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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 [P,s,cost] = polyvalm_ps(c,A,s)
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2 %POLYVALM_PS Evaluate polynomial at matrix argument by Paterson-Stockmeyer alg.
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3 % [P,S,COST] = POLYVALM_PS(C,A,S) evaluates the polynomial whose
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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4 % coefficients are the vector C at the matrix A using the
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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5 % Paterson-Stockmeyer algorithm. If omitted, the integer parameter
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6 % S is chosen automatically and its value is returned as an
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7 % output argument. COST is the number of matrix multiplications used.
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9 m = length(c)-1; % Degree of poly.
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10 c = c(end:-1:1); c = c(:);
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11 n = length(A);
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12
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13 if nargin < 3
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14 % Determine optimum parameter s.
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15 s = ceil(sqrt(m));
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16 end
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17 r = floor(m/s);
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18 cost = s+r-(m==r*s)-1;
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20 % Apower{i+1} = A^i;
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21 Apower = cell(s+1);
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22 Apower{1} = eye(n);
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23 for i=2:s+1
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24 Apower{i} = A*Apower{i-1};
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25 end
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26
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27 B = cell(r+1);
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28 for k=0:r-1
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29 temp = c(s*k+1)*eye(n);
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30 for j=1:s-1
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31 temp = temp + c(s*k+j+1)*Apower{j+1};
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32 end
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33 B{k+1} = temp;
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34 end
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35 B{r+1} = c(m+1)*Apower{m-s*r+1};
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36 for j=m-1:-1:s*r
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37 if j == s*r
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38 B{r+1} = B{r+1} + c(s*r+1)*eye(n);
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39 else
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40 B{r+1} = B{r+1} + c(j+1)*Apower{m-s*r-(m-j)+1};
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41 end
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42 end
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43
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44 As = Apower{s+1};
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45 P = zeros(n);
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46 for k=r:-1:0
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47 P = P*As + B{k+1};
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48 end