SUBROUTINE DGETF2F( 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

*     June 30, 1992

*

*     .. Scalar Arguments ..

      INTEGER            INFO, LDA, M, N

*     ..

*     .. Array Arguments ..

      INTEGER            IPIV( * )

      DOUBLE PRECISION   A( LDA, * )

*     ..

*

*  Purpose

*  =======

*

*  DGETF2 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 2 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 = -k, the k-th argument had an illegal value

*          > 0: if INFO = k, U(k,k) 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, ZERO

      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )

*     ..

*     .. Local Scalars ..

      INTEGER            J, JP

*     ..

*     .. External Functions ..

      INTEGER            IDAMAX

      EXTERNAL           IDAMAX

*     ..

*     .. External Subroutines ..

      EXTERNAL           DGER, DSCAL, DSWAP, 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( 'DGETF2', -INFO )

         RETURN

      END IF

*

*     Quick return if possible

*

      IF( M.EQ.0 .OR. N.EQ.0 )

     $   RETURN

*

      DO 10 J = 1, MIN( M, N )

*

*        Find pivot and test for singularity.

*

         JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )

         IPIV( J ) = JP

         IF( A( JP, J ).NE.ZERO ) THEN

*

*           Apply the interchange to columns 1:N.

*

            IF( JP.NE.J )

     $         CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )

*

*           Compute elements J+1:M of J-th column.

*

            IF( J.LT.M )

     $         CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )

*

         ELSE IF( INFO.EQ.0 ) THEN

*

            INFO = J

         END IF

*

         IF( J.LT.MIN( M, N ) ) THEN

*

*           Update trailing submatrix.

*

            CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,

     $                 A( J+1, J+1 ), LDA )

         END IF

   10 CONTINUE

      RETURN

*

*     End of DGETF2

*

      END