SUBROUTINE DGEMVF ( TRANS, M, N, ALPHA, A, LDA, X, INCX,

     $                   BETA, Y, INCY )

*     .. Scalar Arguments ..

      DOUBLE PRECISION   ALPHA, BETA

      INTEGER            INCX, INCY, LDA, M, N

      CHARACTER*1        TRANS

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )

*     ..

*

*  Purpose

*  =======

*

*  DGEMV  performs one of the matrix-vector operations

*

*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,

*

*  where alpha and beta are scalars, x and y are vectors and A is an

*  m by n matrix.

*

*  Parameters

*  ==========

*

*  TRANS  - CHARACTER*1.

*           On entry, TRANS specifies the operation to be performed as

*           follows:

*

*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

*

*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

*

*              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

*

*           Unchanged on exit.

*

*  M      - INTEGER.

*           On entry, M specifies the number of rows of the matrix A.

*           M must be at least zero.

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry, N specifies the number of columns of the matrix A.

*           N must be at least zero.

*           Unchanged on exit.

*

*  ALPHA  - DOUBLE PRECISION.

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).

*           Before entry, the leading m by n part of the array A must

*           contain the matrix of coefficients.

*           Unchanged on exit.

*

*  LDA    - INTEGER.

*           On entry, LDA specifies the first dimension of A as declared

*           in the calling (sub) program. LDA must be at least

*           max( 1, m ).

*           Unchanged on exit.

*

*  X      - DOUBLE PRECISION array of DIMENSION at least

*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'

*           and at least

*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.

*           Before entry, the incremented array X must contain the

*           vector x.

*           Unchanged on exit.

*

*  INCX   - INTEGER.

*           On entry, INCX specifies the increment for the elements of

*           X. INCX must not be zero.

*           Unchanged on exit.

*

*  BETA   - DOUBLE PRECISION.

*           On entry, BETA specifies the scalar beta. When BETA is

*           supplied as zero then Y need not be set on input.

*           Unchanged on exit.

*

*  Y      - DOUBLE PRECISION array of DIMENSION at least

*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'

*           and at least

*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.

*           Before entry with BETA non-zero, the incremented array Y

*           must contain the vector y. On exit, Y is overwritten by the

*           updated vector y.

*

*  INCY   - INTEGER.

*           On entry, INCY specifies the increment for the elements of

*           Y. INCY must not be zero.

*           Unchanged on exit.

*

*

*  Level 2 Blas routine.

*

*  -- Written on 22-October-1986.

*     Jack Dongarra, Argonne National Lab.

*     Jeremy Du Croz, Nag Central Office.

*     Sven Hammarling, Nag Central Office.

*     Richard Hanson, Sandia National Labs.

*

*

*     .. Parameters ..

      DOUBLE PRECISION   ONE         , ZERO

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

*     .. Local Scalars ..

      DOUBLE PRECISION   TEMP

      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      INFO = 0

      IF     ( .NOT.LSAME( TRANS, 'N' ).AND.

     $         .NOT.LSAME( TRANS, 'T' ).AND.

     $         .NOT.LSAME( TRANS, 'C' )      )THEN

         INFO = 1

      ELSE IF( M.LT.0 )THEN

         INFO = 2

      ELSE IF( N.LT.0 )THEN

         INFO = 3

      ELSE IF( LDA.LT.MAX( 1, M ) )THEN

         INFO = 6

      ELSE IF( INCX.EQ.0 )THEN

         INFO = 8

      ELSE IF( INCY.EQ.0 )THEN

         INFO = 11

      END IF

*

*     Quick return if possible.

*

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

     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )

     $   RETURN

*

*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set

*     up the start points in  X  and  Y.

*

      IF( LSAME( TRANS, 'N' ) )THEN

         LENX = N

         LENY = M

      ELSE

         LENX = M

         LENY = N

      END IF

      IF( INCX.GT.0 )THEN

         KX = 1

      ELSE

         KX = 1 - ( LENX - 1 )*INCX

      END IF

      IF( INCY.GT.0 )THEN

         KY = 1

      ELSE

         KY = 1 - ( LENY - 1 )*INCY

      END IF

*

*     Start the operations. In this version the elements of A are

*     accessed sequentially with one pass through A.

*

*     First form  y := beta*y.

*

      IF( BETA.NE.ONE )THEN

         IF( INCY.EQ.1 )THEN

            IF( BETA.EQ.ZERO )THEN

               DO 10, I = 1, LENY

                  Y( I ) = ZERO

   10          CONTINUE

            ELSE

               DO 20, I = 1, LENY

                  Y( I ) = BETA*Y( I )

   20          CONTINUE

            END IF

         ELSE

            IY = KY

            IF( BETA.EQ.ZERO )THEN

               DO 30, I = 1, LENY

                  Y( IY ) = ZERO

                  IY      = IY   + INCY

   30          CONTINUE

            ELSE

               DO 40, I = 1, LENY

                  Y( IY ) = BETA*Y( IY )

                  IY      = IY           + INCY

   40          CONTINUE

            END IF

         END IF

      END IF

      IF( ALPHA.EQ.ZERO )

     $   RETURN

      IF( LSAME( TRANS, 'N' ) )THEN

*

*        Form  y := alpha*A*x + y.

*

         JX = KX

         IF( INCY.EQ.1 )THEN

            DO 60, J = 1, N

               IF( X( JX ).NE.ZERO )THEN

                  TEMP = ALPHA*X( JX )

                  DO 50, I = 1, M

                     Y( I ) = Y( I ) + TEMP*A( I, J )

   50             CONTINUE

               END IF

               JX = JX + INCX

   60       CONTINUE

         ELSE

            DO 80, J = 1, N

               IF( X( JX ).NE.ZERO )THEN

                  TEMP = ALPHA*X( JX )

                  IY   = KY

                  DO 70, I = 1, M

                     Y( IY ) = Y( IY ) + TEMP*A( I, J )

                     IY      = IY      + INCY

   70             CONTINUE

               END IF

               JX = JX + INCX

   80       CONTINUE

         END IF

      ELSE

*

*        Form  y := alpha*A'*x + y.

*

         JY = KY

         IF( INCX.EQ.1 )THEN

            DO 100, J = 1, N

               TEMP = ZERO

               DO 90, I = 1, M

                  TEMP = TEMP + A( I, J )*X( I )

   90          CONTINUE

               Y( JY ) = Y( JY ) + ALPHA*TEMP

               JY      = JY      + INCY

  100       CONTINUE

         ELSE

            DO 120, J = 1, N

               TEMP = ZERO

               IX   = KX

               DO 110, I = 1, M

                  TEMP = TEMP + A( I, J )*X( IX )

                  IX   = IX   + INCX

  110          CONTINUE

               Y( JY ) = Y( JY ) + ALPHA*TEMP

               JY      = JY      + INCY

  120       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of DGEMV .

*

      END