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31 lines
933 B
Matlab
31 lines
933 B
Matlab
% [USES] ad-hoc/SST, ad-hoc/SIT
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function [L, U, x] = Crout(A, b)
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% U = eye(n) returns an n-by-n identity matrix with ones on the main
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% diagonal and zeros elsewhere
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% L = zeros(n) returns an n-by-n matrix of zeros
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n = length(b);
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L = zeros(n);
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U = eye(n);
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% Decomposition of matrix into L and U
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for i = 1 : n
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% calculate the lower triangular matrix
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sum_for_L = L(i : n, 1 : (i - 1)) * U(1 : (i - 1), i);
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L(i : n, i) = A(i : n, i) - sum_for_L;
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% calculate the upper triangular matrix
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sum_for_U = L(i, 1 : (i - 1)) * U(1 : (i - 1), (i + 1) : n);
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U(i, (i + 1) : n) = (A(i, (i + 1) : n) - sum_for_U) / L(i, i);
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endfor
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% A * x = b; A = L * U
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% L * U * x = b;
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% L * y = b => y (SIT)
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% U * x = y => x (SST)
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% Solve the lower triangular system
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y = SIT(L, b);
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% Solve the upper triangular system
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x = SST(U, y);
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endfunction
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