43 lines
1.1 KiB
Matlab
43 lines
1.1 KiB
Matlab
function [P, Q, L, U] = Alg2_gaussian_elimination_with_complete_pivoting(A)
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% Algorithm 2: Gaussian Elimination with Complete Pivoting.
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% [P, Q, L, U] = Alg2_gaussian_elimination_with_complete_pivoting(A)
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[n, m] = size(A);
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if n ~= m
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error('Matrix is not squared!')
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end
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% if det(A) == 0
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% error('Matrix is not nonsingular!')
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% end
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p = 1:n;
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q = 1:n;
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for k = 1 : n-1
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i = k:n;
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j = k:n;
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[max_val, rows_of_max_in_col] = max(abs(A(i, j)));
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[~, max_col] = max(max_val);
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max_row = rows_of_max_in_col(max_col);
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% Assign value of mu and lambda in respect to the main A matrix
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[mi, lm] = deal(max_row+k-1, max_col+k-1);
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A([k mi], 1:n) = deal(A([mi k], 1:n));
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A(1:n, [k lm]) = deal(A(1:n, [lm k]));
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p([k, mi]) = p([mi, k]);
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q([k, lm]) = q([lm, k]);
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% Perform Gaussian elimination with the greatest pivot
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if A(k, k) ~= 0
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rows = k+1 : n;
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A(rows, k) = A(rows, k)/A(k, k);
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A(rows, rows) = A(rows, rows) - A(rows, k) * A(k, rows);
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end
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end
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I = eye(n);
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U = triu(A);
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L = tril(A, -1) + I;
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P = I(p, :);
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Q = I(:, q); |