19 lines
436 B
Mathematica
19 lines
436 B
Mathematica
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function [Q, R] = Alg13(A)
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% Algorithm 13: The QR algorithm by the Gram-Schmidt ortogonalization
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% [Q, R] = Alg13(A)
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% Based on [GVL96]: Section 5.2.8
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[m,n] = size(A);
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if ~ (m >= n)
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error("m has to be greater or equal n!")
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end
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R = zeros(n, n);
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Q = zeros(m, n);
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for k = 1:n
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R(k, k) = norm(A(:, k));
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Q(:, k) = A(:, k)/R(k, k);
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R(k, k+1:n) = Q(:, k)'*A(:, k+1:n);
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A(:, k+1:n) = A(:, k+1:n) - Q(:, k)*R(k, k+1:n);
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end
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