====================================================================
dgetrf examples
====================================================================

====================================================================
Man Page Details
====================================================================

NAME
       DGETRF - 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 diago-
       nal 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 fac-
               tors L and U from the factorization A = P*L*U; the unit  diago-
               nal 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.

