Lab_SC_02_2_2502012546_Keyla_Azzahra.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Lab - SC 02.2 - 2502012546 - Keyla Azzahra",
      "provenance": [],
      "authorship_tag": "ABX9TyOoaEj/qWANYDz8cMcXOuM/",
      "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/Keywcksn/LAB-Scientific-Computing/blob/main/Lab_SC_02_2_2502012546_Keyla_Azzahra.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "-EMp1cnDJWh8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b060e5b1-7598-4601-ead1-5bd6535a197c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sat Mar 12 12:44:51 2022\n"
          ]
        }
      ],
      "source": [
        "import time\n",
        "print(time.ctime())"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy import optimize\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.style.use('seaborn-poster')\n",
        "\n",
        "# generate x and y\n",
        "x = np.linspace(0, 1, 101)\n",
        "y = 1 + x + x * np.random.random(len(x))\n",
        "\n",
        "# assemble matrix A\n",
        "A = np.vstack([x, np.ones(len(x))]).T\n",
        "\n",
        "# turn y into a column vector\n",
        "y = y[:, np.newaxis]\n",
        "\n",
        "#direct least square regression\n",
        "alpha = np.dot((np.dot(np.linalg.inv(np.dot(A.T, A)), A.T)), y)\n",
        "print(alpha)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rA1lCYGMKRec",
        "outputId": "6a88f13b-2888-4fac-f5e4-24b1ed2abe56"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.45297372]\n",
            " [1.026218  ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# plot the results\n",
        "plt.figure(figsize = (10, 8))\n",
        "plt.plot(x, y, 'b.')\n",
        "plt.plot(x, alpha[0]*x + alpha[1], 'r')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "id": "LfHlL8OsL3JC",
        "outputId": "d258e6c4-f40e-4adc-c276-d4ecec9dcfd1"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pinv = np.linalg.pinv(A)\n",
        "alpha = pinv.dot(y)\n",
        "print(alpha)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_700bee4MQRq",
        "outputId": "e1afa39f-df3d-4d8e-9a3c-78fdbaa58f93"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.45297372]\n",
            " [1.026218  ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = np.linalg.lstsq(A, y, rcond=None)[0]\n",
        "print(alpha)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0jr0EaFSMZ71",
        "outputId": "118c5b13-a6fc-4f2e-c06e-03ef8f73b8dc"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.45297372]\n",
            " [1.026218  ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# generate x and y\n",
        "x = np.linspace(0, 1, 101)\n",
        "y = 1 + x + x * np.random.random(len(x))\n",
        "\n",
        "def func(x, a, b) :\n",
        "  y = a*x + b\n",
        "  return y\n",
        "\n",
        "alpha = optimize.curve_fit(func, xdata = x, ydata = y)[0]\n",
        "print(alpha)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gSYqITuyMkUo",
        "outputId": "b4a92a47-fda7-40a6-8b9d-b71efc22faa1"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1.47774416 1.00326759]\n"
          ]
        }
      ]
    }
  ]
}