Algorithme de la Factorisation LU en Matlab

Algorithme de la Factorisation LU en Matlab :

function [L,U,P] = lu_dcmp(A) %This gives LU decomposition of A with the permutation matrix P % denoting the row switch(exchange) during factorization NA = size(A,1); AP = [A eye(NA)]; %augment with the permutation matrix. for k = 1:NA - 1 %Partial Pivoting at AP(k,k) [akx, kx] = max(abs(AP(k:NA,k))); if akx < eps error(’Singular matrix and No LU decomposition’) end mx = k+kx-1; if kx > 1 % Row change if necessary tmp_row = AP(k,:); AP(k,:) = AP(mx,:); AP(mx,:) = tmp_row; end % LU decomposition for m = k + 1: NA AP(m,k) = AP(m,k)/AP(k,k); %Eq.(2.4.8.2) AP(m,k+1:NA) = AP(m,k + 1:NA)-AP(m,k)*AP(k,k + 1:NA); %Eq.(2.4.9) end end P = AP(1:NA, NA + 1:NA + NA); %Permutation matrix for m = 1:NA for n = 1:NA if m == n, L(m,m) = 1.; U(m,m) = AP(m,m); elseif m > n, L(m,n) = AP(m,n); U(m,n) = 0.; else L(m,n) = 0.; U(m,n) = AP(m,n); end end end if nargout == 0, disp(’L*U = P*A with’); L,U,P, end %You can check if P’*L*U = A?