{ "cells": [ { "cell_type": "markdown", "id": "c12e30ea", "metadata": {}, "source": [ "# Numerická integrace" ] }, { "cell_type": "markdown", "id": "d6464ffc", "metadata": {}, "source": [ "Naimportujeme si knihovny potřebné pro následující příklady:" ] }, { "cell_type": "code", "execution_count": 2, "id": "9479552b", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.integrate as integrate" ] }, { "cell_type": "markdown", "id": "e361df73", "metadata": {}, "source": [ "## Klasické kvadraturní vzorce\n", "- Máme ekvidistantní body $x_{i}$ a vypočteme $f_{i}(x_{i})$\n", "- V 1D aproximujeme integrál pomocí obdélníků/lichoběžníků\n", "- Přesnost je dána šířkou obdélníku\n", "\n", "### Newton–Cotesovy vzorce\n", "1. Obdélníkové pravidlo\n", "$$\n", "\\int_{x_{1}}^{x_{2}}f(x)\\,dx\\approx (x_{2}-x_{1})f\\left( \\dfrac{x_{1}+x_{2}}{2} \\right)\n", "$$\n", "\n", "2. Lichoběžníkové pravidlo\n", "$$\n", "\\int_{x_{1}}^{x_{2}}f(x)\\,dx\\approx (x_{2}-x_{1})\\dfrac{f(x_{1})+f(x_{2})}{2}\n", "$$\n", "\n", "3. Simpsonovo pravidlo\n", " - [Odvození](http://kfe.fjfi.cvut.cz/~vachal/edu/nme/cviceni/07_numint/DOCS/odvozeni_integrace_Lagrange.pdf)\n", "$$\n", "\\int_{x_{1}}^{x_{3}}f(x)\\,dx\\approx (x_{2}-x_{1})\\dfrac{f(x_{1})+4f(x_{2})+f(x_{3})}{3}\n", "$$\n" ] }, { "cell_type": "markdown", "id": "bd57fad7", "metadata": {}, "source": [ "
Cvičení 09.01: Pomocí obdélníkové, lichoběžníkové a Simpsonovy metody numericky vypočtěte integrál $\\int_{1}^{5} \\sin(x)\\,dx$.
" ] }, { "cell_type": "code", "execution_count": 22, "id": "8617f468", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Obdelnikova metoda: 0.256657230544745\n", "Lichobeznikova metoda: 0.2566059008096602\n", "Simpsonovo pravidlo: 0.25664012405560144\n" ] } ], "source": [ "# kod\n", "\n", "pocet_kroku = 100\n", "a = 1\n", "b = 5\n", "\n", "def f(x):\n", " return np.sin(x)\n", "\n", "r = (b-a)/pocet_kroku # velikost kroku\n", "\n", "# obdelnikova metoa\n", "S_obdelnik = 0\n", "for i in range(pocet_kroku):\n", " bod = a + i*r\n", " # DOPLNTE\n", " S_obdelnik = S_obdelnik + r*f((bod+bod+r)/2)\n", "print('Obdelnikova metoda: ',S_obdelnik)\n", "\n", "# lichobeznikova metoda\n", "S_lichobeznik = 0\n", "for i in range(pocet_kroku):\n", " bod = a + i*r \n", " # DOPLNTE\n", " S_lichobeznik = S_lichobeznik + r*(f(bod)+f(bod+r))/2\n", "print('Lichobeznikova metoda: ',S_lichobeznik)\n", "\n", "# Simpsonovo pravidlo\n", "S_simpson = 0\n", "pocet_kroku_simpson = int(np.round(pocet_kroku/2))\n", "for i in range(pocet_kroku_simpson):\n", " bod = a + 2*i*r\n", " # DOPLNTE\n", " S_simpson = S_simpson + r/3*(f(bod) + 4*f(bod+r) + f(bod + 2*r))\n", "print('Simpsonovo pravidlo: ',S_simpson)" ] }, { "cell_type": "markdown", "id": "61aed8b5", "metadata": {}, "source": [ "## Gaussovy kvadratury" ] }, { "cell_type": "markdown", "id": "2eb47caf", "metadata": {}, "source": [ "- Výpočet integrálu při neekvidistantním rozdělení bodů $x_{i}$ s různými váhami $w_{i}$\n", "- Chceme spočítat integrál s minimálním počtem vyčíslení $f(x)$\n", "- Volíme optimální polohu bodů $x_{i}$ a příslušné váhy $w_{i}$\n", "- $n$ bodů dává přesný výsledek pro polynomy řádu $\\leq 2n-1$\n", "- Dvojnásobná přesnost oproti integraci s ekvidistantním rozdělením\n", "- Pro polohu bodů a příslušné váhy používáme tyto polynomy:\n", " - Legenderovy na intervalu $(-1,1)$\n", " - Čebyševovy na intervalu $(-1,1)$\n", " - Laguerrovy na intervalu $(0,+\\infty)$\n", " - Hermiteovy na intervalu $(-\\infty,+\\infty)$\n", "- Funkci $f(x)$ interpolujeme daným typem polynomu, nalezneme $w_{i}$ a $x_{i}$ \n", "- Následně lze integrál numericky vypočítat předpisem:\n", "$$\n", "\\int_{-1}^{1}f(x)dx\\approx \\sum_{i=1}^{n}w_{i}f(x_{i})\n", "$$\n", "- Pokud integrujeme přes interval $\\langle a,b\\rangle$, získáme předpis:\n", "$$\n", "\\int_{a}^{b}f(x)dx\\approx \\sum_{i=1}^{n}\\tilde{w}_{i}f(\\tilde{x}_{i}),\n", "$$\n", "kde\n", "$$\n", "\\tilde{w}_{i} = w_{i}\\dfrac{b-a}{2}\n", "$$\n", "$$\n", "\\tilde{x}_{i} = \\dfrac{(b-a)x_{i}+a+b}{2}\n", "$$" ] }, { "cell_type": "markdown", "id": "779dbadf", "metadata": {}, "source": [ "
Cvičení 09.02: Metodou Gaussovy kvadratury numericky vypočtěte integrál $\\int_{0}^{\\pi} \\sin(x)\\exp[\\cos(x)]\\,dx$.
" ] }, { "cell_type": "code", "execution_count": 9, "id": "7ad34c64", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Nas vypocet: 2.348228171380327\n", "Kontrola: 2.350402387287603\n" ] } ], "source": [ "# kod\n", "\n", "# v kazdem radku je bod a prislusna vaha vypoctena z interpolace Legenderovym polynomem\n", "vahy = np.array([\n", "[ -0.987992518, 0.03075324221],\n", "[-0.9372733924, 0.07036604699],\n", "[-0.8482065834, 0.1071592202],\n", "[-0.7244177314, 0.139570678],\n", "[-0.5709721726, 0.1662692057],\n", "[-0.3941513471 ,0.1861609998],\n", "[-0.201194094 ,0.1984314853],\n", "[0.0, 0.201194094],\n", "[0.201194094, 0.1984314853],\n", "[0.3941513471, 0.1861609998],\n", "[0.5709721726, 0.1662692057],\n", "[0.7244177314, 0.139570678],\n", "[0.8482065834, 0.1071592202],\n", "[0.9372733924, 0.07036604699],\n", "[0.987992518, 0.03075324221 ]\n", "])\n", "\n", "def f(x):\n", " return np.sin(x)*np.exp(np.cos(x))\n", "\n", "# integracni meze\n", "a = 0\n", "b = np.pi\n", "\n", "integral = 0\n", "\n", "m = vahy.shape[0] # pocet bodu\n", "\n", "for i in range(m):\n", " # prvek vahy[i,0] vrati i-ty bod, prvek vahy[i,1] vrati i-tou vahu\n", " # body jsou preskalovane z (-1,1) na (a,b)\n", " # DOPLNTE\n", " #\n", " # DOPLNTE\n", " integral = integral+ vahy[i,1]*(b-a)/2*f(((b-a)*vahy[i,0]+ (a+b))/2)\n", "\n", "print('Nas vypocet: ',integral)\n", "\n", "kontrola = integrate.quad(f, a, b)[0]\n", "print('Kontrola: ', kontrola)\n" ] }, { "cell_type": "markdown", "id": "04b8afa0", "metadata": {}, "source": [ "## Rombergova metoda\n", "- Algoritmus na zpřesnění výpočtu integrálu\n", "- Pro zadanou přesnost integrace sníží počet bodů, ve kterých musíme počítat funkční hodnotu\n", "- [Teorie](http://kfe.fjfi.cvut.cz/~vachal/edu/nme/cviceni/07_numint/DOCS/teorie_Rombergova_metoda.pdf)" ] }, { "cell_type": "markdown", "id": "4dcaf7cc", "metadata": {}, "source": [ "
Cvičení 09.03: Zpřesněte numerický výpočet integrálu $\\int_{0}^{\\pi} \\sin(x)\\exp[\\cos(x)]\\,dx$ Rombergovou metodou.
" ] }, { "cell_type": "code", "execution_count": 11, "id": "af947a1a", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# kod\n", "def f(x):\n", " return np.sin(x)*np.exp(np.cos(x))\n", "\n", "# slozene lichobeznikove pravidlo\n", "def lichobeznik(funkce,odkud,kam,krok):\n", " xArr = np.arange(odkud, kam, krok)\n", " integral = 0 \n", " for x in xArr:\n", " # secteme vsechny funkcni hodnoty\n", " integral = integral + funkce(x)\n", " # a odecteme poloviny kraju\n", " #integral = integral-0.5*funkce(xArr(1)) - 0.5*funkce(xArr(size(xArr,2)));\n", " integral = integral - 0.5 * funkce(xArr[0]) - 0.5 * funkce(xArr[xArr.size-1])\n", " return integral * krok \n", "\n", "\n", "integ = np.zeros((4,1))\n", "h0 = 0.1\n", "for i in range(4):\n", " h = h0/(2**(i))\n", " integ[i,0] = lichobeznik(f,0,np.pi,h)\n", "\n", "# presna hodnota:\n", "v = (np.exp(1)-np.exp(-1))\n", "presna_hodnota = v*np.ones((4,1))\n", "#\n", "\n", "fig, ax = plt.subplots(1,3,figsize=(15,5))\n", "\n", "ax[0].scatter([0,1,2,3],integ,label='numericky vypocet - iterace')\n", "ax[0].plot(presna_hodnota,label='presna hodnota')\n", "ax[0].set_xlabel('iterace')\n", "ax[0].set_ylabel('vysledek')\n", "ax[0].legend()\n", "\n", "# zpresneni Romberg. metodou\n", "r1=4/3*integ[1,0]-1/3*integ[0,0]\n", "ax[1].scatter([0,1,2,3],integ,label='numericky vypocet - iterace')\n", "ax[1].plot(presna_hodnota,label='presna hodnota')\n", "ax[1].scatter(1,r1, marker=\"x\",label='zpresneni Romberg. metodou')\n", "ax[1].set_xlabel('iterace')\n", "ax[1].legend()\n", "\n", "# dalsi zpresneni Romberg. metodou\n", "r2 = 64/45 * integ[2,0] - 20/45 * integ[1,0] + 1/45*integ[0,0]\n", "ax[2].scatter([0,1,2,3],integ,label='numericky vypocet - iterace')\n", "ax[2].plot(presna_hodnota,label='presna hodnota')\n", "ax[2].scatter(1,r1, marker=\"x\",label='zpresneni vypoctu Romberg. metodou')\n", "ax[2].scatter(2,r2, marker=\"x\",color='C8',label='dalsi zpresneni Romberg. metodou')\n", "ax[2].set_xlabel('iterace')\n", "ax[2].legend()" ] }, { "cell_type": "markdown", "id": "55be0a35", "metadata": {}, "source": [ "## Vícedimenzionální integrály\n", "- $N$ dimenzí\n", "- Počet bodů, ve kterých vyčíslujeme funkční hodnotu roste s $N$-tou mocninou\n", " - Např. 30 bodů v jedné dimenzi, ve třech dimenzích počítáme funkci ve $30^{3}=27000$ bodech\n", "- Metody\n", " - 1. Snížení dimenze pomocí symetrie\n", " - 2. Posloupnost opakovaných jednodimenzionálních integrací\n", " - 3. Monte-Carlo\n" ] }, { "cell_type": "markdown", "id": "eb43031b", "metadata": {}, "source": [ "### Metoda Monte-Carlo\n", "- Integrační oblast $V$ uzavřeme do co nejmenší oblasti se známým objemem $\\tilde{V}$, ve které lze snadno generovat náhodné body\n", "- Vygenerujeme $N$ náhodných bodů ve $\\tilde{V}$ a vypočteme integrál\n", "$$\n", "\\int f(\\vec{x})dV\\approx\\dfrac{\\tilde{V}}{N}\\sum_{i=1}^{N}\\tilde{f}(\\vec{x}_{i}),\n", "$$\n", "kde $\\tilde{f}(\\vec{x}) = f(\\vec{x})$, pokud $\\vec{x}\\in V$. Jinak $\\tilde{f}(\\vec{x}) = 0$.\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "ec2eb77f", "metadata": {}, "source": [ "
Cvičení 09.04: Metodou Monte-Carlo určete velikost konstanty $\\pi$.
" ] }, { "cell_type": "code", "execution_count": 16, "id": "cf28c98c", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vypoctena hodnota pi = 2.8\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# kod\n", "\n", "kapek = 0 # pocet kapek\n", "vkruhu = 0 # pocet kapek v kruhu\n", "npi = 0 # odhad pi\n", "steps = 10 # pocet kroku\n", "plotPi = np.zeros((steps,1))\n", "\n", "fig, ax = plt.subplots(1,2,figsize=(15,4.5))\n", "\n", "for i in range(steps): \n", " kapek = kapek+1\n", " x = np.random.rand(1,2) # dve nahodna cisla x[0,0] a x[0,1]\n", " # jsou uvnitr kruhu se stredem (0.5,0.5) a polomerem 0.5?\n", " # DOPLNTE\n", " #\n", " # DOPLNTE\n", " if (x[0,0]-0.5)**2+(x[0,1]-0.5)**2<0.5**2:\n", " vkruhu = vkruhu + 1 # pricteme je\n", " ax[0].scatter(x[0,0], x[0,1], marker=\"x\", color='red')\n", " else:\n", " ax[0].scatter(x[0,0], x[0,1], marker=\"x\", color='blue')\n", " npi = 4 * vkruhu / kapek\n", " plotPi[i] = npi \n", "\n", "ax[0].set_aspect('equal')\n", "ax[0].set_xlim((0,1))\n", "ax[0].set_ylim((0,1))\n", "\n", "ax[1].plot(plotPi,linewidth=2,label=r'numericky vypocet hodnoty $\\pi$')\n", "ax[1].set_ylabel('vysledek')\n", "ax[1].set_xlabel('iterace')\n", "ax[1].legend()\n", "\n", "print('Vypoctena hodnota pi = ',npi)\n" ] }, { "cell_type": "markdown", "id": "95a6df08", "metadata": {}, "source": [ "
Cvičení 09.05: Numericky vypočítejte integrál $\\int_{0}^{1}\\int_{0}^{1}(x+y) dx dy$. Vykreslete výslednou hodnotu, absolutní chybu a odhad přesnosti metody v závislosti na počtu kroků.
" ] }, { "cell_type": "code", "execution_count": 19, "id": "10dcd617", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Numericka integrace = 0.9934831721499284\n", "Kontrola = 1\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# kod\n", "def f(x,y):\n", " return x+y\n", "\n", "kroku = 1000\n", "vysledky = np.zeros((kroku,1)) # vysledky\n", "uspech = 0 # pocet uspesnych pokusu\n", "suma = 0\n", "\n", "for i in range(kroku):\n", " # DOPLNTE\n", " # \n", " # DOPLNTE\n", " r = np.random.rand(1,2) # dve nahodna cisla v intervalu (0,1)\n", " value = f(r[0,0],r[0,1]) # vypocteme funkcni hodnotu v techto dvou nahodnych bodech\n", " suma = suma + value # pricteme ke kumulovane hodnote\n", " vysledky[i,0] = suma / (i+1) # prumer (kumul. hodnota delena poctem kroku)\n", "integral = suma / kroku\n", "\n", "\n", "spravny_vysledek = 1\n", "print('Numericka integrace = ',integral)\n", "print('Kontrola = ',spravny_vysledek)\n", "\n", "spravny_vysledek = spravny_vysledek*np.ones((kroku,1))\n", "\n", "# absolutni chyba\n", "abs_chyba = np.abs(vysledky-spravny_vysledek)\n", "# presnost vypoctu metodou Monte-Carlo je ~ 1/sqrt(N)\n", "odhad_presnosti = np.linspace(1,kroku+1,num=kroku)**(-1/2)\n", "\n", "\n", "fig, ax = plt.subplots(1,2,figsize=(15,5))\n", "ax[0].plot(vysledky[:,0],linewidth=2,label='numericka integrace')\n", "ax[0].plot(spravny_vysledek*np.ones((kroku,1)),linewidth=2,label='presna hodnota')\n", "ax[0].set_xlabel(r'pocet kroku $N$')\n", "ax[0].set_ylabel('vysledek')\n", "ax[0].legend()\n", "\n", "ax[1].plot(abs_chyba,linewidth=2,color='C4',label='absolutni chyba')\n", "ax[1].plot(odhad_presnosti,linewidth=2,color='cyan',label=r'analyticky odhad presnosti metody $1/\\sqrt{N}$')\n", "ax[1].set_xlabel(r'pocet kroku $N$')\n", "ax[1].set_ylabel('chyba')\n", "#ax[1].set_xscale('log')\n", "#ax[1].set_yscale('log')\n", "ax[1].legend()\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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" } }, "nbformat": 4, "nbformat_minor": 5 }