GANS_simplified.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "authorship_tag": "ABX9TyN+d2aGeLAFAMVSP/CWAlwB",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AbhinavJangra29/GANS/blob/main/GANS_simplified.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "rbqNKpmIsotU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "how do gans work? simple , the generator generates and the discriminator distinguishes the generated image as real or fake. They both play a game with each other. The generator gives a generated image to discriminator and the discriminator tells if the image is fake or real and with every iteration of the game they both get better with time. At some point the generator becomes so proficient that it is able to produce completely new samples which the discriminator is unable to distunguish as fake.\n",
        "\n",
        "\n",
        "the generator trains on trying to fool the discriminator,i.e it wants to make the response of discriminator on fake images as real\n",
        "the discriminator is trying to identify a real image as real and a fake image as fake."
      ],
      "metadata": {
        "id": "A6jtVfiJsrL3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# PyTorch GAN Example: Importing Libraries\n",
        "\n",
        "In this section, we import the necessary libraries for our PyTorch Generative Adversarial Network (GAN) example.\n",
        "\n",
        "- **`torch`**: Core PyTorch library for tensor operations.\n",
        "- **`optim`**: Module for optimization algorithms such as Adam used to update model parameters.\n",
        "- **`nn`**: Neural network modules, including layers and loss functions.\n",
        "- **`torch.utils.data`**: Utilities for handling data, including the `DataLoader` class for efficient loading of datasets.\n",
        "- **`torchvision`**: Provides access to popular datasets, model architectures, and image transformations.\n",
        "- **`matplotlib.pyplot`**: Library for creating visualizations and plots.\n",
        "- **`numpy`**: Fundamental package for array operations and numerical computations.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "fit51O23SNFQ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zzhX6iuyBh_R"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.optim as optim\n",
        "import torch.nn as nn\n",
        "from torch.utils import data\n",
        "import torchvision\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Configuration Parameters\n",
        "\n",
        "Here, we define key configuration parameters for our Generative Adversarial Network (GAN) example.\n",
        "\n",
        "- **`learning_rate`**: The learning rate for the optimizer (set to `3e-4` in this case).\n",
        "- **`z_dim`**: The dimensionality of the latent space or noise vector (set to `64`).\n",
        "- **`img_dim`**: The dimensionality of the input image (set to `28*28*1` for a 1-channel image).\n",
        "- **`batch_size`**: The number of samples in each batch during training (set to `32`).\n",
        "- **`num_epochs`**: The total number of training epochs (set to `25`).\n",
        "\n",
        "These parameters will influence the training dynamics and the overall performance of the GAN.\n",
        "\n"
      ],
      "metadata": {
        "id": "xWzUYsXUUSyJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "learning_rate=3e-4\n",
        "z_dim=64\n",
        "img_dim=28*28*1#784\n",
        "batch_size=32\n",
        "num_epochs=25\n"
      ],
      "metadata": {
        "id": "U8UQnyk2KxgH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Generator Architecture and Dimension Sequence\n",
        "\n",
        "Let's break down the Generator's architecture and dimension sequence step by step:\n",
        "\n",
        "1. **Input Layer (`linear1`):**\n",
        "   - **Analogy:** Think of this as the artist's initial sketch.\n",
        "   - **Dimensions:**\n",
        "     - Input: A blank canvas (noise vector of size `z_dim`).\n",
        "     - Output: A rough sketch on the canvas (256 features).\n",
        "\n",
        "2. **Activation Function (`relu`):**\n",
        "   - **Analogy:** Imagine adding more details and refining the sketch.\n",
        "   - **Dimensions:**\n",
        "     - Input: The rough sketch from the previous step (256 features).\n",
        "     - Output: A more detailed and refined sketch.\n",
        "\n",
        "3. **Hidden Layer (`linear2`):**\n",
        "   - **Analogy:** Picture the artist adding colors and finalizing the artwork.\n",
        "   - **Dimensions:**\n",
        "     - Input: The detailed sketch (256 features).\n",
        "     - Output: The final artwork (image with dimensions `img_dim`).\n",
        "\n",
        "4. **Activation Function (`tanh`):**\n",
        "   - **Analogy:** Converting the artwork to grayscale and adjusting the contrast.\n",
        "   - **Dimensions:**\n",
        "     - Input: The final artwork.\n",
        "     - Output: The transformed artwork in a standardized format between -1 and 1.\n",
        "\n",
        "In simple terms, the Generator takes a blank canvas (noise vector), creates a rough sketch, adds details, and then produces the final artwork. The Tanh activation ensures the generated image is in a suitable range for grayscale images.\n"
      ],
      "metadata": {
        "id": "uDfaYLDiUoZ8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class Generator(nn.Module):\n",
        "  def __init__(self,z_dim,img_dim):\n",
        "    super(Generator,self).__init__()\n",
        "    self.linear1=nn.Linear(z_dim,256)\n",
        "    self.relu=nn.LeakyReLU(0.1)\n",
        "    self.linear2=nn.Linear(256,img_dim)\n",
        "    self.tanh=nn.Tanh()\n",
        "\n",
        "  def forward(self,x):\n",
        "    out=self.linear1(x)\n",
        "    out=self.relu(out)\n",
        "    out=self.linear2(out)\n",
        "    out=self.tanh(out)\n",
        "    return out\n"
      ],
      "metadata": {
        "id": "y6PussUNKzOM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Discriminator Architecture and Dimension Sequence\n",
        "\n",
        "Now, let's break down the Discriminator's architecture and dimension sequence:\n",
        "\n",
        "1. **Input Layer (`linear1`):**\n",
        "   - **Analogy:** Think of this as an art critic analyzing an artwork.\n",
        "   - **Dimensions:**\n",
        "     - Input: The artwork (image with dimensions `img_dim`).\n",
        "     - Output: A critical analysis (128 features).\n",
        "\n",
        "2. **Activation Function (`relu`):**\n",
        "   - **Analogy:** The critic giving opinions on different aspects of the artwork.\n",
        "   - **Dimensions:**\n",
        "     - Input: The critical analysis from the previous step (128 features).\n",
        "     - Output: A refined critique.\n",
        "\n",
        "3. **Hidden Layer (`linear2`):**\n",
        "   - **Analogy:** The critic summarizing the overall evaluation.\n",
        "   - **Dimensions:**\n",
        "     - Input: The refined critique (128 features).\n",
        "     - Output: A final verdict (a single value indicating real or fake).\n",
        "\n",
        "4. **Activation Function (`sigmoid`):**\n",
        "   - **Analogy:** The critic providing a score or probability.\n",
        "   - **Dimensions:**\n",
        "     - Input: The final verdict.\n",
        "     - Output: A probability score between 0 and 1 (sigmoid activation).\n",
        "\n",
        "In simple terms, the Discriminator takes an artwork (image), analyzes it, gives opinions, summarizes the evaluation, and provides a probability score indicating whether the artwork is real or fake.\n"
      ],
      "metadata": {
        "id": "5ZM_XgzIVShr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class Discriminator(nn.Module):\n",
        "  def __init__(self,img_dim):\n",
        "    super(Discriminator,self).__init__()\n",
        "    self.linear1=nn.Linear(img_dim,128)\n",
        "    self.relu=nn.LeakyReLU(0.1)\n",
        "    self.linear2=nn.Linear(128,1)\n",
        "    self.sigmoid=nn.Sigmoid()\n",
        "\n",
        "  def forward(self,x):\n",
        "    out=self.linear1(x)\n",
        "    out=self.relu(out)\n",
        "    out=self.linear2(out)\n",
        "    out=self.sigmoid(out)\n",
        "    return out"
      ],
      "metadata": {
        "id": "DoS5S2o1K1m_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Model Initialization and Noise Vector\n",
        "\n",
        "Now, let's initialize our Discriminator and Generator models and create a fixed noise vector for generating images.\n",
        "\n",
        "```python\n",
        "# Initialize Discriminator and Generator models\n",
        "discriminator = Discriminator(img_dim)\n",
        "generator = Generator(z_dim, img_dim)\n",
        "\n",
        "# Create a fixed noise vector for image generation\n",
        "fixed_noise = torch.randn((batch_size, z_dim))\n"
      ],
      "metadata": {
        "id": "jaEJPRbhVbaQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "discriminator=Discriminator(img_dim)\n",
        "generator=Generator(z_dim,img_dim)\n",
        "fix_noise=torch.randn((batch_size,z_dim))"
      ],
      "metadata": {
        "id": "o17rrvL1K3_8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Data Normalization and Transformations\n",
        "\n",
        "In machine learning, data normalization is a process of scaling the values of features to a standardized range. For image data, pixel values are typically normalized to a range between 0 and 1 or -1 and 1. Transformations, on the other hand, are operations applied to the data to augment, preprocess, or manipulate it.\n",
        "\n",
        "## Normalization\n",
        "\n",
        "### What is Normalization?\n",
        "\n",
        "Normalization is like adjusting the brightness and contrast of an image to make it consistent and easy for the model to learn. In the context of our dataset:\n",
        "\n",
        "- **Original Range:** Pixel values in the MNIST dataset are initially between 0 and 255.\n",
        "- **Normalized Range:** We scale them to be between -1 and 1, making it easier for our neural network to process.\n",
        "\n",
        "### How it's Done:\n",
        "\n",
        "```python\n",
        "tf = torchvision.transforms.Compose(\n",
        "    [torchvision.transforms.ToTensor(), torchvision.transforms.Normalize((0.5,), (0.5,)),]\n",
        ")\n"
      ],
      "metadata": {
        "id": "TK5CEViKVv60"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#normalising and transforming\n",
        "tf = torchvision.transforms.Compose(\n",
        "    [torchvision.transforms.ToTensor(),torchvision.transforms.Normalize((0.5,), (0.5,)),]\n",
        ")\n",
        "dataset = torchvision.datasets.MNIST(root=\"dataset/\", transform=tf, download=True)\n",
        "loader = data.DataLoader(dataset, batch_size=batch_size, shuffle=True)"
      ],
      "metadata": {
        "id": "gxom2CxMLENh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Plotting Real Data for Discriminator\n",
        "\n",
        "Here, we visualize a batch of real data samples that will be fed into the Discriminator during training.\n",
        "\n",
        "```python\n",
        "# Get the next batch of real data\n",
        "real_sample = next(iter(loader))[0]\n",
        "\n",
        "# Create an image grid for visualization\n",
        "img_grid_real = torchvision.utils.make_grid(real_sample, normalize=True)\n",
        "\n",
        "# Convert the PyTorch tensor to a NumPy array for plotting\n",
        "npgrid = img_grid_real.numpy()\n",
        "\n",
        "# Plot the image grid\n",
        "plt.imshow(np.transpose(npgrid, (1, 2, 0)), interpolation='nearest')\n",
        "plt.axis('off')\n"
      ],
      "metadata": {
        "id": "qiNFQiHEV4fu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "we plot this to take an observation of how the real data looks like"
      ],
      "metadata": {
        "id": "m8_8en2QWBvg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plotting real data to be fed to the discriminator\n",
        "real_sample = next(iter(loader))[0]  # Get the next batch of real data\n",
        "img_grid_real = torchvision.utils.make_grid(real_sample, normalize=True)\n",
        "npgrid = img_grid_real.numpy()\n",
        "plt.imshow(np.transpose(npgrid, (1, 2, 0)), interpolation='nearest')\n",
        "plt.axis('off')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        },
        "id": "eNqyZNRoLJwX",
        "outputId": "72e77954-e3f4-411f-e24d-3dd30ec8bb1e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-0.5, 241.5, 121.5, -0.5)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Optimizers and Loss Function\n",
        "\n",
        "In this section, we set up the optimizers for our models and define the loss function.\n",
        "\n",
        "## Optimizers\n",
        "\n",
        "```python\n",
        "# Optimizer for the Discriminator\n",
        "opt_discriminator = optim.Adam(discriminator.parameters(), lr=learning_rate)\n",
        "\n",
        "# Optimizer for the Generator\n",
        "opt_generator = optim.Adam(generator.parameters(), lr=learning_rate)\n"
      ],
      "metadata": {
        "id": "KvrddThYWK7x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "#optmizers and loss\n",
        "opt_discriminator=optim.Adam(discriminator.parameters(),lr=learning_rate)\n",
        "opt_generator=optim.Adam(generator.parameters(),lr=learning_rate)\n",
        "#loss\n",
        "criterion=nn.BCELoss()\n"
      ],
      "metadata": {
        "id": "GioSJWM9LMCm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **HOW ARE GANS TRAINING?**\n",
        "# GAN Training Approach: Intuitive Explanation\n",
        "\n",
        "- **Generator's Task:**\n",
        "  - Takes random input noise and attempts to create a synthetic image.\n",
        "  - This generated image is then passed to the Discriminator for evaluation.\n",
        "\n",
        "- **Discriminator's Task:**\n",
        "  - Discriminator is like an art critic; it learns to distinguish between real and fake images.\n",
        "  - It receives both real images from the dataset and synthetic images from the Generator.\n",
        "\n",
        "- **Training Discriminator:**\n",
        "  - Real images are reshaped and labeled as \"real\" (1).\n",
        "  - Discriminator evaluates the likelihood of the real images being real (log(D(real))).\n",
        "  - Fake images generated by the Generator are labeled as \"fake\" (0).\n",
        "  - Discriminator evaluates the likelihood of fake images being fake (log(1 - D(G(z)))).\n",
        "  - The total Discriminator loss is the average of these two.\n",
        "\n",
        "- **Updating Discriminator Weights:**\n",
        "  - Discriminator's weights are adjusted to maximize the total loss.\n",
        "  - It aims to become better at distinguishing real from fake images.\n",
        "\n",
        "- **Training Generator:**\n",
        "  - Generator aims to create images that fool the Discriminator.\n",
        "  - It generates fake images using random noise.\n",
        "  - These fake images are fed into the Discriminator.\n",
        "  - The Generator's loss is based on the likelihood of the Discriminator being fooled (log(D(G(z)))).\n",
        "\n",
        "- **Updating Generator Weights:**\n",
        "  - Generator's weights are adjusted to minimize its loss.\n",
        "  - It aims to generate images that are more realistic and challenging for the Discriminator.\n",
        "\n",
        "This cyclic process of training the Discriminator and Generator iteratively improves both models over time, resulting in the generation of more realistic synthetic images.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "lX_uRgg0XPzt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#training of generator and discriminator\n",
        "\n",
        "for epoch in range(num_epochs):\n",
        "  for batch_idx, (real,_) in enumerate(loader):\n",
        "    real=real.view(-1,784)\n",
        "    batch_size=real.shape[0]\n",
        "    #training discriminator\n",
        "    noise=torch.randn(batch_size,z_dim)\n",
        "\n",
        "    #we generate fake image: the generator takes random noise as input and try to construct an image from it.\n",
        "    fake=generator(noise)\n",
        "    #disc_real is the response of discriminator on real image , ones_like(disc_real) is the target we want to achive\n",
        "    disc_real=discriminator(real).view(-1)\n",
        "    lossD_real=criterion(disc_real,torch.ones_like(disc_real))\n",
        "    #disc_fake is the response of discriminator on fake image , zeroes_like(disc_real) is the target we want to achive\n",
        "    disc_fake=discriminator(fake).view(-1)\n",
        "    lossD_fake=criterion(disc_fake,torch.zeros_like(disc_fake))\n",
        "    '''\n",
        "    so basically here we trained the discriminator to identify fake image as fake\n",
        "    and real image as real\n",
        "    fake->0 and real->1\n",
        "\n",
        "    '''\n",
        "\n",
        "    #total loss we take mean\n",
        "    lossD=(lossD_real+lossD_fake)/2\n",
        "    #update\n",
        "    discriminator.zero_grad()\n",
        "    lossD.backward(retain_graph=True)#retain graph true helps us by checkpointing the particular instance to train generator on the response of discriminator on fake image\n",
        "    opt_discriminator.step()\n",
        "\n",
        "   #training the generator\n",
        "    #retain graph = true helped us to keep a checkpoint on that particular fake instance\n",
        "    output=discriminator(fake).view(-1)\n",
        "    lossG=criterion(output,torch.ones_like(output))\n",
        "    '''\n",
        "    the generator is interested in\n",
        "    what the discriminator responded to a fake(generated) image,\n",
        "    generator wants to fool the discriminator\n",
        "    therefore it will try to make that reponse as 1(1->real)\n",
        "    generator wants to make the reponse of discriminator on fake image\n",
        "    as 1 .\n",
        "\n",
        "    '''\n",
        "    generator.zero_grad()\n",
        "    lossG.backward()\n",
        "    opt_generator.step()\n",
        "\n",
        "    if batch_idx == 0:\n",
        "        print( \"Epoch: {epoch} \\t Discriminator Loss: {lossD} Generator Loss: {lossG}\".format( epoch=epoch, lossD=lossD, lossG=lossG))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KbwHCBA7LOn4",
        "outputId": "e3951eba-f873-4c35-9fe6-6cca9382a9d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch: 0 \t Discriminator Loss: 0.6506878137588501 Generator Loss: 0.728919506072998\n",
            "Epoch: 1 \t Discriminator Loss: 0.2047346979379654 Generator Loss: 1.9376438856124878\n",
            "Epoch: 2 \t Discriminator Loss: 0.5298221111297607 Generator Loss: 0.961971640586853\n",
            "Epoch: 3 \t Discriminator Loss: 0.643018364906311 Generator Loss: 0.9334772229194641\n",
            "Epoch: 4 \t Discriminator Loss: 1.0527551174163818 Generator Loss: 0.6159599423408508\n",
            "Epoch: 5 \t Discriminator Loss: 0.3791605234146118 Generator Loss: 1.2051312923431396\n",
            "Epoch: 6 \t Discriminator Loss: 0.7360836863517761 Generator Loss: 0.8615719079971313\n",
            "Epoch: 7 \t Discriminator Loss: 0.5322799682617188 Generator Loss: 1.1593163013458252\n",
            "Epoch: 8 \t Discriminator Loss: 0.5449835062026978 Generator Loss: 1.1303631067276\n",
            "Epoch: 9 \t Discriminator Loss: 0.7190340757369995 Generator Loss: 0.9333128929138184\n",
            "Epoch: 10 \t Discriminator Loss: 0.7672030925750732 Generator Loss: 1.146661639213562\n",
            "Epoch: 11 \t Discriminator Loss: 0.7313984036445618 Generator Loss: 1.0492466688156128\n",
            "Epoch: 12 \t Discriminator Loss: 0.44428232312202454 Generator Loss: 1.639432430267334\n",
            "Epoch: 13 \t Discriminator Loss: 0.6032383441925049 Generator Loss: 1.0697474479675293\n",
            "Epoch: 14 \t Discriminator Loss: 0.5667535066604614 Generator Loss: 1.2800414562225342\n",
            "Epoch: 15 \t Discriminator Loss: 0.7655940055847168 Generator Loss: 1.223350167274475\n",
            "Epoch: 16 \t Discriminator Loss: 0.6839787364006042 Generator Loss: 1.1370694637298584\n",
            "Epoch: 17 \t Discriminator Loss: 0.4991890788078308 Generator Loss: 1.146500825881958\n",
            "Epoch: 18 \t Discriminator Loss: 0.6836540699005127 Generator Loss: 0.9898819327354431\n",
            "Epoch: 19 \t Discriminator Loss: 0.5843368768692017 Generator Loss: 0.997314453125\n",
            "Epoch: 20 \t Discriminator Loss: 0.7729300260543823 Generator Loss: 0.8148027658462524\n",
            "Epoch: 21 \t Discriminator Loss: 0.6090874671936035 Generator Loss: 1.1887502670288086\n",
            "Epoch: 22 \t Discriminator Loss: 0.6608565449714661 Generator Loss: 1.061275601387024\n",
            "Epoch: 23 \t Discriminator Loss: 0.6364893317222595 Generator Loss: 1.2399706840515137\n",
            "Epoch: 24 \t Discriminator Loss: 0.672309398651123 Generator Loss: 1.0578739643096924\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#now its time to plot the generated images! isnt it awesome? we just made an entity which learned from the data we gave it and now it can generate the data on its own? how amazing it is, it is the first step we took in generating something from scratch."
      ],
      "metadata": {
        "id": "HXmO5qVMZMM0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fake = generator(noise).reshape(-1, 1, 28, 28)\n",
        "img_grid_fake = torchvision.utils.make_grid(fake, normalize=True)\n",
        "npgrid = img_grid_fake.cpu().numpy()\n",
        "plt.imshow(np.transpose(npgrid, (1, 2, 0)), interpolation='nearest')\n",
        "plt.axis('off')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        },
        "id": "abFu5GIyLZp_",
        "outputId": "a3e64614-d229-40f8-bc7e-a043cc8ba9ce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-0.5, 241.5, 121.5, -0.5)"
            ]
          },
          "metadata": {},
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "n_6mxu0CRkCs"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}