SUBROUTINE DGETRFF( M, N, A, LDA, IPIV, INFO )

*

*  -- LAPACK routine (version 3.0) --

*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,

*     Courant Institute, Argonne National Lab, and Rice University

*     March 31, 1993

*

*     .. Scalar Arguments ..

      INTEGER            INFO, LDA, M, N

*     ..

*     .. Array Arguments ..

      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.

*

*  =====================================================================

*

*     .. Parameters ..

      DOUBLE PRECISION   ONE

      PARAMETER          ( ONE = 1.0D+0 )

*     ..

*     .. Local Scalars ..

      INTEGER            I, IINFO, J, JB, NB

*     ..

*     .. External Subroutines ..

      EXTERNAL           DGEMM, DGETF2, DLASWP, DTRSM, XERBLA

*     ..

*     .. 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 XERBLA( '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 = 64

      IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN

*

*        Use unblocked code.

*

         CALL DGETF2( M, N, A, LDA, IPIV, INFO )

      ELSE

*

*        Use blocked code.

*

         DO 20 J = 1, MIN( M, N ), NB

            JB = MIN( MIN( M, N )-J+1, NB )

*

*           Factor diagonal and subdiagonal blocks and test for exact

*           singularity.

*

            CALL 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 10 I = J, MIN( M, J+JB-1 )

               IPIV( I ) = J - 1 + IPIV( I )

   10       CONTINUE

*

*           Apply interchanges to columns 1:J-1.

*

            CALL 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 DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,

     $                      IPIV, 1 )

*

*              Compute block row of U.

*

               CALL DTRSM( 'Left', 'Lower', 'No transpose', '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 DGEMM( 'No transpose', 'No transpose', 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