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