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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.
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1 function X = rootpm_sign(A,p)
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2 %ROOTPM_SIGN Matrix Pth root via matrix sign function.
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3 % X = ROOTPM_SIGN(A,P) computes the principal Pth root X
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4 % of the matrix A using the matrix sign function and a block
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5 % companion matrix approach.
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6
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7 if p == 1, X = A; return, end
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8
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9 n = length(A);
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10 podd = rem(p,2);
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11
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12 Y = A;
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13
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14 if podd
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15 p = 2*p; % Compensate by squaring at end.
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16 else
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17 while mod(p,4) == 0
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18 Y = sqrtm(Y);
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19 p = round(p/2);
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20 end
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21 end
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22
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23 if p == 2
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24 X = sqrtm(Y);
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25 return
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26 end
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27
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28 % Form C, the block companion matrix.
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29 C = zeros(p*n);
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30 C(end-n+1:end, 1:n) = Y;
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31 C = C + diag(ones(n*(p-1),1),n);
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32
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33 S = signm(C);
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34
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35 X = S(n+1:2*n,1:n);
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36
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37 % Scale factor.
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38 c = 0;
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39 for l = 1:floor(p/4)
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40 c = c+cos(2*pi*l/p);
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41 end
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42 c = c*4+2;
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43 c = c/p;
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44 X = X/c;
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45 if podd
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46 X = X*X;
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47 end