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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function [X,k] = sqrtm_newton(A,scal,maxit)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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2 %SQRTM_NEWTON Matrix square root by Newton iteration (unstable).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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3 % [X,k] = SQRTM_NEWTON(A,SCAL,MAXIT) computes the principal
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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4 % square root X of the matrix A by an unstable Newton iteration.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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5 % SCAL specifies whether scaling is used (SCAL = 1) or not
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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6 % (SCAL = 0, default).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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7 % MAXIT (default 25) is the maximum number of iterations allowed.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8 % k is the number of iterations.
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9
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10 n = length(A);
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11 if nargin < 2, scal = 0; end
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12 if nargin < 3, maxit = 25; end
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13
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14 tol = mft_tolerance(A);
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15 accel_tol = 1e-2; % Precise value not important.
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16 need_accel = 1;
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17
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18 X = A;
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20 for k = 1:maxit
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21
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22 if need_accel && scal > 0
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23 mu = (abs(det(X))/sqrt(abs(det(A))))^(-1/n);
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24 X = mu*X;
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25 end
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26
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27 Xold = X;
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28 X = (X + X\A)/2;
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29
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30 reldiff = norm(X-Xold,'fro')/norm(X,'fro');
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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31 if need_accel && (reldiff < accel_tol), need_accel = false; end
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32
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33 if reldiff <= tol, return, end
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34
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35 end
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36 error('Not converged after %2.0f iterations', maxit)