{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import integrate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tento sešit ilustruje jednoduché numerické metody počítání integrálu\n", "$$I=\\int_a^bf$$\n", "\n", "V následující buňce funkci $f$ а meze intervalu $(a,b)$, přes který integrujeme. Dále nastavíme počet $n$ dílů, na který se interval rozdělí, čímž dostaneme krok $h=(b-a)/n$.\n", "\n", "Nakonec proměnná `xint` bude obsahovat pole, ve kterém bude schovaná posloupnost $(x_i)_{i=0}^{n}$, $x_i=a+ih$ (jinými slovy „navzorkujeme“ interval $(a,b)$ pomocí $n+1$ hodnot $x_0,\\dots,x_n$ včetně těch krajních). V proměnné `yint` budou pak obrazy těchto bodů $y_i=f(x_i)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return np.exp(x)\n", "\n", "a,b=1,7\n", "n=4\n", "h=(b-a)/n\n", "xint=np.linspace(a,b,n+1)\n", "yint=f(xint)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pro každou metodu vypočítáme danou aproximaci a její funkci ilustrujeme grafem.\n", "\n", "Začneme metodou levých obdélníků, kde aproximujeme $I\\thickapprox \\sum_{i=0}^{n-1}f(x_i)h$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "471.2862871297907" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x=np.linspace(a,b,200)\n", "plt.plot(x,f(x))\n", "plt.bar(xint[:-1],yint[:-1],width=h,alpha=0.2,align='edge',facecolor='gray')\n", "\n", "sum(yint[:-1])*h" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pokračujeme metodou pravých obdélníků s $I\\thickapprox \\sum_{i=1}^nf(x_i)h$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2112.15860202979" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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bdjkpQ6EvIhnpydfbONA6yCfeVU1pQW7Y5aQMhb6IZJzWvmG+/lIT71gwjRuXZ/733l4Ihb6IZBR35++fbWQk5vzpuxfo4u0ZFPoiklGeqevihcPd/P7V86iZURh2OSkn4dA3s1wz22lmPwzWK83saTM7GLxWjOn7gJnVmdl+M7sl0X2LiIzVMxTlS881sqKqmN++cnbY5aSkyTjT/wSwb8z6/cBmd18ObA7WMbOVwHpgFXAr8FUz09UVEZk0//Tz43QPRnngpoXk5WhYZzwJhb6Z1QDvBR4e03wH8Giw/Chw55j2x9094u5HgDpgTSL7FxE55cWj3fxwbwe/s3oOF1eVhF1Oykr0TP8fgM8A8TFtc9y9GSB4PfU3VjXQMKZfY9D2K8zsXjPbbmbbW1tbEyxRRDJdz1CUBzfXs3RmEffonvy3NOHQN7P3AS3uvuN8Nxmnzcfr6O4PuXutu9dWVWX3jHgicm7/+9lGOgej/Nl7FmX9hGrnkpfAttcCHzCz24EiYLqZ/Rtw0szmuXuzmc0DWoL+jcCCMdvXAE0J7F9EhC0HO3n6QCe/f/U8VszWsM65TPhXors/4O417r6Y0Qu0W9z9w8BG4K6g213AU8HyRmC9mRWa2RJgObBtwpWLSNZr7Rvm755p4NI5JXykdk7Y5aSFRM70z+ZB4AkzuweoBz4I4O57zOwJYC8QBe5z91gS9i8iWSAWd76w6RiRqPPnNy/S3TrnaVJC392fBZ4NltuBdWfptwHYMBn7FJHs9tiOk7za2MfnblqYtV9yPhG64iEiaWd3cz//8nIz65bP4L2XVoZdTlpR6ItIWumNRPn8T48ye1oBn7lRc+tcqGSM6YuIJEXcnb/cVE9L3zBf/Y2LmVaoCLtQOtMXkbTx2I4Wfn6kmz+6rpq3zSsNu5y0pNAXkbTwamMvX3+piXXLZ/DBy/XQ5kQp9EUk5bX0DvPnPznKghmF3L9uocbxE6ABMRFJaYMjMT77w8MMjcT5yq9fpK8+TJBCX0RSVtydv3q6ngOtg3zx/UtZMrM47JLSnoZ3RCRlfXPrCZ6p6+K+6+Zz7ZLysMvJCAp9EUlJmw908s1tJ3jvyko+pG/BmjQKfRFJOftODvCXTx/j8vml/OkNegBrMin0RSSlNHZF+NMfHKKyJJ8Nty/R/PiTTBdyRSRldAyM8Kmn6ojGnX/6L8uoLMkPu6SMo9AXkZTQH4nxJ08dor0/yj/++kUsrtTMmcmgv5tEJHTD0Tj3/8dhDrUNsuH2xVymKRaSRqEvIqGKxZ2/2HSMHY19fO6mRbxzsW7NTCaFvoiEJu7Og1vq2VLXxcevm89tmhs/6RT6IhKKuDt/s7me/9jbwe+tmcvvrNZ33E4Fhb6ITLm4Ow+OCfyPXT0v7JKyhkJfRKZU3J2/3dzAD/d2cPeaudyzdm7YJWUV3bIpIlMmFne+uKWBH+xt57++Yw4fWztXT9tOMYW+iEyJ4WicL2w6xjN1Xdy9Zq4CPyQKfRFJur5IlE//4BDbG/r443dVs14TqIVGoS8iSdXeF+HuR15hz/E+/uw9C7nt0plhl5TVFPoiE9TU1BR2CSmvuWeYTz1Vx4meYf7mvUu5bqkevAqbQl9EkmJ3cz+f/eFhRmLOP9x5EVdUl4VdkqDQF5Ek2LS/g7/+WT1VZfn83fuXafK0FKLQF5FJE3fn4ZebeeSVk1xZXcZf376E8mLFTCrRv4aITIqB4RgbflbPM3VdvH/lTD797hryc/X8Z6qZ8L+ImS0ws2fMbJ+Z7TGzTwTtlWb2tJkdDF4rxmzzgJnVmdl+M7tlMg5ARMJ3pH2Qj33nAM8dGp047f51CxT4KSqRf5Uo8D/c/VLgauA+M1sJ3A9sdvflwOZgneC99cAq4Fbgq2aWm0jxIhK+Tfs7uOc7B+geivLlOy/id1bP0UNXKWzCwzvu3gw0B8u9ZrYPqAbuAG4Iuj0KPAt8Nmh/3N0jwBEzqwPWAC9NtAYRCc9wNM6XXzjOk6+3cfn8Uv7i1iVUlenrDVPdpIzpm9li4EpgKzAn+IWAuzeb2alH76qBl8ds1hi0jfd59wL3AixcuHAyShSRSXS4fZAv/PQYB9sG+d3Vs/mDa+aTl6Oz+3SQcOibWRnw78An3b3nLf6sG+8NH6+juz8EPARQW1s7bh8RmXpxd777Witf+0UTJQW5fPF9euAq3SQU+maWz2jgP+bu3w+aT5rZvOAsfx7QErQ3AgvGbF4D6JFGkTTR2jfMXz1dzysNvVy7eDoP3LSQyhIN56SbRO7eMeAbwD53/9KYtzYCdwXLdwFPjWlfb2aFZrYEWA5sm+j+RWRquDs/3tfOhx97g9eb+/nMjQv44vuXKvDTVCJn+tcCHwFeN7NdQdvngAeBJ8zsHqAe+CCAu+8xsyeAvYze+XOfu8cS2L+IJFlTd4S/3dLAKw29vG1eKf/zPQtZMENP16azRO7e+Tnjj9MDrDvLNhuADRPdp4hMjWjceWJXCw+/fIIcg0/fUMOdb5tFjm7FTHt6IldE3uSXTX186blGDrQOct2Scj59Qw2zpxWEXZZMEoW+iACjF2r/+RdNbNrfyeyyfP7qtsW8+6IZetAqwyj0RbJcJBrn8Z0t/Ov2k8Tizt1r5vLhq2ZTnK8H5jORQl8kS0Xjzk/2dfDw1mZa+ka4YVk5H7+umvnlhWGXJkmk0BfJMu7O84e7+fqLzRztHGLlnBL+/OZFrK6ZFnZpMgUU+iJZwt158WgP39p2gr0nB1hUUcjfvHcJ1y8t17h9FlHoi2S4uDsvHO7mkW0n2N86yNxpBTywbiG3XVqp+XKykEJfJENFY87mg538nx0nOdw+RE15IZ+7aSG3rqgkL1dhn60U+iIZpmcoysY97Xx3Vyut/SMsriji8zcvYt3FFTqzF4W+SKY40j7Ik6+38R/7OhgciVO7oIzPrlvA1Yum60laOU2hL5LGItE4Ww52sXFPG6819ZOXY9y8ooLfvqKK5VUlYZcnKUihL5KGjnYM8dTuNn60r4PeSIwFMwr5+HXzue2SSio0+6W8BYW+SJpo7x/hZwc6+en+Tt5oGSAvx/i1ZeXcedksVteU6bZLOS8KfZEU1h+J8dzhLn76Ric7GnuJO1xcVczHr5vPrZdUak57uWAKfZEU0zMU5RdHunnuUDcvH+thOObMn17AR2rncMuKShZXaj57mTiFvkgKONk7zAuHu3nuUBe7jvcRc6gqzecDq2bynhUVXDa3VMM3MikU+iIhGInF+WVTP1vre9h6rJeDbYMALK4o4nevmsP1y8q5dHaJgl4mnUJfZAq4Ow1dEV5p6GXrsR5ebexjYCRObg5cPq+MP7xmPtcvK2dRhYZuJLkU+iJJEHfnSPsQu473sfN4H7ua+ugYiAIwf3oBt1xSydWLprO6pozSAs1bL1NHoS8yCSLROAdaB9jdPMCupj5ea+qjZygGwJyyfN6xYBpXVJexuqaMmvJCDdtIaBT6IhcoFncOtvTy3J529p7sZ++JAQ63DxLz0fdrygu5fmk5V1SXcWV1GXOnFSjkJWUo9OW0pqamsEtIOQPDMQ61D3GobZC64OdA6yBD0TgA0wpzuWR2CR+uncOls0tYObeUWaW6d15Sl0JfBBgaidPQNUR9Z4QjHUMcah8N+OPdw6f7lBbksGxmMe9fNZOVc0pYObeE6vJCTWYmaUWhL1kj7k5r3wj1naPhfqxziGOdEeq7hjjZO3K6nwELKgpZUVXC7ZfO5KJZxVw0q0jDNJIRFPqSMdyd7qEYTT0RTvQM09QzTHPPMM09EZp6hjnRM8zwqYF3oCQ/h4UVhVw+v4yFMwpZVFHEwopCFswooig/J8QjEUkehb6khbg7nQNRWvtHaO0bobVvmNb+EdpOr49wsneYgZH4m7abXpTL/OkFLK0s5rol5VSXF7JwRiELK4qYVZqnM3fJOgp9CU005nQNRekcGKFrMErnqZ+BKF2Doz/tQbC3DYwQe3Oek2NQWZJPVVk+NTMKqV0wjfnTC5gX/MyfXkhpoe6BFxlLoS8JcXciUac3EqM3EqU3EqMvEqNnKEbfcIzeoWjw3uhPdxDmnYOj7ePJNSgvzqOiOI/KknyuqixiVmk+VaX5zCobDfmq0gIqSvL09X8iF0ihn2XcneFYnKGROIPDMfqHo/RHovRHYjQ0dzMwEmNgJM7gcJyBkRiDI3EGhkfbBobjDAbv9w/H6B0aDfiRuL/lPkvyc5hWmEtZYS7lxXksryqmojiPGcV5VJTkj74G65UleZQV5uqOGJEkmfLQN7NbgS8DucDD7v5gsvaVSvedx90ZiTnRmDMSD5bjcUaC9WjMxyzH/7PP2Pfjo4EdicYZjjqRWJxI1IlET7W9ef3M9yPR0e3PkdFvUphnFOfnUpKfQ0lBDiX5uUwvzGXetAKmFY0G+bTCXKYX5p1enlYUvBbmUVaQS16uAlwkVUxp6JtZLvDPwHuARuAVM9vo7nsne1/feaWeI01txHz0CcqYO7G4Ez+9TrD+n+3R+Jv7jL7HONsG7WP6xN2Jjunzn0EdJxpzYhcQtOerINcozMuhMM8oyM0JlkfXSwtzqczLH9NntP30cm4OxQU5o2Gen0tx/qn1UwGfS1F+joZPRDLMVJ/prwHq3P0wgJk9DtwBTHroP/zCEQ629J1ezzXIMSM3x8gxyM0xcs3IzXlze17Om/vkBH1ygz75uUZRTs6vbHtqOS/YNj93NDDzc+30a36OkZdr5OfmnF4uOP1+zpj3x/QN3ju1nJczGtwFeaYhEBG5YFMd+tVAw5j1RmDtmZ3M7F7g3mC1z8z2T3B/s4C2CW6bajLlWDLlOEDHkqoy5VgSPY5F4zVOdeiPd2r6KwMf7v4Q8FDCOzPb7u61iX5OKsiUY8mU4wAdS6rKlGNJ1nFM9WOHjcCCMes1QOpcbRURyXBTHfqvAMvNbImZFQDrgY1TXIOISNaa0uEdd4+a2ceBnzJ6y+Y33X1PEneZ8BBRCsmUY8mU4wAdS6rKlGNJynGYexLuJRQRkZSkqQRFRLKIQl9EJItkZOib2TfNrMXMdoddSyLMbIGZPWNm+8xsj5l9IuyaJsrMisxsm5m9FhzLF8KuKRFmlmtmO83sh2HXkggzO2pmr5vZLjPbHnY9iTCzGWb2PTN7I/g/886wa5oIM1sR/Huc+ukxs09O2udn4pi+mV0P9AH/6u6XhV3PRJnZPGCeu79qZtOAHcCdyZi2ItlsdOL6UnfvM7N84OfAJ9z95ZBLmxAz+xOgFpju7u8Lu56JMrOjQK27p/3DTGb2KPCCuz8c3B1Y4u5dYdeViGDqmuPAWnc/NhmfmZFn+u7+PNARdh2Jcvdmd381WO4F9jH6VHPa8VGn5sXID37S8ozDzGqA9wIPh12LjDKz6cD1wDcA3H043QM/sA44NFmBDxka+pnIzBYDVwJbw61k4oIhkV1AC/C0u6frsfwD8Bkgfq6OacCBTWa2I5j+JF0tBVqBbwXDbg+bWWnYRU2C9cC3J/MDFfppwMzKgH8HPunuPWHXM1HuHnP3Kxh9EnuNmaXd0JuZvQ9ocfcdYdcySa5199XAbcB9wdBoOsoDVgNfc/crgX7g/nBLSkwwRPUB4LuT+bkK/RQXjH//O/CYu38/7HomQ/Bn97PArSGXMhHXAh8IxsIfB240s38Lt6SJc/em4LUFeJLRmXDTUSPQOOavx+8x+ksgnd0GvOruJyfzQxX6KSy4+PkNYJ+7fynsehJhZlVmNiNYLgZuAt4It6oL5+4PuHuNuy9m9E/vLe7+4ZDLmhAzKw1uECAYCrkZSMs73tz9BNBgZiuCpnUkYcr2KfYhJnloBzL06xLN7NvADcAsM2sEPu/u3wi3qgm5FvgI8HowFg7wOXf/UYg1TdQ84NHgboQc4Al3T+vbHTPAHODJ0XML8oD/6+4/CbekhPwR8FgwLHIYuDvkeibMzEoY/bKpP5j0z87EWzZFRGR8Gt4REckiCn0RkSyi0BcRySIKfRGRLKLQFxHJIgp9EZEsotAXEcki/x9JjLu9G6atGgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x=np.linspace(a,b,200)\n", "plt.plot(x,f(x))\n", "plt.bar(xint[:-1],yint[1:],width=h,alpha=0.2,align='edge',facecolor='gray')\n", "\n", "sum(yint[1:])*h" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Skončíme metodou lichoběžníků, která je vlastně průměrem dvou předchozích. Výpočet lze zapsat jako $I\\thickapprox \\sum_{i=0}^{n-1}{f(x_i)+f(x_{i+1})\\over 2}h$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "1291.7224445797904" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x=np.linspace(a,b,200)\n", "plt.plot(x,f(x))\n", "plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n", "\n", "sum(yint[1:] + yint[:-1])*h/2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Metoda lichoběžníků a Simpsonova metoda jsou v Pythonu ve skutečnosti již naprogramovány:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1291.7224445797904" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate.trapezoid(yint,xint)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "1118.0227226114507" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate.simpson(yint,xint)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Naše odhady můžeme porovnat s hodnotou spočítanou pomocí jakési vestavěné knihovny v Pythonu. (První číslo je hodnota integrálu, druhé je chyba.)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1093.9148765999996, 1.2144894829813064e-11)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate.quad(f,a,b)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 2 }