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