LU LU LU Decomposition for Matrices

Usage

Computes the LU decomposition for a matrix.  The form of the
command depends on the type of the argument.  For full (non-sparse)
matrices, the primary form for lu is

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

where L is lower triangular, U is upper triangular, and
P is a permutation matrix such that L*U = P*A.  The second form is

   [V,U] = lu(A),

where V is P'*L (a row-permuted lower triangular matrix), 
and U is upper triangular.  For sparse, square matrices,
the LU decomposition has the following form:

   [L,U,P,Q,R] = lu(A),

where A is a sparse matrix of either double or dcomplex type.
The matrices are such that L*U=P*R*A*Q, where L is a lower triangular
matrix, U is upper triangular, P and Q are permutation vectors
and R is a diagonal matrix of row scaling factors.  The decomposition
 is computed using UMFPACK for sparse matrices, and LAPACK for dense
 matrices.