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52 lines
1.5 KiB
Matlab
52 lines
1.5 KiB
Matlab
% [USES] ad-hoc/SST
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function [x] = GETotalPivoting(A, b)
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n = size(A)(1);
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% build the augmented matrix so we do less operations (tr. matrice extinsa)
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Ae = [A b];
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% build the permutation vector
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perm = [1:n];
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for p = 1 : n - 1
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% we find the absolute maximum from A(p:n, p:n) to use it as a pivot
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[pivot, pivot_line] = max(abs(Ae(p : n, p : n)));
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[pivot, pivot_column] = max(pivot);
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pivot_line = pivot_line + p - 1;
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pivot_line = pivot_line(pivot_column);
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pivot_column = pivot_column + p - 1;
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% get the new pivot on diagonal position
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temp = Ae(p, :);
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Ae(p, :) = Ae(pivot_line, :);
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Ae(pivot_line, :) = temp;
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temp = Ae(:, p);
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Ae(:, p) = Ae(:, pivot_column);
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Ae(:, pivot_column) = temp;
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% update the permutation vector
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temp = perm(p);
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perm(p) = perm(pivot_column);
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perm(pivot_column) = temp;
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% gaussian elimination
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for i = p + 1 : n
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% check if the pivot is 0, by comparing it to eps (a very small value)
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if abs(A(p, p)) < eps
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disp('One of the pivots is 0');
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x = NaN;
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return;
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endif
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arg = Ae(i, p) / Ae(p, p);
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Ae(i, :) = Ae(i, :) - arg * Ae(p, :);
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endfor
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endfor
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% solve the upper triangular system after separating A and b from Ae
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A = Ae(:, 1 : n);
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b = Ae(:, n + 1);
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x = SST(A, b);
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% apply the permutation vector to the solution
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x = x(perm);
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endfunction
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