{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "# Matematikai Algoritmusok és Felfedezések I.\n", "\n", "## 13. Előadás: Scipy\n", "\n", "### 2021 május 10.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tudományos csomagok (Python Scientific stack)\n", "| csomag | |\n", "| --- | --- |\n", "| NumPy | Hatékony N-dimenziós tömb |\n", "| **SciPy** | **Numerikus számítások** |\n", "| Matplotlib | Grafikonok és rajzok |\n", "| IPython (Jupyter) | Interaktív notebook |\n", "| SymPy | Szimbolikus számítások |\n", "| Pandas | Adatbányászat |" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import sympy as sym\n", "import math\n", "import numpy as np\n", "import matplotlib.pyplot as plt \n", "import scipy\n", " \n", "\n", "# grafikonok stílusának beállítása\n", "plt.rcParams['figure.figsize'] = (20, 10)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "# Numerikus módszerek \n", "A numerikus számítások célja, hogy a matematikai számításokat végezzünk hatékonyan.\n", "\n", "Előnyök:\n", " - Gyors\n", " - Hasznos\n", " - Sok helyzetben alakalmazható\n", " \n", "Hátrányok:\n", " - Csak közelítő eredményt ad \n", " - Emiatt figyelni kell a hiábkra \n", " - A matematikai intuíciónkat hátráltatja elméleti kérdésekben (pl felismernéd, hogy ez melyik algebrai szám közelítése? 2.732050807568877)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SciPy\n", "\n", "\n", "Részletes tutorial: https://docs.scipy.org/doc/scipy/reference/tutorial/\n", "\n", "A háttérben sokszor Fortran fut. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Alcsomagok:\n", "\n", "|||\n", "| --- | --- |\n", "| scipy.cluster\t| Vector quantization / Kmeans |\n", "| scipy.constants |\tPhysical and mathematical constants |\n", "|scipy.fftpack |\tFourier transform\n", "|scipy.integrate |\tIntegration routines\n", "|scipy.interpolate |\tInterpolation\n", "|scipy.io |\tData input and output\n", "|scipy.linalg |\tLinear algebra routines\n", "|scipy.ndimage |\tn-dimensional image package\n", "|scipy.odr |\tOrthogonal distance regression\n", "|scipy.optimize |\tOptimization\n", "|scipy.signal |\tSignal processing\n", "|scipy.sparse |\tSparse matrices\n", "|scipy.spatial |\tSpatial data structures and algorithms\n", "|scipy.special |\tAny special mathematical functions\n", "|scipy.stats |\tStatistics|\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Lineáris algebra\n", "\n", "A numpy lineáris algebra csomagját bővíti ki. Pár függvény hatékonyabb a háttérben. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### LU felbontás\n", "Adott $A$ mátrixot írjunk fel $A=LU$ alakban, ahol $L$ alsó, $U$ pedig felső háromszög mátrix." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from scipy import linalg, optimize" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 5 8 7]\n", " [5 2 2 8]\n", " [7 5 6 6]\n", " [5 4 4 8]]\n", "[[0. 1. 0. 0.]\n", " [0. 0. 0. 1.]\n", " [1. 0. 0. 0.]\n", " [0. 0. 1. 0.]]\n", "[[ 1. 0. 0. 0. ]\n", " [ 0.28571429 1. 0. 0. ]\n", " [ 0.71428571 0.12 1. 0. ]\n", " [ 0.71428571 -0.44 -0.46153846 1. ]]\n", "[[ 7. 5. 6. 6. ]\n", " [ 0. 3.57142857 6.28571429 5.28571429]\n", " [ 0. 0. -1.04 3.08 ]\n", " [ 0. 0. 0. 7.46153846]]\n", "[[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00]\n", " [ 8.8817842e-16 0.0000000e+00 -4.4408921e-16 0.0000000e+00]\n", " [ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00]\n", " [ 8.8817842e-16 0.0000000e+00 0.0000000e+00 0.0000000e+00]]\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.linalg import lu\n", "A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])\n", "p, l, u = lu(A)\n", "print(A,p,l,u, sep=\"\\n\")\n", "print(A - p @ l @ u)\n", "np.allclose(A - p @ l @ u, np.zeros((4, 4)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### QR felbontás\n", "Adott $A$ mátrixot írjunk fel $A=QR$ alakban, ahol $Q$ ortogonális, $R$ pedig felső háromszög mátrix." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-1.44840301 0.67738334 1.43656256 -1.78688189]\n", " [ 0.41986004 1.58434968 0.97647205 -1.36177752]\n", " [-1.36852932 -1.15752736 0.69033396 -0.78003637]\n", " [ 0.22152299 -0.29598561 -1.43680908 0.16168519]]\n", "[[-0.70707678 -0.54274783 0.3340504 -0.30639444]\n", " [ 0.20496594 -0.72731261 -0.16693366 0.63335494]\n", " [-0.66808429 0.38019553 -0.26065223 0.58410201]\n", " [ 0.10814239 0.17858476 0.89028304 0.40473301]]\n", "[[ 2.0484381 0.58709294 -1.43219775 1.52295975]\n", " [ 0. -2.01291109 -1.48402198 1.69257241]\n", " [ 0. 0. -1.14222561 -0.0223183 ]\n", " [ 0. 0. 0. -0.70517932]]\n" ] } ], "source": [ "A = np.random.randn(4, 4)\n", "print(A)\n", "q, r = linalg.qr(A)\n", "print(q,r,sep='\\n') " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1.00000000e+00, -1.19749865e-17, -1.03130015e-16,\n", " 1.50165469e-16],\n", " [-1.19749865e-17, 1.00000000e+00, 5.06667007e-17,\n", " -2.36702558e-16],\n", " [-1.03130015e-16, 5.06667007e-17, 1.00000000e+00,\n", " -1.74345312e-16],\n", " [ 1.50165469e-16, -2.36702558e-16, -1.74345312e-16,\n", " 1.00000000e+00]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q @ q.T" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-1.44840301, 0.67738334, 1.43656256, -1.78688189],\n", " [ 0.41986004, 1.58434968, 0.97647205, -1.36177752],\n", " [-1.36852932, -1.15752736, 0.69033396, -0.78003637],\n", " [ 0.22152299, -0.29598561, -1.43680908, 0.16168519]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q @ r" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Lineáris egyenlet megoldás\n", "\n", "Oldjuk meg az $Ax=y$ egyeneletet. \n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "A=np.array([[1,2],[3,4]])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "array([[-3.],\n", " [ 4.]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = np.array([[5.], [7.]])\n", "x=np.linalg.solve(A, y)\n", "x" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "array([[5.],\n", " [7.]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A @ x" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Integrálás" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Számístuk ki $\\int_a^b f$ értékét.\n", "\n", "A `scipy.integrate.quad(f, a, b)` integrálja $a$-tól $b$-ig az $f$ függvényt. Két értékkel tér vissza, az inregrálás eredményével és egy hibahatárral." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.0, 1.1102230246251565e-14)\n" ] } ], "source": [ "import scipy.integrate\n", "f= lambda x:2*x\n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.0, 1.1102230246251565e-14)\n" ] } ], "source": [ "import scipy.integrate\n", "\n", "def f(x):\n", " return 2*x\n", "\n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.7468241328124271, 8.291413475940725e-15)\n" ] } ], "source": [ "f= lambda x:np.exp(-x**2)\n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(x \\right)}}{2}$" ], "text/plain": [ "sqrt(pi)*erf(x)/2" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## szimbolikus számítással\n", "xval = sym.Symbol('x')\n", "sym.integrate(sym.exp(-xval ** 2), xval)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0.746824132812427$" ], "text/plain": [ "0.746824132812427" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((sym.erf(1)-sym.erf(0))*np.pi**(1/2)/2).evalf() " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Próbáljunk ki egy ronda függvényt\n", "\n", "$$\\int_0^1 e^{\\sin(\\log(x^2+x)-x)}dx$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#sym.integrate(sym.exp(sym.sin(-sym.log(xval ** 2+xval)-xval)), xval)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.1008683826459191, 9.950209101106111e-09)\n" ] } ], "source": [ "f= lambda x:np.exp(np.sin(-np.log(x ** 2+x)-x)) \n", "i = scipy.integrate.quad(f, 0, 1)\n", "print(i)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Több változóban is tudunk integrálni a ` scipy.integrate.dblquad(func, a, b, gfun, hfun)` paranccsal. A gfun és hfun parancsok adják meg a belső integrál határait. \n", "\n", "\n", "$$\\int_{0}^{1/2} \\left( \\int_{0}^{\\sqrt{1-4y^2}} 16xy \\:dx\\right)dy$$\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.5, 1.7092350012594845e-14)\n" ] } ], "source": [ "f = lambda x, y : 16*x*y\n", "g = lambda x : 0\n", "h = lambda y : math.sqrt(1-4*y**2)\n", "i = scipy.integrate.dblquad(f, 0, 0.5, g, h)\n", "print(i)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Interpoláció\n", "\n", "A fő gondolat:\n", "- Adott két adat tömb, $x_g$ és $y_g$, gondolhatunk rájuk úgy, hogy $y_g$ a mérési eredmény $x_g$ pontokban.\n", "- Egy köztes $(x,y)$ adatpontot szeretnénk megbecsülni. \n", "- Ha adott $x_g,y_g$ és $x$, akkor mi legyen $y$?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Módszerek\n", "- Illeszünk egy görbét a pontokra és értékeljük ki a görbét $x$-nél \n", "- Vegyük a legközelebbi adat pontot\n", "- Lineárisan interpoláljunk\n", "- Magasabb rendű polinommal interpoláljunk" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Mi a különbség görbe illesztés és interpoláció között?\n", "\n", "- Általában az interpoláció lokális, csak néhány környező adatpontot használ\n", "- A görbe illesztés az összes pontra nézve próbál optimális görbét találni\n", "- Ezért a görbe illesztés nem fog átmenni az adatpontokon általában\n", "- Ezért a görbe illesztés akkor hasznos, ha az adat \"zajos\" és mi a zajtól szeretnénk megszabadulni vagy modelt szeretnénk felállítani\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0.36363636 0.72727273 1.09090909 1.45454545 1.81818182\n", " 2.18181818 2.54545455 2.90909091 3.27272727 3.63636364 4. ] \n", "\n", " [-0.65364362 -0.61966189 -0.51077021 -0.31047698 -0.00715476 0.37976236\n", " 0.76715099 0.99239518 0.85886263 0.27994201 -0.52586509 -0.99582185]\n" ] } ], "source": [ "from scipy import interpolate\n", " \n", "xg = np.linspace(0, 4, 12)\n", "yg = np.cos(xg**2/3+4)\n", "print (xg,'\\n\\n',yg)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure, axis = plt.subplots(1, 1,figsize=(8,8))\n", "axis.plot(xg, yg,'o')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "f1 = interpolate.interp1d(xg, yg,kind = 'linear')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xnew = np.linspace(0, 4,100)\n", "\n", "figure, axis = plt.subplots(1, 1,figsize=(8,8))\n", "axis.plot(xg, yg, 'o')\n", "axis.plot( xnew, f1(xnew), '-')\n", "axis.legend(['data', 'linear'], loc = 'best')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f2 = interpolate.interp1d(xg, yg, kind = 'cubic')\n", "xnew = np.linspace(0, 4,100)\n", "#plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')\n", "figure, axis = plt.subplots(1, 1,figsize=(8,8))\n", "axis.plot(xg, yg, 'o')\n", "#axis.plot( xnew, f1(xnew), '-')\n", "axis.plot( xnew, f2(xnew), '--')\n", " \n", "axis.legend(['data', 'cubic'], loc = 'best')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Legkisebb négyzetek módszere\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = np.poly1d([5, 1])\n", "\n", "x = np.linspace(0, 10, 30)\n", "y = f(x) + 6*np.random.normal(size=len(x))\n", "xn = np.linspace(0, 10, 200)\n", "\n", "figure, axis = plt.subplots(1, 1,figsize=(6,6))\n", "axis.plot(x, y, 'or')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4.82023058, 0.0604941 ])" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.vstack([x, np.ones(len(x))]).T\n", "np.dot(np.linalg.inv(np.dot(a.T, a)), np.dot(a.T, y))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4.82023058, 0.0604941 ])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.lstsq(a, y,rcond=None)[0]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4.82023058, 0.0604941 ])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.polyfit(x, y, 1)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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5xqQrOzHpyk5nXzVHXEkBLhLilm47yMTZKeQXWKaPjuXKi1s5XZL4iAJcJERZa0n4ZgfPfbqZDi0akPDrWNo3r+90WeJDCnCREHQyJ59H5q3l43X7+GX383nhlp7Ur6Nf91Cjf1GRELPz4EnGzkxie8YJHru2C2N/cmFoLgErCnCRULJk0wEemLuaGhGGGXf147JOLZwuSfxIAS4SAgoLLa/9axuvfLGNbhecx1/u6Eu7ppHlP1BcTQEu4nLHsvN4cO5qvtiUwc292/Cnm7tX/JJn4moKcBG38njY+twbjB1wJ7san8+TbXIYfWtP9XeHEQW4iBt5PPzjuek8dNVviczNZtbsx+l3aCc0z3XdkqhSdVp6TMRlCgotz879jnt/+Vs6Z6axeMYD9Nu9wXtF9cmTnS5PAkgtcBEXOXwyl4mzV7G06y+4fdUnPLHkLeoU5J8+IMgvwiu+pQAXcYn1e44ydmYymcdzeO67REZ8Oefcg4L8IrziW+pCEXGBD1J2M3zacgqt5b1xAxkx5npXXoRXfKvcADfG1DXGfGeMWWOM2WCMeapof3tjzApjzHZjzFxjjK7DJOJjeQWFPLlwAw++t4Ze7RqzaOIQerVr7B2oTEiA6GgwxnubkKABzDBTkRZ4DnCFtbYn0Au4xhgzAHgOeNla2xE4DIzxW5UiZfF4ICYGIiK8tx6P0xX5TMbxbOL+uoJ3lqdy1+D2JN7dn+YN6pw+IC4OUlOhsNB7q/AOO+X2gVtrLXCiaLNW0R8LXAHcXrR/BvAkMM33JYqUweOB+Hjv7AuAtDTvNrg+zFLSDzM+MZmjp/J4dWQvhvZq43RJEoQq1AdujKlhjFkNZACfA98DR6y1xcPfu4FS/4cZY+KNMUnGmKTMzEwflCxSZPLk0+FdLASm0s16/X1GvP4NtdPT+GDR0wzd8JXTJUmQqlCAW2sLrLW9gLZAP6BLRV/AWptgrY211sa2aKGFdcSHypoy59KpdNl5BTz23Ac8vieSgWlrWDTjAbquWe79VlHdrqEQ7moKZ5WahWKtPQJ8CQwEGhtjirtg2gJ7fFuaSDnKmjLnwql0e4+cYkTCf5hzuA73LZ/L3+c9RePsop7L6n6rKO5qSksDa093NSnEXa8is1BaGGMaF92vB/wc2IQ3yG8pOmw0sMBPNYqUbsqUkJhK958dP3DD60vZfuA4f/lwCg//eyY1bOHZB1XnW0WIdjVJxVrgrYEvjTFrgZXA59baxcCjwIPGmO1AM2C6/8oUKYXLp9JZa5m+dCdxf1tBo8haLJgwmGty9pZ+cHW+Vfirq0ndMs6z1gbsT9++fa1ISElMtDY62lpjvLeJiRV6WFZOvr1/doqNfnSxvXvGSnvsVO7p54uMtNbb2eH9ExlZ4ectVXT02c9X/Cc6uurP6Y86pUxAki0lUxXgIlVVxRBLO3jSXvPKNzbmscX2tS+22oKCwnOftwofCr6u80f540NBylRWgBvvzwIjNjbWJiUlBez1RPwqJsY7IFhSdLT3xJpSfL01k/tnr8Jay6u39eZnnVv6tcT/8ni8fd7p6d7umClTqtfVFBHhjeySjPGeWCQ+ZYxJttbGltyvxaxEqqoSfcvWWt786nte/OcWOrdqyFuj+hLdrL6fCzxDXJxvxwaiokr/8HLhDCA302JWIlVVwWmMJ3LyGZeYzAufbeH6Hhfwwb2DAhve/hAiM4DcTgEuwckNMxwqEGLfZ55g6BtL+WJTBr+77mJeG9mLyNoh8MXX5TOAQkUI/E+SkOOWNU6Kaymjb/mfG/bz4HtrqF0zgplj+jGoQ3MHi/UDX3fLSKVpEFOCTxUGB4NJQaHllS+28vq/ttOjbSOm3dGXNo3rOV2WuJgGMcU9XLzGydGsPCbNXcVXWzL5Vd+2/HHYJdStVcPpsiREKcAl+Lh0hsPm/ccYOzOZvUdO8cdhl3BH/yiMMU6XJSFMg5gSfFw4w2Hhmr3cNHU5p3ILmBM/gFEDohXe4ndqgUvwKWdwMJjkFxTy3Keb+eu/dxIb3YQ34/rQ8ry6TpclYUIBLsHJBTMcfjiRw4RZq/h2xw/8emA0v7uuK7Vr6kutBI4CXKQK1u4+wriZyRw8mcuLv+rJLX3bOl2ShCEFuEglvZe0i999tJ4WDeowf9wgurdt5HRJEqYU4CIVlJtfyB8WbyDxP+kM6tCM12/rTbMzrxIvEmAKcJEKOHAsm3s9KSSnHSb+JxfyyNWdqVlD/d3iLAW4SDmSUg8x3pPCiex8Xr+tNzf0vMDpkkQABbhImay1JP4njacWbaRNk3okjulP5/MbOl2WyH8pwEVKkZ1XwO8+Ws+85N38rHMLXhnZm0b1ajldlshZFOAiJew+nMX4xBTW7TnK/Vd24oErOxERobMqJfgowEXOsHz7QSbMXkVefiF//XUsP+/ayumSRMqkABfB29/913/v4NlPNnNhiwa8NaovHVo0cLoskR+lAJewl5WbzyPz1rJ47T6uveR8XvhVTxrU0a+GBD/9L5WwlnrwJGNnJrMt4ziPXNOZ8T/toFUExTUU4BK2vtycwaQ5q4iIMLxzZz9+clELp0sSqRQFuISdwkLLG19u5+UvtnLx+efx1qi+tGsaWf4DRYKMzgWWsHIsO4/4mcm89PlWhvVqw/zxg84Nb4/He13OiAjvrcfjRKki5VILXMLGtgPHGTszmbRDWTxxQ1f+Z1DMuf3dHg/Ex0NWlnc7Lc27DUG/PrmEH7XAJSx8sm4fw6Yu41h2HrPu7s+dg9uXPlg5efLp8C6WleXdLxJkFOAS0goKLc99upnxnhQ61chhkedh+ndsUXbXSHp66U9U1n4RB6kLRULW4ZO53D9nFf/edpDbmuTw5NN3UufEMe8Py+oaiYry/qykqCj/FyxSSWqBS0jasPcoN7yxlBU7DvHMzd15ZtqDp8O7WGldI1OmQGSJQc3ISO9+kSCjAJeQ89GqPQyftpz8AsvcsQO4rV9UxbtG4uIgIQGio8EY721CggYwJSipC0VCRl5BIX/6xyb+viyVfu2bMvX2PrRoWHTJs8p0jcTFKbDFFdQCl5CQeTyHuL+t4O/LUrlzcAyeu/ufDm9Q14iEJLXAxfVWpR9mfGIKR07l8vKIntzUu+25BxW3qCdP9nabREV5w1stbXExBbi42uzv0nliwQZanleH+eMH0e2CRmUfrK4RCTEKcHGlnPwCnly4gdnf7eKyTs15bWRvmtSv7XRZIgGlABfX2Xf0FOMTU1i96wjjL+/AQ7/oTA1d8kzCkAJcXGXFjh+4b1YKp3ILmBbXh2u7t3a6JBHHKMDFFay1vLM8lSkfbyKqaSSz7xlAp1YNnS5LxFHlBrgxph3wLtAKsECCtfZVY0xTYC4QA6QCt1prD/uvVAlXp3ILePzDdXy4ag9XXdyKl0b05Ly6tZwuS8RxFZkHng/81lrbFRgA3GeM6Qo8Biyx1nYClhRti/jUrkNZDJ+2nI9W7+HBn19Ewqi+Cm+RIuW2wK21+4B9RfePG2M2AW2AocDlRYfNAL4CHvVLlRKWvtmayf1zVlFQaHl79KX8rEtLp0sSCSqV6gM3xsQAvYEVQKuicAfYj7eLpbTHxAPxAFFa0U0qwFrLtK+/58XPttCpZUPeGtWXmOb1nS5LJOhUOMCNMQ2A+cAD1tpjZy6Gb621xhhb2uOstQlAAkBsbGypx4gUO5GTz8Pvr+GT9fu5rkdrnh/eg/p1NNYuUpoK/WYYY2rhDW+PtfaDot0HjDGtrbX7jDGtgQx/FSnhYUfmCcbOTOb7zBM8/ssu3HPZhaVfNUdEgAoMYhrvb9B0YJO19qUzfrQQGF10fzSwwPflSbj4fOMBhr6xjIMncpg5pj/xP+mg8BYpR0Va4IOBUcA6Y8zqon2PA88C7xljxgBpwK1+qVBCWmGh5ZUl23htyTa6t2nEtDv60LZJZPkPFJEKzUJZCpTVFLrSt+VIODl6Ko8H5qziyy2Z3NK3LU8Pu4S6tWo4XZaIa2h0SByxZf9x4mcmsefwKf44tBt3DIhWl4lIJSnAJeAWr93Lw++vpUHdmsyJH0BsTFOnSxJxJQW4BEx+QSHPf7aFhG920De6CW/G9aHVeXWdLkvEtRTgEhCHTuYycXYKy7b/wB0Dovi/67tRu6au6CdSHQpw8bt1u48yLjGZzBM5PH9LD26Nbed0SSIhQQEufjUveTePf7iO5vVrM2/cQHq0bex0SSIhQwEufpGbX8jTH2/k3W/TGHhhM964vTfNGtQp/4EiUmEKcPG5jGPZ3OtJISntMPdc1p5Hr+lCzRrq7xbxNQW4+FRy2iHGJ6ZwPDuf127rzY09L3C6JJGQpQAXn7DWkrginT8s2kDrRvWYcVc/Lm59ntNliYQ0BbhUW3ZeAb//aD3vJ+/m8s4teHVEbxpF6qo5Iv6mAJdq2XPkFOMTk1m7+ygTr+jIA1ddRI0InRIvEggKcKmy5d8fZMKsVeTmF/LWqL5c3e18p0sSCSsKcKk0ay3Tl+7kmU82E9MskrdGxdKxZQOnyxIJOwpwqZSs3Hwenb+ORWv2ck2383nx1p400CXPRByhybnBzOOBmBiIiPDeejyOlpP2w0lufnO5dzXBqzsz7Y4+Cm8RB+m3L1h5PBAfD1lZ3u20NO82QFxcwMv5cksGk2avwhjDO3f246cXtQh4DSJyNrXAg9XkyafDu1hWlnd/ABUWWl5fso273llJmyaRLJowROEtEiTUAg9W6emV2+8Hx7PzePC9Nd4LDve6gGdv7kG92rrkmUiwUAs8WEVFVW6/j/vLt2ccZ+jUZfxrcwa/v74rr4zopfAWCTIK8GA1ZQpElrg6e2Skd39Jxf3laWlg7en+8iqG+Kfr9zP0jWUczcojcUx/xgxpr+tVigQhBXiwiouDhASIjgZjvLcJCaUPYPqov7yg0PLCZ5sZl5hMx1YNWXz/EAZ2aFaNNyEi/mSstQF7sdjYWJuUlBSw1wsbERHelndJxkBhYYWe4khWLvfPWc03WzMZeWk7nryxG3VrqctEJBgYY5KttbEl92sQMxRERXm7TUrbXwEb9x5jbGIS+49m86ebunN7/4o9TkScpS6UUFCZ/vISFqzew83TlpGbX8jcsQMV3iIuohZ4KCjuF5882TvNMCrKG94/csJPXkEhz/xjM28v20m/mKa8Edeblg3rBqhgEfEFBXioiIur8BmaB0/kcJ8nhRU7D/E/g2KYfN3F1NIlz0RcRwEeZlbvOsL4xGQOnczl5RE9ual3W6dLEpEqUoCHkbkr0/n9RxtoeV4d5o8fxCVtGjldkohUgwI8DOTkF/DUoo3MWpHOZZ2a89rI3jSpX9vpskSkmhTgIW7/0WzGe5JZlX6E8Zd34KFfdNYlz0RChEauQth3Ow9x/etL2bL/ONPi+vDoNV2cDe8gW99cxO3UAg9B1lpmLE/l6Y830a5pJLPv6U+nVg2dLSrI1jcXCQVqgYeY7LwCfvveGp5ctJHLO7dgwYTBzoc3BM365iKhRC3wELLrUBbjEpPZuO8Yv7nqIiZe0ZGIYOnvDoL1zUVCjQI8RCzddpCJs1PIL7RMHx3LFV1aOV3S2aq5XouInEtdKC5nreUvX3/Pr99eQYuGdVg4YUjwhTdUa70WESmdWuAudjInn0fmreXjdfu4rkdrnh/eg/rBepX4KqzXIiI/Lvhb4Jp6VqqdB08ybOoyPlm/j8d/2YU3busdvOFdLC4OUlO9a5Snpiq8RaopuH/jNfWsVEs2HeCBOaupWcMwc0x/Bnds7nRJIuKA4G6Ba+rZWQoLLS9/vpUxM5KIbh7JoolDFN4iYazcADfGvG2MyTDGrD9jX1NjzOfGmG1Ft038Up2mnv3X0VN53PNuEq8u2cbwPm2ZN24QbZtElv9AEQlZFWmBvwNcU2LfY8ASa20nYEnRtu+VNcUszKaebT1wnGFTl/H11kz+MLQbL/6qh65XKSLlB7i19hvgUIndQ4EZRfdnAMN8W1YRTT3j47X7GDZ1GSdy8pkdP4BfD4zBmCA5OUdEHFXVPvBW1tp9Rff3A2VOPDbGxBtjkowxSZmZmZV7lbg4SEiA6GjvFdajo73bYTCAmV9QyDOfbOK+WSl0Ob8hiycO4dKYpk6XJSJBxFhryz/ImBhgsbX2kqLtI9baxmf8/LC1ttx+8NjYWJuUlFT1asPEoZO53D97FUu3HySufxRP3NCN2jWDe7xZRPzHGJNsrY0tub+q0wgPGGNaW2v3GWNaAxnVK0+Krd9zlLEzk8k8kcPzw3tw66XtnC5JRIJUVZt1C4HRRfdHAwt8U054m5+8m+HTlmOt5f2xAxXeIvKjym2BG2NmA5cDzY0xu4EngGeB94wxY4A04FZ/Fhnq8goKeXrxRmZ8m8aAC5vyxu19aN6gjtNliUiQKzfArbW3lfGjK31cS1jKOJ7NfZ4UVqYe5u4h7Xns2i7UrKH+bhEpX3CfSh/iktMOc68nmaOn8nh1ZC+G9mrjdEki4iKh1dRzycJX1lo8K9IYmfAtdWrW4MN7Byu8RaTSQqcF7pKFr7LzCnjipQXMPVyHn+5I5tXVc2jcZnJQ1Sgi7hA6LXAXLHy198gpRvxpMXMP12HC8jm8Pe8pGm/b5P2gCdS3BZd8SxGR8lXoRB5f8euJPBERUNp7Mca7/rTDvv3+BybMSiHnyFH+vOjPXL3tP2cfEB3tXSPbn0p+SwHv0gRhcnariFuVdSJP6LTAg3ThK2stf/v3Du6YvoLGkbX4aMaD54Y3BGaFRRd8SxGRigudAA/Cha9O5RbwwNzVPP3xJq66uCUf3TeYjg3K+CsPxAeNlucVCSmhE+BBtvBV+g9Z3PTmMhau2cvDV3dmWlxfGtat5ewHTWW/pai/XCS4WWsD9qdv3742HHy5+YDt8eRntseTn9kvNx8494DERGujo601xnubmBiYwhITrY2MtNY7WuD9ExlZ+utX5lgR8SsgyZaSqaEziBkErLW8+dX3vPjPLXRu1ZCEUbFENQuyq+Z4PBW7MnxMjHcqZkmBGGwVkbOUNYipAPeR49l5PPT+Gj7bcIAbe17As8O7E1nbxdPsg3xWj0g4Cf1ZKA7annGCYVOX8cWmDH5/fVdeHdnL3eENlesvV1+5iCMU4NX02Yb9DJu6jCNZeSSO6c+YIe1D45JnFR1sLZ5bnpbmbbEXnwGrEBfxOwV4FRUUWl74bDNjZybToUV9Fk0cwsAOzZwuy3cqOqtHc8tFHKM+8Co4kpXLpDmr+XprJiNi2/HU0G7he5V49ZWL+J2vL6kWtjbuPca4xGT2HT3FlJsu4fZ+UaHRZVJVUVGlz1Zx+AxYkXCgLpRKWLB6DzdPW0ZOfgFz4gcS1z86vMMbgvIMWJFwoQCvgPyCQv64eCOT5qyme5tGLJo4hL7RTc4+KFxnYgTZGbAi4URdKOU4eCKHCbNS+M+OQ4weGM3k67pSu2aJzz2XrEXuN3Fx4fE+RYKMBjF/xJpdRxiXmMyhk7n86abuDO/btvQDddaiiPiRBjEr6b2Vu/jdgvW0aFCH+eMHcUmbRmUfrFX+RMQBCvAScvILeGrRRmatSGdIx+a8dltvmtav/eMP0kwMEXGABjHPcOBYNiMT/sOsFemM/emFvHPnpeWHN2gmhog4Qi3wIitTDzE+MYWs3Hym3t6H63q0rviDiwfwKrLKn4iIj4R9gFtreffbNP64eCNtm9TDc3d/Op/fsPJPpJkYIhJgYR3g2XkFPP7hOj5I2cOVXVry0oheNKpXy+myREQqJGwDfPfhLMYlJrN+zzEmXdmJSVd2IiIizM+qFBFXCcsAX7rtIBNnp5BfYJk+OpYrL27ldEkiIpUWVgFurSXhmx089+lmOrRoQMKvY2nfvL7TZYmIVEnYBPjJnHwembeWj9ft45fdz+eFW3pSv07YvH0RCUFhkWA7D55k7Mwktmec4LFruzD2JxdqFUERcb2QD/Almw7wwNzV1IgwzLirH5d1auF0SSIiPhGyAV5YaHntX9t45YttdLvgPP5yR1/aNY0s/4EiIi4RkgF+LDuPB+eu5otNGdzcuw1/url7+F7yTERCVsgF+NYDxxk7M5ldh7J48oaujB4Uo/5uEQlJIRXg/1i3j4feX0Nk7ZrMumcA/do3dbokERG/CYkALyi0vPDZFv7y9ff0jmrMtLi+nN+ortNliYj4lesD/PDJXCbOXsXS7Qe5vX8UT9zQlTo11d8tIqHP1QG+fs9Rxs5MJvN4Ds8N786IS3UBBREJH64N8A9SdvO/H6yjaf3avDduIL3aNXa6JBGRgHJdgOcVFDLl4028szyV/u2bMjWuD80b1HG6LBGRgKvWJdWMMdcYY7YYY7YbYx7zVVFlyTieTdxfV/DO8lTuGtyexLv7K7xFJGxVuQVujKkBTAV+DuwGVhpjFlprN/qquDOlpB9mfGIyR0/l8erIXgzt1cYfLyMi4hrVaYH3A7Zba3dYa3OBOcBQ35R1tlkr0hnx1rfUrhnBB+MHK7xFRKheH3gbYNcZ27uB/iUPMsbEA/EAUVGVnyVirSU57TADOzTntZG9aBxZgavEi4iEAb8PYlprE4AEgNjYWFvZxxtj+NPNl1AzIoIauuSZiMh/VSfA9wDtzthuW7TP53RijojIuarTB74S6GSMaW+MqQ2MBBb6piwRESlPlVvg1tp8Y8wE4DOgBvC2tXaDzyoTEZEfVa0+cGvtP4B/+KgWERGphGqdyONaHg/ExEBEhPfW43G6IhGRSnPdqfTV5vFAfDxkZXm309K82wBxcc7VJSJSSeHXAp88+XR4F8vK8u4XEXGR8Avw9PTK7Vd3i4gEqfAL8LLOBi1tf3F3S1oaWHu6u0UhLiJBIPwCfMoUiIw8e19kpHd/SepuEZEgFn4BHhcHCQkQHQ3GeG8TEkofwKxsd4uISACF3ywU8IZ1RWacREV5u01K2y8i4rDwa4FXRmW6W0REAkwB/mMq090iIhJg4dmFUhkV7W4REQkwtcBFRFxKAS4i4lIKcBERl1KAi4i4lAJcRMSlFOAiIi6lABcRcSkFuIiISynARURcSgEuIuJSxlobuBczJhMoZXm/CmkOHPRhOW6g9xwe9J5DX3Xfb7S1tkXJnQEN8OowxiRZa2OdriOQ9J7Dg95z6PPX+1UXioiISynARURcyk0BnuB0AQ7Qew4Pes+hzy/v1zV94CIicjY3tcBFROQMrghwY8w1xpgtxpjtxpjHnK7Hn4wx7YwxXxpjNhpjNhhjJjldU6AYY2oYY1YZYxY7XUsgGGMaG2PmGWM2G2M2GWMGOl2TvxljflP0/3q9MWa2Maau0zX5mjHmbWNMhjFm/Rn7mhpjPjfGbCu6beKL1wr6ADfG1ACmAtcCXYHbjDFdna3Kr/KB31pruwIDgPtC/P2eaRKwyekiAuhV4FNrbRegJyH+3o0xbYD7gVhr7SVADWCks1X5xTvANSX2PQYssdZ2ApYUbVdb0Ac40A/Ybq3dYa3NBeYAQx2uyW+stfustSlF94/j/aVu42xV/meMaQtcB/zN6VoCwRjTCPgJMB3AWptrrT3iaFGBUROoZ4ypCUQCex2ux+estd8Ah0rsHgrMKLo/Axjmi9dyQ4C3AXadsb2bMAg0AGNMDNAbWOFwKYHwCvAIUOhwHYHSHsgE/l7UbfQ3Y0x9p4vyJ2vtHuBFIB3YBxy11v7T2aoCppW1dl/R/f1AK188qRsCPCwZYxoA84EHrLXHnK7Hn4wx1wMZ1tpkp2sJoJpAH2CatbY3cBIffa0OVkX9vkPxfnhdANQ3xtzhbFWBZ71T/3wy/c8NAb4HaHfGdtuifSHLGFMLb3h7rLUfOF1PAAwGbjTGpOLtIrvCGJPobEl+txvYba0t/nY1D2+gh7KrgJ3W2kxrbR7wATDI4ZoC5YAxpjVA0W2GL57UDQG+EuhkjGlvjKmNd9BjocM1+Y0xxuDtF91krX3J6XoCwVr7v9battbaGLz/vv+y1oZ0y8xaux/YZYzpXLTrSmCjgyUFQjowwBgTWfT//EpCfOD2DAuB0UX3RwMLfPGkNX3xJP5krc03xkwAPsM7av22tXaDw2X502BgFLDOGLO6aN/j1tp/OFeS+MlEwFPUMNkB3OlwPX5lrV1hjJkHpOCdbbWKEDwj0xgzG7gcaG6M2Q08ATwLvGeMGYN3RdZbffJaOhNTRMSd3NCFIiIipVCAi4i4lAJcRMSlFOAiIi6lABcRcSkFuIiISynARURcSgEuIuJS/w/N8PiehQCNvAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "m, c = np.polyfit(x, y, 1)\n", "yn = np.polyval([m, c], xn)\n", "\n", "figure, axis = plt.subplots(1, 1,figsize=(6,6))\n", "axis.plot(x, y, 'or')\n", "axis.plot(xn, yn)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Gyök keresés\n", "\n", "Keressük a $2x+3cos(x)$ függvény egy gyökét.\n", "\n", "A ` scipy.optimize.root(fn,x0)` függvényt használhatjuk. A hátterben különböző iteratív módszerek futnak, amik folyamatosan javítanak a megoldáson. A második paraméter a kezdeti tipp a gyökre. \n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fjac: array([[-1.]])\n", " fun: array([0.])\n", " message: 'The solution converged.'\n", " nfev: 9\n", " qtf: array([-3.65345532e-10])\n", " r: array([-4.37742425])\n", " status: 1\n", " success: True\n", " x: array([-0.91485648])\n" ] } ], "source": [ "from scipy.optimize import root\n", "\n", "def func(x):\n", " return 2*x + 3 * np.cos(x)\n", "\n", "sol = root(func,0)\n", "print(sol)\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-6.797106655298535e-09" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "func(-0.91485648) " ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{x\\; \\middle|\\; x \\in \\mathbb{C} \\wedge 2 x + 2 \\cos{\\left(x \\right)} = 0 \\right\\}$" ], "text/plain": [ "ConditionSet(x, Eq(2*x + 2*cos(x), 0), Complexes)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sym.solveset( xval*2 + 2 * sym.cos(xval), xval) # a szimolikus megoldó csak széttárja a kezét." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Optimalizáció\n", "\n", "Adott egy célfüggvény, amit bizonyos feltélek mellett szeretnék minimalizálni (maximalizálni). Például:\n", "\n", "$$\\min(x_0^3+x_1^2-x_2)$$\n", "Feltéve hogy:\n", "$$x_0^2+x_1^2=10 $$\n", "$$x_0x_2\\le4 $$\n", "$$0\\le x_0,x_1,x_2\\le100$$\n", "\n", "Legyen a kiindulási tipp (2,3,4)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import minimize" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "# cél és feltételek\n", "def objective(x):\n", " return x[0]**3+x[1]**2-x[2] \n", "\n", "def constraint1(x):\n", " return x[0]**2+x[1]**2-10.0\n", "\n", "def constraint2(x):\n", " return 4-x[0]*x[2]" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cél függvény értéke a kiindulási pontban: 13\n" ] } ], "source": [ "#Kezdeti tipp\n", "x0=np.array([2,3,4]) \n", "\n", "#Kezdeti érték\n", "print(\"Cél függvény értéke a kiindulási pontban:\",objective(x0))" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cél függvény értéke: -89.9999999999999\n", "Optimális értékek:\n", "x1 = 0.0\n", "x2 = 3.162277660168381\n", "x3 = 99.99999999999991\n" ] } ], "source": [ "# optimalizálás\n", "b = (0.0,100.0)\n", "bnds = (b, b, b)\n", "con1 = {'type': 'eq', 'fun': constraint1}\n", "con2 = {'type': 'ineq', 'fun': constraint2}\n", "cons = ([con1,con2])\n", "solution = minimize(objective,x0,method='SLSQP',bounds=bnds,constraints=cons)\n", "x = solution.x\n", "\n", "# show final objective\n", "print('Cél függvény értéke: ' + str(objective(x)))\n", "\n", "# print solution\n", "print('Optimális értékek:')\n", "print('x1 = ' + str(x[0]))\n", "print('x2 = ' + str(x[1]))\n", "print('x3 = ' + str(x[2]))" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "8.881784197001252e-15\n", "4.0\n" ] } ], "source": [ "#Ellenőrzés\n", "print(constraint1(x))\n", "print(constraint2(x))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Közönséges differenciálegyenletek\n", "\n", "Oldjuk meg az $f'(x)=-kf(x)$ egyenletet. \n", "\n", "Használhatjuk az `scipy.integrate.odeint` függvényt." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# függvény, ami visszatért a derivált értékével\n", "def model(f,x):\n", " k = 0.3\n", " deri = -k * f\n", " return deri\n", "\n", "# kezdeti érték\n", "f0 = 5\n", "\n", "# x értékek, ahol ki akarjuk számolni a függvényt\n", "x = np.linspace(0,20)\n", "\n", "# egyenelet megoldása\n", "f = odeint(model,f0,x)\n", "\n", "# plot results\n", "plt.plot(x,f)\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Geometriai algoritmusok\n", "\n", "- Alapvetően nem ajánlott, mivel a Scipy ezen a területen keveset tud" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Delaunay háromszögelés\n", "\n", "Adott egy ponthalmaz. Kössük össze azokat a pontpárokat, akikhez létezik olyan körlap, ami csak őket tartalmazza a ponthalmazból." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.spatial import Delaunay\n", "points = np.random.rand(30, 2) # 30 random points in 2-D\n", "tri = Delaunay(points)\n", "import matplotlib.pyplot as plt\n", "plt.triplot(points[:,0], points[:,1], tri.simplices.copy())\n", "plt.plot(points[:,0], points[:,1], 'o')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Konvex burok\n", "Adott egy ponthalmaz, számítsuk ki a konvex burkát." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.spatial import ConvexHull\n", "points = np.random.rand(30, 2) # 30 random points in 2-D\n", "hull = ConvexHull(points)\n", "plt.plot(points[:,0], points[:,1], 'o')\n", "for simplex in hull.simplices:\n", " plt.plot(points[simplex,0], points[simplex,1], 'k-')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "# Köszönöm a figyelmet!\n" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 5 }