35 lines
720 B
Matlab
35 lines
720 B
Matlab
function [L, U] = Alg7(A)
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% LU Factorization without pivoting
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% [L, U] = Alg7(A) decomposes matrix A using Crout's algorithm into
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% U – upper triangular matrix and L – unit lower triangular matrix
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% such that A = LU.
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[m, n] = size(A);
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% This solution is mathematically correct, however computationaly
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% inefficient.
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%
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% A = Alg1_outer_product_gaussian_elimination(A);
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%
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% U = triu(A);
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% L = tril(A, -1) + eye(m);
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% Instead, we should use the Crout's algorithm
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L = zeros(m, n);
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U = eye(m, n);
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for k = 1:n
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for j = k : n
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U(k, j) = A(k, j) - dot(L(k, 1:k-1), U(1:k-1, j));
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end
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for i = k:n
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L(i, k) = (A(i, k) - dot(L(i,1:k-1), U(1:k-1, k))) / U(k,k);
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end
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end
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end |