Lineares Modell in numpy

LinearesModell.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = (lambda x: x*x)(x) + np.random.normal(0, N, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(t):\n",
    "    return np.array([1, t, t*t])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   0,   0],\n",
       "       [  1,   1,   1],\n",
       "       [  1,   2,   4],\n",
       "       [  1,   3,   9],\n",
       "       [  1,   4,  16],\n",
       "       [  1,   5,  25],\n",
       "       [  1,   6,  36],\n",
       "       [  1,   7,  49],\n",
       "       [  1,   8,  64],\n",
       "       [  1,   9,  81],\n",
       "       [  1,  10, 100],\n",
       "       [  1,  11, 121],\n",
       "       [  1,  12, 144],\n",
       "       [  1,  13, 169],\n",
       "       [  1,  14, 196],\n",
       "       [  1,  15, 225]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [model(k) for k in range(N)]\n",
    "X = np.array(X)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate(t):\n",
    "    return np.array(model(t)).dot(gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.linspace(0, N, 100), estimate(np.linspace(0, N, 100)))\n",
    "plt.scatter(x, y);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}