10_1_1D_Convolution.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "view-in-github"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/udlbook/udlbook/blob/main/Notebooks/Chap10/10_1_1D_Convolution.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "el8l05WQEO46"
      },
      "source": [
        "# **Notebook 10.1: 1D Convolution**\n",
        "\n",
        "This notebook investigates 1D convolutional layers.\n",
        "\n",
        "Work through the cells below, running each cell in turn. In various places you will see the words \"TO DO\". Follow the instructions at these places and make predictions about what is going to happen or write code to complete the functions.\n",
        "\n",
        "Contact me at udlbookmail@gmail.com if you find any mistakes or have any suggestions.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ggQrHkFZcUiV"
      },
      "source": [
        "NOTE!!\n",
        "\n",
        "If you have the first edition of the printed book, it mistakenly refers to a convolutional filter with no spaces between the elements (i.e. a normal filter without dilation) as having dilation zero.  Actually, the convention is (weirdly) that this has dilation one.  And when there is one space between the elements, this is dilation two.   This notebook reflects the correct convention and so will be out of sync with the printed book.  If this is confusing, check the [errata](https://github.com/udlbook/udlbook/blob/main/UDL_Errata.pdf) document."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "nw7k5yCtOzoK"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "lSSHuoEqO3Ly"
      },
      "outputs": [],
      "source": [
        "# Define a signal that we can apply convolution to\n",
        "x = [5.2, 5.3, 5.4, 5.1, 10.1, 10.3, 9.9, 10.3, 3.2, 3.4, 3.3, 3.1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "zVssv_wiREc2"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Draw the signal\n",
        "fig,ax = plt.subplots()\n",
        "ax.plot(x, 'k-')\n",
        "ax.set_xlim(0,11)\n",
        "ax.set_ylim(0, 12)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "MmfXED12RvNq"
      },
      "outputs": [],
      "source": [
        "def zero_pad(arr, index):\n",
        "    if index >= 0 and index < len(arr):\n",
        "        return arr[index]\n",
        "    return 0\n",
        "\n",
        "# Now let's define a zero-padded convolution operation\n",
        "# with a convolution kernel size of 3, a stride of 1, and a dilation of 1\n",
        "# as in figure 10.2a-c.  Write it yourself, don't call a library routine!\n",
        "# Don't forget that Python arrays are indexed from zero, not from 1 as in the book figures\n",
        "def conv_3_1_1_zp(x_in, omega):\n",
        "    x_out = np.zeros_like(x_in)\n",
        "    # TODO✅ -- write this function\n",
        "    # replace this line\n",
        "    # --- MY METHOD ---\n",
        "    for i, v in enumerate(x_out):\n",
        "        xinomega0 = zero_pad(x_in, i-1) * omega[0]\n",
        "        xinomega1 = x_in[i] * omega[1]\n",
        "        xinomega2 = zero_pad(x_in, i+1) * omega[2]\n",
        "        x_out[i] = xinomega0 + xinomega1 + xinomega2\n",
        "    \n",
        "    # --- PROFESSOR'S METHOD ---\n",
        "    # padding_size = 1\n",
        "    # x_padded = padding_size*[0] + list(x_in) + padding_size*[0]\n",
        "    # for i in range(len(x_in)):\n",
        "    #     window = [x_padded[i+j] for j in range(len(omega))]\n",
        "    #     x_out[i] = sum([omega[j]*window[j] for j in range(len(omega))])\n",
        "\n",
        "    return x_out"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fof_Rs98Zovq"
      },
      "source": [
        "Now let's see what kind of things convolution can do\n",
        "First, it can average nearby values, smoothing the function:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "HOcPZR6iWXsa"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sum of output is 71.1, should be 71.1\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# 🔵 with these values of omega, weights are evenly distributed, creating an 'average'\n",
        "omega = [0.33,0.33,0.33]\n",
        "h = conv_3_1_1_zp(x, omega)\n",
        "\n",
        "# Check that you have computed this correctly\n",
        "print(f\"Sum of output is {np.sum(h):3.3}, should be 71.1\")\n",
        "\n",
        "# Draw the signal\n",
        "fig,ax = plt.subplots()\n",
        "ax.plot(x, 'k-',label='before')\n",
        "ax.plot(h, 'r-',label='after')\n",
        "ax.set_xlim(0,11)\n",
        "ax.set_ylim(0, 12)\n",
        "ax.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PBkNKUylZr-k"
      },
      "source": [
        "Notice how the red function is a smoothed version of the black one as it has averaged adjacent values.  The first and last outputs are considerably lower than the original curve though.  Make sure that you understand why!<br><br>\n",
        "\n",
        "With different weights, the convolution can be used to find sharp changes in the function:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "o8T5WKeuZrgS"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# 🔵 with these values of omega, the left and right weights are calculated, but not the center, like a derivative\n",
        "omega = [-0.5,0,0.5]\n",
        "h2 = conv_3_1_1_zp(x, omega)\n",
        "\n",
        "# Draw the signal\n",
        "fig,ax = plt.subplots()\n",
        "ax.plot(x, 'k-',label='before')\n",
        "ax.plot(h2, 'r-',label='after')\n",
        "ax.set_xlim(0,11)\n",
        "# ax.set_ylim(0, 12)\n",
        "ax.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ogfCVThJgtPx"
      },
      "source": [
        "Notice that the convolution has a peak where the original function went up and trough where it went down.  It is roughly zero where the function is locally flat.  This convolution approximates a derivative. <br> <br>\n",
        "\n",
        "Now let's define the convolutions from figure 10.3.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "5QYrQmFMiDBj"
      },
      "outputs": [],
      "source": [
        "# Now let's define a zero-padded convolution operation\n",
        "# with a convolution kernel size of 3, a stride of 2, and a dilation of 1\n",
        "# as in figure 10.3a-b.  Write it yourself, don't call a library routine!\n",
        "def conv_3_2_1_zp(x_in, omega):\n",
        "    x_out = np.zeros(int(np.ceil(len(x_in)/2)))\n",
        "    # TODO✅ -- write this function\n",
        "    # --- MY METHOD ---\n",
        "    for i, v in enumerate(x_out):\n",
        "        ridx = i*2\n",
        "        xinomega0 = zero_pad(x_in, ridx-1) * omega[0]\n",
        "        xinomega1 = x_in[ridx] * omega[1]\n",
        "        xinomega2 = zero_pad(x_in, ridx+1) * omega[2]\n",
        "        x_out[i] = xinomega0 + xinomega1 + xinomega2\n",
        "\n",
        "    return x_out"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "CD96lnDHX72A"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[ 3.465  5.247  5.214  6.798  8.415  9.999 10.065  7.722  5.577  3.267\n",
            "  3.234  2.112]\n",
            "[ 3.465  5.214  8.415 10.065  5.577  3.234]\n"
          ]
        }
      ],
      "source": [
        "omega = [0.33,0.33,0.33]\n",
        "h3 = conv_3_2_1_zp(x, omega)\n",
        "\n",
        "# If you have done this right, the output length should be six and it should\n",
        "# contain every other value from the original convolution with stride 1\n",
        "print(h)\n",
        "print(h3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "lw46-gNUjDw7"
      },
      "outputs": [],
      "source": [
        "# Now let's define a zero-padded convolution operation\n",
        "# with a convolution kernel size of 5, a stride of 1, and a dilation of 1\n",
        "# as in figure 10.3c.  Write it yourself, don't call a library routine!\n",
        "def conv_5_1_1_zp(x_in, omega):\n",
        "    x_out = np.zeros_like(x_in)\n",
        "    # TODO✅ -- write this function\n",
        "    for i, v in enumerate(x_out):\n",
        "        xinomegan2 = zero_pad(x_in, i-2) * omega[0]\n",
        "        xinomegan1 = zero_pad(x_in, i-1) * omega[1]\n",
        "        xinomega0 = x_in[i] * omega[2]\n",
        "        xinomega1 = zero_pad(x_in, i+1) * omega[3]\n",
        "        xinomega2 = zero_pad(x_in, i+2) * omega[4]\n",
        "        x_out[i] = xinomegan1 + xinomegan2 + xinomega0 + xinomega1 + xinomega2\n",
        "\n",
        "    return x_out"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "JkKBL-nFk4bf"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sum of output is 69.6, should be 69.6\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "\n",
        "omega2 = [0.2, 0.2, 0.2, 0.2, 0.2]\n",
        "h4 = conv_5_1_1_zp(x, omega2)\n",
        "\n",
        "# Check that you have computed this correctly\n",
        "print(f\"Sum of output is {np.sum(h4):3.3}, should be 69.6\")\n",
        "\n",
        "# Draw the signal\n",
        "fig,ax = plt.subplots()\n",
        "ax.plot(x, 'k-',label='before')\n",
        "ax.plot(h4, 'r-',label='after')\n",
        "ax.set_xlim(0,11)\n",
        "ax.set_ylim(0, 12)\n",
        "ax.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "_aBcW46AljI0"
      },
      "outputs": [],
      "source": [
        "# Finally let's define a zero-padded convolution operation\n",
        "# with a convolution kernel size of 3, a stride of 1, and a dilation of 2\n",
        "# as in figure 10.3d.  Write it yourself, don't call a library routine!\n",
        "# Don't forget that Python arrays are indexed from zero, not from 1 as in the book figures\n",
        "def conv_3_1_2_zp(x_in, omega):\n",
        "    x_out = np.zeros_like(x_in)\n",
        "    # TODO✅ -- write this function\n",
        "    for i, v in enumerate(x_out):\n",
        "        xinomega0 = zero_pad(x_in, i-2) * omega[0]\n",
        "        xinomega1 = x_in[i] * omega[1]\n",
        "        xinomega2 = zero_pad(x_in, i+2) * omega[2]\n",
        "        x_out[i] = xinomega0 + xinomega1 + xinomega2\n",
        "\n",
        "    return x_out"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "En-ByCqWlvMI"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sum of output is 68.3, should be 68.3\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "omega = [0.33,0.33,0.33]\n",
        "h5 = conv_3_1_2_zp(x, omega)\n",
        "\n",
        "# Check that you have computed this correctly\n",
        "print(f\"Sum of output is {np.sum(h5):3.3}, should be 68.3\")\n",
        "\n",
        "# Draw the signal\n",
        "fig,ax = plt.subplots()\n",
        "ax.plot(x, 'k-',label='before')\n",
        "ax.plot(h5, 'r-',label='after')\n",
        "ax.set_xlim(0,11)\n",
        "ax.set_ylim(0, 12)\n",
        "ax.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "loBwu125lXx1"
      },
      "source": [
        "Finally, let's investigate representing convolutions as full matrices, and show we get the same answer."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "U2RFWfGgs72j"
      },
      "outputs": [],
      "source": [
        "# Compute matrix in figure 10.4 d\n",
        "def get_conv_mat_3_1_1_zp(n_out, omega):\n",
        "  omega_mat = np.zeros((n_out,n_out))\n",
        "  # TODO✅ Fill in this matrix\n",
        "  for i, v in enumerate(omega_mat):\n",
        "    if i-1 >= 0:\n",
        "      omega_mat[i][i-1] = omega[0]\n",
        "    omega_mat[i][i] = omega[1]\n",
        "    if i+1 < len(omega_mat):\n",
        "      omega_mat[i][i+1] = omega[2]\n",
        "\n",
        "  return omega_mat"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "20IYxku8lMty"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[ 1.54 -3.63 -3.62 -4.87 -2.11 -6.93 -7.41 -5.39 -9.38 -2.16 -2.37 -1.75]\n",
            "[ 1.54 -3.63 -3.62 -4.87 -2.11 -6.93 -7.41 -5.39 -9.38 -2.16 -2.37 -1.75]\n"
          ]
        }
      ],
      "source": [
        "# Run original convolution\n",
        "omega = np.array([-1.0,0.5,-0.2])\n",
        "h6 = conv_3_1_1_zp(x, omega)\n",
        "print(h6)\n",
        "\n",
        "# If you have done this right, you should get the same answer\n",
        "omega_mat = get_conv_mat_3_1_1_zp(len(x), omega)\n",
        "h7 = np.matmul(omega_mat, x)\n",
        "print(h7)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rYoQVhBfu8R4"
      },
      "source": [
        "TODO✅:  What do you expect to happen if we apply the last convolution twice?  Can this be represented as a single convolution?  If so, then what is it?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {},
      "outputs": [],
      "source": [
        "'''\n",
        "If we apply the last convolution twice, we can basically calculate new values through new passes. For example, if you were to have an even omega value, such as 0.33, 0.33, 0.33 and reapply it again, you would basically blur an image even more. You can represent this as one convolution, by increasing the kernel size and rerepresenting the weights. \n",
        "\n",
        "For example: \n",
        "\n",
        "h4 = xo3 + xo4 + xo5\n",
        "h5 = xo4 + xo5 + xo6\n",
        "h6 = xo5 + xo6 + xo7\n",
        "\n",
        "where xon = x[n] * omega[m]\n",
        "then the next one would be: \n",
        "\n",
        "h`5 = ho4 + ho5 + ho6\n",
        "\n",
        "where hon = h[n] * omega[m]:\n",
        "\n",
        "h`5 = (xo3 + xo4 + xo5) * omega[0] + (xo4 + xo5 + xo6) * omega[1] + (xo5 + xo6 + xo7) * omega[2]\n",
        "\n",
        "which would expand to:\n",
        "\n",
        "h`5 = \n",
        "    (x[3] * omega[0] + x[4] * omega[1] + x[5] * omega[2]) * omega[0] +\n",
        "    (x[4] * omega[0] + x[5] * omega[1] + x[6] * omega[2]) * omega[1] +\n",
        "    (x[5] * omega[0] + x[6] * omega[1] + x[7] * omega[2]) * omega[2]\n",
        "\n",
        "h'5 =\n",
        "    x[3] * (omega[0]^2) +\n",
        "    x[4] * (omega[0] * omega[1] * 2) +\n",
        "    x[5] * (omega[0] * omega[2] * 2 + omega[1]^2) +\n",
        "    x[6] * (omega[1] * omega[2] * 2) +\n",
        "    x[7] * (omega[2]^2)\n",
        "\n",
        "so in conclusion:\n",
        "\n",
        "if we have omega as [w0, w1, w2] and do the convolution twice, we can represent the new omega as:\n",
        "[w0^2, 2*w0*w1, w1^2 + 2*w0*w1, 2*w1*w2, w2^2]\n",
        "\n",
        "''' and None"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "authorship_tag": "ABX9TyML7rfAGE4gvmNUEiK5x3PS",
      "include_colab_link": true,
      "provenance": []
    },
    "kernelspec": {
      "display_name": ".venv",
      "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": "3.12.1"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}