54 lines
1.3 KiB
Matlab
54 lines
1.3 KiB
Matlab
function [L, U, P] = Alg8(A)
|
||
% LU Factorization with partial pivoting
|
||
% [L, U, P] = Alg8(A) decomposes matrix A using Crout's algorithm into
|
||
% U – upper triangular matrix and L – unit lower triangular matrix
|
||
% using partial pivoting, interchanging A's rows, such that AP = LU.
|
||
|
||
[m, n] = size(A);
|
||
|
||
L = zeros(m, n);
|
||
U = eye(m, n);
|
||
P = eye(m, n);
|
||
|
||
for k = 1:m
|
||
if A(k, k) == 0
|
||
non_zero_col = find(A(k, :), 1);
|
||
A(:, [k non_zero_col]) = deal(A(:, [non_zero_col k]));
|
||
P(:, [k non_zero_col]) = deal(P(:, [non_zero_col k]));
|
||
end
|
||
end
|
||
|
||
% TODO: Permutation A*P does not work
|
||
|
||
|
||
%
|
||
% for i = m + 1 : M
|
||
% A(i:end, m+1:end); % Partial matrix (in which we are looking for non-zero pivots)
|
||
% A(i:end, m+1); % Left-most column
|
||
% if ~any(A(i:end, m+1)) % If the left-most column has only zeros check the next one
|
||
% m = m + 1;
|
||
% end
|
||
% A(i:end, m+1:end);
|
||
% if A(i, m+1) == 0
|
||
% non_zero_row = find(A(i:end,m+1), 1);
|
||
% if isempty(non_zero_row)
|
||
% continue
|
||
% end
|
||
% A([i, i+non_zero_row-1], :) = deal(A([i+non_zero_row-1, i], :));
|
||
% end
|
||
% end
|
||
|
||
for k = 1:n
|
||
|
||
for j = k : n
|
||
U(k, j) = A(k, j) - dot(L(k, 1:k-1), U(1:k-1, j));
|
||
end
|
||
|
||
for i = k:n
|
||
L(i, k) = (A(i, k) - dot(L(i,1:k-1), U(1:k-1, k))) / U(k,k);
|
||
end
|
||
|
||
|
||
end
|
||
|
||
end |