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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,m] = logm_iss(A)
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2 %LOGM_ISS Matrix logarithm by inverse scaling and squaring method.
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3 % X = LOGM_ISS(A) computes the logarithm of A, for a matrix with no
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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4 % nonpositive real eigenvalues, using the inverse scaling and squaring
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5 % method with Pade approximation.
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6 % Matrix square roots are computed by the product form of the
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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7 % Denman-Beavers teration.
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8 % [X,K,M] = LOGM_ISS(A) returns the number K of square roots
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 % computed and the degree M of the Pade approximant.
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10
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11 e = eig(A);
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12 if any( imag(e) == 0 & real(e) <= 0 )
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13 error('A must not have any nonpositive real eigenvalues!')
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14 end
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16 n = length(A);
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17
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18 load log_pade_err_opt % mmax-by-3 matrix DATA.
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19 % mvals = data(:,1);
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20 xvals = data(:,2);
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21
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22 X = A;
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23 k = 0; p = 0; itk = 5;
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24
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25 while 1
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27 normdiff = norm(X-eye(n),1);
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28 if normdiff <= xvals(16)
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29
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30 p = p+1;
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31 j1 = find(normdiff <= xvals(3:16));
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32 j1 = j1(1) + 2;
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33 j2 = find(normdiff/2 <= xvals(3:16));
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34 j2 = j2(1) + 2;
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35 if 2*(j1-j2)/3 < itk || p == 2, m = j1; break, end
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37 end
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39 [X,M,itk] = sqrtm_dbp(X,1); k = k+1;
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41 end
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43 X = 2^k*logm_pade_pf(X-eye(n),m);
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44 if isreal(A), X = real(X); end