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author Antonio Pino Robles <data.script93@gmail.com>
date Fri, 29 May 2015 09:48:36 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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1 function [C,S,cost,s] = cosmsinm(A)
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2 %COSMSINM Matrix cosine and sine by double angle algorithm.
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3 % [C,S,COST,s] = COSMSINM(A) computes the cosine C and the sine S
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4 % of the matrix A using the double angle algorithm with Pade
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5 % approximation. The total number of matrix multiplications and
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6 % linear systems solved is returned as COST and s specifies the
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7 % amount of scaling (A is scaled to 2^(-s)*A).
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8
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9 n = length(A);
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10 theta = [0.00613443965526 0.11110098037055 0.43324697422211 0.98367255274344 ...
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11 1.72463663220280 2.61357494421368 3.61521023400301 4.70271938553349 ...
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12 5.85623410320942 7.06109053959248 0 9.58399601173102];
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13
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14 normA = norm(A,inf);
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15 d = [2 4 6 8 10 12 14 16 20];
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16 for i = d(1:8)
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17 if normA <= theta(i/2);
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18 m = i;
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19 cost = m/2+3;
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20 [C,S] = cosmsinm_pade(A,m);
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21 s = m;
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22 return
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23 end
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24 end
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25
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26 s = 0;
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27 if normA > theta(20/2)
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28 s = max( ceil( log2( normA/theta(20/2) ) ), 1 );
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29 A = A/(2^s);
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30 normA = normA/(2^s);
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31 end
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32
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33 if normA > 2*theta(12/2)
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34 m = 20; cost = 12;
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35 elseif normA > theta(16/2)
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36 A = A/2; m = 12; cost = 9; s = s+1;
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37 else
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38 m = 16; cost = 11;
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39 end
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40
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41 [C,S] = cosmsinm_pade(A,m);
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42 for i = 1:s
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43 S = 2*S*C;
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44 C = 2*(C^2) - eye(n);
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45 end
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46 cost = cost + 2*s;