From fb341026cd63e81638865e5beed8f13f1dc8d86a Mon Sep 17 00:00:00 2001 From: Frederic Weidling <fweidli@client61.num.math.uni-goettingen.de> Date: Fri, 16 Dec 2016 12:30:25 +0100 Subject: [PATCH] lsg blatt 8 --- 08_GN_Ellipse.ipynb | 256 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 256 insertions(+) create mode 100644 08_GN_Ellipse.ipynb diff --git a/08_GN_Ellipse.ipynb b/08_GN_Ellipse.ipynb new file mode 100644 index 0000000..8859372 --- /dev/null +++ b/08_GN_Ellipse.ipynb @@ -0,0 +1,256 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aufgabe 31\n", + "## Implementation Gauß-Newton\n", + "Verfahren wie in der Vorlesung besprochen, mit der Änderung, dass auch alle Zwischenschritte des Verfahrens mit ausgegeben werden." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from numpy.linalg import lstsq,norm\n", + "from numpy import concatenate\n", + "\n", + "def gauss_newton(f,df,x0,tol):\n", + " delta_x = lstsq(df(x0),-f(x0))[0]\n", + " x=x0+delta_x\n", + " all_x=array([x0,x])\n", + " k=1\n", + " \n", + " while True:\n", + " k=k+1\n", + " delta_x_new=lstsq(df(x),-f(x))[0]\n", + " x=x+delta_x_new\n", + " all_x=concatenate((all_x,[x]),axis=0)\n", + " q=norm(delta_x_new)/norm(delta_x)\n", + " if q>=1:\n", + " print('Verfahren scheint nicht zu konvergieren')\n", + " return all_x,k\n", + " if q/(1-q)*norm(delta_x_new)<=tol:\n", + " return all_x,k\n", + " else:\n", + " delta_x=delta_x_new.copy()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ellipsen Fit\n", + "Wir schreiben zunächst die Funktionen $r_p(t)$ und $D_p r_p(t)$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import cos,sin,zeros,array,pi,squeeze\n", + "\n", + "# Bestimmung des Radius bei gegebenen Parametern zu einem Zeitpunkt\n", + "def radius_single(p,t):\n", + " a=1-p[1]*cos(t-p[2])\n", + " return p[0]/a\n", + "\n", + "# Bestimmung der Jacobimatrix an gegebnen Parmetern zu einem Zeitpunkt\n", + "def jacobi_radius_single(p,t):\n", + " J=zeros([1,3])\n", + " t=t-p[2]\n", + " J[0,0]=1./(1-p[1]*cos(t))\n", + " J[0,1]=p[0]*cos(t)/(1-p[1]*cos(t))**2\n", + " J[0,2]=p[0]*p[1]*sin(t)/(1-p[1]*cos(t))**2\n", + " return J\n", + "\n", + "# Auswertung der Radien zu vielen Zeitpunkten bei festen Parametern\n", + "def radius(p,T):\n", + " r=[radius_single(p,t) for t in T]\n", + " return squeeze(array(r))\n", + "\n", + "# Auswertung der Jacobimatrix zu vielen Zeitpunkten bei festen Parametern\n", + "def jacobi_radius(p,T):\n", + " J=[jacobi_radius_single(p,t) for t in T]\n", + " return squeeze(array(J))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mit den gegeben Daten können wir daraus nun die Funktionen für unser Gauß-Newton Verfahren erstellen" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from numpy import load\n", + "\n", + "l=load('data31.npz')\n", + "t_data=l['t']\n", + "r_data=l['r']\n", + "\n", + "F= lambda x: radius(x,t_data)-r_data\n", + "DF= lambda x: jacobi_radius(x,t_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Das Verfahren liefert das folgende Ergebnis:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Anzahl benötigter Iterationen: 3\n", + "Iterate:\n", + "[[ 1. 0.5 0. ]\n", + " [ 0.88970882 0.61388071 0.36853493]\n", + " [ 0.89655494 0.70531879 0.39076027]\n", + " [ 0.89812593 0.71296859 0.38936107]]\n" + ] + } + ], + "source": [ + "x0=array([1.,1./2.,0.])\n", + "a,k=gauss_newton(F,DF,x0,0.01*norm(r_data))\n", + "print('Anzahl benötigter Iterationen: {0}\\nIterate:\\n{1}'.format(k,a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir plotten nun Daten und die berechneten Ellipsen zusammen mit der wahren Ellipse." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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6TTTlP5aTvjCdXSN24XeLH6FPheLk33oKb0fHwKvw8BhPdvYjZGY+QFHRJ0RE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\nT+bq8ddReCBGm+XTVVFhrUdeudIa3wT+b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BDXdUEcY9vaNDUfm9fmDyLylYiUichhEXlX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\nJAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff49f3a36a0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from numpy import arange\n", + "\n", + "def ellipse_coo(p):\n", + " T=arange(1000)*pi/500\n", + " r=radius(p,T)\n", + " x=cos(T)*r\n", + " y=sin(T)*r\n", + " return x,y\n", + "\n", + "x_data=cos(t_data)*r_data\n", + "y_data=sin(t_data)*r_data\n", + "\n", + "plt.plot(x_data,y_data,'x',label='Daten')\n", + "\n", + "for j in range(k+1):\n", + " x,y=ellipse_coo(a[j,:])\n", + " plt.plot(x,y,label='{}-te Iteration'.format(j))\n", + " \n", + "truth=array([0.9,23./32,pi/8])\n", + "x,y=ellipse_coo(truth)\n", + "plt.plot(x,y,label='truth')\n", + "\n", + "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n", + "plt.axis([-1, 3.5, -1, 2])\n", + "plt.gca().set_aspect('equal')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Der folgende Code wurde verwendet um die Daten zu erzeugen." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# from numpy import arange\n", + "# from numpy.random import randn\n", + "\n", + "# samples=20\n", + "# truth=array([0.9,23./32,pi/8])\n", + "# t_data=(arange(samples)/samples)*3*pi/4+7/8*pi\n", + "# r_data=radius(truth,t_data)\n", + "\n", + "# e=randn(samples)\n", + "# r_data=0.01*e*r_data+r_data\n", + "\n", + "# from numpy import savez\n", + "# savez('data31.npz',t=t_data,r=r_data)" + ] + } + ], + "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": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- GitLab