47 lines
1.3 KiB
Matlab
47 lines
1.3 KiB
Matlab
function [P, Q, L, U] = Alg2(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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% computes the complete pivoting factorization PAQ = LU.
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[m, n] = size(A);
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if m ~= n
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error('Matrix is not square!')
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end
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% p and q are permutation vectors – respectively rows and columns
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p = 1:m;
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q = 1:m;
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% The following algorithm is based on the Algrotihm 3.4.2 from [2].
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for k = 1 : m-1
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i = k:m;
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j = k:m;
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% Find the maximum entry to be the next pivot
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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 matrix A
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[mi, lm] = deal(max_row+k-1, max_col+k-1);
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% Interchange the rows and columns of matrix A...
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A([k mi], 1:m) = deal(A([mi k], 1:m));
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A(1:m, [k lm]) = deal(A(1:m, [lm k]));
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% ...and respective permutation vectors entries.
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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 : m;
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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(m);
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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);
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end |