Man Scilab

lu
Scilab Function

lu - LU factors of Gaussian elimination

Calling Sequence

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

Parameters

Description

[L,U]= lu(A) 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.

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

If A is a real matrix, using the function lufact and luget it is possible to obtain the permutation matrices and also when A is not full rank the column compression of the matrix L .

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.

Back