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author Antonio Pino Robles <data.script93@gmail.com>
date Fri, 29 May 2015 09:48:36 +0200
parents 8f23314345f4
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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1 function [P,Q,k] = sqrtm_db(A,scale)
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2 %SQRTM_DB Matrix square root by Denman-Beavers iteration.
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3 % [P,Q,k] = SQRTM_DB(A,SCAL) computes the principal square root
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4 % P of the matrix A using the Denman-Beavers iteration.
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5 % It also returns Q = INV(P).
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6 % SCAL specifies the scaling:
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7 % SCAL == 0, no scaling.
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8 % SCAL == 1, determinantal scaling (default).
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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 P = A;
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16 Q = eye(n);
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17 reldiff = inf;
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18 maxit = 25;
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19
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20 for k = 1:maxit
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21
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22 if scale == 1
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23 g = (abs(det(P)*det(Q)))^(-1/(2*n));
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24 P = g*P; Q = g*Q;
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25 end
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26
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27 Pold = P;
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28
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29 Poldinv = inv(Pold);
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30 P = (P + inv(Q))/2;
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31 Q = (Q + inv(Pold))/2;
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32
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33 diff_F = norm(P-Pold,'fro');
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34 reldiff_old = reldiff;
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35 reldiff = diff_F/norm(P,'fro');
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36 if reldiff < 1e-2, scale = 0; end % Switch to no scaling.
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37
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38 cged = (diff_F <= sqrt( tol*norm(P)/norm(Poldinv) ) || ...
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39 reldiff > reldiff_old/2 && ~scale);
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40 if cged, return, end
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41
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42 end
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43 error('Not converged after %2.0f iterations', maxit)