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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Chris Sullivan | Fast QR eigenvalue iteration with deflation and Wilkinson shifts" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In this work, we will explore a fast eigenvalue decomposition using QR factorization with reduction to upper-hessenberg (via householder reflections), tridiaganol in the case of symmetric matrices, and the use of givens rotators for the factorization. In addition, we will show how the Wilkinson shift converges with near cubic accuracy." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"hideCode": true, | |
"hideOutput": true, | |
"hidePrompt": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import numpy.linalg as la\n", | |
"from scipy.sparse import dia_matrix\n", | |
"from scipy.linalg import solve_banded" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"hideCode": true, | |
"hideOutput": true, | |
"hidePrompt": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import seaborn as sns\n", | |
"import matplotlib.pyplot as plt\n", | |
"sns.set_context(\"paper\",font_scale=1.75)\n", | |
"sns.set_style(\"ticks\")\n", | |
"%matplotlib inline\n", | |
"from scipy.optimize import curve_fit\n", | |
"from scipy.linalg import hilbert" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"hideCode": true, | |
"hideOutput": true, | |
"hidePrompt": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import contextlib\n", | |
"@contextlib.contextmanager\n", | |
"def printoptions(*args, **kwargs):\n", | |
" original = np.get_printoptions()\n", | |
" np.set_printoptions(*args, **kwargs)\n", | |
" try:\n", | |
" yield\n", | |
" finally: \n", | |
" np.set_printoptions(**original)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Using householder reflection matrices, we can build a routine to convert any matrix to upper-hessenberg form. For a symmetric matrix, reduction to upper-hessenberg will result in a tridiaganol matrix with which fast QR decomposition can be applied." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"hideOutput": true, | |
"hidePrompt": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def householder_reflector(x):\n", | |
" v = np.copy(x)\n", | |
" v[0] += np.sign(x[0])*np.linalg.norm(x,ord=2)\n", | |
" v /= la.norm(v,ord=2)\n", | |
" return v\n", | |
"\n", | |
"def householder_reduction_to_upper_hessenberg(A):\n", | |
" for i in range(len(A)-2):\n", | |
" v = householder_reflector(A[i+1:,i])\n", | |
" A[i+1:,i:] -= 2*np.outer(v,v.dot(A[i+1:,i:]))\n", | |
" A[:,i+1:] -= 2*np.outer(A[:,i+1:].dot(v),v)\n", | |
" return A" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Testing this implementation on the symmetric positive definite hilbert matrix of rank 4, a tridiagonal matrix is produced:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"hidePrompt": true | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"[ 1. -0.65085414 -0. -0. ]\n", | |
"[-0.65085414 0.65058548 0.06391188 0. ]\n", | |
"[ 0. 0.06391188 0.02532014 -0.00116521]\n", | |
"[ 0. -0. -0.00116521 0.00028485]\n" | |
] | |
} | |
], | |
"source": [ | |
"mat = householder_reduction_to_upper_hessenberg(hilbert(4))\n", | |
"with printoptions(precision=8, suppress=True):\n", | |
" for row in mat:\n", | |
" print(row)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"hidePrompt": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def givens_factors(x,y):\n", | |
" h = np.sqrt(np.square(x)+np.square(y))\n", | |
" return np.array([x,y])/h\n", | |
"\n", | |
"def qr_step(A):\n", | |
" givensfactors = []\n", | |
"\n", | |
" # R = G^T_n-1 ... G^T_1 * A where G^T is the transpose of the givens matrix\n", | |
" for i in range(len(A)-1):\n", | |
" c,s = givens_factors(A[i,i],A[i+1,i])\n", | |
" givensfactors.append([c,s])\n", | |
" A[i:i+2,i:] = np.array([[c,s],[-s,c]]).dot(A[i:i+2,i:])\n", | |
"\n", | |
" # A_k+1 = R * G_1 ... G_n-1\n", | |
" for i,(c,s) in enumerate(givensfactors):\n", | |
" A[:i+2, i:i+2] = A[:i+2,i:i+2].dot(np.array([[c,-s],[s,c]]))\n", | |
" return A\n", | |
"\n", | |
"\n", | |
"def qr(mat, qr_iteration=qr_step):\n", | |
" mat = np.copy(mat)\n", | |
" \n", | |
" m,n = mat.shape\n", | |
" niter = 0\n", | |
" mxm1 = []\n", | |
" diag = []\n", | |
" diagonal = np.zeros(m)\n", | |
" while True:\n", | |
" \n", | |
" mat = qr_iteration(mat)\n", | |
" mxm1.append(np.abs(mat[m-1,m-2]))\n", | |
" diagonal[0:m] = np.diag(mat)\n", | |
" diag.append(np.asarray(list(diagonal)))\n", | |
" niter += 1\n", | |
"\n", | |
" if mxm1[-1] < 1e-12:\n", | |
" yield niter,mat,mxm1,diag\n", | |
" mxm1 = []\n", | |
" diag = []\n", | |
" mat = mat[:-1,:-1]\n", | |
" m,n = mat.shape\n", | |
" if m < 2:\n", | |
" yield 0,mat,[],[]\n", | |
" return\n", | |
" niter = 0\n", | |
" \n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here is a small example of the qr method above in action, notice the matrix deflation that occurs at each step." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"hidePrompt": true | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Num iterations: 3\n", | |
"[ 1.61888942 -0.00379094 0. -0. 0. 0. ]\n", | |
"[-0.00379094 0.24237131 0.00003143 0. -0. 0. ]\n", | |
"[ 0. 0.00003143 0.01632153 -0.00000024 0. -0. ]\n", | |
"[ 0. 0. -0.00000024 0.00061575 0. 0. ]\n", | |
"[-0. 0. 0. 0. 0.00001257 0. ]\n", | |
"[ 0. 0. 0. 0. 0. 0.00000011]\n", | |
"\n", | |
"Num iterations: 2\n", | |
"[ 1.61889985 -0.00008496 0. -0. 0. ]\n", | |
"[-0.00008496 0.24236088 0.00000014 0. -0. ]\n", | |
"[ 0. 0.00000014 0.01632152 -0. 0. ]\n", | |
"[ 0. 0. -0. 0.00061575 0. ]\n", | |
"[-0. 0. 0. 0. 0.00001257]\n", | |
"\n", | |
"Num iterations: 2\n", | |
"[ 1.61889986 -0.0000019 0. -0. ]\n", | |
"[-0.0000019 0.24236087 0. 0. ]\n", | |
"[ 0. 0. 0.01632152 -0. ]\n", | |
"[ 0. 0. -0. 0.00061575]\n", | |
"\n", | |
"Num iterations: 3\n", | |
"[ 1.61889986 -0.00000001 0. ]\n", | |
"[-0.00000001 0.24236087 0. ]\n", | |
"[ 0. 0. 0.01632152]\n", | |
"\n", | |
"Num iterations: 5\n", | |
"[ 1.61889986 -0. ]\n", | |
"[-0. 0.24236087]\n", | |
"\n", | |
"Num iterations: 0\n", | |
"[ 1.61889986]\n", | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"mat = householder_reduction_to_upper_hessenberg(hilbert(6))\n", | |
"with printoptions(precision=8, suppress=True):\n", | |
" for n,T,mxm1,diag in qr(mat):\n", | |
" print(\"Num iterations: \",n)\n", | |
" for row in T:\n", | |
" print(row)\n", | |
" print()\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def driver(mat,qr_iteration=qr_step):\n", | |
" H = householder_reduction_to_upper_hessenberg(mat)\n", | |
" evals = []\n", | |
" ntotal = 0\n", | |
" mxm1s = []\n", | |
" diags = []\n", | |
" for niter,T,mxm1,diag in qr(H,qr_iteration=qr_iteration):\n", | |
" evals.append(T[-1,-1])\n", | |
" ntotal += niter\n", | |
" mxm1s.extend(mxm1)\n", | |
" diags.extend(diag)\n", | |
" return evals,[list(range(ntotal)),mxm1s],np.asarray(diags)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": { | |
"hideCode": true, | |
"hidePrompt": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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TjdeRgme3op5rinq3l1SZ3eDvJVXm91oAHEGatHICadTwCyNidtU2xwB/Twqu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\nQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b2697518>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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EzKwo26sZQZiZmVnz5d2gZn/SjnOHAR/IynYAbo+I97QuPDMzM6tX3pb854CPS3o9L61d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\nAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b281cbe0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"evals,semiology,diags = driver(hilbert(4))\n", | |
"fig,axes = plt.subplots()\n", | |
"axes.scatter(*semiology, color='red')\n", | |
"axes.set_yscale('log')\n", | |
"axes.set_ylim(1e-30,1e10)\n", | |
"axes.set_xlabel('QR iteration step')\n", | |
"axes.set_ylabel('|t$_{m,m-1}$|')\n", | |
"\n", | |
"fig,axes=plt.subplots()\n", | |
"color_idx = np.linspace(0, 1, len(diags[0]))\n", | |
"for n in range(len(diags[0])):\n", | |
" axes.plot(semiology[0],diags[:,n],color=plt.cm.inferno(color_idx[n]),label='$\\lambda_{'+str(n+1)+'}$')\n", | |
"axes.set_xlabel('QR iteration step')\n", | |
"axes.set_ylabel('Eigenvalue estimate')\n", | |
"axes.legend(loc='center right', bbox_to_anchor=(1.3,0.5))\n", | |
"axes.set_yscale('log')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"hidePrompt": true | |
}, | |
"source": [ | |
"Let's now define a different qr_step routine which incorporates the Wilkinson shift." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"metadata": { | |
"hidePrompt": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def qr_step_wilkinson(A):\n", | |
" \n", | |
" def shift(mat):\n", | |
" [[am1,bm1],[bm1,am]] = mat[-2:,-2:]\n", | |
" delta = (am1-am)/2\n", | |
" s = max(np.sign(delta),1)\n", | |
" return am-s*bm1*bm1/(np.abs(delta) + np.sqrt(delta*delta + bm1*bm1))\n", | |
" \n", | |
" \n", | |
" givensfactors = []\n", | |
" mu = shift(A)\n", | |
" A -= np.diag(np.ones(A.shape[0])*mu)\n", | |
" \n", | |
" # R = G^T_n-1 ... G^T_1 * A where G^T is the transpose of the givens matrix\n", | |
" for i in range(len(A)-1):\n", | |
" c,s = givens_factors(A[i,i],A[i+1,i])\n", | |
" givensfactors.append([c,s])\n", | |
" A[i:i+2,i:] = np.array([[c,s],[-s,c]]).dot(A[i:i+2,i:])\n", | |
"\n", | |
" # A_k+1 = R * G_1 ... G_n-1\n", | |
" for i,(c,s) in enumerate(givensfactors):\n", | |
" A[:i+2, i:i+2] = A[:i+2,i:i+2].dot(np.array([[c,-s],[s,c]]))\n", | |
" \n", | |
" A += np.diag(np.ones(A.shape[0])*mu)\n", | |
"\n", | |
" \n", | |
" return A" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": { | |
"hideCode": true, | |
"hidePrompt": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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5D1WP71WU8DsX+GBEvCwz729ZfejYD87MH46y6dbfWTPGW5uazWta6luZ+Xvg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\nsCw/AAAAAElFTkSuQmCC\n", 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"<matplotlib.figure.Figure at 0x7f07b263c908>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
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n0CR5YEOgE3iqrvwp4IC8N2lm6kFEzCJtFLBSthjOQ3nrNTMzG2wGU5IvTFFT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\nrKKc5M3MzCrq/wPYFwzhXadl7gAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b27b02b0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"evals,semiology,diags = driver(hilbert(6),qr_iteration=qr_step_wilkinson)\n", | |
"fig,axes = plt.subplots()\n", | |
"axes.scatter(*semiology, color='red')\n", | |
"axes.set_yscale('log')\n", | |
"axes.set_ylim(1e-30,1e10)\n", | |
"axes.set_xlabel('QR iteration step')\n", | |
"axes.set_ylabel('|t$_{m,m-1}$|')\n", | |
"\n", | |
"fig,axes=plt.subplots()\n", | |
"color_idx = np.linspace(0, 1, len(diags[0]))\n", | |
"for n in range(len(diags[0])):\n", | |
" axes.plot(semiology[0],diags[:,n],color=plt.cm.inferno(color_idx[n]),label='$\\lambda_{'+str(n+1)+'}$')\n", | |
"axes.set_xlabel('QR iteration step')\n", | |
"axes.set_ylabel('Eigenvalue estimate')\n", | |
"axes.legend(loc='center right', bbox_to_anchor=(1.3,0.5))\n", | |
"axes.set_yscale('log')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": { | |
"hideCode": true, | |
"hidePrompt": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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9QbrNU0DHWorf393frFHWMOBkd/92QQwbA9OB4929nivztcbfC3jlwQcfZKut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\nABhpZvqbNE4HYDdgWsHy7wG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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b2549630>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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WTo/WTZdC0BcqKXYBiaqqrV8m3eLuLWZ2OfAYUeX3QXf/W7bLyTSJVwI/LPb+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\nEKB/lyBuyc0AAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b266fcf8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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yycnfl7TvYJxDDrGT49q1yd4XRKvY1e20aSZmd96Zj2hNmVJ5vfhVaBrRqkXm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\nBweDlQV2HB58sPhreVtaYMc8FLiuXl3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MnGhtqHbsGJihePlyKyouNf1PvJNGKWusTril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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b296bf98>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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ZRrfTqza3w8oVm2neNp0mbRrXUu3EcaYR8L1SCsAOfKC1XlTThQQdxJVStwE3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\nUipMaRBXSimlwpQGcaWUUipM/X8mnyf8S2HdFAAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f07b25fd8d0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"mat = np.ones((15,15)) + np.diag(list(reversed(range(16)[:-1])))\n", | |
"for step in [qr_step,qr_step_wilkinson]:\n", | |
" evals,semiology,diags = driver(mat,qr_iteration=step)\n", | |
" fig,axes = plt.subplots()\n", | |
" axes.plot(*semiology, color='red')\n", | |
" axes.set_yscale('log')\n", | |
" axes.set_ylim(1e-30,1e10)\n", | |
" axes.set_xlabel('QR iteration step')\n", | |
" axes.set_ylabel('|t$_{m,m-1}$|')\n", | |
" axes.set_title(str(step.__name__))\n", | |
"\n", | |
" fig,axes=plt.subplots()\n", | |
" color_idx = np.linspace(0, 1, len(diags[0]))\n", | |
" for n in range(len(diags[0])):\n", | |
" axes.plot(semiology[0],diags[:,n],color=plt.cm.inferno(color_idx[n]),label='$\\lambda_{'+str(n+1)+'}$')\n", | |
" axes.set_xlabel('QR iteration step')\n", | |
" axes.set_ylabel('Eigenvalue estimate')\n", | |
" axes.set_title(str(step.__name__))\n", | |
" axes.legend(loc='center right', bbox_to_anchor=(1.3,0.5))\n", | |
" axes.set_yscale('log')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The convergence we observe in the standard QR step is linear for each eigenvalue, as can be clearly seen for the individual eigenvalues in the first plot above. For the QR step with the Wilkinson shift we see convergence in most cases which is between superlinear and quadratic (for a few of the eigenvalues we see it converging near cubicly, see the third plot above). The theoretical convergence rate is cubic with the Wilkinson shift. \n", | |
"\n", | |
"The number of QR itererations per eigenvalue is not particularly meaningful, as the number of steps to convergence is variable for each eigenvalue depending on the method utilized. For example, in the power iteration QR decomposition, the largest eigenvalues converge much more slowly than the smallest eigenvalues. Trying to describe the number of iterations per eigenvalue in a global way ignores these subtleties." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"celltoolbar": "Hide code", | |
"hide_code_all_hidden": false, | |
"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": "3.4.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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