{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# unit 4.0 - Convolutional layers\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://githubtocolab.com/culurciello/deep-learning-course-source/blob/main/source/lectures/40-conv-layer.ipynb)\n",
    "\n",
    "\n",
    "What are convolutional layers and what do they compute?\n",
    "\n",
    "Convolution are a mathematical operation defines as:\n",
    "\n",
    "$$\n",
    "y[n] = \\sum x[a] w[n-a]\n",
    "$$\n",
    "\n",
    "where $x(t)$ is the input signal, $w(t)$ is the kernel (or filter) and $y(t)$ is the output signal.\n",
    "\n",
    "\n",
    "Convolutional layers are the basic building blocks of Convolutional Neural Networks (CNNs). They are designed to extract features from input data.\n",
    "\n",
    "Convoultion and correlation are two closely related operations. In convolution, the kernel is flipped before applying it to the input. In correlation, the kernel is not flipped. In practice, the difference is not important, as the kernel weights are learned by the network.\n",
    "\n",
    "\n",
    "## 1D convolution\n",
    "\n",
    "\n",
    "Here we show the [animation of a 1d convolution](https://e2eml.school/convolution_one_d.html) filter and what it does to an input sequence:\n",
    "\n",
    "![](images/1d-conv-animation.gif)\n",
    "\n",
    "In this animation you see a 1D convolution filter (blue) moving across an input sequence (dark red). The filter is a 1x3 kernel, which means it has 3 weights. The filter is applied to the input sequence by moving it across the sequence and computing the dot product of the filter weights and the input sequence at each position. The result of the dot product is the output of the convolution at that position.\n",
    "\n",
    "\n",
    "\n",
    "We have already seen an [example of 1D convolution applied to a sequence](https://githubtocolab.com/culurciello/deep-learning-course-source/blob/main/source/lectures/22-seq-cnn-1d.ipynb). What  transformation did it perform?\n",
    "\n",
    "A convolution, similar to a linear layer, is designed to extract \"features\" in ain input signal. Features are repeating patterns in the signal, for examples oriented edges in an image, or short waveforms in an audio file.\n",
    "\n",
    "A 1D convolution is basically similar to a liner layer applied to a sequence of data points. The difference is that a convolution is applied many times in the sequence by moving the weights kernel across the sequence.\n",
    "\n",
    "See this figure for more detail:\n",
    "\n",
    "![](images/1d-conv.png)\n",
    "\n",
    "In this example you see an input sequence $x_1$ to $x_n$. A 1D convolution wit a kernel of 1x3 weights is applied to the sequence in the first layer and also the second layer.\n",
    "\n",
    "a 1D convolution can have multiple plains as inputs (multiple sequences or a sequence with many features), and also can usually generate an output with even more features (5 in this example).\n",
    "\n",
    "The red kernel moves across the sequence down vertically to take the next set of 3 elements and produce another output.\n",
    "\n",
    "\n",
    "In this example below we show how a convolution affects an input sequence of numbers (here a sin wave). Notice how different random filters find different features in the input sequence. Some filters invert the signal, some follow it, and most introduce a small phase change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "31106a39",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8e1f80db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([136])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'gaussian')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# seq = torch.rand(1,64)\n",
    "t = torch.cat([torch.ones(18), torch.zeros(18), torch.linspace(0,10,64), torch.zeros(18), torch.ones(18)])\n",
    "\n",
    "print(t.shape)\n",
    "seq = torch.sin(t).unsqueeze(0)\n",
    "# seq = (torch.sin(t)+torch.sin(2*t)).unsqueeze(0)\n",
    "# print(seq.shape)\n",
    "sp = seq.permute(1,0)\n",
    "m = torch.nn.Conv1d(1, 4, 5, padding=2) # implements 4 filters with a kernel of 5 numbers\n",
    "# print(m.weight)\n",
    "# print(m.weight.shape)\n",
    "f = torch.Tensor([[[-1,-1, 0, 1, 1]],  # right edge \n",
    "                  [[ 1/5, 1/5, 1/5, 1/5, 1/5]],  # average\n",
    "                  [[ 1, 1, 0,-1,-1]],  # left edge\n",
    "                  [[-1, 0, 2, 0,-1]]]) # gaussian\n",
    "# print(m.weight.shape)\n",
    "m.weight = torch.nn.Parameter(f)\n",
    "# print(\"convolution filer: \")\n",
    "# print(m.weight)\n",
    "output = m(seq)\n",
    "# print(output.shape)\n",
    "op = output.permute(1,0).detach()\n",
    "\n",
    "# plot\n",
    "fig, axs = plt.subplots(2, 2) # 2x2 plots\n",
    "axs[0,0].plot(sp, 'r--', label=\"input\") # plot original sin wave in red\n",
    "axs[0,0].plot(op[:,0], label=\"right edge\") # plot 4 outputs in green\n",
    "axs[0,0].set_title('right edge')\n",
    "\n",
    "axs[0,1].plot(sp, 'r--', label=\"input\") # plot original sin wave in red\n",
    "axs[0,1].plot(op[:,1], label=\"average\") # plot 4 outputs in green\n",
    "axs[0,1].set_title('average')\n",
    "\n",
    "axs[1,0].plot(sp, 'r--', label=\"input\") # plot original sin wave in red\n",
    "axs[1,0].plot(op[:,2], label=\"left edge\") # plot 4 outputs in green\n",
    "axs[1,0].set_title('left edge')\n",
    "\n",
    "axs[1,1].plot(sp, 'r--', label=\"input\") # plot original sin wave in red\n",
    "axs[1,1].plot(op[:,3], label=\"gaussian\") # plot 4 outputs in green\n",
    "axs[1,1].set_title('gaussian')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c0b72cf",
   "metadata": {},
   "source": [
    "## 2D convolution\n",
    "\n",
    "A 2D convolution can be applied to data arranged in 2D, for example images and image planes. \n",
    "An image is convolved by a 2d filter to produce a feature map - another image usually of smaller size. See this example illustration:\n",
    "\n",
    "![](images/2dconv.png)\n",
    "\n",
    "We can learn what a convolution does with a few examples. Let us load an image and plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d0b2257",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x316a8c500>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ima = torchvision.io.read_image(\"images/home.png\")\n",
    "iman = ima.permute(1, 2, 0)\n",
    "# iman.shape\n",
    "plt.imshow(iman)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can try to run a convolutional operation from PyTorch.\n",
    "\n",
    "Here we run 16 convolution filters of 5x5 pixels and with a stride of 2 pixels.\n",
    "\n",
    "This runs on all 4 channels of the input image (RGBW).\n",
    "\n",
    "You will recognize these numbers in the Conv2d operator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6ebd5799",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([16, 42, 51])\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    conv_layer = torch.nn.Conv2d(4, 16, 3, stride=2)\n",
    "ima.shape\n",
    "processed = conv_layer(ima.float())\n",
    "print(processed.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we will now plot all the 16 images output of the Conv2d operator. You will see how each convolution processes the image. \n",
    "\n",
    "The convolution filter weights were randomly generated, so you will see 16 different outputs.\n",
    "\n",
    "Some enhance vertical edges, some horizontal edges, some will blur the image, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b9711254",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x2000 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20, 20))\n",
    "for i in range(len(processed)):\n",
    "    a = fig.add_subplot(5, 4, i+1)\n",
    "    processed_display = processed[i].detach().unsqueeze(0).permute(1, 2, 0)\n",
    "#     print(processed_display.shape)\n",
    "    imgplot = plt.imshow(processed_display, cmap='gray')\n",
    "    a.axis(\"off\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "3.12",
   "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",
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