Mercurial > matrix-functions
view matrixcomp/strassenw.m @ 0:8f23314345f4 draft
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 |
parents | |
children |
line wrap: on
line source
function C = strassenw(A, B, nmin) %STRASSENW Strassen's fast matrix multiplication algorithm (Winograd variant). % C = STRASSENW(A, B, NMIN), where A and B are matrices of dimension % a power of 2, computes the product C = A*B. % Winograd's variant of Strassen's algorithm is % used recursively until dimension <= NMIN is reached, % at which point standard multiplication is used. % The default is NMIN = 8 (which minimizes the total number of % operations). % Reference: % N. J. Higham, Accuracy and Stability of Numerical Algorithms, % Second edition, Society for Industrial and Applied Mathematics, % Philadelphia, PA, 2002; chap. 23. if nargin < 3, nmin = 8; end n = length(A); if n ~= 2^( log2(n) ) error('The matrix dimension must be a power of 2.') end if n <= nmin C = A*B; else m = n/2; i = 1:m; j = m+1:n; S1 = A(j,i) + A(j,j); S2 = S1 - A(i,i); S3 = A(i,i) - A(j,i); S4 = A(i,j) - S2; S5 = B(i,j) - B(i,i); S6 = B(j,j) - S5; S7 = B(j,j) - B(i,j); S8 = S6 - B(j,i); M1 = strassenw( S2, S6, nmin); M2 = strassenw( A(i,i), B(i,i), nmin); M3 = strassenw( A(i,j), B(j,i), nmin); M4 = strassenw( S3, S7, nmin); M5 = strassenw( S1, S5, nmin); M6 = strassenw( S4, B(j,j), nmin); M7 = strassenw( A(j,j), S8, nmin); T1 = M1 + M2; T2 = T1 + M4; C = [ M2+M3 T1+M5+M6; T2-M7 T2+M5 ]; end