlDlrw336tULffv2hU6nQ3FxMbZv347CwsIW6wMDAxEVFQU3NzdUVFRgz549yM7OVtRERkYiLCwMzs7OyM/PR1JSEiorK60+1+rVq7F7926cO3cOzs7OCAkJwcyZM9G5c+frLrdz50688847+Pnnn+Hj44OZM2fivvvuk+dLkoSVK1fiiy++QHV1NUJDQ/HKK6/Ax8fHqnNdS8TxFDmXvb09nn76aQwYMAAGgwFGoxEHDx7EsmXLUFZWdt1lJ0yYgMmTJ0Ov1yMrKwsLFy7EyZMn5fmOjo6YPXs2hg8fDkdHRxw4cACvvfYaKioqrD6bqOMpaq5rtXoPJSgoCEOGDMG+ffuQmJiIkpISxMfHQ6PRWKw3GAwYO3Ys0tLSkJiYiKysLMTFxcHDw0Ou6devH8LDw5GUlIQ1a9agvr4e8fHxsLOzs/pcR44cwYQJE/Dpp59i9erVuHLlCh577DHU1ta2uExaWhpmzZqFMWPG4IsvvkB0dDSeeuopnD17Vq754IMPsGHDBiQkJODTTz9Fu3btMHXqVNTV1Vl1LjNRx1PUXADg7OyMe++9F++99x7GjRuHZ555Bp07d8bKlSuvu9ywYcMwe/Zs/Otf/8K4ceOQlZWFxMRE3HHHHXLN888/j8jISMycOROTJk2Ch4cHVqxYYfXZRB1PUXM11eqG0qdPHxw7dgzp6ekoLy/H1q1b0dDQgNDQUIv14eHhyM7ORkpKCsrLy5GcnIyioiL07t1bUbN//35kZWWhtLQUW7ZsgYuLCwICAqw+1/vvv4/Ro0fDz88PAQEBWLBgAYqKiq77/4CsX78e/fv3x6OPPoouXbrg6aefRmBgID755BMAV/cCPv74Y0ybNg3R0dG45557sGjRIpSWlmLv3r1WnctM1PEUNRcAGI1GPPbYY9i5cyfy8vJw4sQJLFiwAN26dUOnTp1aXG7SpEn44osvsGXLFuTk5GDevHm4fPkyxowZAwDQ6XQYO3YslixZgtTUVJw+fRovv/wyQkND0aNHD6vOJup4ipqrqVY1FFtbW3h5eSE3N1cxPTc3FwaDweIy3t7ezepzcnLkejc3N7i4uChq6urqUFBQAG9vb6vOZUl1dTUAwNXVtcWa9PR09OnTRzGtX79+SE9PBwAUFBSgvLxcUePi4oIePXrg+PHjVp9L1PEUNdf16HQ6mEwm/PLLLxbnOzg4IDAwEAcPHpSnSZKEQ4cOITg4GMDVrWUHBwdFzblz51BYWIiQkBCrzSbqeIqay2LW214SgEajga2tLWpqahTTa2pqoNPpLC6j0+ma1RuNRrne/GhpnVqt1qpzNWUymbB48WKEhoaia9euLdaVl5fD3d1dMc3d3V0+JlxeXg4A0Ov1zWrM86w5l6jjKWquljg6OmLmzJnYtm1bs/Wbubm5wd7evtn5hoqKCnkc9Xo96uvr5Y0OSzXWmE3U8RQ1lyW8yqsNzZ8/H2fPnsWbb77Z1lEURM1F1zdixAgcOXJE/goLC5Pn2dvbY+nSpbCxscGrr77KbPSraNVVXrW1tTCZTM06mlarhdFotLiM0WhsVq/T6eR682PTdWi1WpSUlFh1rmvNnz8f+/btw0cffYSOHTtet1av11vcKjPvHZi3vMrLyxUn3SoqKm75eKiIuUQdT9FyJScnK652Mtfb29vjrbfegpeXFyZPntziHgAAVFVV4cqVKxb3PM17leXl5XB0dISLi4tiT+B6e54iZzMTbTxFz2VJq/ZQTCYTCgsL4evrq5ju6+uLgoICi8vk5+c3uxT12vqqqipUV1cr1uno6AiDwYD8/HyrzgVcPeY7f/587N27F//+979bPAZ6rZCQEBw6dEgx7eDBg/IxYYPBAL1ej9TUVHm+0WjEiRMn5GPL1poLEHc8RctVW1uL8+fPy191dXXyL2wfHx9MmTIFFy9evO46GhoacPr0acV5LxsbG4SHh8vnvTIyMtDQ0KCoufvuu+Hl5SWfP7OmbGaijafouSxp9SGvQ4cOISwsDMHBwdDr9Rg5ciQcHBzkwYuNjcWgQYPk+tTUVPj5+SEiIgLu7u4YOHAgvLy8cPjwYUXNgAED4O/vD09PT4wePRrV1dXIzMy0+lyvvfYatm7diiVLlkCj0aCsrAxlZWW4fPmyXDNnzhwsW7ZMfh4fH48DBw7gww8/RG5uLt59912cOnUKDz30EICrH6qHH34YiYmJ+Pbbb3HmzBnMmTMHnp6eiu/RGnOZiTqeouYCrm79L1u2DEFBQXj++edhZ2cHvV4PvV4PBwcHue6DDz6QxwwAPvroIzz44IMYNWoUfH198corr6Bdu3b46quvAFzdKPjyyy8xe/Zs9O7dG4GBgZg/fz7S0tJw4sQJq84m6niKmqupVt/YmJGRAY1Gg8jISPmGmw0bNsi7rq6urpAkSa4vKCjA5s2bERUVhejoaFRWVmLjxo2Km5kOHDgABwcHxMTEwNnZGefPn8f69evR2Nho9bk+++wzAMAjjzyimD5//nyMHj0aAFBUVAQbGxt5XmhoKJYsWYK3334by5cvh4+PD9555x3FCfMpU6bg0qVLmDt3LqqrqxEWFobExEQ4OTlZdS4zUcdT1FwA4OnpiejoaADA5s2bFfMeeeQRHDlyBMDVK4Lc3NzkeTt27MAdd9yBGTNmQK/XIzMzE9OmTVMc3ly8eDEkScLy5cvh4OCAAwcOYP78+VafTdTxFDVXUzbStSmuY968ebf9In9U48aNa+sIVmfTpk1tHcHqfP75520dweqMHz++rSNYnYSEhBvW8CovIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSpa/f+hUMsCAwPbOgL9AZw+fbqtIxAB4B4KERGphA2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSpU+WvDvXr1Qt++faHT6VBcXIzt27ejsLCwxfrAwEBERUXBzc0NFRUV2LNnD7KzsxU1kZGRCAsLg7OzM/Lz85GUlITKykqrz7Vq1SqsWrUKeXl5AICgoCC88sorGD58eIvLbNq0Cf/85z+Rl5eHrl27YvHixXjggQfk+ZIkISEhAatXr0ZVVRX69euHVatWoWvXrlaf61oijqfIuQAgISEBcXFx8Pb2Rn19PX788Ue89NJLOHz48HWXe/LJJzFr1ix07NgRx48fx1NPPYUjR47I852cnPDWW28hLi4OTk5O2LlzJ5588kmUlpZafTZRx1PUXNdq9R5KUFAQhgwZgn379iExMRElJSWIj4+HRqOxWG8wGDB27FikpaUhMTERWVlZiIuLg4eHh1zTr18/hIeHIykpCWvWrEF9fT3i4+NhZ2dn9bkMBgNef/11/Pjjjzh69Ciio6MxatQoZGRkWKxPSUnBhAkTMGXKFKSlpSE2NhaxsbE4deqUXLNkyRK8/fbbeO+995CamgqtVouhQ4fi8uXLVp/LTNTxFDWX2ZkzZzBjxgx0794d/fv3R15eHnbt2gW9Xt/iMuPHj8fSpUsxb948hIWF4fjx49i5c6ci47JlyxATE4Nx48Zh4MCB8PLywubNm60+m6jjKWquplrdUPr06YNjx44hPT0d5eXl2Lp1KxoaGhAaGmqxPjw8HNnZ2UhJSUF5eTmSk5NRVFSE3r17K2r279+PrKwslJaWYsuWLXBxcUFAQIDV54qJicEDDzyArl27wt/fHwsWLIBOp8OhQ4cs1q9YsQLDhg3DrFmzcO+99+K1115DWFgYVq5cCeDqXsDy5cvx8ssvY9SoUejRowfWrVuHwsJCbNmyxepzmYk6nqLmMvv000+xd+9enDt3DqdPn8bMmTPh6uqKHj16tLjMzJkzsXr1anz44Yf473//i8cffxy1tbV49NFHAQDt27fHlClTMHPmTCQnJ+PYsWOYPHmy/AvKmrOJOp6i5mqqVQ3F1tYWXl5eyM3NVUzPzc2FwWCwuIy3t3ez+pycHLnezc0NLi4uipq6ujoUFBTA29vbqnM11djYiI0bN6KmpgYREREWaw4ePIj7779fMW3o0KE4ePAgAODcuXMoLi5W1Li6uiI8PFyusfZcoo6nqLla4uDggKlTp6KqqgrHjx9vsaZnz57Ys2ePPE2SJOzZs0d+L/Ts2ROOjo6KmqysLPz0008tvl+sIZuo4ylqLktadQ5Fo9HA1tYWNTU1iuk1NTUt7rbqdLpm9UajETqdTp5vXkfTdWq1WqvOZXby5ElERETg8uXL0Ol0+Oqrr1r83x2Li4vxpz/9STHtT3/6E4qLi+X55mkt1Vh7LlHHU9RcTY0YMQIbN26ERqNBUVERBg8ejIqKCou1er0e9vb2KCkpUUwvKSmRt1w7duyIuro6XLx4sVlNx44drTabqOMpai5LeJVXG7jnnnuQnp6O1NRUPPHEE5g0aZIQ/42rqLno5jz00EOorq6Wv/r37w8ASE5ORkhICPr27YsdO3bg888/VxxL/6NnI/W0qqHU1tbCZDI162harRZGo9HiMkajsVm9TqeT682PltbZtJtaWy4zR0dH+Pn5oWfPnli0aBGCg4OxYsUKi7UdO3a0uEVm3toyP16vxtpziTqeouX6+uuvERISIn8dPXpUzpmTk4PU1FT87W9/w5UrVzBlyhSL6ygvL8eVK1duuPfp5OQEV1fXFmusKZuZaOMpei5LWtVQTCYTCgsL4evrq5ju6+uLgoICi8vk5+ejc+fOLdZXVVWhurpasU5HR0cYDAbk5+dbda7r5a2rq7M4LyIiAnv37lVM2717t3w8uHPnzujYsaOi5pdffkFqauptH88WLZeo4ylaLqPRiJycHPmrpavpbG1t4eTkZHFeQ0MDfvzxRwwaNEieZmNjg0GDBsnnvn788UfU19cravz9/eHj49Pi+TGRs5mJNp6i57Kk1Ye8Dh06hLCwMAQHB0Ov12PkyJFwcHBAeno6ACA2NlYxuKmpqfDz80NERATc3d3ly/quvfY8NTUVAwYMgL+/Pzw9PTF69GhUV1cjMzPT6nPNmTMH+/fvR15eHk6ePIk5c+bgu+++w1//+lcAwMSJEzFnzhy5/plnnsGOHTvw1ltvITMzE3PnzsXRo0cxY8YMAFc/UM8++yzmz5+Pr7/+GidPnsTEiRPh5eWF2NhYq89lJup4ipoLuHrsfcGCBQgPD8ddd92FsLAwfPDBB7jzzjuxadMmuW7Pnj2YPn26/Hzp0qV47LHHMHHiRAQEBGDVqlXQarVYu3YtgKsbBh988AGWLl0q38ewdu1apKSkIDU11aqziTqeouZqqtU3NmZkZECj0SAyMlK+4WbDhg3ybpOrqyskSZLrCwoKsHnzZkRFRSE6OhqVlZXYuHEjysrK5JoDBw7AwcEBMTExcHZ2xvnz57F+/Xo0NjZafa7S0lJMnDgRRUVF8iWSO3fuxODBgwEA58+fh63t//p837598cknn+Dll1/Giy++iK5du2LLli3o1q2bXDN79mzU1NTIV8n0798fO3bsgLOzs9XnMhN1PEXNBVy9Wi8gIACTJk2CXq9HRUUFjhw5ggEDBijOjXXp0kVxctd8HuPVV19Fx44dkZ6ejmHDhiluDHzuuedgMpnw5ZdfKm4etPZsoo6nqLmaspGuTXEd8+bNu+0X+aNKSEho6whWh++zWzd37ty2jmB1+DO7dTfz+4xXeRERkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAp7NVbSq1cv9O3bFzqdDsXFxdi+fTsKCwtbrA8MDERUVBTc3NxQUVGBPXv2IDs7W1ETGRmJsLAwODs7Iz8/H0lJSaisrLT6XKtWrcKqVauQl5cHAAgKCsIrr7yC4cOHt7jMpk2b8M9//hN5eXno2rUrFi9ejAceeECeL0kSEhISsHr1alRVVaFfv35YtWoVunbtavW5riXieIqcCwASEhIQFxcHb29v1NfX48cff8RLL72Ew4cPX3e5J598ErNmzULHjh1x/PhxPPXUUzhy5Ig838nJCW+99Rbi4uLg5OSEnTt34sknn0RpaanVZxN1PEXNda1W76EEBQVhyJAh2LdvHxITE1FSUoL4+HhoNBqL9QaDAWPHjkVaWhoSExORlZWFuLg4eHh4yDX9+vVDeHg4kpKSsGbNGtTX1yM+Ph52dnZWn8tgMOD111/Hjz/+iKNHjyI6OhqjRo1CRkaGxfqUlBRMmDABU6ZMQVpaGmJjYxEbG4tTp07JNUuWLMHbb7+N9957D6mpqdBqtRg6dCguX75s9bnMRB1PUXOZnTlzBjNmzED37t3Rv39/5OXlYdeuXdDr9S0uM378eCxduhTz5s1DWFgYjh8/jp07dyoyLlu2DDExMRg3bhwGDhwILy8vbN682eqziTqeouZqqtUNpU+fPjh27BjS09NRXl6OrVu3oqGhAaGhoRbrw8PDkZ2djZSUFJSXlyM5ORlFRUXo3bu3omb//v3IyspCaWkptmzZAhcXFwQEBFh9rpiYGDzwwAPo2rUr/P39sWDBAuh0Ohw6dMhi/YoVKzBs2DDMmjUL9957L1577TWEhYVh5cqVAK7uBSxfvhwvv/wyRo0ahR49emDdunUoLCzEli1brD6XmajjKWous08//RR79+7FuXPncPr0acycOROurq7o0aNHi8vMnDkTq1evxocffoj//ve/ePzxx1FbW4tHH30UANC+fXtMmTIFM2fORHJyMo4dO4bJkyfLv6CsOZuo4ylqrqZa1VBsbW3h5eWF3NxcxfTc3FwYDAaLy3h7ezerz8nJkevd3Nzg4uKiqKmrq0NBQQG8vb2tOldTjY2N2LhxI2pqahAREWGx5uDBg7j//vsV04YOHYqDBw8CAM6dO4fi4mJFjaurK8LDw+Uaa88l6niKmqslDg4OmDp1KqqqqnD8+PEWa3r27Ik9e/bI0yRJwp49e+T3Qs+ePeHo6KioycrKwk8//dTi+8Uasok6nqLmsqRV51A0Gg1sbW1RU1OjmF5TU9PibqtOp2tWbzQaodPp5PnmdTRdp1artepcZidPnkRERAQuX74MnU6Hr776CoGBgRZri4uL8ac//Ukx7U9/+hOKi4vl+eZpLdVYey5Rx1PUXE2NGDECGzduhEajQVFREQYPHoyKigqLtXq9Hvb29igpKVFMLykpkbdcO3bsiLq6Oly8eLFZTceOHa02m6jjKWouS3iVVxu45557kJ6ejtTUVDzxxBOYNGkSTp8+3daxhM1FN+ehhx5CdXW1/NW/f38AQHJyMkJCQtC3b1/s2LEDn3/+ueJY+h89G6mnVQ2ltrYWJpOpWUfTarUwGo0WlzEajc3qdTqdXG9+tLTOpt3U2nKZOTo6ws/PDz179sSiRYsQHByMFStWWKzt2LGjxS0y89aW+fF6NdaeS9TxFC3X119/jZCQEPnr6NGjcs6cnBykpqbib3/7G65cuYIpU6ZYXEd5eTmuXLlyw71PJycnuLq6tlhjTdnMRBtP0XNZ0qqGYjKZUFhYCF9fX8V0X19fFBQUWFwmPz8fnTt3brG+qqoK1dXVinU6OjrCYDAgPz/fqnNdL29dXZ3FeREREdi7d69i2u7du+XjwZ07d0bHjh0VNb/88gtSU1Nv+3i2aLlEHU/RchmNRuTk5MhfLV1NZ2trCycnJ4vzGhoa8OOPP2LQoEHyNBsbGwwaNEg+9/Xjjz+ivr5eUePv7w8fH58Wz4+JnM1MtPEUPZclrT7kdejQIYSFhSE4OBh6vR4jR46Eg4MD0tPTAQCxsbGKwU1NTYWfnx8iIiLg7u4uX9Z37bXnqampGDBgAPz9/eHp6YnRo0ejuroamZmZVp9rzpw52L9/P/Ly8nDy5EnMmTMH3333Hf76178CACZOnIg5c+bI9c888wx27NiBt956C5mZmZg7dy6OHj2KGTNmALj6gXr22Wcxf/58fP311zh58iQmTpwILy8vxMbGWn0uM1HHU9RcwNVj7wsWLEB4eDjuuusuhIWF4YMPPsCdd96JTZs2yXV79uzB9OnT5edLly7FY489hokTJyIgIACrVq2CVqvF2rVrAVzdMPjggw+wdOlS+T6GtWvXIiUlBampqVadTdTxFDVXU62+sTEjIwMajQaRkZHyDTcbNmyQd5tcXV0hSZJcX1BQgM2bNyMqKgrR0dGorKzExo0bUVZWJtccOHAADg4OiImJgbOzM86fP4/169ejsbHR6nOVlpZi4sSJKCoqki+R3LlzJwYPHgwAOH/+PGxt/9fn+/bti08++QQvv/wyXnzxRXTt2hVbtmxBt27d5JrZs2ejpqZGvkqmf//+2LFjB5ydna0+l5mo4ylqLuDq1XoBAQGYNGkS9Ho9KioqcOTIEQwYMEBxbqxLly6Kk7vm8xivvvoqOnbsiPT0dAwbNkxxY+Bzzz0Hk8mEL7/8UnHzoLVnE3U8Rc3VlI10bYrrmDdv3m2/yB9VQkJCW0ewOnyf3bq5c+e2dQSrw5/ZrbuZ32e8youIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkilb/fyjUMv5/7PRbCAwMbOsIRAC4h0JERCphQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkClX+2nCvXr3Qt29f6HQ6FBcXY/v27SgsLGyxPjAwEFFRUXBzc0NFRQX27NmD7OxsRU1kZCTCwsLg7OyM/Px8JCUlobKy0upzrV69Grt378a5c+fg7OyMkJAQzJw5E507d77ucjt37sQ777yDn3/+GT4+Ppg5cybuu+8+eb4kSVi5ciW++OILVFdXIzQ0FK+88gp8fHysOte1RBxPkXPZ29vj6aefxoABA2AwGGA0GnHw4EEsW7YMZWVl1112woQJmDx5MvR6PbKysrBw4UKcPHlSnu/o6IjZs2dj+PDhcHR0xIEDB/Daa6+hoqLC6rOJOp6i5rpWq/dQgoKCMGTIEOzbtw+JiYkoKSlBfHw8NBqNxXqDwYCxY8ciLS0NiYmJyMrKQlxcHDw8POSafv36ITw8HElJSVizZg3q6+sRHx8POzs7q8915MgRTJgwAZ9++ilWr16NK1eu4LHHHkNtbW2Ly6SlpWHWrFkYM2YMvvjiC0RHR+Opp57C2bNn5ZoPPvgAGzZsQEJCAj799FO0a9cOU6dORV1dnVXnMhN1PEXNBQDOzs6499578d5772HcuHF45pln0LlzZ6xcufK6yw0bNgyzZ8/Gv/71L4wbNw5ZWVlITEzEHXfcIdc8//zziIyMxMyZMzFp0iR4eHhgxYoVVp9N1PEUNVdTrW4offr0wbFjx5Ceno7y8nJs3boVDQ0NCA0NtVgfHh6O7OxspKSkoLy8HMnJySgqKkLv3r0VNfv370dWVhZKS0uxZcsWuLi4ICAgwOpzvf/++xg9ejT8/PwQEBCABQsWoKio6Lr/d8r69evRv39/PProo+jSpQuefvppBAYG4pNPPgFwdS/g448/xrRp0xAdHY177rkHixYtQmlpKfbu3WvVucxEHU9RcwGA0WjEY489hp07dyIvLw8nTpzAggUL0K1bN3Tq1KnF5SZNmoQvvvgCW7ZsQU5ODubNm4fLly9jzJgxAACdToexY8diyZIlSE1NxenTp/Hyyy8jNDQUPXr0sOpsoo6nqLmaalVDsbW1hZeXF3JzcxXTc3NzYTAYLC7j7e3drD4nJ0eud3Nzg4uLi6Kmrq4OBQUF8Pb2tupcllRXVwMAXF1dW6xJT09Hnz59FNP69euH9PR0AEBBQQHKy8sVNS4uLujRoweOHz9u9blEHU9Rc12PTqeDyWTCL7/8YnG+g4MDAgMDcfDgQXmaJEk4dOgQgoODAVzdWnZwcFDUnDt3DoWFhQgJCbHabKKOp6i5LGa97SUBaDQa2NraoqamRjG9pqYGOp3O4jI6na5ZvdFolOvNj5bWqdVqrTpXUyaTCYsXL0ZoaCi6du3aYl15eTnc3d0V09zd3eVjwuXl5QAAvV7frMY8z5pziTqeouZqiaOjI2bOnIlt27Y1W7+Zm5sb7O3tm51vqKiokMdRr9ejvr5e3uiwVGON2UQdT1FzWcKrvNrQ/PnzcfbsWbz55pttHUVB1Fx0fSNGjMCRI0fkr7CwMHmevb09li5dChsbG7z66qvMRr+KVl3lVVtbC5PJ1KyjabVaGI1Gi8sYjcZm9TqdTq43PzZdh1arRUlJiVXnutb8+fOxb98+fPTRR+jYseN1a/V6vcWtMvPegXnLq7y8XHHSraKi4paPh4qYS9TxFC1XcnKy4monc729vT3eeusteHl5YfLkyS3uAQBAVVUVrly5YnHP07xXWV5eDkdHR7i4uCj2BK635ylyNjPRxlP0XJa0ag/FZDKhsLAQvr6+ium+vr4oKCiwuEx+fn6zS1Gvra+qqkJ1dbVinY6OjjAYDMjPz7fqXMDVY77z58/H3r178e9//7vFY6DXCgkJwaFDhxTTDh48KB8TNhgM0Ov1SE1NlecbjUacOHFCPrZsrbkAccdTtFy1tbU4f/68/FVXVyf/wvbx8cGUKVNw8eLF666joaEBp0+fVpz3srGxQXh4uHzeKyMjAw0NDYqau+++G15eXvL5M2vKZibaeIqey5JWH/I6dOgQwsLCEBwcDL1ej5EjR8LBwUEevNjYWAwaNEiuT01NhZ+fHyIiIuDu7o6BAwfCy8sLhw8fVtQMGDAA/v7+8PT0xOjRo1FdXY3MzEyrz/Xaa69h69atWLJkCTQaDcrKylBWVobLly/LNXPmzMGyZcvk5/Hx8Thw4AA+/PBD5Obm4t1338WpU6fw0EMPAbj6oXr44YeRmJiIb7/9FmfOnMGcOXPg6emp+B6tMZeZqOMpai7g6tb/smXLEBQUhOeffx52dnbQ6/XQ6/VwcHCQ6z744AN5zADgo48+woMPPohRo0bB19cXr7zyCtq1a4evvvoKwNWNgi+//BKzZ89G7969ERgYiPnz5yMtLQ0nTpyw6myijqeouZpq9Y2NGRkZ0Gg0iIyMlG+42bBhg7zr6urqCkmS5PqCggJs3rwZUVFRiI6ORmVlJTZu3Ki4menAgQNwcHBATEwMnJ2dcf78eaxfvx6NjY1Wn+uzzz4DADzyyCOK6fPnz8fo0aMBAEVFRbCxsZHnhYaGYsmSJXj77bexfPly+Pj44J133lGcMJ8yZQouXbqEuXPnorq6GmFhYUhMTISTk5NV5zITdTxFzQUAnp6eiI6OBgBs3rxZMe+RRx7BkSNHAFy9IsjNzU2et2PHDtxxxx2YMWMG9Ho9MjMzMW3aNMXhzcWLF0OSJCxfvhwODg44cOAA5s+fb/XZRB1PUXM1ZSNdm+I65s2bd9sv8kc1bty4to5gdTZt2tTWEazO559/3tYRrM748ePbOoLVSUhIuGENr/IiIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUkWr/3w9tSwjI6OtI9AfQFBQUFtHIALAPRQiIlIJGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVajy14Z79eqFvn37QqfTobi4GNu3b0dhYWGL9YGBgYiKioKbmxsqKiqwZ88eZGdnK2oiIyMRFhYGZ2dn5OfnIykpCZWVlVaf6/Tp0/j6669x7tw5XLhwAf/4xz/Qu3fv6y6TkZGBdevWIT8/H+7u7hg7diwiIyMVNTt27MA333yDqqoq+Pj44NFHH4Wfn99N5xI9GyDmeIqcCwB69+6NwYMHw9fXFy4uLpg1axZ++umnGy7Xp08f/OUvf4GHhweKi4uxYcMGpKWlKWrGjx+PQYMGQavVIjMzE2vWrEFxcbHVZxN1PEXNda1W76EEBQVhyJAh2LdvHxITE1FSUoL4+HhoNBqL9QaDAWPHjkVaWhoSExORlZWFuLg4eHh4yDX9+vVDeHg4kpKSsGbNGtTX1yM+Ph52dnZWn6uurg533303pkyZclP1paWleP311xEUFIQlS5ZgxIgReO+995Ceni7XpKSkYN26dXjwwQexePFi+Pj4YMGCBbh48eJN5xI9m6jjKWouMycnJ2RmZmLDhg03vYy/vz+eeeYZfPvtt3j++edx5MgRzJo1C97e3nLNqFGjMHz4cKxevRovvvgi6urq8NJLL8HBwcGqs4k6nqLmaqrVDaVPnz44duwY0tPTUV5ejq1bt6KhoQGhoaEW68PDw5GdnY2UlBSUl5cjOTkZRUVFii3h8PBw7N+/H1lZWSgtLcWWLVvg4uKCgIAAq88VGhqKuLi4G275m+3atQuenp6YOHEiDAYDhg0bhj59+iApKUmu2bp1KwYNGoSoqCgYDAY89thjcHR0RHJy8k3nEj2bqOMpai6z77//Hl9++SVOnjx508s88MADSE9PxzfffIOff/4Zn332GXJzczFs2DBFzebNm3H06FGcP38eK1euRIcOHdCrVy+rzibqeIqaq6lWNRRbW1t4eXkhNzdXMT03NxcGg8HiMt7e3s3qc3Jy5Ho3Nze4uLgoaurq6lBQUKDYCrHGXLfj7Nmz6N69u2JacHAwzpw5AwC4cuUKcnNzFTW2trbo3r27XGPt2UQdT1FztZa/v3+zX/LHjx9H165dAQCenp7o0KEDTpw4Ic+/dOkSsrOz4e/vb7XZRB1PUXNZzHrbSwLQaDSwtbVFTU2NYnpNTQ10Op3FZXQ6XbN6o9Eo15sfLa1Tq9Vada7bUVVVBVdXV8U0V1dXXLp0CfX19fjll19gMpng5uamqHFzc0NVVdWvluu3zCbqeIqaq7Xc3NyaHZK8ePGiPI7mx+vVWGM2UcdT1FyW8L8AJvqd6N+/P6ZOnSo/X7hwITIzM9sw0f+InI3U06qGUltbC5PJ1KyjabVaGI1Gi8sYjcZm9TqdTq43PzZdh1arRUlJiVXnuh0tbZG1a9cOjo6OaN++PWxtbZtt8VdVVbXZ1qLa2UQdT9FyHT16FGfPnpWf3+7VOi3teZrH0fx47TTz87y8PKvLZibaeIqey5JWHfIymUwoLCyEr6+vYrqvry8KCgosLpOfn4/OnTu3WF9VVYXq6mrFOh0dHWEwGJCfn2/VuW5H165dmx0zPnHihHw82N7eHr6+vjh16pQ832Qy4dSpU7/68ezfKpuo4ylarsuXL6OkpET+amhouKnvo6kzZ840OzfWo0cPuSGUlpbiwoULipp27drBz8+vxXNjImczE208Rc9lSauv8jp06BDCwsIQHBwMvV6PkSNHwsHBQb50NDY2FoMGDZLrU1NT4efnh4iICLi7u2PgwIHw8vLC4cOHFTUDBgyAv78/PD09MXr0aFRXV9/SLrKouS5fvoy8vDx5a6m0tBR5eXkoLy8HAHzyySdYuXKlXD9kyBCUlpZi/fr1+Pnnn7Fz504cPHgQI0aMkGtGjhyJvXv34rvvvkNBQQHWrFmDurq6ZveDWHM2UcdT1FxmWq0WPj4+8slYLy8v+Pj4KLbyp0+fjgkTJsjPt23bhuDgYIwcORJeXl4YN24cunTpgh07dihqxowZg549e8Lb2xszZszAhQsXcOTIEavOJup4ipqrqVafQ8nIyIBGo0FkZKR8w82GDRvkkz2urq6QJEmuLygowObNmxEVFYXo6GhUVlZi48aNKCsrk2sOHDgABwcHxMTEwNnZGefPn8f69evR2Nho9blycnIwb948+fm6desAAAMHDsT06dNx4cIF+Rc4cPWqlRdeeAEfffQRtm3bBnd3dzz++OMICQmRa/r27YtffvkFn3/+OaqqqnD33XfjxRdfvOVDXiJnE3U8Rc1l9uc//xnTp0+Xnz/33HMAgE2bNmHTpk0AAL1er8h45swZvP3224iLi8OECRNQVFSEN954Q7Hl+p///AdOTk6YNm0aNBoNMjMzsXDhwlva8xAxm6jjKWqupmyka1Ncx7W/aOjmBAYGtnUEq3P69Om2jmB1MjIy2jqC1QkKCmrrCFYnISHhhjX8W15ERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVfD/lP8V8U+x02+Bf4qdRME9FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVqPLXhnv16oW+fftCp9OhuLgY27dvR2FhYYv1gYGBiIqKgpubGyoqKrBnzx5kZ2craiIjIxEWFgZnZ2fk5+cjKSkJlZWVv4tcImcTNZfI2UTNJXI2UXOJnE3UXNdq9R5KUFAQhgwZgn379iExMRElJSWIj4+HRqOxWG8wGDB27FikpaUhMTERWVlZiIuLg4eHh1zTr18/hIeHIykpCWvWrEF9fT3i4+NhZ2dn9blEziZqLpGziZpL5Gyi5hI5m6i5mmp1Q+nTpw+OHTuG9PR0lJeXY+vWrWhoaEBoaKjF+vDwcGRnZyMlJQXl5eVITk5GUVERevfurajZv38/srKyUFpaii1btsDFxQUBAQFWn0vkbKLmEjmbqLlEziZqLpGziZqrqVY1FFtbW3h5eSE3N1cxPTc3FwaDweIy3t7ezepzcnLkejc3N7i4uChq6urqUFBQAG9vb6vOJXI2UXOJnE3UXCJnEzWXyNlEzWUx620vCUCj0cDW1hY1NTWK6TU1NdDpdBaX0el0zeqNRqNcb360tE6tVmvVuUTOJmoukbOJmkvkbKLmEjmbqLks4VVeRESkilY1lNraWphMpmYdTavVwmg0WlzGaDQ2q9fpdHK9+dHSOpt2U2vLJXI2UXOJnE3UXCJnEzWXyNlEzWVJqxqKyWRCYWEhfH19FdN9fX1RUFBgcZn8/Hx07ty5xfqqqipUV1cr1uno6AiDwYD8/HyrziVyNlFziZxN1FwiZxM1l8jZRM1lSasPeR06dAhhYWEIDg6GXq/HyJEj4eDggPT0dABAbGwsBg0aJNenpqbCz88PERERcHd3x8CBA+Hl5YXDhw8ragYMGAB/f394enpi9OjRqK6uRmZmptXnEjmbqLlEziZqLpGziZpL5Gyi5mqq1Tc2ZmRkQKPRIDIyUr7hZsOGDfJuk6urKyRJkusLCgqwefNmREVFITo6GpWVldi4cSPKysrkmgMHDsDBwQExMTFwdnbG+fPnsX79ejQ2Nlp9LpGziZpL5Gyi5hI5m6i5RM4maq6mbKRrU1zHvHnzbvtFiIjIuiUkJNywhld5ERGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKQKNhQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUgUbChERqYINhYiIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCns1VtKrVy/07dsXOp0OxcXF2L59OwoLC1usDwwMRFRUFNzc3FBRUYE9e/YgOztbURMZGYmwsDA4OzsjPz8fSUlJqKys/F3kEjmbqLlEziZqLpGziZpL5Gyi5rpWq/dQgoKCMGTIEOzbtw+JiYkoKSlBfHw8NBqNxXqDwYCxY8ciLS0NiYmJyMrKQlxcHDw8POSafv36ITw8HElJSVizZg3q6+sRHx8POzs7q88lcjZRc4mcTdRcImcTNZfI2UTN1VSrG0qfPn1w7NgxpKeno7y8HFu3bkVDQwNCQ0Mt1oeHhyM7OxspKSkoLy9HcnIyioqK0Lt3b0XN/v37kZWVhdLSUmzZsgUuLi4ICAiw+lwiZxM1l8jZRM0lcjZRc4mcTdRcTbWqodja2sLLywu5ubmK6bm5uTAYDBaX8fb2blafk5Mj17u5ucHFxUVRU1dXh4KCAnh7e1t1LpGziZpL5Gyi5hI5m6i5RM4mai6LWW97SQAajQa2traoqalRTK+pqYFOp7O4jE6na1ZvNBrlevOjpXVqtVqrziVyNlFziZxN1FwiZxM1l8jZRM1lCa/yIiIiVbSqodTW1sJkMjXraFqtFkaj0eIyRqOxWb1Op5PrzY+W1tm0m1pbLpGziZpL5Gyi5hI5m6i5RM4mai5LWtVQTCYTCgsL4evrq5ju6+uLgoICi8vk5+ejc+fOLdZXVVWhurpasU5HR0cYDAbk5+dbdS6Rs4maS+RsouYSOZuouUTOJmouS1p9yOvQoUMICwtDcHAw9Ho9Ro4cCQcHB6SnpwMAYmNjMWjQILk+NTUVfn5+iIiIgLu7OwYOHAgvLy8cPnxYUTNgwAD4+/vD09MTo0ePRnV1NTIzM60+l8jZRM0lcjZRc4mcTdRcImcTNVdTrb6xMSMjAxqNBpGRkfINNxs2bJB3m1xdXSFJklxfUFCAzZs3IyoqCtHR0aisrMTGjRtRVlYm1xw4cAAODg6IiYmBs7Mzzp8/j/Xr16OxsdHqc4mcTdRcImcTNZfI2UTNJXI2UXM1ZSNdm+I65s2bd9svQkRE1i0hIeGGNbzKi4iIVMGGQkREqmBDISIiVbChEBGRKthQiIhIFWwoRESkCjYUIiJSBRsKERGpgg2FiIhUwYZCRESqYEMhIiJVsKEQEZEq2FCIiEgVbChERKSKm/7z9URERNfDPRQiIlIFGwoREamCDYWIiFTBhkJERKpgQyEiIlWwoRARkSrYUIiISBVsKEREpAo2FCIiUsX/AyRpvyuMoKgPAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MbxxvlRdp20x"
      },
      "source": [
        "### Horizontal Edge\n",
        "TODO:\n",
        "Create a similar filter to detect horizontal edges."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "ZAydg700qLsw",
        "outputId": "6f0c1dfd-a7f1-454e-e692-5d4854c595f8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "edge_filter_y = np.zeros((3,3))\n",
        "edge_filter_y[0,:] = 1\n",
        "edge_filter_y[2,:] = -1\n",
        "plot_image_with_values(edge_filter_y, 'Edge Filter to calculate gradient in y-direction')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "edge_filter_tensor_y = torch.tensor(edge_filter_y, dtype = torch.float32)\n",
        "edge_filter_tensor_y = edge_filter_tensor_y.unsqueeze(0)\n",
        "edge_filter_tensor_y = edge_filter_tensor_y.unsqueeze(1)\n",
        "\n",
        "conv3 = nn.Conv2d(1,1,kernel_size = 3, padding = 1, bias = False)\n",
        "conv3.weight.data = edge_filter_tensor_y\n",
        "image_edge_y = conv3(image_tensor)"
      ],
      "metadata": {
        "id": "M2RyIsRhbXV6"
      },
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "image_conv_edge_y = image_edge_y.squeeze().detach().numpy()\n",
        "plot_image_with_values(image_conv_edge_y,'Edge Detection for gradient in Y-direction')"
      ],
      "metadata": {
        "id": "qqwqd3OJbcWf",
        "outputId": "5c4d7b3e-127b-4f66-bf0a-f49268396982",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kle9PjhE8wXY"
      },
      "source": [
        "### Laplacian Sharpening\n",
        "Lapalacian filters can increase the regions of the image with rapid intensity. It is very helpful in hding the fine details of images. Any features with a sharp discontunioty will be enhanced.\n",
        "\n",
        "One of the Laplacian filter is\n",
        "\n",
        "\\begin{bmatrix}\n",
        " 0 & -1 &  0 \\\\\n",
        "-1 &  4 & -1 \\\\\n",
        " 0 & -1 &  0 \\\\\n",
        "\\end{bmatrix}\n",
        "\n",
        "To sharpen an image ```img```:\n",
        "\n",
        "1. use the Laplacian filter to convolve the original image to obtained a filter.\n",
        "2. scale the filter into the range of the oringal image.\n",
        "3. add the filter to the original image.\n",
        "4. scale the summation to the range of the original image.\n",
        "\n",
        "\n",
        "TODO: Create this filter and visualize it. Plot the filter as a grid with black or white colors and write the value of each cell on it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "VHwADQcH9ZiA",
        "outputId": "8973f571-ea14-441b-9e34-31954b2f82af"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "laplacian_filter = np.array([[0,-1,0],[-1,4,-1],[0,-1,0]])\n",
        "plot_image_with_values(laplacian_filter,'Laplacian Filter')\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gTgdF9z9--ox"
      },
      "source": [
        "TODO: Apply this filter on the original image.\n",
        "\n",
        "Plot the image as a grid with black or white colors and write value of each cell on it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "id": "Sbr-naJ3-sXC"
      },
      "outputs": [],
      "source": [
        "laplacian_tensor = torch.tensor(laplacian_filter, dtype=torch.float32)\n",
        "laplacian_tensor = laplacian_tensor.unsqueeze(0)\n",
        "laplacian_tensor = laplacian_tensor.unsqueeze(1)\n",
        "conv4 = nn.Conv2d(1,1,kernel_size = 3, padding = 1)\n",
        "conv4.weight.data = laplacian_tensor\n",
        "image_laplacian = conv4(image_tensor)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "image_laplacian_array = image_laplacian.squeeze().detach().numpy()\n",
        "plot_image_with_values(image_laplacian_array,'Original Image with Laplacian Filter')"
      ],
      "metadata": {
        "id": "2dx9hUSseUi-",
        "outputId": "974bcfbc-b66b-4697-e064-7325bdb4cffb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Scaling the image obtained after applying the filter."
      ],
      "metadata": {
        "id": "_HQ8PhvxfQmi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def scale(x,xmax,xmin):\n",
        "  return (x - xmin)/(xmax - xmin)"
      ],
      "metadata": {
        "id": "_1Jd51tCfQP_"
      },
      "execution_count": 75,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "xmax = np.amax(image)\n",
        "xmin = np.amin(image)\n",
        "image_laplacian_scale = np.zeros((10,10))\n",
        "\n",
        "for j in range(image.shape[0]):\n",
        "  for i in range(image.shape[1]):\n",
        "    image_laplacian_scale[j][i] = scale(image_laplacian_array[j][i],xmax,xmin)\n",
        "\n",
        "plot_image_with_values(image_laplacian_scale,'Scaled Laplacian Image')"
      ],
      "metadata": {
        "id": "9iPh8bO1fv6O",
        "outputId": "288d34bc-380e-4ec2-bc3b-5cc76aea2f58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Adding the Scaled Filtered Image to Original Image"
      ],
      "metadata": {
        "id": "-rzncOCng4iz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "add_img = image + image_laplacian_scale\n",
        "plot_image_with_values(add_img,'Added Image')"
      ],
      "metadata": {
        "id": "bi5TDBE3g4Ov",
        "outputId": "591ead02-c43e-4178-c64c-a8466ff686bb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Scaling the Added Image in the range of Original Image."
      ],
      "metadata": {
        "id": "YBG0yhWuhrTl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fin_img = np.zeros((add_img.shape))\n",
        "for j in range(add_img.shape[0]):\n",
        "  for i in range(add_img.shape[1]):\n",
        "    fin_img[j][i] = scale(add_img[j][i], xmax, xmin)\n",
        "plot_image_with_values(fin_img,'Sharpened Image after implementing Laplacian Filter ')\n"
      ],
      "metadata": {
        "id": "LB0k3pufh1Py",
        "outputId": "491c0fd8-2014-4984-a451-c6bd579f568d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        }
      },
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vcXeVjszchQz"
      },
      "source": [
        "## Applying Filters on an Image\n",
        "\n",
        "In this section we apply several filters on a real image.\n",
        "\n",
        "**TODO**\n",
        "Use `PIL` library to read the attached image called `cars-1638594_1280.jpg` as a numpy array. Convert that image to grayscale so that it only has a single channel and plot the image."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1dPoNC39r8zS"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pcRb4WApdJHt"
      },
      "source": [
        "**TODO**:\n",
        "Apply the vertical edge detection to the image and plot both original and converted image."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wO9S-oDotMvD"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LbCgGFpudPyA"
      },
      "source": [
        "**TODO**:\n",
        "Apply the horizontal edge detection to the image and plot both original and converted image.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hsL3jjKXuCIz"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UXOXAXCU_Skn"
      },
      "source": [
        "**TODO**:\n",
        "Apply the sharpening to the image and plot both original and converted image.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "knmKRg_X_NTp"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mhB85-1NNfGP"
      },
      "source": [
        "### Bluring the image with the Gaussian filter\n",
        "\n",
        "One commonly used filter for blurring is the Gaussian filter. Its values are determined by the Gaussian function, which results in a bell-shaped curve.\n",
        "\n",
        "A Gaussian filter tends to give more weight to the central pixels and gradually decreasing weight as one moves to the periphery, unlike the uniform averaging filter we discussed earlier.\n",
        "\n",
        "**TODO**:\n",
        "Create a 5x5 Gaussian blur filter with these values:\n",
        "\n",
        "\\begin{bmatrix}\n",
        "1 & 4 & 6 & 4 & 1 \\\\\n",
        "4 & 16 & 24 & 16 & 4 \\\\\n",
        "6 & 24 & 36 & 24 & 6 \\\\\n",
        "4 & 16 & 24 & 16 & 4 \\\\\n",
        "1 & 4 & 6 & 4 & 1 \\\\\n",
        "\\end{bmatrix}\n",
        "\n",
        "Apply the filter to the image and plot both original and converted image.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lKodFHxQNtaI"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "allKLfTvSHmv"
      },
      "source": [
        "## Pooling\n",
        "\n",
        "Pooling is an operation frequently used in the context of Convolutional Neural Networks (CNNs) for image processing. The main idea behind pooling is to reduce the spatial size of the representation, thereby reducing the number of parameters and computational complexity in the network. This helps in making the network less prone to overfitting and also reduces computation time.\n",
        "\n",
        "There are several types of pooling operations, with the most common ones being:\n",
        "\n",
        "**Max Pooling**: In this method, for each segment of the input, the maximum value is selected. For instance, if we consider a 2x2 pooling window (often called a \"kernel\" in this context) and slide it over an image tensor, the largest value within each 2x2 window will be selected for the pooled output.\n",
        "\n",
        "- **Average Pooling**: Instead of taking the maximum value in each window, average pooling takes the average value. So for a 2x2 window, it would take the average of all 4 values in that window.\n",
        "- **Min Pooling**: This operation selects the minimum value from each window, though it's less commonly used than max or average pooling.\n",
        "- **Global Pooling**: Instead of using a fixed size window, global pooling operates over the entire height and width of the feature map, effectively transforming the spatial dimensions of the feature map to 1x1 (retaining the depth/channels).\n",
        "\n",
        "The main benefits of pooling include:\n",
        "\n",
        "- **Dimensionality Reduction**: It reduces the spatial dimensions of the feature maps, which in turn reduces the number of parameters in subsequent layers, leading to faster computations.\n",
        "- **Invariance to Small Translations**: Small translations in the input image might not lead to significant changes in the pooled feature map. This can be particularly useful when the exact location of features is less relevant than their presence.\n",
        "- **Prevents Overfitting**: By reducing the spatial resolution and thus the total number of parameters, pooling can help prevent overfitting.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JL0GQXY6UYSp"
      },
      "source": [
        "### Max Pooling:\n",
        "Create a Max Pooling filter of size 8 with stride 2 and run it on the original image.\n",
        "\n",
        "**TODO:** Explain the output and its shape dimensions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rBmFUrJQR8Yf"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mKgFIc4bW4_y"
      },
      "source": [
        "### Average Pooling:\n",
        "Create an average pooling filter of size 8 with stride 2 and run it on the original image.\n",
        "\n",
        "**TODO:** Explain the output and its shape dimensions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FSZunSLCWXca"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nCaMDWYArEXO"
      },
      "source": [
        "# Section 2: Convolutional Neural Networks\n",
        "\n",
        "The construction of neural networks is facilitated through the utilization of the ``torch.nn`` package within the PyTorch framework.\n",
        "\n",
        "A standard process for training a neural network involves the following steps:\n",
        "\n",
        "1. **Neural Network Definition:** The first step entails defining the architecture of the neural network, which encompasses the design of its interconnected layers and the inclusion of learnable parameters, often referred to as weights.\n",
        "\n",
        "2. **Iterative Data Processing:** Next, the training procedure involves iterating through a dataset containing input samples. Each input is fed into the neural network for processing.\n",
        "\n",
        "3. **Forward Propagation:** During this phase, the input data is passed through the neural network's layers, activating its neurons through weighted connections and producing an output prediction.\n",
        "\n",
        "4. **Loss Computation:** The output generated by the network is then compared to the actual desired output, leading to the computation of a loss value. This loss signifies the discrepancy between the predicted outcome and the true value.\n",
        "\n",
        "5. **Backpropagation:** After calculating the loss, the gradients of the loss with respect to the network's parameters are computed through a process called backpropagation. This entails tracing how changes in the parameters affect the loss.\n",
        "\n",
        "6. **Gradient Update:** The gradients computed during backpropagation are used to adjust the network's weights. A common method involves updating the weights by subtracting a scaled gradient value from the current weights. The scale factor, known as the learning rate, determines the step size of the update. This update rule can be expressed as: ``weight = weight - learning_rate * gradient``.\n",
        "\n",
        "Throughout this iterative process, the neural network's parameters are fine-tuned to minimize the loss and enhance its predictive accuracy. This sequence of steps forms the backbone of training neural networks, enabling them to learn and improve their performance over time.\n",
        "\n",
        "In this assignment we will create a simple CNN.\n",
        "\n",
        "\n",
        "To begin this section, we will load the CIFAR10 dataset and train a simple convolutional neural network (CNN) to classify the images.\n",
        "\n",
        "The CIFAR10 dataset has the classes:\n",
        "\n",
        "* `airplane`\n",
        "* `automobile`\n",
        "* `bird`\n",
        "* `cat`\n",
        "* `deer`\n",
        "* `dog`\n",
        "* `frog`\n",
        "* `horse`\n",
        "* `ship`\n",
        "* `truck`\n",
        "\n",
        "The images in CIFAR-10 are of size:\n",
        "\n",
        "* `3x32x32`\n",
        "\n",
        "i.e. 3-channel color images of `32x32` pixels in size.\n",
        "\n",
        "To load the data, we use a package called\n",
        "``torchvision``, that has data loaders for common datasets such as\n",
        "ImageNet, CIFAR10, MNIST, etc. and data transformers for images, namely,\n",
        "``torchvision.datasets`` and ``torch.utils.data.DataLoader``.\n",
        "\n",
        "\n",
        "In the following code, we perform the following:\n",
        "\n",
        "* Define a batch size for processing multiple images in each iteration.\n",
        "* Create a series of transformations to be applied to the images in the dataset: converting images to tensors and normalizing the pixel values.\n",
        "* Load the CIFAR10 **training** and **test** datasets, specifying the root directory, training mode, and transformations.\n",
        "* Construct a DataLoader for the **training** and **test** datasets with batch processing, shuffling, and parallel data loading.\n",
        "\n",
        "TODO: Complete the next code block."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_5UuOjjrnogR"
      },
      "outputs": [],
      "source": [
        "# Set the batch size for data processing\n",
        "batch_size = 4\n",
        "\n",
        "# Define the mean values and standard deviation values for normalization\n",
        "mean_values = (0.5, 0.5, 0.5)  # Mean values for red, green, and blue channels\n",
        "std_values = (0.5, 0.5, 0.5)   # Standard deviation values for red, green, and blue channels\n",
        "\n",
        "# Define the transformation pipeline\n",
        "\n",
        "# Load the CIFAR10 training dataset and apply the defined transformations\n",
        "\n",
        "\n",
        "# Create a DataLoader to efficiently load and process training data in batches\n",
        "\n",
        "\n",
        "# Load the CIFAR10 test dataset and apply the same transformations as for training\n",
        "\n",
        "\n",
        "# Create a DataLoader for test data\n",
        "\n",
        "# classes\n",
        "classes = ('plane', 'car', 'bird', 'cat',\n",
        "           'deer', 'dog', 'frog', 'horse', 'ship', 'truck')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4LMb7NPmiNfo"
      },
      "source": [
        "Let's view some of the images."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "01HjHP7EiQDq"
      },
      "outputs": [],
      "source": [
        "\n",
        "# Define a function to display images\n",
        "def imshow(img):\n",
        "    # Unnormalize the image\n",
        "    # The normalization was done using this formula:\n",
        "    # img_norm = (img - mean) / std\n",
        "    # So we unnormalize as follows:\n",
        "    img = img * 0.5 + 0.5\n",
        "\n",
        "    npimg = img.numpy()\n",
        "\n",
        "\n",
        "    #The image array is typically stored in the order [height, width, channels],\n",
        "    #but the plt.imshow function expects the image array to be stored in the\n",
        "    #order [channels, width, height].\n",
        "    #The np.transpose function transposes the image array,\n",
        "    #so that it is stored in the correct order.\n",
        "    plt.imshow(np.transpose(npimg, (1, 2, 0)))\n",
        "\n",
        "    # Display the image\n",
        "    plt.show()\n",
        "\n",
        "# Get some random training images\n",
        "dataiter = iter(trainloader)\n",
        "images, labels = next(dataiter)\n",
        "\n",
        "# Show the images using the imshow function\n",
        "imshow(torchvision.utils.make_grid(images))\n",
        "\n",
        "# Print labels\n",
        "print('Labels:', ' '.join(f'{classes[labels[j]]:5s}' for j in range(batch_size)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l62CkyIwtSOv"
      },
      "source": [
        "TODO: Define a simple CNN that classifies CIFAR images."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9fL3F-7Rntog"
      },
      "outputs": [],
      "source": [
        "class Net(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(Net, self).__init__()\n",
        "\n",
        "        # Define the layers of the neural network architecture\n",
        "\n",
        "        # First convolutional layer: 3 input channels, 6 output channels, kernel size 5x5,no bias\n",
        "        self.conv1 =\n",
        "\n",
        "        # Max pooling layer with kernel size 2x2 and stride 2\n",
        "        self.pool =\n",
        "\n",
        "        # Second convolutional layer: 6 input channels, 16 output channels, kernel size 5x5, no bias\n",
        "        self.conv2 =\n",
        "\n",
        "        # Fully connected (dense) layers\n",
        "\n",
        "        # First fully connected layer: 16*5*5 input features, 120 output features, no bias\n",
        "        self.fc1 =\n",
        "\n",
        "        # Second fully connected layer: 120 input features, 84 output features, no bias\n",
        "        self.fc2 =\n",
        "\n",
        "        # Third fully connected layer: 84 input features, 10 output features (for classification), no bias\n",
        "        self.fc3 =\n",
        "\n",
        "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
        "        # Forward pass through the neural network\n",
        "\n",
        "        # Apply first convolutional layer, followed by ReLU activation and max pooling\n",
        "\n",
        "        # Apply second convolutional layer, followed by ReLU activation and max pooling\n",
        "\n",
        "        # The output from the convolutional and pooling layers is in the form of a\n",
        "        # 3D tensor (height, width, depth or channels).\n",
        "        # To feed this tensor into a fully connected layer,\n",
        "        # it needs to be flattened into a 1D tensor.\n",
        "        # Reshape tensor for fully connected layers\n",
        "        # A2D tensor with a shape of [batch_size, 16 * 5 * 5].\n",
        "\n",
        "        # Apply first fully connected layer, followed by ReLU activation\n",
        "\n",
        "        # Apply second fully connected layer, followed by ReLU activation\n",
        "\n",
        "        # Apply third fully connected layer (output layer)\n",
        "\n",
        "        return x\n",
        "\n",
        "# Create an instance of the neural network and move it to the specified device (e.g., GPU)\n",
        "net = Net().to(device)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nijieuxptag6"
      },
      "source": [
        "Train this CNN on the training dataset (this may take a few moments)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CzK6ohj5oNCT"
      },
      "outputs": [],
      "source": [
        "def train(model: nn.Module, dataloader: DataLoader):\n",
        "    # Define the loss criterion and optimizer\n",
        "    criterion = nn.CrossEntropyLoss()  # Cross-entropy loss for classification\n",
        "    optimizer = optim.SGD(model.parameters(), lr=0.001, momentum=0.9)  # SGD optimizer with momentum\n",
        "\n",
        "    for epoch in range(2):  # Loop over the dataset for multiple epochs\n",
        "        running_loss = 0.0\n",
        "\n",
        "        # Iterate over mini-batches of data\n",
        "        for i, data in enumerate(dataloader, 0):\n",
        "            # Get the inputs; data is a list of [inputs, labels]\n",
        "            inputs, labels = data\n",
        "\n",
        "            inputs = inputs.to(device)  # Move inputs to the specified device\n",
        "            labels = labels.to(device)  # Move labels to the specified device\n",
        "\n",
        "            # Zero the gradients in the optimizer\n",
        "            optimizer.zero_grad()\n",
        "\n",
        "            # Forward pass + backward pass (backpropagation) + optimization\n",
        "            outputs = model(inputs)  # Forward pass through the model\n",
        "            loss = criterion(outputs, labels)  # Calculate the loss\n",
        "            loss.backward()  # Compute gradients\n",
        "            optimizer.step()  # Update model parameters\n",
        "\n",
        "            # Print statistics\n",
        "            running_loss += loss.item()\n",
        "            if i % 2000 == 1999:  # Print every 2000 mini-batches\n",
        "                print('[%d, %5d] loss: %.3f' %\n",
        "                    (epoch + 1, i + 1, running_loss / 2000))\n",
        "                running_loss = 0.0\n",
        "\n",
        "    print('Finished Training')  # Training loop is complete\n",
        "    PATH = os.path.join(weights_dir, 'cifar_net.pth')\n",
        "    torch.save(net.state_dict(), PATH)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HixhBHaqtmZU"
      },
      "outputs": [],
      "source": [
        "train(net, trainloader)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EJggxnCVuRxU"
      },
      "source": [
        "Now that the CNN has been trained, let's test it on our test dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ifYWr5qFrzdc"
      },
      "outputs": [],
      "source": [
        "dataiter = iter(testloader)\n",
        "images, labels = next(dataiter)\n",
        "\n",
        "# print images\n",
        "imshow(torchvision.utils.make_grid(images))\n",
        "print('GroundTruth: ', ' '.join(f'{classes[labels[j]]:5s}' for j in range(4)))\n",
        "\n",
        "\n",
        "# net = Net()\n",
        "# net.load_state_dict(torch.load(PATH))\n",
        "net.cuda()\n",
        "images = images.cuda()\n",
        "outputs = net(images)\n",
        "_, predicted = torch.max(outputs, 1)\n",
        "\n",
        "print('Predicted: ', ' '.join(f'{classes[predicted[j]]:5s}'\n",
        "                              for j in range(4)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vW3U7pourwjT"
      },
      "source": [
        "Let us look at how the network performs on the whole dataset.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "y27_n-djuEdz"
      },
      "outputs": [],
      "source": [
        "\n",
        "# A function to evaluate the performance of a given neural network model\n",
        "# using a test dataset.\n",
        "# It calculates the accuracy of the model's predictions on the test data.\n",
        "def calculate_accuracy(model: nn.Module, dataloader: DataLoader, max_samples=None) -> float:\n",
        "    correct_predictions = 0  # Initialize the count of correctly predicted samples\n",
        "    total_samples = 0    # Initialize the count of total samples\n",
        "    inference_count = 0  # Initialize the count of inferences made\n",
        "\n",
        "    with torch.no_grad():  # Disable gradient calculation for inference\n",
        "        for batch_data in dataloader:\n",
        "            images, labels = batch_data  # Separate images and labels from the batch\n",
        "\n",
        "            images = images.to(device)  # Move images to the specified device\n",
        "            labels = labels.to(device)  # Move labels to the specified device\n",
        "\n",
        "            outputs = model(images)  # Forward pass to get model predictions\n",
        "            _, predicted = torch.max(outputs.data, 1)  # Get predicted class indices\n",
        "\n",
        "            total_samples += labels.size(0)  # Increment the total count of samples\n",
        "            correct_predictions += (predicted == labels).sum().item()  # Count correct predictions\n",
        "\n",
        "            if max_samples:  # Check if a maximum number of samples for testing is specified\n",
        "                inference_count += images.shape[0]  # Increment the count of inferences made\n",
        "                if inference_count > max_samples:  # Stop testing if maximum samples reached\n",
        "                    break\n",
        "\n",
        "    accuracy = 100 * correct_predictions / total_samples  # Calculate the accuracy as a percentage\n",
        "    return accuracy\n",
        "\n",
        "score = calculate_accuracy(net, testloader)\n",
        "print('Accuracy of the network on the test images: {}%'.format(score))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SQZoEjBSveV8"
      },
      "source": [
        "## Question 1: Visualize Weights\n",
        "\n",
        "Write a function that takes one layer of our network and plots the historgram of its paramters. Use this signature:\n",
        "\n",
        "```python\n",
        "def analyze_layer_weights(layer: nn.Module):\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PoySOC4WDk5F"
      },
      "outputs": [],
      "source": [
        "def analyze_layer_weights(layer: nn.Module):\n",
        "    # Extract and flatten the weights of the given layer\n",
        "    layer_weights = layer.weight.data.cpu().view(-1)\n",
        "\n",
        "    # Get layer type (Conv2d or Linear) for better title\n",
        "    layer_type = type(layer).__name__\n",
        "\n",
        "    # Plot a histogram of the flattened layer weights\n",
        "    plt.hist(layer_weights, density=True, bins=50)\n",
        "    plt.title(f\"{layer_type} Layer Weights Histogram\")\n",
        "    plt.xlabel(\"Weight Value\")\n",
        "    plt.ylabel(\"Density\")\n",
        "    plt.show()\n",
        "\n",
        "    # Calculate the upper and lower bounds of the range within 3 standard deviations\n",
        "    layer_weights_3sigma_max = (layer_weights.mean() + 3 * layer_weights.std()).item()\n",
        "    layer_weights_3sigma_min = (layer_weights.mean() - 3 * layer_weights.std()).item()\n",
        "\n",
        "    # Calculate the range of weights and the 3-sigma range for the layer\n",
        "    weight_range = layer_weights.max() - layer_weights.min()\n",
        "    sigma_range = layer_weights_3sigma_max - layer_weights_3sigma_min\n",
        "\n",
        "    print(f\"{layer_type} Layer Weight Range: {weight_range.item()}\")\n",
        "    print(f\"{layer_type} Layer 3-Sigma Range: {sigma_range}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7qv8ZLXiDgrf"
      },
      "outputs": [],
      "source": [
        "analyze_layer_weights(net.conv1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5xjQyehq5lA4"
      },
      "outputs": [],
      "source": [
        "analyze_layer_weights(net.conv2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j9CnTZCD5lmn"
      },
      "outputs": [],
      "source": [
        "analyze_layer_weights(net.fc1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VYWkOW145mJE"
      },
      "outputs": [],
      "source": [
        "analyze_layer_weights(net.fc2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v893WZ9_5wpW"
      },
      "outputs": [],
      "source": [
        "analyze_layer_weights(net.fc3)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g2_4MK0B1f1z"
      },
      "source": [
        "## Question 2: Model Dimensions.\n",
        "TODO:\n",
        "In the CNN model we have created, how many layers have trainable weights? Please list all the dimensions of each layer's weights.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xg8xNrUe12kw"
      },
      "source": [
        "TODO: For all the layers with traiable weights, please list their input and output dimension."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "omnAgQS6yfwu"
      },
      "source": [
        "TODO: For all the layers, please list their total number of multiplications and summations in both forward and backward pass."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K_UMA22B2UXa"
      },
      "source": [
        "TODO: Calculate the maximum memory requirements to run the training for this CNN model. Hint: Weights + gradients + maximum intermediate feature."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AiEzZ1gL345L"
      },
      "source": [
        "## Question 3: Model without MaxPooling2D\n",
        "TODO: remove the MaxPooling2D layer in the CNN model we have created and adjust the dimension of FC layers to have a matching layer.\n",
        "\n",
        "TODO: Evaluate the model accuracy and compare it with the CNN model with MaxPooling.\n",
        "\n",
        "TODO: repeat question 2 for the CNN model without MaxPooling2D."
      ]
    }
  ],
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      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
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