CDS104-Databases-and-Data-P.../code/online-part-1/Linear Algebra Assignment 3.ipynb
2025-05-18 17:24:28 +02:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Übung\n",
"\n",
"Gegeben ist das folgende Array:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"n = np.array([\n",
" [0. , 0. , 0.5, 1. , 1. , 0. , 1. , 0. , 1. ],\n",
" [0. , 1. , 1.5, 1. , 0. , 1. , 1. , 0. , 0. ]\n",
"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Die erste Zeile sind dabei x-Werte, die zweite Zeile y-Werte von Punkten. Plotten Sie die Punkte als Linienzug mit `plt.plot(...)`."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Linienzug plotten\n",
"plt.figure()\n",
"plt.plot(n[0], n[1])\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Als nächstes sollen die Punkte rotiert werden. Eine Matrix, die eine Rotation um einen Winkel $\\theta$ durchführt, lautet wie folgt:\n",
"\n",
"\\begin{equation}\n",
"m_1 =\n",
"\\begin{bmatrix}\n",
"\\cos \\theta & -\\sin \\theta \\\\ \n",
"\\sin \\theta & \\cos \\theta \\\\\n",
"\\end{bmatrix}\n",
"\\end{equation}\n",
"\n",
"Implementieren Sie eine Funktion, die für einen gegeben Winkel diese Matrix als `ndarray` erzeugt:\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# angle soll in Grad angegeben werden\n",
"def rotation_matrix(angle):\n",
" theta = np.deg2rad(angle)\n",
" c = np.cos(theta)\n",
" s = np.sin(theta)\n",
" return np.array([[c, -s], [s, c]])\n",
"\n",
"# mögliche Tests\n",
"assert np.allclose(rotation_matrix(90).dot(np.array([1,0])), np.array([0,1]))\n",
"assert np.allclose(rotation_matrix(-90).dot(np.array([1,0])), np.array([0,-1]))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Zum Rotieren aller Punkte muss jeder Punkt mit der Matrix `m` multipliziert werden. Rotieren Sie alle Punkte um 60 Grad und plotten Sie das Ergebnis erneut (Bonus: Versuchen Sie ohne `for`-Schleife auszukommen):"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# n_rot soll die rotierten Punkte enthalten, n_rot.shape == n.shape\n",
"n_rot = rotation_matrix(60).dot(n)\n",
"\n",
"plt.figure()\n",
"plt.plot(n_rot[0], n_rot[1])\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Als nächstes sollen die Punkte bezüglich des Ursprungs skaliert werden werden. Eine Matrix, die eine Skalierung in x-Richtung mit Faktor $s_x$ und in y-Richtung mit Faktor $s_y$ durchführt, lautet:\n",
"\n",
"\\begin{equation}\n",
"m_2 =\n",
"\\begin{bmatrix}\n",
"s_x & 0 \\\\ \n",
"0 & s_y \\\\\n",
"\\end{bmatrix}\n",
"\\end{equation}\n",
"\n",
"Implementieren Sie eine Funktion, die für einen gegeben Winkel diese Matrix als `ndarray` erzeugt:\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def scale_matrix(sx, sy):\n",
" return np.array([[sx, 0], [0, sy]])\n",
"\n",
"assert np.allclose(scale_matrix(2, 3).dot(np.array([1,1])), np.array([2,3]))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Skalieren Sie die gegebenen Punkte um beliebige Faktoren und plotten Sie die ursprünglichen und skalierten Punkte im selben Diagramm:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"scaled = scale_matrix(2, 0.5).dot(n)\n",
"plt.figure()\n",
"plt.plot(n[0], n[1], label=\"original\")\n",
"plt.plot(scaled[0], scaled[1], label=\"scaled\")\n",
"plt.legend()\n",
"plt.show()\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "code (3.13.2)",
"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": "3.13.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}