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annotate matrixcomp/strassenw.m @ 0:8f23314345f4 draft
Create local repository for matrix toolboxes. Step #0 done.
author | Antonio Pino Robles <data.script93@gmail.com> |
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date | Wed, 06 May 2015 14:56:53 +0200 |
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Create local repository for matrix toolboxes. Step #0 done.
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1 function C = strassenw(A, B, nmin) |
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2 %STRASSENW Strassen's fast matrix multiplication algorithm (Winograd variant). |
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3 % C = STRASSENW(A, B, NMIN), where A and B are matrices of dimension |
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4 % a power of 2, computes the product C = A*B. |
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5 % Winograd's variant of Strassen's algorithm is |
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6 % used recursively until dimension <= NMIN is reached, |
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7 % at which point standard multiplication is used. |
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8 % The default is NMIN = 8 (which minimizes the total number of |
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9 % operations). |
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10 |
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11 % Reference: |
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12 % N. J. Higham, Accuracy and Stability of Numerical Algorithms, |
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13 % Second edition, Society for Industrial and Applied Mathematics, |
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14 % Philadelphia, PA, 2002; chap. 23. |
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15 |
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16 if nargin < 3, nmin = 8; end |
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17 |
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18 n = length(A); |
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19 if n ~= 2^( log2(n) ) |
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20 error('The matrix dimension must be a power of 2.') |
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21 end |
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22 |
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23 if n <= nmin |
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24 C = A*B; |
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25 else |
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26 m = n/2; i = 1:m; j = m+1:n; |
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27 |
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28 S1 = A(j,i) + A(j,j); |
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29 S2 = S1 - A(i,i); |
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30 S3 = A(i,i) - A(j,i); |
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31 S4 = A(i,j) - S2; |
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32 S5 = B(i,j) - B(i,i); |
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33 S6 = B(j,j) - S5; |
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34 S7 = B(j,j) - B(i,j); |
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35 S8 = S6 - B(j,i); |
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36 |
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37 M1 = strassenw( S2, S6, nmin); |
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38 M2 = strassenw( A(i,i), B(i,i), nmin); |
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39 M3 = strassenw( A(i,j), B(j,i), nmin); |
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40 M4 = strassenw( S3, S7, nmin); |
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41 M5 = strassenw( S1, S5, nmin); |
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42 M6 = strassenw( S4, B(j,j), nmin); |
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43 M7 = strassenw( A(j,j), S8, nmin); |
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44 |
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45 T1 = M1 + M2; |
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46 T2 = T1 + M4; |
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47 |
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48 C = [ M2+M3 T1+M5+M6; T2-M7 T2+M5 ]; |
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49 |
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