DLO_Aufg4.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "DLO_Aufg4.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPCcCbVP9WkxqNDXz7m9et4",
      "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/DomTHK/DLO_Lab/blob/main/DLO_Aufg4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Aufgabe 4\n",
        "\n",
        "Gegeben sind die vier Punkte (1, 1), (3,4), (6, 2), (7, 3).\n",
        "* Wie lautet Ihre Fehlerfunktion L, die aussagt, wie sehr ein\n",
        "Polynom ˆy(x) = a0 + a1x + a2x\n",
        "2 + . . . + ad x\n",
        "d mit Grad d die\n",
        "Punkte verfehlt?\n",
        "* Wie sehen dann die partiellen Ableitungen nach a0, a1, usw.\n",
        "aus?\n",
        "* Nutzen Sie Gradientenabsteig, um Polynome verschiedenen\n",
        "Grades an die Punkte zu fitten\n",
        "* Achtung: Initialisierung der ai sowie Schrittweite η haben\n",
        "großen Einfluss!\n"
      ],
      "metadata": {
        "id": "ZfVpR_9_eADf"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "ump8jdKYd8rA"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#was wird gemacht?\n",
        "# 0) Funktion auswählen [besser gesagt anzahl Polynome]\n",
        "# 1) 4 mal 'y_' für jedes der 4 'x' berechnen\n",
        "# 2) y_ mit y vergleichen, differenz berechnen, ableitung berechnen, a (=gewichtsvektor) anpassen\n",
        "# 3) Dies für alle gewünschten Polynomgrade wiederholen\n",
        "\n",
        "def calc_y(x, a, grades, k, i):                                                                                                                                                   \n",
        "    y = 0\n",
        "    for j in range(int(grades[i])+1): \n",
        "      y = y + a[i, j] * x[k]**j \n",
        "      #print(j)\n",
        "    return y\n",
        "\n",
        "def calc_y_(x, a, grades, k, i):                                      #für jedes der 4 'x' jeweils 'y_' berechnen und Gradientenabstieg durchführen                                                                                                              \n",
        "    y_ = 0\n",
        "    for j in range(int(grades[i])+1): y_ = y_ + a[i, j] * x[k, 0]**j  #calculate 'y' for the chosen 'x', based on function         \n",
        "    #print(a[i, j])\n",
        "    #print('y,ai,\\nxk:',i,  y_, a[i, :], x[k, 0])\n",
        "    return y_\n",
        "\n",
        "def perform_gd(y_, x, lr, a, i, k, grades):\n",
        "    L = y_ - x[k, 1]                                               #calculate loss based on calculated y\n",
        "    #print('before:', a[i,:])\n",
        "    for l in range(int(grades[i])+1): a[i, l] = a[i, l] - (lr/((10**l)*(1+l))) * L * x[k,0]**l    #perform gradient-descent \n",
        "    #print('after:', a[i,:])\n",
        "    return a\n",
        "\n",
        "def fit_polynom(x, grades, n_epochs, lr):\n",
        "    a = np.full((len(grades), np.max(grades)+1), 0.9)\n",
        "    #a = np.matrix([[0.1, 3, 3, 5/10, 5/100],\n",
        "    #               [0.1, 3, 3, 5/10, 5/100],\n",
        "    #               [0.1, 3, 3, 5/10, 5/100]])\n",
        "    for i in range(len(grades)):                                       #Eine Iteration steht für eine Funktion eines best. Grades \n",
        "        for e in range(n_epochs):                                      #über e Iterationen laufen lassen\n",
        "            for k in range(len(x)):                                    #change weights for one 'x' at a time\n",
        "                for h in range(len(grades)):\n",
        "                  y_ = 0\n",
        "                  y_ = calc_y_(x, a, grades, k, i)                       #Einmal die y-Werte der Funktion mit aktuellen a1..ad berechnen\n",
        "                  a = perform_gd(y_, x, lr, a, i, k, grades)\n",
        "        print(a)\n",
        "    return a                                                                                      \n",
        "          \n",
        "\n",
        "    \n",
        "         "
      ],
      "metadata": {
        "id": "W5lLJh2egaBW"
      },
      "execution_count": 109,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b = np.matrix([[3.e-05, 3.e-05, 3.e-05, 3.e-05, 3.e-05],\n",
        " [3.e-05, 3.e-05, 3.e-05, 3.e-05, 3.e-05],\n",
        " [3.e-05, 3.e-05, 3.e-05, 3.e-05, 3.e-05]])\n",
        "\n",
        "print(np.mean(b))"
      ],
      "metadata": {
        "id": "u3yumC1Yl-wF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "53f77ac0-b428-46e0-eb5a-8f40884b6163"
      },
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3.000000000000001e-05\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#initializing\n",
        "x = np.array([[1, 1], \n",
        "              [3, 4], \n",
        "              [6, 2], \n",
        "              [7, 3]])\n",
        "grades = np.array([[3], [4], [5]])\n",
        "n_epochs = 100000\n",
        "lr = 0.0078\n",
        "\n",
        "#training\n",
        "a = fit_polynom(x, grades, n_epochs, lr)\n",
        "\n",
        "#plotting\n",
        "x_range = np.linspace(1, 8, num=100)\n",
        "y_ = np.full((100, 3), 0.0)\n",
        "\n",
        "for k in range(100):\n",
        "    for j in range(3): y_[k, j] = calc_y(x_range, a, grades, k, j)\n",
        "\n",
        "color = (['blue', 'green', 'yellow'])\n",
        "for h in range(3): plt.plot(x_range, y_[:, h], color = color[h]) \n",
        "plt.ylim(0, 5)\n",
        "plt.scatter(x[:,0], x[:,1], color='red')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 477
        },
        "id": "aRiEIfa6i_ts",
        "outputId": "fd413570-7d08-481a-8284-13b2e1f2dbb9"
      },
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-4.25174103  6.93835584 -1.81440986  0.1387278   0.9         0.9       ]\n",
            " [ 0.9         0.9         0.9         0.9         0.9         0.9       ]\n",
            " [ 0.9         0.9         0.9         0.9         0.9         0.9       ]]\n",
            "[[-4.25174103  6.93835584 -1.81440986  0.1387278   0.9         0.9       ]\n",
            " [-1.78927602  2.85142965  0.121351   -0.20382784  0.02032321  0.9       ]\n",
            " [ 0.9         0.9         0.9         0.9         0.9         0.9       ]]\n",
            "[[-4.25174103e+00  6.93835584e+00 -1.81440986e+00  1.38727800e-01\n",
            "   9.00000000e-01  9.00000000e-01]\n",
            " [-1.78927602e+00  2.85142965e+00  1.21351002e-01 -2.03827839e-01\n",
            "   2.03232062e-02  9.00000000e-01]\n",
            " [ 5.31963781e-01 -1.48840798e-01  5.72374084e-01  1.09020037e-01\n",
            "  -7.09710331e-02  6.45392808e-03]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "ut8MvSzeQrxY"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}