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% LU Matrix decomposition algorithm | |
% Author: Farhad Mehryari | |
% Web: blog.mrfarhad.ir | |
function [ L, U ] = LU(A) | |
% A شرط بررسی مربعی بودن ماتریس | |
sz = size(A); | |
if sz(1)~=sz(2) | |
fprintf('A is not square !\n'); | |
clear x; | |
return; | |
end | |
n = sz(1); | |
L = eye(n); | |
P = eye(n); | |
U = A; | |
for i=1:sz(1) | |
% کاهش سطری | |
if U(i,i)==0 | |
maximum = max(abs(U(i:end,1))); | |
for k=1:n | |
if maximum == abs(U(k,i)) | |
temp = U(1,:); | |
U(1,:) = U(k,:); | |
U(k,:) = temp; | |
temp = P(:,1); | |
P(1,:) = P(k,:); | |
P(k,:) = temp; | |
end | |
end | |
end | |
if U(i,i)~=1 | |
temp = eye(n); | |
temp(i,i)=U(i,i); | |
L = L * temp; | |
U(i,:) = U(i,:)/U(i,i); % بررسی اینکه محور ها الزاما یک باشند | |
end | |
if i~=sz(1) | |
for j=i+1:length(U) | |
temp = eye(n); | |
temp(j,i) = U(j,i); | |
L = L * temp; | |
U(j,:) = U(j,:)-U(j,i)*U(i,:); | |
end | |
end | |
end | |
end | |
% Author: Farhad Mehryari | |
% Web: blog.mrfarhad.ir |
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A=[4 5;6 8] | |
[l u]=LU(A) |
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