AAE-NA-Labs/Direct Methods for Solving Linear Systems/Alg11.m

25 lines
370 B
Matlab

function [Q R] = Alg11(A)
% Algorithm 11: QR factorization via Householder algorithm.
[m, n] = size(A);
if ~ (m>=n)
error("m has to be greater or equal n!")
end
for j = 1:n
[v, beta] = householder(A(j:m, j))
A(j:m, j:n) = (eye(m-j+1)-beta*(v*v.'))*A(j:m, j:n)
if j < m
A(j+1:m, j) = v(2:m-j+1)
end
end
R = triu(A)
H = tril(A, -1)
end