dgetrf(3F)

NAME
     DGETRF - compute an LU factorization of a general M-by-N matrix A using
     partial pivoting with row interchanges

SYNOPSIS
     SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )

         INTEGER        INFO, LDA, M, N

         INTEGER        IPIV( * )

         DOUBLE         PRECISION A( LDA, * )

PURPOSE
     DGETRF computes an LU factorization of a general M-by-N matrix A using
     partial pivoting with row interchanges.

     The factorization has the form
        A = P * L * U
     where P is a permutation matrix, L is lower triangular with unit diagonal
     elements (lower trapezoidal if m > n), and U is upper triangular (upper
     trapezoidal if m < n).

     This is the right-looking Level 3 BLAS version of the algorithm.


ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A.  M >= 0.

     N       (input) INTEGER
             The number of columns of the matrix A.  N >= 0.

     A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
             On entry, the M-by-N matrix to be factored.  On exit, the factors
             L and U from the factorization A = P*L*U; the unit diagonal
             elements of L are not stored.

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,M).

     IPIV    (output) INTEGER array, dimension (min(M,N))
             The pivot indices; for 1 <= i <= min(M,N), row i of the matrix
             was interchanged with row IPIV(i).

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, U(i,i) is exactly zero. The factorization has
             been completed, but the factor U is exactly singular, and
             division by zero will occur if it is used to solve a system of
             equations.