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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,M,k] = sqrtm_dbp(A,scale)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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2 %SQRTM_DBP Matrix square root by product form of Denman-Beavers iteration.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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3 % [X,M,k] = SQRTM_DBP(A,SCAL) computes the principal square root X
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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4 % of the matrix A using the product form of the Denman-Beavers
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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5 % iteration. The matrix M tends to EYE.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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6 % SCAL specifies the scaling:
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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7 % SCAL == 0, no scaling.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8 % SCAL == 1, determinantal scaling (default).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 % k is the number of iterations.
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10
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11 n = length(A);
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12 if nargin < 2, scale = 1; end
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13
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14 tol = mft_tolerance(A);
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15 X = A;
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16 M = A;
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17 maxit = 25;
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18
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19 for k = 1:maxit
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20
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21 if scale == 1
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22 g = (abs(det(M)))^(-1/(2*n));
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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23 X = g*X; M = g^2*M;
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24 end
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25
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26 Xold = X; invM = inv(M);
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27
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28 X = X*(eye(n) + invM)/2;
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29 M = 0.5*(eye(n) + (M + invM)/2);
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31 Mres = norm(M - eye(n),'fro');
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33 reldiff = norm(X - Xold,'fro')/norm(X,'fro');
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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34 if reldiff < 1e-2, scale = 0; end % Switch to no scaling.
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35
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36 if Mres <= tol, return; end
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37
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38 end
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39 error('Not converged after %2.0f iterations', maxit)