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@robert-marik
Created December 6, 2021 17:39
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Konecne_diference.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Konecne_diference.ipynb",
"provenance": [],
"authorship_tag": "ABX9TyOMAdpOo+/WRbkrojBwdjqb",
"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/gist/robert-marik/a545aa84f0ec91ab3fe62611835ee300/konecne_diference.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "oLsm6bCmwy7A"
},
"source": [
"# Derivace a konečné diference\n",
"\n",
"Derivace je užitečná veličina. Udává, jak rychle se mění data. Umíme ji počítat pro symbolicky zadané funkce, ale tato dovednost není použitelná v případě, že potřebujeme derivovat numerická data. Například výstupy z měření. V takovém případě používáme místo derivace (okamžité rychlosti růstu) konečné diference (průměrné rychlosti růstu). V pratických případech používáme nejčastěji dopřednou a centrální diferenci. \n",
"\n",
"Mějme funkci $f$ definovanou v bodech vzdálených od sebe o hodnotu $h$.\n",
"\n",
"* **Dopředná diference** $$\\frac{\\mathrm df}{\\mathrm dx}\\approx \\frac{f(x+h)-f(x)}{h}$$ je průměrná rychlost na následujícím intervalu. Je jednoduchá, dává přesné výsledky pro lineární funkce a není definována v posledním bodě definičního oboru. Varianta dopředné diference je **zpětná diference** $$\\frac{\\mathrm df}{\\mathrm dx}\\approx \\frac{f(x)-f(x-h)}{h}$$ pracující s předchozím intervalem.\n",
"* **Centrální diference** $$\\frac{\\mathrm df}{\\mathrm dx}\\approx \\frac{f(x+h)-f(x-h)}{2h}$$ je průměrná rychlost na předchozím a následujícícm intervalu. Je přesnější, protože dává přesné výsledky pro lineární a kvadratické funkce. Není definována v krajních bodech definičního oboru.\n",
"* Je-li to možné, používáme centrální diferenci. Ta je v programech jako Python, Octave nebo Matlab přístupná přes funkci `gradient`. Někdy oba přístupy kombinujeme. Například při modelování vedení tepla v tyči používáme centrální diferenci pro derivaci podle prostorových proměnných a dopřednou nebo zpětnou diferenci pro časovou derivaci."
]
},
{
"cell_type": "code",
"metadata": {
"id": "x-qTCbq8iXy5"
},
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"execution_count": 36,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "D0g7YjfCi3Bk"
},
"source": [
"x = np.linspace(0, 1, 10)"
],
"execution_count": 37,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "_Br63983znCn"
},
"source": [
"# Grafické porovnání konečných diferencí s derivací"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 281
},
"id": "jz5q6PbIjM9k",
"outputId": "ba551a0f-d018-4008-d57a-297b99fabd9b"
},
"source": [
"def porovnani(x, fx, dfx):\n",
" plt.plot(x, np.gradient(fx,x)) # centralni diference\n",
" plt.plot(x[:-1], np.diff(fx)/(x[1]-x[0])) # dopredna diference\n",
" plt.plot(x, dfx)\n",
" plt.legend([\"centralni diference\", \"dopredna diference\", \"symbolicka (presna) derivace\"])\n",
"\n",
"porovnani(x, 4*x**2+2*x, 8*x+2)\n",
"plt.title(\"Diference pro polynom druheho stupne\")\n",
"plt.show()"
],
"execution_count": 41,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 281
},
"id": "hjn2kEO8kOMU",
"outputId": "d177bb4b-03b9-441c-f7ec-a07895d62354"
},
"source": [
"porovnani(x, 4*x**3+2*x, 12*x**2+2)\n",
"plt.title(\"Diference pro polynom tretiho stupne\")\n",
"plt.show()"
],
"execution_count": 42,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 281
},
"id": "IgCY36ZwusQg",
"outputId": "db7f76d1-8f9b-4ed9-8fc3-02b73b39ba8f"
},
"source": [
"porovnani(x, 4*x**4-2*x**2, 16*x**3-4*x)\n",
"plt.title(\"Diference pro polynom tretiho stupne\")\n",
"plt.show()"
],
"execution_count": 45,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "WSsrhnBlztzG"
},
"source": [
""
]
},
{
"cell_type": "code",
"metadata": {
"id": "GSS7U9IxmKdM"
},
"source": [
"from sympy import symbols, expand, diff\n",
"x, a, b, c, h = symbols('x a b c h')\n",
"f = a*x**2 + b*x + c"
],
"execution_count": 31,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "AqfvS3tBzzfe"
},
"source": [
"Dopředná diference kvadratické funkce $$y=ax^2+bx+c$$ závisí na $h$. "
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 39
},
"id": "25tImogcoJpN",
"outputId": "698d267e-4fd6-4223-9409-37a06ff5c6b7"
},
"source": [
"expand((f.subs(x, x+h)-f)/(h)) # dopredna diference"
],
"execution_count": 32,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/latex": "$\\displaystyle a h + 2 a x + b$",
"text/plain": [
"a*h + 2*a*x + b"
]
},
"metadata": {},
"execution_count": 32
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "wJL_efKTz9T2"
},
"source": [
"Centrální diference kvadratické funkce $$y=ax^2+bx+c$$ na $h$ nezávisí je je rovna derivaci $$y'=2ax+b$$ vypočtené analytickou metodou. "
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 39
},
"id": "WIkRb1RMokX8",
"outputId": "5963ed55-70b7-400f-81d6-e10dd7e88d7d"
},
"source": [
"expand((f.subs(x, x+h)-f.subs(x, x-h))/(2*h)) # centralni diference"
],
"execution_count": 33,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/latex": "$\\displaystyle 2 a x + b$",
"text/plain": [
"2*a*x + b"
]
},
"metadata": {},
"execution_count": 33
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 39
},
"id": "iO7UCJF2pQqd",
"outputId": "23cec2c8-1162-4636-e337-8b2be982ab87"
},
"source": [
"diff(f, x) # presna derivace"
],
"execution_count": 34,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/latex": "$\\displaystyle 2 a x + b$",
"text/plain": [
"2*a*x + b"
]
},
"metadata": {},
"execution_count": 34
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "4kqvl9JQplw8"
},
"source": [
""
],
"execution_count": 8,
"outputs": []
}
]
}
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