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.
 