786 lines
2.6 MiB
Plaintext
786 lines
2.6 MiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "d1bcc8a7-466b-4610-b58a-9d6fd89d3534",
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"metadata": {},
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"source": [
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"#### Zadanie 1 (4pkt):\n",
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"\n",
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"Zadanie polega na wizualizacji algorytmu gradientu prostego. Rozważamy dwa typy powierzchni w $\\mathbb{R}^3$: z jednym ekstremum oraz z jedym punktem siodłowym - przykady pokazuje <a href=https://fraktal.faculty.wmi.amu.edu.pl/symulowanie_wizualne/lab4_r1.png>rysunek 1</a>. Dla każdej z nich należy wykonać dwa typy wizualizacji, pokazujących ciąg zbieżny do punktu ekstremalnego: 2D oraz 3D - przykład pokazuje \n",
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" pokazuje to <a href=https://fraktal.faculty.wmi.amu.edu.pl/symulowanie_wizualne/lab4_r2.png>rysunek 2</a>. \n",
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"Wizualizacje powinny pokazywać działanie algorytmu z różnymi współczynnikami szybkości zbiegania, w tym przypadek kiedy zbieżność nie zostaje osiągnięta.\n",
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"Gradient należy zakodować analitycznie.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5ced1d1c-a5bf-4224-a001-f2007ec8fdee",
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"metadata": {},
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"source": [
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"#### Zadanie 2 (2pkt):\n",
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"\n",
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"Zadanie jest identyczne jak Zadanie 1, z jednym wyjątkiem: gradient należy zakodować stosując aproksymację przez różnice skończone.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9ec21f33-322d-4d99-a065-274430b02185",
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"metadata": {},
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"source": [
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"### Zadanie 1 ###"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 307,
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"id": "7d5f3d90-c154-4fad-8850-1ca10f09198c",
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"metadata": {
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"deletable": false,
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"nbgrader": {
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"cell_type": "code",
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"checksum": "74517e974d221748786da140f21ed16a",
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"grade": true,
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"grade_id": "cell-4b4826b612a1a9b4",
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"locked": false,
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"points": 4,
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"schema_version": 3,
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"solution": true,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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" \n",
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"def f(x, y):\n",
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" return x ** 2 + y ** 2\n",
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"\n",
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"def f2(x, y):\n",
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" return x ** 2 - y ** 2\n",
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"\n",
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"x = np.linspace(-4, 4, 100)\n",
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"y = np.linspace(-4, 4, 100)\n",
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"\n",
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"X, Y = np.meshgrid(x, y)\n",
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"Z = f(X, Y)\n",
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"Z2 = f2(X, Y)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 308,
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"id": "06492973-e74b-4022-a9af-9116f8677bf3",
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"metadata": {},
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"outputs": [],
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"source": [
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"#pochodna jest identyczna względem wartości x oraz y \n",
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"def df(x):\n",
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" return 2*x\n",
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"\n",
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"def gradient(xi, yi, steps, lr):\n",
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" xline = []\n",
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" yline = []\n",
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" zline = []\n",
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" \n",
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" for i in range(0, steps):\n",
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" xi = xi - lr * df(xi)\n",
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" xline.append(xi)\n",
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" \n",
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" yi = yi - lr * df(yi)\n",
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" yline.append(yi)\n",
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" \n",
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" res = f(xi, yi)\n",
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" zline.append(res)\n",
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" \n",
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" return xline, yline, zline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 309,
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"id": "f4de1c41",
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"metadata": {},
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"outputs": [],
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"source": [
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|
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"def dfx2(x):\n",
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" return 2*x\n",
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"\n",
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"def dfy2(y):\n",
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" return -2*y\n",
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"\n",
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"def gradient2(xi, yi, steps, lr):\n",
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" xline = []\n",
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" yline = []\n",
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" zline = []\n",
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" \n",
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" for i in range(0, steps):\n",
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" xi = xi - lr * dfx2(xi)\n",
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" xline.append(xi)\n",
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" \n",
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" yi = yi - lr * dfy2(yi)\n",
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" yline.append(yi)\n",
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" \n",
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" res = f(xi, yi)\n",
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" zline.append(res)\n",
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" \n",
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" return xline, yline, zline"
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]
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},
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{
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"cell_type": "markdown",
|
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|
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"id": "e00f3e1d-4d3d-42d0-9e51-07f56702573e",
|
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|
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"metadata": {
|
||
|
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"tags": []
|
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|
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},
|
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|
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"source": [
|
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|
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"### Learning rate = 0.1 ###"
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|
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]
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},
|
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|
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{
|
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|
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"cell_type": "code",
|
||
|
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"execution_count": 310,
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||
|
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"id": "e8ffc7db-4a38-4e6d-b888-9f7e5184c30c",
|
||
|
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"metadata": {},
|
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|
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"outputs": [
|
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|
|
{
|
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"data": {
|
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|
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"text/plain": [
|
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|
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"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcf71932250>"
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]
|
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|
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},
|
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|
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"execution_count": 310,
|
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|
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"metadata": {},
|
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|
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"output_type": "execute_result"
|
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|
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},
|
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|
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{
|
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"data": {
|
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|
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"image/png": "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
|
||
|
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"text/plain": [
|
||
|
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"<Figure size 1000x1000 with 1 Axes>"
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]
|
||
|
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},
|
||
|
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"metadata": {},
|
||
|
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"output_type": "display_data"
|
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|
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}
|
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|
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],
|
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"source": [
|
||
|
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"xline, yline, zline = gradient(-4, 4, 1500, 0.1)\n",
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|
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"fig = plt.figure(figsize=[10,10])\n",
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"ax = plt.axes(projection='3d')\n",
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"ax.set_xlabel('x', fontsize=20)\n",
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|
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"ax.set_ylabel('y', fontsize=20)\n",
|
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|
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"ax.set_zlabel('z', fontsize=20)\n",
|
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|
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"ax.contour3D(X, Y, Z, 50, cmap='viridis')\n",
|
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|
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"ax.plot3D(xline, yline, zline, 'blue')\n",
|
||
|
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"ax.scatter(xline, yline, zline, color='deeppink', marker='v')"
|
||
|
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]
|
||
|
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},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 311,
|
||
|
|
"id": "76788cb4-dc45-488a-9e50-e6e693f74050",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z)\n",
|
||
|
|
"cp = plt.plot(xline, yline, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline, yline, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "6f16a2ff-53b2-4df1-918f-e461a24b6de1",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Learning rate = 0.01 ###"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 312,
|
||
|
|
"id": "0be9e978-cf9e-4ace-9a4d-359636981c32",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcf719f4b50>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 312,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 1000x1000 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"xline, yline, zline = gradient(-4, 4, 1500, 0.01)\n",
|
||
|
|
"fig = plt.figure(figsize=[10,10])\n",
|
||
|
|
"ax = plt.axes(projection='3d')\n",
|
||
|
|
"ax.set_xlabel('x', fontsize=20)\n",
|
||
|
|
"ax.set_ylabel('y', fontsize=20)\n",
|
||
|
|
"ax.set_zlabel('z', fontsize=20)\n",
|
||
|
|
"ax.contour3D(X, Y, Z, 50, cmap='viridis')\n",
|
||
|
|
"ax.plot3D(xline, yline, zline, 'blue')\n",
|
||
|
|
"ax.scatter(xline, yline, zline, color='deeppink', marker='v')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 313,
|
||
|
|
"id": "da9d138f-e1dc-431e-8f8f-a23477510f9d",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z)\n",
|
||
|
|
"cp = plt.plot(xline, yline, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline, yline, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "6bba592a",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Druga funkcja"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "1fd1ddd8-9034-498a-9b01-c05f867a2e22",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Learning rate = 0.1"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 314,
|
||
|
|
"id": "30276af9-9ed2-4355-a0b0-5566bc911bff",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcfd73b8040>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 314,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 1000x1000 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"xline2, yline2, zline2 = gradient2(-2, -1, 15, 0.1)\n",
|
||
|
|
"fig = plt.figure(figsize=[10,10])\n",
|
||
|
|
"ax = plt.axes(projection='3d')\n",
|
||
|
|
"ax.set_xlabel('x', fontsize=20)\n",
|
||
|
|
"ax.set_ylabel('y', fontsize=20)\n",
|
||
|
|
"ax.set_zlabel('z', fontsize=20)\n",
|
||
|
|
"ax.contour3D(X, Y, Z2, 30, cmap='viridis')\n",
|
||
|
|
"ax.plot3D(xline2, yline2, zline2, 'blue')\n",
|
||
|
|
"ax.scatter(xline, yline, zline, color='deeppink', marker='v')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 315,
|
||
|
|
"id": "1865802c-5b43-419a-9c4b-39de287438c2",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z2, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z2, cmap='viridis')\n",
|
||
|
|
"cp = plt.plot(xline2, yline2, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline, yline, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "298e097b-96bf-4561-996f-029bf90b0896",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Learning rate = 0.01"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 316,
|
||
|
|
"id": "0a174218-d7b5-44e0-af25-ea315793f2ee",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcfb4895eb0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 316,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 1000x1000 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"xline2, yline2, zline2 = gradient2(-4.5, 0, 1500, 0.01)\n",
|
||
|
|
"fig = plt.figure(figsize=[10,10])\n",
|
||
|
|
"ax = plt.axes(projection='3d')\n",
|
||
|
|
"ax.set_xlabel('x', fontsize=20)\n",
|
||
|
|
"ax.set_ylabel('y', fontsize=20)\n",
|
||
|
|
"ax.set_zlabel('z', fontsize=20)\n",
|
||
|
|
"ax.contour3D(X, Y, Z2, 30, cmap='viridis')\n",
|
||
|
|
"ax.plot3D(xline2, yline2, zline2, 'blue')\n",
|
||
|
|
"ax.scatter(xline, yline, zline, color='deeppink', marker='v')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 317,
|
||
|
|
"id": "d3c27a35-9162-4b27-bd26-98ecc59a5fb4",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z2, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z2, cmap='viridis')\n",
|
||
|
|
"cp = plt.plot(xline2, yline2, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline2, yline2, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "b0ac88f0-a730-48da-8a56-b68efd5e2d85",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Zmiana punktu startowego - brak zbieżności ###"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 318,
|
||
|
|
"id": "d283d6c3-6c61-4abb-8355-7c3956bf9ce6",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcfb1d0f0d0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 318,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 1000x1000 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"xline2, yline2, zline2 = gradient2(-4.5, 1, 1500, 0.01)\n",
|
||
|
|
"fig = plt.figure(figsize=[10,10])\n",
|
||
|
|
"ax = plt.axes(projection='3d')\n",
|
||
|
|
"ax.set_xlabel('x', fontsize=20)\n",
|
||
|
|
"ax.set_ylabel('y', fontsize=20)\n",
|
||
|
|
"ax.set_zlabel('z', fontsize=20)\n",
|
||
|
|
"ax.contour3D(X, Y, Z2, 30, cmap='viridis')\n",
|
||
|
|
"ax.plot3D(xline2, yline2, zline2, 'blue')\n",
|
||
|
|
"ax.scatter(xline, yline, zline, color='deeppink', marker='v')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 319,
|
||
|
|
"id": "74869483-6584-4e4c-93e5-e01ba48f7a61",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z2, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z2, cmap='viridis')\n",
|
||
|
|
"cp = plt.plot(xline2, yline2, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline2, yline2, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "cc28229a-2ce9-4830-b0f3-fef3cdf048e2",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Zadanie 2 ###"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 320,
|
||
|
|
"id": "04a92a75",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "93f80346581dfbf0111ea2eb79f851ac",
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-81f6af67fad17986",
|
||
|
|
"locked": false,
|
||
|
|
"points": 2,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"def dfx_differences(x, y, h):\n",
|
||
|
|
" return (f(x + h, y) - f(x - h, y)) / 2*h\n",
|
||
|
|
"\n",
|
||
|
|
"def dfy_differences(x, y, h):\n",
|
||
|
|
" return (f(x, y + h) - f(x, y - h)) / 2*h\n",
|
||
|
|
"\n",
|
||
|
|
"def gradient_differences(xi, yi, steps, lr, h):\n",
|
||
|
|
" xline = []\n",
|
||
|
|
" yline = []\n",
|
||
|
|
" zline = []\n",
|
||
|
|
" \n",
|
||
|
|
" for i in range(0, steps):\n",
|
||
|
|
" xi_new = xi - lr * dfx_differences(xi, yi, h)\n",
|
||
|
|
" xline.append(xi)\n",
|
||
|
|
" \n",
|
||
|
|
" yi_new = yi - lr * dfy_differences(xi, yi, h)\n",
|
||
|
|
" yline.append(yi)\n",
|
||
|
|
" \n",
|
||
|
|
" res = f(xi, yi)\n",
|
||
|
|
" zline.append(res)\n",
|
||
|
|
" \n",
|
||
|
|
" xi = xi_new\n",
|
||
|
|
" yi = yi_new\n",
|
||
|
|
" \n",
|
||
|
|
" return xline, yline, zline\n",
|
||
|
|
"\n",
|
||
|
|
"def gradient_differences2(xi, yi, steps, lr, h):\n",
|
||
|
|
" xline = []\n",
|
||
|
|
" yline = []\n",
|
||
|
|
" zline = []\n",
|
||
|
|
" \n",
|
||
|
|
" for i in range(0, steps):\n",
|
||
|
|
" xi_new = xi - lr * dfx_differences(xi, yi, h)\n",
|
||
|
|
" xline.append(xi)\n",
|
||
|
|
" \n",
|
||
|
|
" yi_new = yi - lr * dfy_differences(xi, yi, h)\n",
|
||
|
|
" yline.append(yi)\n",
|
||
|
|
" \n",
|
||
|
|
" res = f2(xi, yi)\n",
|
||
|
|
" zline.append(res)\n",
|
||
|
|
" \n",
|
||
|
|
" xi = xi_new\n",
|
||
|
|
" yi = yi_new\n",
|
||
|
|
" \n",
|
||
|
|
" return xline, yline, zline"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 325,
|
||
|
|
"id": "d3b2f0d0-68fb-4024-b92a-a7c2b91183be",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcfe58b2760>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 325,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 1000x1000 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"xline_diff, yline_diff, zline_diff = gradient_differences(-4, 4, 1000, 0.1, 0.001)\n",
|
||
|
|
"fig = plt.figure(figsize=[10,10])\n",
|
||
|
|
"ax = plt.axes(projection='3d')\n",
|
||
|
|
"ax.set_xlabel('x', fontsize=20)\n",
|
||
|
|
"ax.set_ylabel('y', fontsize=20)\n",
|
||
|
|
"ax.set_zlabel('z', fontsize=20)\n",
|
||
|
|
"ax.contour3D(X, Y, Z, 30, cmap='viridis')\n",
|
||
|
|
"ax.plot3D(xline_diff, yline_diff, zline_diff, 'blue')\n",
|
||
|
|
"ax.scatter(xline_diff, yline_diff, zline_diff, color='deeppink', marker='v')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 322,
|
||
|
|
"id": "5247eda5-50c3-440d-b71b-9474666790a2",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z, cmap='viridis')\n",
|
||
|
|
"cp = plt.plot(xline_diff, yline_diff, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline_diff, yline_diff, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 323,
|
||
|
|
"id": "e31d5217-114e-4ee3-b0f2-8372f0db3308",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fcfe57d33d0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 323,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 1000x1000 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"xline_diff2, yline_diff2, zline_diff2 = gradient_differences2(-4, -4, 1500, 0.1, 0.1)\n",
|
||
|
|
"fig = plt.figure(figsize=[10,10])\n",
|
||
|
|
"ax = plt.axes(projection='3d')\n",
|
||
|
|
"ax.set_xlabel('x', fontsize=20)\n",
|
||
|
|
"ax.set_ylabel('y', fontsize=20)\n",
|
||
|
|
"ax.set_zlabel('z', fontsize=20)\n",
|
||
|
|
"ax.contour3D(X, Y, Z2, 30, cmap='viridis')\n",
|
||
|
|
"ax.plot3D(xline_diff2, yline_diff2, zline_diff2, 'blue')\n",
|
||
|
|
"ax.scatter(xline_diff2, yline_diff2, zline_diff2, color='deeppink', marker='v')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 324,
|
||
|
|
"id": "28887dab-8d71-4cb2-a7dc-6aaf00cb7cac",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cp = plt.contour(X, Y, Z2, colors='black', linestyles='dashed', linewidths=1)\n",
|
||
|
|
"plt.clabel(cp, inline=1, fontsize=10)\n",
|
||
|
|
"cp = plt.contour(X, Y, Z2, cmap='viridis')\n",
|
||
|
|
"cp = plt.plot(xline_diff2, yline_diff2, color='blue')\n",
|
||
|
|
"cp = plt.scatter(xline_diff2, yline_diff2, color='deeppink', marker='.')\n",
|
||
|
|
"plt.xlabel('x')\n",
|
||
|
|
"plt.ylabel('y')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3.9.13 ('base')",
|
||
|
|
"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": "3.9.13"
|
||
|
|
},
|
||
|
|
"latex_envs": {
|
||
|
|
"LaTeX_envs_menu_present": true,
|
||
|
|
"autoclose": false,
|
||
|
|
"autocomplete": true,
|
||
|
|
"bibliofile": "biblio.bib",
|
||
|
|
"cite_by": "apalike",
|
||
|
|
"current_citInitial": 1,
|
||
|
|
"eqLabelWithNumbers": true,
|
||
|
|
"eqNumInitial": 1,
|
||
|
|
"hotkeys": {
|
||
|
|
"equation": "Ctrl-E",
|
||
|
|
"itemize": "Ctrl-I"
|
||
|
|
},
|
||
|
|
"labels_anchors": false,
|
||
|
|
"latex_user_defs": false,
|
||
|
|
"report_style_numbering": false,
|
||
|
|
"user_envs_cfg": false
|
||
|
|
},
|
||
|
|
"toc": {
|
||
|
|
"base_numbering": 1,
|
||
|
|
"nav_menu": {},
|
||
|
|
"number_sections": false,
|
||
|
|
"sideBar": true,
|
||
|
|
"skip_h1_title": false,
|
||
|
|
"title_cell": "Table of Contents",
|
||
|
|
"title_sidebar": "Contents",
|
||
|
|
"toc_cell": false,
|
||
|
|
"toc_position": {},
|
||
|
|
"toc_section_display": true,
|
||
|
|
"toc_window_display": false
|
||
|
|
},
|
||
|
|
"vscode": {
|
||
|
|
"interpreter": {
|
||
|
|
"hash": "83181d593ff87630d4a0d7997796f399a1d96b6a7eabd5b16ad531f517f6300b"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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