SLATEC Routines --- SSBMV ---


    Note: this is a BLAS routine and is not in libslatec.a

*DECK SSBMV
      SUBROUTINE SSBMV (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
     $   INCY)
C***BEGIN PROLOGUE  SSBMV
C***PURPOSE  Multiply a real vector by a real symmetric band matrix.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B4
C***TYPE      SINGLE 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  SSBMV  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  - REAL            .
C           On entry, ALPHA specifies the scalar alpha.
C           Unchanged on exit.
C
C  A      - REAL             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      - REAL             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   - REAL            .
C           On entry, BETA specifies the scalar beta.
C           Unchanged on exit.
C
C  Y      - REAL             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  SSBMV