# dsbmv.f

          SUBROUTINE DSBMV (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
         $   INCY)
    C***BEGIN PROLOGUE  DSBMV
    C***PURPOSE  Perform the matrix-vector operation.
    C***LIBRARY   SLATEC (BLAS)
    C***CATEGORY  D1B4
    C***TYPE      DOUBLE PRECISION (SSBMV-S, DSBMV-D, CSBMV-C)
    C***KEYWORDS  LEVEL 2 BLAS, LINEAR ALGEBRA
    C***AUTHOR  Dongarra, J. J., (ANL)
    C           Du Croz, J., (NAG)
    C           Hammarling, S., (NAG)
    C           Hanson, R. J., (SNLA)
    C***DESCRIPTION
    C
    C  DSBMV  performs the matrix-vector  operation
    C
    C     y := alpha*A*x + beta*y,
    C
    C  where alpha and beta are scalars, x and y are n element vectors and
    C  A is an n by n symmetric band matrix, with k super-diagonals.
    C
    C  Parameters
    C  ==========
    C
    C  UPLO   - CHARACTER*1.
    C           On entry, UPLO specifies whether the upper or lower
    C           triangular part of the band matrix A is being supplied as
    C           follows:
    C
    C              UPLO = 'U' or 'u'   The upper triangular part of A is
    C                                  being supplied.
    C
    C              UPLO = 'L' or 'l'   The lower triangular part of A is
    C                                  being supplied.
    C
    C           Unchanged on exit.
    C
    C  N      - INTEGER.
    C           On entry, N specifies the order of the matrix A.
    C           N must be at least zero.
    C           Unchanged on exit.
    C
    C  K      - INTEGER.
    C           On entry, K specifies the number of super-diagonals of the
    C           matrix A. K must satisfy  0 .le. K.
    C           Unchanged on exit.
    C
    C  ALPHA  - DOUBLE PRECISION.
    C           On entry, ALPHA specifies the scalar alpha.
    C           Unchanged on exit.
    C
    C  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
    C           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
    C           by n part of the array A must contain the upper triangular
    C           band part of the symmetric matrix, supplied column by
    C           column, with the leading diagonal of the matrix in row
    C           ( k + 1 ) of the array, the first super-diagonal starting at
    C           position 2 in row k, and so on. The top left k by k triangle
    C           of the array A is not referenced.
    C           The following program segment will transfer the upper
    C           triangular part of a symmetric band matrix from conventional
    C           full matrix storage to band storage:
    C
    C                 DO 20, J = 1, N
    C                    M = K + 1 - J
    C                    DO 10, I = MAX( 1, J - K ), J
    C                       A( M + I, J ) = matrix( I, J )
    C              10    CONTINUE
    C              20 CONTINUE
    C
    C           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
    C           by n part of the array A must contain the lower triangular
    C           band part of the symmetric matrix, supplied column by
    C           column, with the leading diagonal of the matrix in row 1 of
    C           the array, the first sub-diagonal starting at position 1 in
    C           row 2, and so on. The bottom right k by k triangle of the
    C           array A is not referenced.
    C           The following program segment will transfer the lower
    C           triangular part of a symmetric band matrix from conventional
    C           full matrix storage to band storage:
    C
    C                 DO 20, J = 1, N
    C                    M = 1 - J
    C                    DO 10, I = J, MIN( N, J + K )
    C                       A( M + I, J ) = matrix( I, J )
    C              10    CONTINUE
    C              20 CONTINUE
    C
    C           Unchanged on exit.
    C
    C  LDA    - INTEGER.
    C           On entry, LDA specifies the first dimension of A as declared
    C           in the calling (sub) program. LDA must be at least
    C           ( k + 1 ).
    C           Unchanged on exit.
    C
    C  X      - DOUBLE PRECISION array of DIMENSION at least
    C           ( 1 + ( n - 1 )*abs( INCX ) ).
    C           Before entry, the incremented array X must contain the
    C           vector x.
    C           Unchanged on exit.
    C
    C  INCX   - INTEGER.
    C           On entry, INCX specifies the increment for the elements of
    C           X. INCX must not be zero.
    C           Unchanged on exit.
    C
    C  BETA   - DOUBLE PRECISION.
    C           On entry, BETA specifies the scalar beta.
    C           Unchanged on exit.
    C
    C  Y      - DOUBLE PRECISION array of DIMENSION at least
    C           ( 1 + ( n - 1 )*abs( INCY ) ).
    C           Before entry, the incremented array Y must contain the
    C           vector y. On exit, Y is overwritten by the updated vector y.
    C
    C  INCY   - INTEGER.
    C           On entry, INCY specifies the increment for the elements of
    C           Y. INCY must not be zero.
    C           Unchanged on exit.
    C
    C***REFERENCES  Dongarra, J. J., Du Croz, J., Hammarling, S., and
    C                 Hanson, R. J.  An extended set of Fortran basic linear
    C                 algebra subprograms.  ACM TOMS, Vol. 14, No. 1,
    C                 pp. 1-17, March 1988.
    C***ROUTINES CALLED  LSAME, XERBLA
    C***REVISION HISTORY  (YYMMDD)
    C   861022  DATE WRITTEN
    C   910605  Modified to meet SLATEC prologue standards.  Only comment
    C           lines were modified.  (BKS)
    C***END PROLOGUE  DSBMV