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      SUBROUTINE SSBMVF( UPLO, N, K, ALPHA, A, LDA, X, INCX,
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     $                   BETA, Y, INCY )
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*     .. Scalar Arguments ..
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      REAL               ALPHA, BETA
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      INTEGER            INCX, INCY, K, LDA, N
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      CHARACTER*1        UPLO
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*     .. Array Arguments ..
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      REAL               A( LDA, * ), X( * ), Y( * )
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  SSBMV  performs the matrix-vector  operation
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*
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*     y := alpha*A*x + beta*y,
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*
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*  where alpha and beta are scalars, x and y are n element vectors and
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*  A is an n by n symmetric band matrix, with k super-diagonals.
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*
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*  Parameters
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*  ==========
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*
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*  UPLO   - CHARACTER*1.
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*           On entry, UPLO specifies whether the upper or lower
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*           triangular part of the band matrix A is being supplied as
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*           follows:
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*
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*              UPLO = 'U' or 'u'   The upper triangular part of A is
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*                                  being supplied.
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*
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*              UPLO = 'L' or 'l'   The lower triangular part of A is
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*                                  being supplied.
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*
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*           Unchanged on exit.
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*
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*  N      - INTEGER.
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*           On entry, N specifies the order of the matrix A.
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*           N must be at least zero.
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*           Unchanged on exit.
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*
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*  K      - INTEGER.
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*           On entry, K specifies the number of super-diagonals of the
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*           matrix A. K must satisfy  0 .le. K.
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*           Unchanged on exit.
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*
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*  ALPHA  - REAL            .
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*           On entry, ALPHA specifies the scalar alpha.
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*           Unchanged on exit.
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*
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*  A      - REAL             array of DIMENSION ( LDA, n ).
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*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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*           by n part of the array A must contain the upper triangular
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*           band part of the symmetric matrix, supplied column by
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*           column, with the leading diagonal of the matrix in row
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*           ( k + 1 ) of the array, the first super-diagonal starting at
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*           position 2 in row k, and so on. The top left k by k triangle
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*           of the array A is not referenced.
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*           The following program segment will transfer the upper
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*           triangular part of a symmetric band matrix from conventional
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*           full matrix storage to band storage:
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*
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*                 DO 20, J = 1, N
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*                    M = K + 1 - J
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*                    DO 10, I = MAX( 1, J - K ), J
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*                       A( M + I, J ) = matrix( I, J )
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*              10    CONTINUE
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*              20 CONTINUE
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*
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*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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*           by n part of the array A must contain the lower triangular
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*           band part of the symmetric matrix, supplied column by
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*           column, with the leading diagonal of the matrix in row 1 of
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*           the array, the first sub-diagonal starting at position 1 in
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*           row 2, and so on. The bottom right k by k triangle of the
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*           array A is not referenced.
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*           The following program segment will transfer the lower
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*           triangular part of a symmetric band matrix from conventional
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*           full matrix storage to band storage:
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*
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*                 DO 20, J = 1, N
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*                    M = 1 - J
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*                    DO 10, I = J, MIN( N, J + K )
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*                       A( M + I, J ) = matrix( I, J )
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*              10    CONTINUE
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*              20 CONTINUE
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*
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*           Unchanged on exit.
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*
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*  LDA    - INTEGER.
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*           On entry, LDA specifies the first dimension of A as declared
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*           in the calling (sub) program. LDA must be at least
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*           ( k + 1 ).
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*           Unchanged on exit.
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*
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*  X      - REAL             array of DIMENSION at least
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*           ( 1 + ( n - 1 )*abs( INCX ) ).
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*           Before entry, the incremented array X must contain the
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*           vector x.
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*           Unchanged on exit.
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*
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*  INCX   - INTEGER.
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*           On entry, INCX specifies the increment for the elements of
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*           X. INCX must not be zero.
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*           Unchanged on exit.
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*
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*  BETA   - REAL            .
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*           On entry, BETA specifies the scalar beta.
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*           Unchanged on exit.
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*
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*  Y      - REAL             array of DIMENSION at least
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*           ( 1 + ( n - 1 )*abs( INCY ) ).
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*           Before entry, the incremented array Y must contain the
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*           vector y. On exit, Y is overwritten by the updated vector y.
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*
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*  INCY   - INTEGER.
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*           On entry, INCY specifies the increment for the elements of
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*           Y. INCY must not be zero.
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*           Unchanged on exit.
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*
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*
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*  Level 2 Blas routine.
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*
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*  -- Written on 22-October-1986.
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*     Jack Dongarra, Argonne National Lab.
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*     Jeremy Du Croz, Nag Central Office.
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*     Sven Hammarling, Nag Central Office.
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*     Richard Hanson, Sandia National Labs.
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*
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*
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*     .. Parameters ..
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      REAL               ONE         , ZERO
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      PARAMETER        ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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*     .. Local Scalars ..
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      REAL               TEMP1, TEMP2
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      INTEGER            I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
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*     .. External Functions ..
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      LOGICAL            LSAME
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      EXTERNAL           LSAME
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*     .. External Subroutines ..
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      EXTERNAL           XERBLA
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*     .. Intrinsic Functions ..
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      INTRINSIC          MAX, MIN
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*     ..
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*     .. Executable Statements ..
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*
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*     Test the input parameters.
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*
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      INFO = 0
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      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
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     $         .NOT.LSAME( UPLO, 'L' )      )THEN
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         INFO = 1
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      ELSE IF( N.LT.0 )THEN
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         INFO = 2
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      ELSE IF( K.LT.0 )THEN
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         INFO = 3
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      ELSE IF( LDA.LT.( K + 1 ) )THEN
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         INFO = 6
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      ELSE IF( INCX.EQ.0 )THEN
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         INFO = 8
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      ELSE IF( INCY.EQ.0 )THEN
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         INFO = 11
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      END IF
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      IF( INFO.NE.0 )THEN
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         CALL XERBLA( 'SSBMV ', INFO )
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         RETURN
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      END IF
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*
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*     Quick return if possible.
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*
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      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
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     $   RETURN
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*
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*     Set up the start points in  X  and  Y.
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*
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      IF( INCX.GT.0 )THEN
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         KX = 1
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      ELSE
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         KX = 1 - ( N - 1 )*INCX
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      END IF
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      IF( INCY.GT.0 )THEN
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         KY = 1
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      ELSE
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         KY = 1 - ( N - 1 )*INCY
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      END IF
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*
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*     Start the operations. In this version the elements of the array A
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*     are accessed sequentially with one pass through A.
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*
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*     First form  y := beta*y.
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*
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      IF( BETA.NE.ONE )THEN
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         IF( INCY.EQ.1 )THEN
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            IF( BETA.EQ.ZERO )THEN
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               DO 10, I = 1, N
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                  Y( I ) = ZERO
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   10          CONTINUE
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            ELSE
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               DO 20, I = 1, N
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                  Y( I ) = BETA*Y( I )
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   20          CONTINUE
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            END IF
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         ELSE
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            IY = KY
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            IF( BETA.EQ.ZERO )THEN
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               DO 30, I = 1, N
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                  Y( IY ) = ZERO
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                  IY      = IY   + INCY
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   30          CONTINUE
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            ELSE
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               DO 40, I = 1, N
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                  Y( IY ) = BETA*Y( IY )
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                  IY      = IY           + INCY
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   40          CONTINUE
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            END IF
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         END IF
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      END IF
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      IF( ALPHA.EQ.ZERO )
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     $   RETURN
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      IF( LSAME( UPLO, 'U' ) )THEN
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*
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*        Form  y  when upper triangle of A is stored.
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*
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         KPLUS1 = K + 1
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         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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            DO 60, J = 1, N
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               TEMP1 = ALPHA*X( J )
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               TEMP2 = ZERO
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               L     = KPLUS1 - J
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               DO 50, I = MAX( 1, J - K ), J - 1
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                  Y( I ) = Y( I ) + TEMP1*A( L + I, J )
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                  TEMP2  = TEMP2  + A( L + I, J )*X( I )
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   50          CONTINUE
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               Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
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   60       CONTINUE
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         ELSE
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            JX = KX
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            JY = KY
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            DO 80, J = 1, N
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               TEMP1 = ALPHA*X( JX )
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               TEMP2 = ZERO
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               IX    = KX
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               IY    = KY
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               L     = KPLUS1 - J
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               DO 70, I = MAX( 1, J - K ), J - 1
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                  Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
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                  TEMP2   = TEMP2   + A( L + I, J )*X( IX )
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                  IX      = IX      + INCX
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                  IY      = IY      + INCY
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   70          CONTINUE
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               Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
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               JX      = JX      + INCX
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               JY      = JY      + INCY
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               IF( J.GT.K )THEN
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                  KX = KX + INCX
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                  KY = KY + INCY
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               END IF
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   80       CONTINUE
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         END IF
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      ELSE
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*
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*        Form  y  when lower triangle of A is stored.
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*
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         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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            DO 100, J = 1, N
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               TEMP1  = ALPHA*X( J )
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               TEMP2  = ZERO
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               Y( J ) = Y( J )       + TEMP1*A( 1, J )
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               L      = 1            - J
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               DO 90, I = J + 1, MIN( N, J + K )
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                  Y( I ) = Y( I ) + TEMP1*A( L + I, J )
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                  TEMP2  = TEMP2  + A( L + I, J )*X( I )
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   90          CONTINUE
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               Y( J ) = Y( J ) + ALPHA*TEMP2
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  100       CONTINUE
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         ELSE
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            JX = KX
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            JY = KY
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            DO 120, J = 1, N
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               TEMP1   = ALPHA*X( JX )
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               TEMP2   = ZERO
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               Y( JY ) = Y( JY )       + TEMP1*A( 1, J )
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               L       = 1             - J
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               IX      = JX
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               IY      = JY
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               DO 110, I = J + 1, MIN( N, J + K )
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                  IX      = IX      + INCX
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                  IY      = IY      + INCY
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                  Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
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                  TEMP2   = TEMP2   + A( L + I, J )*X( IX )
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  110          CONTINUE
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               Y( JY ) = Y( JY ) + ALPHA*TEMP2
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               JX      = JX      + INCX
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               JY      = JY      + INCY
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  120       CONTINUE
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         END IF
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      END IF
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*
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      RETURN
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*
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*     End of SSBMV .
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*
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      END