lu - LU factors of Gaussian elimination

Calling Sequence

[L,U]= lu(A)

[L,U,E]= lu(A)

Parameters

• A : real or complex matrix (m x n).
• L : real or complex matrices (m x min(m,n)).
• U : real or complex matrices (min(m,n) x n ).
• E : a (n x n) permutation matrix.

Description

produces two matrices L and U such that A = L*U with U upper triangular and E*L lower triangular for a permutation matrix E.

If A has rank k, rows k+1 to n of U are zero.

produces three matrices L, U and E such that E*A = L*U with U upper triangular and E*L lower triangular for a permutation matrix E.

Examples

a=rand(4,4);
[l,u]=lu(a)
norm(l*u-a)


[h,rk]=lufact(sparse(a))  // lufact fonctionne avec des matrices creuses 
[P,L,U,Q]=luget(h);
ludel(h)
P=full(P);L=full(L);U=full(U);Q=full(Q); 
norm(P*L*U*Q-a) // P,Q sont des matrices de permutation

 

See Also

lufact  luget  lusolve  qr  svd  

Used Function

lu decompositions are based on the Lapack routines DGETRF for real matrices and ZGETRF for the complex case.