33 lines
637 B
Matlab
33 lines
637 B
Matlab
function b = Alg4(U,b)
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% Argorithm 4: Back Substitution
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% b = Alg4_back_substitution(U,b) returns vetor b with solution to the
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% Ux = b.
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[m, n] = size(U);
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if U ~= triu(U)
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error('Matrix U is not upper triangular!')
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end
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if m ~= n
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error('Matrix is not squared!')
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end
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if length(b) ~= m
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error('Vector b has wrong length!')
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end
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% if det(U) < eps
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% error('Matrix is not nonsingular!')
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% end
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% The following algorithm is based on the Algrotihm 3.1.2 from [2].
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% b(m, :) so that matrices are also accepted
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b(m, :) = b(m, :)/U(m, m);
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for i = m-1:-1:1
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b(i, :) = (b(i, :) - U(i, i+1 : m)*b(i+1 : m, :))/U(i, i);
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end
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end |