{ "cells": [ { "cell_type": "markdown", "id": "c12e30ea", "metadata": {}, "source": [ "# Aproximace funkcí" ] }, { "cell_type": "markdown", "id": "d6464ffc", "metadata": {}, "source": [ "Naimportujeme si knihovny potřebné pro následující příklady:" ] }, { "cell_type": "code", "execution_count": 1, "id": "9479552b", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "9eb351a6", "metadata": {}, "source": [ "## Typy aproximací:\n", "* Interpolační \n", "* Čebyševovy\n", "* Aproximace metodou nejmenších čtverců" ] }, { "cell_type": "markdown", "id": "6b299f80", "metadata": {}, "source": [ "## Interpolační aproximace" ] }, { "cell_type": "markdown", "id": "8ab9b329", "metadata": {}, "source": [ "* Máme zadané diskrétní funkční hodnoty nějaké funkce $f(x)$ v bodech $x_{0},\\dots ,x_{n}$.\n", "* Hledáme interpolační funkci, která má v zadaných bodech $x_{0},\\dots ,x_{n}$ stejné hodnoty jako funkce $f(x)$.\n", " * Globální interpolace\n", " * V celém intervalu jsou koeficienty interpolační funkce stejné\n", " * Např. Lagrangeův, Newtonův interpolační polynom\n", " * Lokální interpolace\n", " * V každém podintervalu má interpolační funkce různé koeficienty\n", " * Např. spline" ] }, { "cell_type": "markdown", "id": "b5063be0", "metadata": {}, "source": [ "### Lagrangeův interpolační polynom (globální interpolace )\n", "* [Konstrukce Lagrangeova interpolačního polynomu](http://pascal.fjfi.cvut.cz/~vachal/edu/nme/cviceni/03_aprox/DOCS/priklad_Lagrangeova_interpolace.pdf) řádu $n$:\n", " * Známe $n+1$ bodů $x_{0},\\dots ,x_{n}$ a jim odpovídající funkční hodnoty $y_{0}=f(x_{0}),\\dots ,y_{n}=f(x_{n})$ \n", "$$\n", "L_{n}(x)=\\sum_{i=0}^{n}y_{i}F_{i}(x),\n", "$$\n", "přičemž $L_{n}(x_{0})=y_{0},\\dots,L_{n}(x_{n})=y_{n},$\n", "$$\n", "F_{i}(x) = \\dfrac{x-x_{0}}{x_{i}-x_{0}}\\dots\\dfrac{x-x_{i-1}}{x_{i}-x_{i-1}}\\dfrac{x-x_{i+1}}{x_{i}-x_{i+1}}\\dots\\dfrac{x-x_{n}}{x_{i}-x_{n}}=\\prod_{j = 0,j \\neq i}^{n}\\dfrac{x-x_{j}}{x_{i}-x_{j}}\n", "$$" ] }, { "cell_type": "markdown", "id": "779960b8", "metadata": {}, "source": [ "
Cvičení 05.01: Naprogramujte výpočet Lagrangeovy interpolace v libovolném bodě pro $x=\\{-4, -1, 0, 2\\}$ a $f(x)=\\{-28, -16, -36, -40\\}$.
" ] }, { "cell_type": "code", "execution_count": 2, "id": "2278ff2d", "metadata": {}, "outputs": [], "source": [ "#\n", "bod = -0.5\n", "x = np.array([-4, -1, 0, 2])\n", "y = np.array([-28, -16, -36, -40])\n", "# DOPLNTE KOD" ] }, { "cell_type": "markdown", "id": "4f9de571", "metadata": {}, "source": [ "### Spline (lokální interpolace)" ] }, { "cell_type": "markdown", "id": "90b6bf75", "metadata": {}, "source": [ "* Lokální interpolace\n", " * Celý interval je rozdělený na podintervaly\n", " * V každém podintervalu má interpolační funkce různé koeficienty\n", " \n", "* Interpolační spline:\n", " * Prochází všemi uzly.\n", " * V uzlech má spojitou alespoň první derivaci.\n", " \n", "* Kubický spline - [odvození](http://pascal.fjfi.cvut.cz/~vachal/edu/nme/cviceni/03_aprox/DOCS/teorie_kubicky_spline.pdf)" ] }, { "cell_type": "markdown", "id": "3a663203", "metadata": {}, "source": [ "
Cvičení 05.02: Můžete vyzkoušet skript pro kubický spline a vstupní data pro Matlab (dostupný též online pro studenty ČVUT).
" ] }, { "cell_type": "markdown", "id": "372d97e2", "metadata": {}, "source": [ "## Aproximace Čebyševovými polynomy" ] }, { "cell_type": "markdown", "id": "3966f8ab", "metadata": {}, "source": [ "* Čebyševův polynom $T_{n}(x)$:\n", " * $T_{0}(x)=1$\n", " * $T_{1}(x)=x$\n", " * $T_{n+1}(x)=2xT_{n}(x)-T_{n-1}(x)$\n", "* Pro interpolaci [Čebyševovými polynomy](https://en.wikipedia.org/wiki/Chebyshev_polynomials#/media/File:Chebyshev_Polynomials_of_the_First_Kind.svg) se libovolný interval lineárně transformuje na interval $\\langle-1,1\\rangle$.\n", "* Každému $t \\in \\langle a,b\\rangle$ přiřadíme hodnotu $x \\in \\langle-1,1\\rangle$ předpisem $x = \\left[2t-(a+b)\\right]/(b-a)$.\n", "* Funkci $f(x)$ aproximujeme:\n", "$$\n", "f(x)\\approx T(x)=\\dfrac{1}{2}c_{0}+\\sum_{j=1}^{N-1}c_{j}T_{j}(x)\n", "$$\n", "$$\n", "c_{j}=\\dfrac{2}{N}\\sum_{k=1}^{N}f\\left[ \\cos\\left( \\dfrac{\\pi(k-0.5)}{N}\\right) \\right]\\cos\\left( \\dfrac{\\pi j(k-0.5)}{N}\\right)\n", "$$\n", "* Hodnoty funkce $f(x)$ jsou rovny hodnotám funkce $T(x)$ ve všech $N$ kořenech (nulových bodech) polynomu $T_{n}(x)$.\n" ] }, { "cell_type": "markdown", "id": "b7c942c3", "metadata": {}, "source": [ "
Cvičení 05.03: Aproximujte funkci $f(x)=x^{4}\\log(10+\\lvert x \\rvert)\\cos(x)$ pomocí prvních 20 Čebyševových polynomů.
" ] }, { "cell_type": "code", "execution_count": 7, "id": "634b0d99", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#\n", "N = 20 # stupen aproximace (pocet Cebysevovych polynomu)\n", "a = -10 # levy kraj intervalu\n", "b = 10 # pravy kraj intervalu\n", "def zadanafce(t):\n", " return t**4 * np.log(10+np.abs(t)) * np.cos(t)\n", "# t interval \n", "bodu = 1000 # pocet bodu, ze kterych chceme funkci aproximovat\n", "\n", "\n", "# transformace intervalu z do <-1,1>\n", "def trans(t):\n", " return ( 2*t - (a+b) ) / (b-a)\n", "\n", "\n", "def func(xx): # hodnota funkce pro xx transformovane z na <-1,1>\n", " t = ( xx*(b-a) + (a+b) ) / 2 # \"roztahneme\" hodnoty z intervalu <-1,1> na \n", " return zadanafce(t)# aproximovana funkce\n", "\n", "def c(j): # koeficienty cj (viz. prednaska)\n", " suma = 0\n", " for k in range(N):\n", " suma = suma + func(np.cos(np.pi/N*(k-0.5)) ) * np.cos(np.pi/N*(k-0.5)*j )\n", " return 2*suma/N\n", "\n", "# rekurentni definice n Cebysevovych polynomu v bode xx\n", " \n", "def T(xx): # Cebysevovy polynomy\n", " T0 = 1 \n", " T = np.zeros(N-1) \n", " T[1] = xx\n", " T[2] = 2*xx*T[1] - T0\n", " for ii in range(3,N-2):\n", " T[ii] = 2*xx*T[ii-1] - T[ii-2]\n", " return T\n", "\n", "cj = np.zeros((N-1))\n", "c0 = c(0) \n", "for i in range(N-1):\n", " cj[i] = c(i)\n", "\n", "krok = (b-a) / bodu\n", "x = a\n", "\n", "xarr = np.zeros(bodu)\n", "yarr = np.zeros(bodu)\n", "\n", "for i in range(bodu):\n", " ## DOPLNIT\n", " y = 1\n", " ## DOPLNIT\n", " xarr[i] = x # ulozime aktualni x\n", " yarr[i] = y # a aktualni y\n", " x = x+krok # posuneme se na dalsi x\n", "\n", "x1 = np.arange(a,b,krok)\n", "y1= zadanafce(x1)\n", "\n", "fig, ax = plt.subplots(1,2,figsize=(10,5))\n", "ax[0].plot(x1,y1,label='Puvodni funkce')\n", "ax[0].plot(xarr,yarr,label='Aproximace')\n", "ax[0].set_xlim(-10,10)\n", "ax[0].legend()\n", "\n", "ax[1].plot(x1,yarr-y1,label='Chyba aproximace')\n", "ax[1].set_xlim(-10,10)\n", "ax[1].set_ylim(-1000,1000)\n", "ax[1].legend()" ] }, { "cell_type": "markdown", "id": "b439fa1a", "metadata": {}, "source": [ "## Aproximace derivací konečnými diferencemi" ] }, { "cell_type": "markdown", "id": "b627a496", "metadata": {}, "source": [ "* Na 2. cvičení jsme ukazovali jednoduchý vzorec pro aproximaci derivace z funkčních hodnot ve dvou blízkých bodech \n", "* Ukážeme si [příklad metody vyššího řádu](http://pascal.fjfi.cvut.cz/~vachal/edu/nme/cviceni/03_aprox/DOCS/priklad_aproximace_derivaci.pdf) pro přesnější aproximaci derivace." ] }, { "cell_type": "markdown", "id": "a767d474", "metadata": {}, "source": [ "
Cvičení 05.04: Implementujte uvedenou metodu vyššího řádu v následujícím příkladu pro výpočet derivace (zadání stejné jako Cvičení 02.04).
" ] }, { "cell_type": "code", "execution_count": 5, "id": "3b7cf85d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# kod\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def f(x):\n", " return np.sin(x)\n", "\n", "def df(x):\n", " return np.cos(x)\n", "\n", "def num1_df(x, h):\n", " return (f(x+h) - f(x))/h\n", "\n", "def num2_df(x, h):\n", " return (f(x+h) - f(x-h))/(2*h)\n", "\n", "def num4_df(x, h): # odhad derivace metodou ctvrteho radu\n", " ## DOPLNIT\n", " return 1.0\n", "\n", "x = np.pi/6\n", "h = x # Pocatecni hodnota h\n", "\n", "der_a = df(x) # Hodnota derivace analyticky\n", "der_1 = num1_df(x,h) # Derivace metodou prvniho radu\n", "der_2 = num2_df(x,h) # Derivace metodou druheho radu\n", "der_4 = num4_df(x,h) # Derivace metodou ctvrteho radu\n", "krok = h # Seznam pouzitych velikosti kroku\n", "\n", "# Hledame hodnoty derivace v bode x v zavislosti na kroku h\n", "while h > np.finfo(float).eps:\n", " der_a = np.append(der_a, df(x))\n", " der_1 = np.append(der_1, num1_df(x,h))\n", " der_2 = np.append(der_2 ,num2_df(x,h))\n", " der_4 = np.append(der_4 ,num4_df(x,h))\n", " krok = np.append(krok, h)\n", " h = 0.9 * h\n", "\n", "fig, ax = plt.subplots(1,2,figsize=(10,5))\n", "ax[0].plot(krok,der_a,linewidth=2,label='Ananlyticka hodnota')\n", "ax[0].plot(krok,der_1,linewidth=2,label='Metoda prvniho radu')\n", "ax[0].plot(krok,der_2,linewidth=2,label='Metoda druheho radu')\n", "ax[0].plot(krok,der_4,linewidth=2,label='Metoda ctvrteho radu')\n", "ax[0].set_xlabel('h')\n", "ax[0].set_ylabel(r'$df(x)/dx$ pro $x=\\pi/6$')\n", "ax[0].set_xlim((0,0.5))\n", "#ax[0].set_xscale('log')\n", "ax[0].legend()\n", "\n", "ax[1].plot(krok, np.abs((der_1-der_a)/der_a),c='C1',linewidth=2,label='Chyba metody 1. radu')\n", "ax[1].plot(krok, np.abs((der_2-der_a)/der_a),color='C2',linewidth=2,label='Chyba metody 2. radu')\n", "ax[1].plot(krok, np.abs((der_4-der_a)/der_a),color='C3',linewidth=2,label='Chyba metody 4. radu')\n", "ax[1].set_xlabel('h')\n", "ax[1].set_ylabel('Relativni chyba')\n", "ax[1].set_xlim((0,0.5))\n", "ax[1].legend()\n", "\n", "fig.tight_layout()" ] } ], "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 }