From c093826f6d107a8e843394a170213f3f9dd65c1e Mon Sep 17 00:00:00 2001 From: Frederic Weidling <fweidli@client61.num.math.uni-goettingen.de> Date: Mon, 14 Nov 2016 08:32:40 +0100 Subject: [PATCH] blatt 3 --- 03_Cholesky_Poisson2d.ipynb | 400 ++++++++++++++++++++++++++++++++++++ 03_ellipsen_fits.ipynb | 191 +++++++++++++++++ 2 files changed, 591 insertions(+) create mode 100644 03_Cholesky_Poisson2d.ipynb create mode 100644 03_ellipsen_fits.ipynb diff --git a/03_Cholesky_Poisson2d.ipynb b/03_Cholesky_Poisson2d.ipynb new file mode 100644 index 0000000..9945ac8 --- /dev/null +++ b/03_Cholesky_Poisson2d.ipynb @@ -0,0 +1,400 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aufgabe 11\n", + "## Aufgabe 11.1\n", + "__Aufgabe:__ Implementieren Sie Vorwärts- und Rückwärtselimination.\n", + "\n", + "Zunächst die Vorwärtselimination:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import array, tril, diagonal, zeros, arange" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def vorwaertselimination(L,b):\n", + " # Überprüfen ob Matrix und Vektor die gewünschte Form haben:\n", + " n,m =L.shape\n", + " k=max(b.shape)\n", + " if not((n==m) & (n==k)):\n", + " print('Dimensionen passen nicht zusammen')\n", + " return None \n", + " if not((L==tril(L)).all()):\n", + " print('Matrix ist nicht vom passenden Dreieckstyp.')\n", + " return None\n", + " if (diagonal(L)==0).any():\n", + " print('Matrix ist singulär')\n", + " return None\n", + " \n", + " # Start des Algorithmus:\n", + " x=zeros(max(b.shape))\n", + " for iii in range(n):\n", + " l=L[iii,:]\n", + " x[iii]=(b[iii]-l@x)/L[iii,iii]\n", + " \n", + " return x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test mit einem Beispiel in dem erst $b=L\\cdot x$ berechnet wird und dann mit L,b getestet wird:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., 3.])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "L=array([[1,0,0],[1,2,0],[1,3,1]])\n", + "x=array([1,2,3])\n", + "b=L@x \n", + "vorwaertselimination(L,b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Die Rückwärtselimination wird jetzt so geschrieben, dass sie die Vorwärtselimination aufruft, der das Gleichungssystem \"von unten gelesen\" übergeben wird." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def rueckwaertselimination(U,b):\n", + " n,m= U.shape\n", + " rueckwaerts=arange(n-1,-1,-1)\n", + " z=vorwaertselimination(U[rueckwaerts,:][:,rueckwaerts],b[rueckwaerts])\n", + " if z==None:\n", + " return None\n", + " else:\n", + " return z[rueckwaerts]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:5: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n" + ] + }, + { + "data": { + "text/plain": [ + "array([ 1., 2., 3.])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U=array([[1,2,3],[0,2,1],[0,0,1]])\n", + "c=U@x \n", + "rueckwaertselimination(U,c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aufgabe 11.2\n", + "__Aufgabe:__ Implementieren Sie die Cholesky Zerlegung" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def cholesky(A):\n", + " # Test ob Matrix quadratisch ist\n", + " n,m = A.shape\n", + " if not(n==m):\n", + " print('Matrix ist nicht quadratisch')\n", + " return None\n", + " # Test ob Matrix hermitesch ist\n", + " if not((A==A.T.conj()).all()):\n", + " print('Matrix ist nicht hermitesch')\n", + " return None\n", + " # Es gibt keine kluge Variante im Vorfeld festzustellen, ob die Matrix A positiv definit ist. Das\n", + " # \"ergibt\" sich im Laufe der Zerlegung. Jede Variante das festzustellen (z.B. Eigenwerte bestimmen)\n", + " # dauert etwa genauso lange wie den Algorithmus selbst durchzuführen.\n", + " \n", + " for kkk in range(n):\n", + " A[kkk,kkk]=A[kkk,kkk]-A[kkk,:kkk]@A[kkk,:kkk].conj()\n", + " if A[kkk,kkk]>0:\n", + " A[kkk,kkk]=A[kkk,kkk]**(1/2)\n", + " else:\n", + " print('Matrix ist nicht positiv definit')\n", + " return None\n", + " A[kkk+1:,kkk]=(A[kkk+1:,kkk]-A[kkk+1:,:kkk]@ A[kkk,:kkk].conj())/A[kkk,kkk]\n", + " return A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Testen der Zerlegung, indem wir zunächst eine positiv definite Matrix per $A=LL^*$ konstruieren und zeigen, dass die Zerlegung L zurück gibt." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 4.44089210e-16+0.j]]\n" + ] + } + ], + "source": [ + "L=array([[2,0,0],[1j,2,0],[-1j,2,3]])*1.0\n", + "A=L@L.T.conj()\n", + "B=cholesky(A.copy())\n", + "print(tril(B)-L)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Aufgabe 11.3\n", + "__Aufgabe:__ Lösen Sie zu gegebener rechter Seite die 2d Poissongleichung\n", + "\n", + "Zunächst kopieren wir die Funktion von Blatt 2 die die Matrix erstellt." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import eye\n", + "\n", + "def tridiag(a,b,c,n):\n", + " A=zeros([n,n]) \n", + " for iii in range(n):\n", + " if iii==0:\n", + " A[iii,iii]=b \n", + " A[iii,iii+1]=c\n", + " elif iii==n-1:\n", + " A[iii,iii]=b\n", + " A[iii,iii-1]=a\n", + " else:\n", + " A[iii,iii]=b\n", + " A[iii,iii-1]=a\n", + " A[iii,iii+1]=c\n", + " return A\n", + "\n", + "def poisson2d_matrix(n):\n", + " A=zeros([(n-1)**2,(n-1)**2]) # Hier speichern wie die Poissonmatrix rein\n", + " B=tridiag(-1,4,-1,n-1) # Die Matrix entlang der Diagonalen\n", + " C=-eye(n-1) # Die Matrix auf den Matrixnebendiagonalen\n", + " # Jetzt bauen wir Matrix nach dem selben Prinzip zusammen, wie in tridiag:\n", + " for iii in range(n-1): # für \"blockweise\" durchlaufen der Matrix\n", + " ind=iii*(n-1) # Umrechnen von Blockindex zu Matrixindex\n", + " A[ind:ind+(n-1),ind:ind+n-1]=B #Setzen des Diagonalblocks\n", + " # Setzen der Nebendiagonalblöcke\n", + " if iii==0:\n", + " A[ind:ind+(n-1),ind+(n-1):ind+2*(n-1)]=C\n", + " elif iii==n-2:\n", + " A[ind:ind+(n-1),ind-(n-1):ind]=C\n", + " else:\n", + " A[ind:ind+(n-1),ind+(n-1):ind+2*(n-1)]=C\n", + " A[ind:ind+(n-1),ind-(n-1):ind]=C\n", + " return n**2*A" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from numpy import array,zeros,ogrid,broadcast_arrays\n", + "\n", + "def rechte_seite(n):\n", + " rechteSeite=zeros([n-1,n-1])\n", + " x,y=ogrid[1/n:1-1/n:(n-1)*1j,1/n:1-1/n:(n-1)*1j]\n", + " x, y = broadcast_arrays(x, y)\n", + " rechteSeite[(1/8<=x) & (x<=1/4) & (1/8<=y) & (y<=5/8)]=2\n", + " rechteSeite[(1/8<=y) & (y<=1/4) & (1/8<=x) & (x<=5/8)]=2\n", + " z=(x-2/3)**2+(y-2/3)**2\n", + " rechteSeite[z<=1/16]=-1\n", + " return rechteSeite.ravel()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "Bevor wir die Gleichung lösen, plotten wir zunächst einmal die rechte Seite als Bild\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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NTCUGL5+ahSOZsHc4Ps9HioKX7B6tJPNaTGaLf3QhFpU8uhgfRIu1+Da9sBJB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\nTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7fd5bc480b00>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "n=50\n", + "x=rechte_seite(n)\n", + "x=x.reshape(n-1,n-1)\n", + "plt.imshow(x)\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Jetzt, lösen der Gleichung und anschließend plotten des Bildes:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:5: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n" + ] + }, + { + "data": { + "image/png": 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yX06n6urxbv0tsgkJtFlMizYkFiR1t5XT8XNERZ1T5Z76OwR6OrHILdUtYTea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\n/ngpEvfuCQ7/8cb4fSGGzNbDzTvxvFTuOhB9DerQK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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fd59ac2fc50>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n=50\n", + "x=rechte_seite(n)\n", + "A=poisson2d_matrix(n)\n", + "\n", + "L=tril(cholesky(A))\n", + "u=rueckwaertselimination(L.T.conj(),vorwaertselimination(L,x))\n", + "u=u.reshape(n-1,n-1)\n", + "plt.imshow(u)\n", + "plt.colorbar()\n", + "plt.show()" + ] + } + ], + "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 +} diff --git a/03_ellipsen_fits.ipynb b/03_ellipsen_fits.ipynb new file mode 100644 index 0000000..340d815 --- /dev/null +++ b/03_ellipsen_fits.ipynb @@ -0,0 +1,191 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aufgabe 12\n", + "__Aufgabe:__ Fitten Sie an die gegebenen Daten Ellipsen an:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from numpy import array,load\n", + "\n", + "daten=load('dataEllipse.npz')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Da wir mehrfach die gleichen Auswertungen vornehmen, schreiben wir uns eine Funktion, die das lineare Ausgleichsproblem aufstellt und löst." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ -2. -0.5 -1. 1. 20. ]\n" + ] + } + ], + "source": [ + "from numpy import ones\n", + "from numpy.linalg import lstsq\n", + "\n", + "def fit_ellipse_coeff(xData,yData):\n", + " # rechte Seite des Gleichungsstems, gegeben durch x^2\n", + " b=xData**2\n", + " # Die Matrix hat die Spalten yData^2, xData*yData , xData, yData ,1\n", + " n=max(xData.shape)\n", + " A=ones([n,5])\n", + " A[:,0]=yData**2\n", + " A[:,1]=xData*yData\n", + " A[:,2]=xData\n", + " A[:,3]=yData\n", + " x=lstsq(A,b)\n", + " return x[0]\n", + "\n", + "coeffTrue=fit_ellipse_coeff(daten['xtrue'],daten['ytrue'])\n", + "print(coeffTrue)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Die ausgegebenen Daten geben Die Koeffizienten a,...,e der Ellipse an. Diese entsprechen auch tatsächlich den Werten die benutzt wurden um die Daten zu erstellen." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "from numpy import array, ogrid, broadcast_arrays\n", + "\n", + "def plotEllipseData(xData,yData,ellipsenCoeff):\n", + " # Input:\n", + " # xData: Vektor, behinhaltet die x-Koordianten die zum fitten verwendet wurden\n", + " # yData: Vektor, behinhaltet die y-Koordianten die zum fitten verwendet wurden\n", + " # ellipsenCoeff: Vektor der Form [a,b,c,d,e]\n", + " x,y=ogrid[-5.5:4.5:1000j,-4:4:1000j]\n", + " x, y = broadcast_arrays(x, y)\n", + " z=-x**2+ellipsenCoeff[0]*y**2+ellipsenCoeff[1]*x*y+ellipsenCoeff[2]*x+ellipsenCoeff[3]*y+ellipsenCoeff[4]\n", + " \n", + " plt.plot(xData,yData,'x')\n", + " plt.contour(x,y,z,[0],colors='red')\n", + " plt.show()\n", + " return None " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Jetzt plotten wir alle vier Ellipsen und ihre zugehörigen Daten:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XG8Ri8m/Z0ur8T5oUdCQiIhKnQiErAJT+x33kTPwJVq36c0XAAMVe8ncOTjoJ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\nICIiRdp5AXDKCjLPeZL0euM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++8LYsWFHIiIiCaawEIauHcikGicwdHBJzGz2o+QP0KsXvPkmlJSEHYmIiCSI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\niCQZJX8REZEko+QvIiKSZJT8RUREkoy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ghz9JUo4VCslCfw0Nyay/eQh+8MpfkpRjpRJMm5YE/7Rpy+4EONgY/pKkXOr+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\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f3b00267a90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plotEllipseData(daten['xtrue'],daten['ytrue'],coeffTrue)\n", + "plotEllipseData(daten['x1'],daten['y1'],fit_ellipse_coeff(daten['x1'],daten['y1']))\n", + "plotEllipseData(daten['x2'],daten['y2'],fit_ellipse_coeff(daten['x2'],daten['y2']))\n", + "plotEllipseData(daten['x3'],daten['y3'],fit_ellipse_coeff(daten['x3'],daten['y3']))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Während der Unterschied zwischen den ersten beiden Ellipsen fast nicht sichtbar ist, unterscheiden sich die letzten beiden stark von der \"wahren\" Ellipse." + ] + } + ], + "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