{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "*ENSAM-Bordeaux, Mathématiques et informatique. Date : le 11/10/19. Auteur : Éric Ducasse. Version : 1.0*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
*On pourra faire exécuter ce notebook cellule par cellule $\\left(\\mathtt{Maj+Entrée}\\right)$ ou intégralement par $\\mathtt{\\;Kernel\\rightarrow Restart\\;\\&\\;Run\\;All}$.*
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import sympy as sb\n", "sb.init_printing() # Pour avoir de jolies formules mathématiques à l'écran" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Version de sympy : 1.4\n" ] } ], "source": [ "print(f\"Version de sympy : {sb.__version__}\") " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# **Évaluation immédiate / évaluation différée**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voir aussi le tutoriel **sympy** :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "https://docs.sympy.org/latest/tutorial/index.html#tutorial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. *Exemple* : Développement en série entière de $\\exp(x)$ " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAQCAYAAAAWGF8bAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABJElEQVQ4EZ2TgW3CMBBFHdQBkLpBugFSN0g3qMQGjEDVEdoNOgMjhA2qdIOwQQsbhPeDz7oIuTic9OM72/d9Z/+EYRhCKUIIDdiCnc8hbi0uJlMC9hFHBcvor/CPswlJqkUCXkGfCC4VpwofWCwyCA7aWFXVmuHLJT3jtym2k0pHEo+gsf0xVtu15hY495hVq0fSNSjWVYRKrHOMlpX4AjrwB3QF3+AHrv2EkM067R38AtkTeGPjaYxKPqowVqnye7Byc7qbUSo2d2s0MklCvW98ArFEnB7Ar+V8k43JYEnbInkEMulrf3ELvzoJ02fyO+UquDXvZTNKobCO7DYjzJJFmWQJrhZiyxsWOt8OsSSkux3/AL/2n5906B7DNCgFfEI4y87e/q1injtwwwAAAABJRU5ErkJggg==\n", "text/latex": [ "$\\displaystyle e^{u}$" ], "text/plain": [ " u\n", "ℯ " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u,v = sb.symbols(\"u,v\")\n", "n = sb.symbols(\"n\", integer=True, nonnegative=True)\n", "sb.summation(u**n/sb.factorial(n), (n,0,sb.oo) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### On veut calculer la somme de la série pour les éléments de la liste suivante :" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[ x, \\ y, \\ 0, \\ \\log{\\left(2 \\right)}, \\ \\log{\\left(3 \\right)}, \\ \\log{\\left(4 \\right)}, \\ \\log{\\left(5 \\right)}, \\ \\log{\\left(6 \\right)}, \\ \\log{\\left(7 \\right)}, \\ \\log{\\left(8 \\right)}, \\ \\log{\\left(9 \\right)}, \\ \\log{\\left(10 \\right)}, \\ \\log{\\left(11 \\right)}, \\ \\log{\\left(12 \\right)}, \\ \\log{\\left(13 \\right)}, \\ \\log{\\left(14 \\right)}, \\ \\log{\\left(15 \\right)}, \\ \\log{\\left(16 \\right)}, \\ \\log{\\left(17 \\right)}, \\ \\log{\\left(18 \\right)}, \\ \\log{\\left(19 \\right)}, \\ \\log{\\left(20 \\right)}\\right]$" ], "text/plain": [ "[x, y, 0, log(2), log(3), log(4), log(5), log(6), log(7), log(8), log(9), log(\n", "10), log(11), log(12), log(13), log(14), log(15), log(16), log(17), log(18), l\n", "og(19), log(20)]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x,y = sb.symbols(\"x,y\")\n", "liste = [x,y] +[sb.log(i) for i in range(1,21)] ; liste" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Évaluation différée** : calcul répété à chaque appel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Boucle simple :" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 2.01 s\n" ] }, { "data": { "image/png": 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, "text/latex": [ "$\\displaystyle \\left[ e^{x}, \\ e^{y}, \\ 1, \\ 2, \\ 3, \\ 4, \\ 5, \\ 6, \\ 7, \\ 8, \\ 9, \\ 10, \\ 11, \\ 12, \\ 13, \\ 14, \\ 15, \\ 16, \\ 17, \\ 18, \\ 19, \\ 20\\right]$" ], "text/plain": [ "⎡ x y \n", "⎣ℯ , ℯ , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\n", "\n", "⎤\n", "⎦" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time L1 = [ sb.summation(u**n/sb.factorial(n), (n,0,sb.oo) ) for u in liste ]\n", "L1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Boucle avec définition standard d'une fonction :" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 1.39 s\n" ] }, { "data": { "image/png": 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, "text/latex": [ "$\\displaystyle \\left[ e^{x}, \\ e^{y}, \\ 1, \\ 2, \\ 3, \\ 4, \\ 5, \\ 6, \\ 7, \\ 8, \\ 9, \\ 10, \\ 11, \\ 12, \\ 13, \\ 14, \\ 15, \\ 16, \\ 17, \\ 18, \\ 19, \\ 20\\right]$" ], "text/plain": [ "⎡ x y \n", "⎣ℯ , ℯ , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\n", "\n", "⎤\n", "⎦" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def s_differee(t) :\n", " return sb.summation(t**n/sb.factorial(n), (n,0,sb.oo) )\n", "%time L2 = [s_differee(u) for u in liste]\n", "L2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Évaluation immédiate** : calcul fait une fois pour toutes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Calcul symbolique avant la boucle et réécriture dans la boucle :" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 64 ms\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAQCAYAAAAbBi9cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVQ4EZ1Tiw2CQAzljAOQuAFuQOIGjKAr4AYQR8ANdAVGwBV0A9xA4wb43tkjleTOwyal7V1ff1fMMAxJLBljCvjm4A1wO+Jw1lAmDBTLcG8kMbOnom+ht3OCZASDWVWvk8NujESFHkeuFeBqIqTdea1J0h74wlUEvaK+YNQ/6EkMqmG7N6tLFupRJK3s4dwRAPyZ8mtGcOIwD+AHL0FrcA3nl7VCH1YkVdnXgG+uzrgz9sndmU+6IOyVu1FqR9gVeBysvpvqSziSTh+RpGiP4JXYHQAX0cOCkUH8tNMsc2z9/PdwyvCtC+QNglb5L/0maa2E51W3ApurwNll+tynj3ukhux2iC96RKAoegOLqV5hZJvQwQAAAABJRU5ErkJggg==\n", "text/latex": [ "$\\displaystyle e^{v}$" ], "text/plain": [ " v\n", "ℯ " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time resultat = sb.summation(v**n/sb.factorial(n), (n,0,sb.oo) )\n", "resultat" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 12.5 ms\n" ] }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[ e^{x}, \\ e^{y}, \\ 1, \\ 2, \\ 3, \\ 4, \\ 5, \\ 6, \\ 7, \\ 8, \\ 9, \\ 10, \\ 11, \\ 12, \\ 13, \\ 14, \\ 15, \\ 16, \\ 17, \\ 18, \\ 19, \\ 20\\right]$" ], "text/plain": [ "⎡ x y \n", "⎣ℯ , ℯ , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\n", "\n", "⎤\n", "⎦" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time L3 = [ resultat.replace(v,u) for u in liste]\n", "L3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Définition d'une fonction mémorisant le résultat du calcul symbolique grâce à la fonction $\\mathtt{lambdify}$ :" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 36.5 ms\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAQCAYAAAAbBi9cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVQ4EZ1Tiw2CQAzljAOQuAFuQOIGjKAr4AYQR8ANdAVGwBV0A9xA4wb43tkjleTOwyal7V1ff1fMMAxJLBljCvjm4A1wO+Jw1lAmDBTLcG8kMbOnom+ht3OCZASDWVWvk8NujESFHkeuFeBqIqTdea1J0h74wlUEvaK+YNQ/6EkMqmG7N6tLFupRJK3s4dwRAPyZ8mtGcOIwD+AHL0FrcA3nl7VCH1YkVdnXgG+uzrgz9sndmU+6IOyVu1FqR9gVeBysvpvqSziSTh+RpGiP4JXYHQAX0cOCkUH8tNMsc2z9/PdwyvCtC+QNglb5L/0maa2E51W3ApurwNll+tynj3ukhux2iC96RKAoegOLqV5hZJvQwQAAAABJRU5ErkJggg==\n", "text/latex": [ "$\\displaystyle e^{v}$" ], "text/plain": [ " v\n", "ℯ " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time s_immediate = sb.lambdify(x,sb.summation(x**n/sb.factorial(n), (n,0,sb.oo)),\"sympy\")\n", "s_immediate(v)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 0 ns\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAAVCAYAAACjdONZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAOVElEQVR4Ae2djXHcNhCFZY0LcJQKknQQWx3YHUhJBbY7SCYVeJIOHFeQnw7sVOCfDpxUYFsdOO+jsBSOx7tbksDenQzMQCRBcPftYvm4BMnTnZOTk59Un6pSLj9//vzuetX3986dOxxP+U71V1Vk3WNdsv7VMqwIy0Mp+171XLovTbHaX2r7kW23ZfNA80DzQPNA80DzQPNA88CX6YGUu/a576nc8LXqUyWL36nOSYT/1nG/ScaZ6nOt/6zlA1WS0ujyKGG5kKEk5CdaggM8rXyBHkjjv2I5saH67UrjkWyAW/UJNhwJ5AazeaB54AA9IA5Zu0bDK6pHyY01XIwvVBvf1nDunmWSK6oyifu36tndhXiuJMxmf7k4v0zyHqt9UmK9EAdJLyfwMy2ZHf5X+q+STLbfpPXiC+mDUP5SvZ/pLKYn2cUNBoWk/qPqzzX8m3TZnRLjiU+Z4X+lZbWSfMgNmekuqesfyccWi0fWKfevF2X/ShdPR/LyR+GxIt6eU6Ur12PrnJNf2caSZfLbL5LxQZWbZnz3V614kD7ssnKmFXjkyhpKLqVr53mrPjaW2N89+RIe47uScDpZHkx09PYrAXCXLu2HI0L4yexxYjIuIWar89guTIbdlql/Lc7r1DgwhXIjoByYDLude922/pTmUZO7C1MY3/aAtLLLT9pPXIdxM9h2YUp9qnO4cLg5R30tjnZy+KJkWBeG33FAKiSdHSmq3RIP21d9aRcpGQ8JkulbOdeKJenWtmgpHQTiC1USUxJUBqd4SYNOMpq/8sHgvtU+ZsGLJanJJpJsu4gQ/E+k66WWvD6T+7S0rdxM1IoZxogKqZHIYMcz2VM0yZKPiAHijAtcNy5qwy4qiVSpQjzjK2zBrrz052DeuGCd2OvjATnYpHqvZDwgT6LfqvJkiadMRrz/aR83mUUS0KTHdd6qL3iIky7uDaOWnHdF8CQ7XVwyBTtylxSvLvWzJDOKn3aOXcIewmNeP20YiyqcNxFTFDe6Yhw/pZiqzqMT/BTGtxMw4apIbvaedxEc7uYc+XMyh5NcPRTBn8ytOp5EQ4dfy9D6t7YevZTu96q9PVr/pPp9LRySzTvTn1VJEGb7cOxYyYQw1+SqDZs+jR0zt03yzI4Lk4FuVWx7a22ll0kvY8aMY1H/Ia+W3CFW6TEi6G1QG6TO++p929J1ySNhXJOndkhidN9Y/11tksWN0JNhP7V1ieuwfcm2ZBLna/GsNvxXzKYco+RavI+dX9j+Pu/PugpcWXQ8cx2SvRHTnH75MXPXt2HSvjB+yvHvwGQ+3AePua4DCX81zjNfbfMTfVSqcK7pH1s6MIXwaI5tGybtG+UftRfl2xwP6zswhXFzjmsHphAOFwYX56ifm8PVt8uBT7Uyq3AHp0pSRvlRldkqKyuzSdYYuOxmzISPmTIudjm2QBiLVYH/k+wgAckLM4+l3+3CR1epdrrkN7arFdnFTdSKzmrKKgqWHRcSjy32uLjTJv8xi1j6w00SxLGyNlMw1mlCG7PZ/YzfhOPmdMV/Y7OtxCSkFl2we4wzXqv94cj5GI3vUPRF8pPX5nAe8wKj323hvCk2e/sG86gXVhTfevHQL5KbvbiiONzLOZM5fHYyLA99VH2lAOZiRcCw/pMqWfYz1X0VEpKnCRfrYxe1fWGbqpekN3//eXj8MEke7ndvK2l7pfoVSztIPiTAKfl7QNctZf7+KH35qzZlpMZL4d2tK9lS9eYBs6Rj7XWVSucc5zSJH6/J5HHG+V0sHjLZ8MmwfKBBfbjRiCwQ7hgeG1/2tyLOlxNC+MnrbPhLNZrHvPDod1s4b4rN3r5hPOoFFMi3Xkj0C+FmL6BgDvdyzmQOv7vN4GQkAdpdlLTkjoT3sezCn88c9UnUNplL9m3Dg9y0/50FsLbBV+zCvQT7nGNlR+7fXESXHGh/tURfviOYSHx4B7Z4wir5PM4MGRvp4obNEjpimEdfJX3HeLyTHpY8JeF8QU+1j80kuyvSyeM6XgNamZVOu2cvJI+bWxJvboh4OoF8bOI1gbWEXO2zimRdSTbHno0I4KM9yti+6z2F/wqLxck2yWF4toHY9z6N3d74yWu7xrMqj3lx0E9YwjjPi0uYanOjFwr94M+98KgXpPxVhW+9+ukXxc1eTJEc7uEcjdEsDt+YDEsgJEKy0v/2sNoIVpLjohdeydtZnHheSBCPMn9L/c/kvOKJ3E6wFTukMeCErDIGST5jf65KwvhGtWiRDvBzQzX2aLyoLgnjxPiTExbBSfd7LYt8gCg5+Yn3QHr6cdE+ksjHaiuWPGLDoHDDQi1ehPtS+JHNRZwl8VBDF/4h5oYFvqEQL1HFEt0uXgZKP6btfMwHXb7sTcULY1aNn7zeTTiq8pgXC/2EJ5LzvNCI42rc6AVBP/knP6f2waNeuPBfDQ706u/6BXKzF9feOHyEc2Zx+OmYpenEZSqe9xDzGTTIhfbQMgHPHwLGTBMXb5KdKj+fFWr8ujJeIP9dtnVf3a/vXtbCeCNblVkf/MkvV9jrEsuE3xxdZbb5RvzNmuwgDvrERusk4DzFKD0rzezs8MbrT+l5If/lRH8DbuFaOi/4UKjKU5ls3JkRRgeJDjcSY4nrEmsec3AuV+vosnGzJHSJjpLH2ox1SZm3RVZVfvI6SedEBI954dAvjPO8oOSjKG70QqJfOI96wYmTuKGpxrdeHPQTFrsm1+ZmL6x9cvgczlnj8LsbLLVEgY+0SCztQB6RVrnwbsBhzS48wlZzBs6w7G2pscAPvBMX8oEi/pROEhJ+Tov38Cw5me0DyeGxnI3nbDkLDyQh5n1YfvVk0ew0PpEc4IzJ4cto7H2gWuO8IQ7ym1VtlilpnPhZM4u1R2qDgCEe4uGbEvEA2uTDb7T6q+SSBMM3r1NF55hv1VylbEu8bcbBXhurAuBYhWrsQvnJ6yfFV3Ee8+qmn/xyCJznhVyMG70K6Zc4gNWxc702j6LXU6rxrUe59UnxFMLNpnPXcl8cvoFzZnH4pmSYmR/7z3K7/BCx/9DwRNi8oiOdAJCGJScr+5duSD5JCPKHydUbNeP/bgzoM7dIB3fW/LrHGOHNFbvxOOnjKQavytzf0KnUjC32bLtRwO4apWaiyKNAEtS+yI8kFcxEdD9fqGWxm0/Jxn8rsS1ddtMUEi8YCg7pZXUsNqwtDA9AjqHIZyR81fjJ6wPhqM5jXiz0E55QzvNiE64obvRCot++eNSLsSbfejHQL5SbvcCiOXwT58zl8LtbDD00wj80PFtcV3aXBp2TkH+X3ScLiWS5+Cz2i2RxkefuG/IuMgOMrJHCheFcOphdzAsXMH6qj3a+Tu/fu807zVh/oGPG7hK7GT7pGSb+M1R0hzAG2xLexWM0BJbGDJ2lbOhVJNnctJCgrhTiTftJgjsfruwsv8H48SRkDUd5VSsSmcUfG0+zucYs/wqAY9pQPFTlJ68vUtxG8JgXEv2iOc+LLYobvXjoF86jXnAptqrwrRcD/RKOQ+BmL+wqHO7gnMkcfrrBoo0X7wRiw2Gbm9Mgbu6wfc+h4dmONtu70G6Cn0TxXAnBMEHkAtQnekv0pGSDhIOnAcPEg2Cm9AnAXF2STWLDB5krVbLRaft6O+fqAWwqvFvNTOawMMvd28POhbq4Ux9LnpiR5kPBXtdCPUC1YuPSx4DtsOVcXcLLeDBDOmYT4u+pFrNJei5UV35PO+km9vt4QLHa0V27cFNm/s11MZ68i4p/uhKEx9S5lpGYpKs6P7mMVieLW61W5TEvHvpx7quu8B3b2kUM2b4+xgPHLoobcYO37INHvdiMD4rzrRcA/SzGFSch3OzFJjxhHO7kHDeHm42bkmGCkoShL5ykqjy2nDwTxbE6jotdd9feC/WvHBoeF/Kldut4Ap5B7Xyv7eep0sYHGd1FeameZAyEvPJxpOReoLuCrqSyX6CD2pdCNnX+6oVqRXJ5B57S/yzUUl0aBxJDfoqMOO1KkvmDNroPC2hcqqcTfPPH/HV103SzVkAX/un+9fKN1M4GHofz7UB3g1pAD+KJ8+FFBq4hxnu+KaQLfVuLdPIh5EfpI/67knTXHE9TtWgZ5SNASlckP3n9sk8e82KkXy3O82II4UYvGPrtiUe9EGvzrRcH/SK52YsrhMO9nOPl8Nw4Xo7jAr72YZyU2odzH+wAKZj9CwaSx3uGFF78Hr2AX+8e/3uAeLokVWi5Y+REITngwv0699MSu3UsNw/MvIwVZqj6d2GX6DHhksENUJ8kap0A5xdF+llA+pbQleSQ8OA/sxE9xGIXZyX0SAY22MzLmdZJurrfytayL4V0cS4ZaaLrmWzpkzmUldCT5GAX8bHxp9uW6tLxjMsvqvjMytpvJy/Vg2DJ6G8ktIkP1/Skfkt5xHveggHbjf/OtV5lPGW7F5O33yIfJT/v1CXc0fy0E1PCHsZj3rEDF0X9IzjP66dIbnRhSj4K4dEpY6e+1fk22e7yk/BEcrMXU3UOl91TOMfL4eB+uTEZZmBKFxnCTAuPhq5Ky54jLwrPbdODr5tNcyLu+pgo37Vxmj9GU46MHE8vrobJ56nmp+Ynnwd8vVo8HZ+fNGZdMnzqg16sF+++HkQinCyKwnPb9OC+ZtP80yLKd22c5o/RlCMjx9OLq2Hyear5qfnJ5wFfrxZPR+qnsGRY2TdT1vbI0eeuir2i8Nw2PQxJs2l+YEb5ro3T/DGacmTkeHpxNUw+TzU/NT/5PODr1eLpeP0E8rBkWLp+sHdBfS6r3isKz23Tw8A0m+aHZ5Tv2jjNH6MpR0aOpxdXw+TzVPNT85PPA75eLZ6O108n9s6wfTV9Ofzgx2db69U80DzQPNA80DzQPNA80DzQPHD4HtBMPj8Swf9u4GP3y/8BjDpGm5pKY1kAAAAASUVORK5CYII=\n", "text/latex": [ "$\\displaystyle \\left[ e^{x}, \\ e^{y}, \\ 1, \\ 2, \\ 3, \\ 4, \\ 5, \\ 6, \\ 7, \\ 8, \\ 9, \\ 10, \\ 11, \\ 12, \\ 13, \\ 14, \\ 15, \\ 16, \\ 17, \\ 18, \\ 19, \\ 20\\right]$" ], "text/plain": [ "⎡ x y \n", "⎣ℯ , ℯ , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\n", "\n", "⎤\n", "⎦" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time L4 = [s_immediate(u) for u in liste]\n", "L4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Remarque : la fonction $\\mathtt{lambdify}$ permet aussi de définir une fonction numérique (vectorisée) à partir du résultat d'un calcul symbolique :" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 0 ns\n" ] }, { "data": { "text/plain": [ "array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11.,\n", " 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,\n", " 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33.,\n", " 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44.,\n", " 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55.,\n", " 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66.,\n", " 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77.,\n", " 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88.,\n", " 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99.,\n", " 100.])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s_immediate_num = sb.lambdify(x,sb.summation(x**n/sb.factorial(n), (n,0,sb.oo)), \"numpy\")\n", "vec_num = np.log(np.arange(1,101))\n", "%time V5 = s_immediate_num( vec_num )\n", "V5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. La fonction $\\mathtt{sympy.lambdify}$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "https://docs.sympy.org/latest/tutorial/basic_operations.html#lambdify" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[ x, \\ \\frac{x^{2}}{2}, \\ \\frac{x^{3}}{6}, \\ \\frac{x^{4}}{24}, \\ \\frac{x^{5}}{120}\\right]$" ], "text/plain": [ "⎡ 2 3 4 5⎤\n", "⎢ x x x x ⎥\n", "⎢x, ──, ──, ──, ───⎥\n", "⎣ 2 6 24 120⎦" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = sb.symbols(\"k\", integer=True, nonnegative=True)\n", "p = sb.lambdify([x,k], x**k/sb.factorial(k), \"sympy\")\n", "[p(x,i) for i in range(1,6)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **Ne fonctionne pas :**" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Erreur : name 'factorial' is not defined\n" ] } ], "source": [ "p_num = sb.lambdify([x,k], x**k/sb.factorial(k), \"numpy\")\n", "try : \n", " [p_num(1,i) for i in range(1,6)]\n", "except Exception as e :\n", " print(\"Erreur :\",e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **Version correcte :**" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 120.0$" ], "text/plain": [ "120.0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.special import factorial as sc_fact\n", "float(sc_fact(5))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[ 1.0, \\ 0.5, \\ 0.16666666666666666, \\ 0.041666666666666664, \\ 0.008333333333333333\\right]$" ], "text/plain": [ "[1.0, 0.5, 0.16666666666666666, 0.041666666666666664, 0.008333333333333333]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p_num = sb.lambdify([x,k], x**k/sb.factorial(k), {\"factorial\":sc_fact})\n", "[p_num(1,i) for i in range(1,6)]" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1. , 0.5 , 0.16666667, 0.04166667, 0.00833333])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p_num(1,np.arange(1,6)) # Fonction vectorisée" ] } ], "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }