*> \brief \b DGETRF
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
* 
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, M, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,M).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*>          IPIV is 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).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is 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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup doubleGEcomputational
*
*  =====================================================================
      SUBROUTINE GAL_DGETRF(M,N,A,LDA,IPIV,INFO)
*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER INFO,LDA,M,N
*     ..
*     .. Array Arguments ..
      INTEGER IPIV(*)
      DOUBLE PRECISION A(LDA,*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE
      PARAMETER (ONE=1.0D+0)
*     ..
*     .. Local Scalars ..
      INTEGER I,IINFO,J,JB,NB
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_DGEMM,GAL_DGETF2,GAL_DLASWP,GAL_DTRSM,GAL_XERBLA
*     ..
*     .. External Functions ..
      INTEGER GAL_ILAENV
      EXTERNAL GAL_ILAENV
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX,MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO=0
      IF(M.LT.0)THEN
      INFO=-1
      ELSE IF(N.LT.0)THEN
      INFO=-2
      ELSE IF(LDA.LT.MAX(1,M))THEN
      INFO=-4
      END IF
      IF(INFO.NE.0)THEN
      CALL GAL_XERBLA('GAL_DGETRF',-INFO)
      RETURN
      END IF
*
*     Quick return if possible
*
      IF(M.EQ.0.OR.N.EQ.0)
     $RETURN
*
*     Determine the block size for this environment.
*
      NB=GAL_ILAENV(1,'GAL_DGETRF','',M,N,-1,-1)
      IF(NB.LE.1.OR.NB.GE.MIN(M,N))THEN
*
*        Use unblocked code.
*
      CALL GAL_DGETF2(M,N,A,LDA,IPIV,INFO)
      ELSE 
*
*        Use blocked code.
*
      DO 20J=1,MIN(M,N),NB
      JB=MIN(MIN(M,N)-J+1,NB)
*
*           Factor diagonal and subdiagonal blocks and test for exact
*           singularity.
*
      CALL GAL_DGETF2(M-J+1,JB,A(J,J),LDA,IPIV(J),IINFO)
*
*           Adjust INFO and the pivot indices.
*
      IF(INFO.EQ.0.AND.IINFO.GT.0)
     $INFO=IINFO+J-1
      DO 10I=J,MIN(M,J+JB-1)
      IPIV(I)=J-1+IPIV(I)
   10 CONTINUE
*
*           Apply interchanges to columns 1:J-1.
*
      CALL GAL_DLASWP(J-1,A,LDA,J,J+JB-1,IPIV,1)
*
      IF(J+JB.LE.N)THEN
*
*              Apply interchanges to columns J+JB:N.
*
      CALL GAL_DLASWP(N-J-JB+1,A(1,J+JB),LDA,J,J+JB-1,
     $IPIV,1)
*
*              Compute block row of U.
*
      CALL GAL_DTRSM('LEFT','LOWER','NOTRANSPOSE','UNIT',JB,
     $N-J-JB+1,ONE,A(J,J),LDA,A(J,J+JB),
     $LDA)
      IF(J+JB.LE.M)THEN
*
*                 Update trailing submatrix.
*
      CALL GAL_DGEMM('NOTRANSPOSE','NOTRANSPOSE',M-J-JB+1,
     $N-J-JB+1,JB,-ONE,A(J+JB,J),LDA,
     $A(J,J+JB),LDA,ONE,A(J+JB,J+JB),
     $LDA)
      END IF
      END IF
   20 CONTINUE
      END IF
      RETURN
*
*     End of DGETRF
*
      END 
