SUBROUTINE SGBMVF( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,

     $                   BETA, Y, INCY )

*     .. Scalar Arguments ..

      REAL               ALPHA, BETA

      INTEGER            INCX, INCY, KL, KU, LDA, M, N

      CHARACTER*1        TRANS

*     .. Array Arguments ..

      REAL               A( LDA, * ), X( * ), Y( * )

*     ..

*

*  Purpose

*  =======

*

*  SGBMV  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 band matrix, with kl sub-diagonals and ku super-diagonals.

*

*  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.

*

*  KL     - INTEGER.

*           On entry, KL specifies the number of sub-diagonals of the

*           matrix A. KL must satisfy  0 .le. KL.

*           Unchanged on exit.

*

*  KU     - INTEGER.

*           On entry, KU specifies the number of super-diagonals of the

*           matrix A. KU must satisfy  0 .le. KU.

*           Unchanged on exit.

*

*  ALPHA  - REAL            .

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

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

*           Before entry, the leading ( kl + ku + 1 ) by n part of the

*           array A must contain the matrix of coefficients, supplied

*           column by column, with the leading diagonal of the matrix in

*           row ( ku + 1 ) of the array, the first super-diagonal

*           starting at position 2 in row ku, the first sub-diagonal

*           starting at position 1 in row ( ku + 2 ), and so on.

*           Elements in the array A that do not correspond to elements

*           in the band matrix (such as the top left ku by ku triangle)

*           are not referenced.

*           The following program segment will transfer a band matrix

*           from conventional full matrix storage to band storage:

*

*                 DO 20, J = 1, N

*                    K = KU + 1 - J

*                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )

*                       A( K + I, J ) = matrix( I, J )

*              10    CONTINUE

*              20 CONTINUE

*

*           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

*           ( kl + ku + 1 ).

*           Unchanged on exit.

*

*  X      - REAL             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   - REAL            .

*           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      - REAL             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, 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 ..

      REAL               ONE         , ZERO

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

*     .. Local Scalars ..

      REAL               TEMP

      INTEGER            I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY,

     $                   LENX, LENY

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     .. Intrinsic Functions ..

      INTRINSIC          MAX, MIN

*     ..

*     .. 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( KL.LT.0 )THEN

         INFO = 4

      ELSE IF( KU.LT.0 )THEN

         INFO = 5

      ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN

         INFO = 8

      ELSE IF( INCX.EQ.0 )THEN

         INFO = 10

      ELSE IF( INCY.EQ.0 )THEN

         INFO = 13

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'SGBMV ', INFO )

         RETURN

      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 the band part of 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

      KUP1 = KU + 1

      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 )

                  K    = KUP1 - J

                  DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL )

                     Y( I ) = Y( I ) + TEMP*A( K + 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

                  K    = KUP1 - J

                  DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL )

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

                     IY      = IY      + INCY

   70             CONTINUE

               END IF

               JX = JX + INCX

               IF( J.GT.KU )

     $            KY = KY + INCY

   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

               K    = KUP1 - J

               DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL )

                  TEMP = TEMP + A( K + 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

               K    = KUP1 - J

               DO 110, I = MAX( 1, J - KU ), MIN( M, J + KL )

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

                  IX   = IX   + INCX

  110          CONTINUE

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

               JY      = JY      + INCY

               IF( J.GT.KU )

     $            KX = KX + INCX

  120       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of SGBMV .

*

      END