{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Analyse\n", "\n", "Ce notebook est relatif au troisième chapitre de cours de Prolégomènes de Mathématiques du [Master Sciences et Numérique pour la Santé](https://sns.edu.umontpellier.fr).\n", "\n", "> **⚠️ Rappel ⚠️**: Ce chapitre a pour objectif de synthétiser les notions et formules essentielles à l’utilisation des nombres complexes. Dans le cadre du Master, elles trouvent leurs applications dans les\n", "modules suivants : HAH807E - Chaîne d’Acquisition / Traitement du Signal, HAH710E - Ingénierie\n", ": Électronique, HAH802E - Capteurs et Traitement d’Images, HAH808E - Capteurs US\n", "pour le Biomédical, HAH805E - Robotique médicale, HAH806E - Neuroprothèse, HAH906E -\n", "Acquisition de données et traitement du signal pour le biomédical, HAH908E - Thermographie\n", "IR, détecteurs optiques et US, HAH909E - Robotique médicale 2, HAH910E - Neuroprothèse 2.\n", "\n", "Notebook réalisé par E. Le Clézio, le 21 août 2023. \n", "[Master Sciences et Numérique pour la Santé](https://sns.edu.umontpellier.fr) \n", "[Université de Montpellier](https://www.umontpellier.fr)\n", "\n", "## Import des bibliothèques nécessaires au fonctionnement du Notebook" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "from matplotlib.ticker import LinearLocator, FormatStrFormatter, MaxNLocator\n", "from matplotlib.colors import BoundaryNorm\n", "import numpy as np\n", "import cmath\n", "from fractions import Fraction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Intégration numérique :\n", "\n", "### Méthode de Riemann" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.cos(x)\n", "a = 0; b = 5 ; N = 10\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "x = np.linspace(a,b,N+1)\n", "y = f(x)\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "\n", "plt.figure(figsize=(15,5))\n", "\n", "plt.subplot(1,3,1)\n", "plt.plot(X,Y,'b')\n", "x_left = x[:-1] # Left endpoints\n", "y_left = y[:-1]\n", "plt.plot(x_left,y_left,'b.',markersize=10)\n", "plt.bar(x_left,y_left,width=(b-a)/N,alpha=0.2,align='edge',edgecolor='b')\n", "plt.title('Left Riemann Sum, N = {}'.format(N))\n", "\n", "plt.subplot(1,3,2)\n", "plt.plot(X,Y,'b')\n", "x_mid = (x[:-1] + x[1:])/2 # Midpoints\n", "y_mid = f(x_mid)\n", "plt.plot(x_mid,y_mid,'b.',markersize=10)\n", "plt.bar(x_mid,y_mid,width=(b-a)/N,alpha=0.2,edgecolor='b')\n", "plt.title('Midpoint Riemann Sum, N = {}'.format(N))\n", "\n", "plt.subplot(1,3,3)\n", "plt.plot(X,Y,'b')\n", "x_right = x[1:] # Left endpoints\n", "y_right = y[1:]\n", "plt.plot(x_right,y_right,'b.',markersize=10)\n", "plt.bar(x_right,y_right,width=-(b-a)/N,alpha=0.2,align='edge',edgecolor='b')\n", "plt.title('Right Riemann Sum, N = {}'.format(N))\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "intabfxdxR = 1.0075866899102104\n" ] } ], "source": [ "# Méthode Riemann\n", "\n", "intabfxdxR = 0.\n", "\n", "a = 0\n", "b = np.pi/2\n", "\n", "N = 100\n", "x = a + np.arange(0, N, 1)*(b-a)/N\n", "#print(x)\n", "deltax = (b-a)/N\n", "\n", "for n in range(N-1):\n", " intabfxdxR += np.cos(x[n]) * deltax\n", " \n", "print('intabfxdxR = ', intabfxdxR)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Méthode du milieu" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "intabfxdxM = 0.9995168362046273\n" ] } ], "source": [ "# Méthode milieu\n", "\n", "intabfxdxM = 0.\n", "\n", "a = 0\n", "b = np.pi/2\n", "\n", "x = a + np.arange(0, N, 1)*(b-a)/N\n", "#print(x)\n", "deltax = (b-a)/N\n", "\n", "for n in range(1,N-1):\n", " intabfxdxM += np.cos((x[n-1] + x[n])/2) * deltax\n", " \n", "print('intabfxdxM = ', intabfxdxM)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Méthode des trapèzes" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "intabfxdxT = 0.9994860087513269\n", "9.99\n", "intunsurx2 = 10.132439534607286\n" ] } ], "source": [ "# Méthode trapèze\n", "\n", "intabfxdxT = 0.\n", "\n", "a = 0\n", "b = np.pi/2\n", "\n", "N = 100\n", "x = a + np.arange(0, N, 1)*(b-a)/N\n", "#print(x)\n", "deltax = (b-a)/N\n", "\n", "for n in range(1,N-1):\n", " intabfxdxT += (np.cos(x[n-1]) + np.cos(x[n]))/2 * deltax\n", " \n", "print('intabfxdxT = ', intabfxdxT)\n", "\n", "\n", "a = 1\n", "b = 1000\n", "x = a + np.arange(0, N, 1)*(b-a)/N\n", "deltax = (b-a)/N\n", "print(deltax)\n", "intunsurx2 = 0\n", "for n in range(N-1):\n", " #print(x[n])\n", " intunsurx2 += 1/(x[n]**2)*deltax\n", "print('intunsurx2 = ', intunsurx2)\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.cos(x)\n", "a = 0; b = 5; N = 20\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "x = np.linspace(a,b,N+1)\n", "y = f(x)\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "\n", "plt.figure(figsize=(10,10))\n", "\n", "\n", "plt.subplot(1,1,1)\n", "plt.plot(X,Y,'b')\n", "x_right = x[1:] # Left endpoints\n", "y_right = y[1:]\n", "plt.plot(x_right,y_right,'b.',markersize=10)\n", "for ip in range(len(x_right)-1):\n", " plt.fill_between([x_right[ip],x_right[ip+1]],[y_right[ip],y_right[ip+1]], color = 'lightblue', alpha=1, edgecolor='k')\n", "plt.title('Trapezoid Sum, N = {}'.format(N))\n", "\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Notion de dérivée :" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.cos(x)\n", "a = 0; b = 5; N = 10\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "\n", "plt.figure(figsize=(15,5))\n", "\n", "plt.subplot(1,3,1)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = 1\n", "A = (f(x+dx)-f(x))/dx\n", "B = f(x)\n", "y = A*(X-x)+B\n", "\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "plt.plot(x+dx,f(x+dx),'k.',markersize=10)\n", "plt.plot(X, y,'k')\n", "plt.ylim([-1.5, 1.5])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.subplot(1,3,2)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = 0.5\n", "A = (f(x+dx)-f(x))/dx\n", "B = f(x)\n", "y = A*(X-x)+B\n", "\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "plt.plot(x+dx,f(x+dx),'k.',markersize=10)\n", "plt.plot(X, y,'k')\n", "plt.ylim([-1.5, 1.5])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.subplot(1,3,3)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = 0.05\n", "A = (f(x+dx)-f(x))/dx\n", "B = f(x)\n", "y = A*(X-x)+B\n", "\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "plt.plot(x+dx,f(x+dx),'k.',markersize=10)\n", "plt.plot(X, y,'k')\n", "plt.ylim([-1.5, 1.5])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.cos(x)\n", "a = 0; b = 5; N = 10\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "\n", "plt.figure(figsize=(15,5))\n", "\n", "plt.subplot(1,3,1)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = 1\n", "A = (f(x+dx)-f(x))/dx\n", "B = f(x)\n", "y = A*(X-x)+B\n", "\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "plt.plot(x+dx,f(x+dx),'k.',markersize=10)\n", "plt.plot(X, y,'k')\n", "#plt.xlim([2, 4])\n", "#plt.ylim([-1, -0.7])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.subplot(1,3,2)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = 0.3\n", "A = (f(x+dx)-f(x))/dx\n", "B = f(x)\n", "y = A*(X-x)+B\n", "\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "plt.plot(x+dx,f(x+dx),'k.',markersize=10)\n", "plt.plot(X, y,'k')\n", "#plt.xlim([2, 3])\n", "#plt.ylim([-1, -0.7])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.subplot(1,3,3)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = 0.1\n", "A = (f(x+dx)-f(x))/dx\n", "B = f(x)\n", "y = A*(X-x)+B\n", "\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "plt.plot(x+dx,f(x+dx),'k.',markersize=10)\n", "plt.plot(X, y,'k')\n", "#plt.xlim([2, 3])\n", "#plt.ylim([-1, -0.7])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = lambda x : np.cos(x)\n", "a = 0; b = 5; N = 10\n", "n = 10 # Use n*N+1 points to plot the function smoothly\n", "\n", "X = np.linspace(a,b,n*N+1)\n", "Y = f(X)\n", "\n", "plt.figure(figsize=(10,10))\n", "\n", "#plt.subplot(1,3,1)\n", "plt.plot(X,Y,'b')\n", "\n", "x = np.pi-np.pi/6\n", "dx = np.linspace(1e-6,1,10)\n", "plt.plot(x,f(x),'b.',markersize=10)\n", "\n", "for idx in range(len(dx)):\n", " A = (f(x+dx[idx])-f(x))/dx[idx]\n", " B = f(x)\n", " y = A*(X-x)+B\n", "\n", " plt.plot(x+dx[idx],f(x+dx[idx]),'k.',markersize=10, alpha=1-dx[idx])\n", " plt.plot(X, y,'k',alpha=1-dx[idx])\n", "\n", "plt.xlim([2, 4])\n", "plt.ylim([-1, -0.7])\n", "plt.title('Dérivée en 5$\\pi$/6')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 4 }