AAE-NA-Labs/Direct Methods for Solving Linear Systems/gauss_jordan_elimination.m
2021-03-06 20:58:52 +01:00

31 lines
696 B
Matlab

function A = gauss_jordan_elimination(A)
[n, m] = size(A);
if n ~= m
error('Matrix is not squared!')
end
if det(A) == 0
error('Matrix is not nonsingular!')
end
A
for k = 1 : n-1
i = k:n;
j = k:n;
A(i, j);
maximum = max(abs(A(i, j)), [], 'all');
max_idx = find(abs(A==maximum));
[mi, lm] = ind2sub(size(A), max_idx(1));
A([k mi], 1:n) = deal(A([mi k], 1:n));
A(1:n, [k lm]) = deal(A(1:n, [lm k]));
p(k) = mi;
q(k) = lm;
% Perform Gaussian elimination with the greatest pivot
if A(k, k) ~= 0
rows = k+1 : n;
A(rows, k) = A(rows, k)/A(k, k);
A(rows, rows) = A(rows, rows) - A(rows, k) * A(k, rows);
end
end