Mercurial > matrix-functions
comparison matrixcomp/gs_c.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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-1:000000000000 | 0:8f23314345f4 |
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1 function [Q, R] = gs_c(A) | |
2 %GS_C Classical Gram-Schmidt QR factorization. | |
3 % [Q, R] = GS_C(A) uses the classical Gram-Schmidt method to compute the | |
4 % factorization A = Q*R for m-by-n A of full rank, | |
5 % where Q is m-by-n with orthonormal columns and R is n-by-n. | |
6 | |
7 % Reference: | |
8 % N. J. Higham, Accuracy and Stability of Numerical Algorithms, | |
9 % Second edition, Society for Industrial and Applied Mathematics, | |
10 % Philadelphia, PA, 2002; sec 19.8. | |
11 | |
12 [m, n] = size(A); | |
13 Q = zeros(m,n); | |
14 R = zeros(n); | |
15 | |
16 for j=1:n | |
17 R(1:j-1,j) = Q(:,1:j-1)'*A(:,j); | |
18 temp = A(:,j) - Q(:,1:j-1)*R(1:j-1,j); | |
19 R(j,j) = norm(temp); | |
20 Q(:,j) = temp/R(j,j); | |
21 end |