Task2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOM4uG2QpBF32Cj7dz8f+0Z",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sf-balaba/DA-in-GameDev-lab1/blob/main/Task2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "id": "J5yLABIqYtRM",
        "outputId": "704daa43-a3b3-4800-c914-2b801547559f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.44852871]\n",
            "[0.11869413]\n",
            "[0.45261935] [0.11875337] 2837.1090023385655\n",
            "[0.46076212] [0.11887127] 2804.001667704202\n",
            "[0.47288063] [0.11904666] 2755.115188369313\n",
            "[0.48886179] [0.11927782] 2691.3519895466\n",
            "[0.50855754] [0.11956249] 2613.871559765211\n",
            "[1.75150804] [0.10813616] 189.0791449368985\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f95db82d650>]"
            ]
          },
          "metadata": {},
          "execution_count": 1
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#Import the required modules, numpy for calculation, and Matplotlib for drawing\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# define data, and change list to array\n",
        "x = [3,21,22,34,54,34,55,67,89,99]\n",
        "x = np.array(x)\n",
        "y = [2,22,24,65,79,82,55,130,150,199]\n",
        "y = np.array(y)\n",
        "\n",
        "#Show the effect of a scatter plot\n",
        "plt.scatter(x,y)\n",
        "#The basic linear regression model is wx + b, and sinse this is a two-dementional space, the model is ax + b\n",
        "\n",
        "def model(a, b, x):\n",
        "  return a*x+b\n",
        "\n",
        "#The most commonly used ioss function of linear regression model is the loss function of mean variance difference\n",
        "def loss_function(a, b, x, y):\n",
        "  num = len(x)\n",
        "  prediction = model(a, b, x)\n",
        "  return (0.5/num) * (np.square(prediction-y)).sum()\n",
        "\n",
        "#The optimization function mainly USES partial derivatives to update two parameters a and b\n",
        "def optimize(a, b, x, y):\n",
        "  num = len(x)\n",
        "  prediction = model(a,b,x)\n",
        "  #Update the values of A and B by sinding the partial derivatives of the loss function on a and b\n",
        "  da = (1.0/num) * ((prediction -y)*x).sum()\n",
        "  db = (1.0/num) * ((prediction -y).sum())\n",
        "  a = a-Lr*da\n",
        "  b = b-Lr*db\n",
        "  return a, b\n",
        "\n",
        "#iterated function, return a and b\n",
        "def iterate(a,b,x,y,times):\n",
        "  for i in range(times):\n",
        "    a,b = optimize(a,b,x,y)\n",
        "  return a, b\n",
        "\n",
        "#Initialize parameters and display\n",
        "a = np.random.rand(1)\n",
        "print(a)\n",
        "b = np.random.rand(1)\n",
        "print(b)\n",
        "Lr = 0.000001\n",
        "\n",
        "#For thw first iteartion, thw parameter values, losses and visualization after the iteration are displayed\n",
        "a,b = iterate(a,b,x,y,1)\n",
        "prediction = model(a,b,x)\n",
        "loss = loss_function(a,b,x,y)\n",
        "print(a,b,loss)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x, prediction)\n",
        "\n",
        "\n",
        "a,b = iterate(a,b,x,y,2)\n",
        "prediction = model(a,b,x)\n",
        "loss = loss_function(a,b,x,y)\n",
        "print(a,b,loss)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x, prediction)\n",
        "\n",
        "a,b = iterate(a,b,x,y,3)\n",
        "prediction = model(a,b,x)\n",
        "loss = loss_function(a,b,x,y)\n",
        "\n",
        "print(a,b,loss)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x, prediction)\n",
        "\n",
        "a,b = iterate(a,b,x,y,4)\n",
        "prediction = model(a,b,x)\n",
        "loss = loss_function(a,b,x,y)\n",
        "print(a,b,loss)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x, prediction)\n",
        "\n",
        "a,b = iterate(a,b,x,y,5)\n",
        "prediction = model(a,b,x)\n",
        "loss = loss_function(a,b,x,y)\n",
        "print(a,b,loss)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x, prediction)\n",
        "\n",
        "a,b = iterate(a,b,x,y,10000)\n",
        "prediction = model(a,b,x)\n",
        "loss = loss_function(a,b,x,y)\n",
        "print(a,b,loss)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x, prediction)"
      ]
    }
  ]
}