SLATEC Routines --- SGBMV ---


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

*DECK SGBMV
      SUBROUTINE SGBMV (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
     $   BETA, Y, INCY)
C***BEGIN PROLOGUE  SGBMV
C***PURPOSE  Multiply a real vector by a real general band matrix.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B4
C***TYPE      SINGLE PRECISION (SGBMV-S, DGBMV-D, CGBMV-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  SGBMV  performs one of the matrix-vector operations
C
C     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
C
C  where alpha and beta are scalars, x and y are vectors and A is an
C  m by n band matrix, with kl sub-diagonals and ku super-diagonals.
C
C  Parameters
C  ==========
C
C  TRANS  - CHARACTER*1.
C           On entry, TRANS specifies the operation to be performed as
C           follows:
C
C              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
C
C              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
C
C              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.
C
C           Unchanged on exit.
C
C  M      - INTEGER.
C           On entry, M specifies the number of rows of the matrix A.
C           M must be at least zero.
C           Unchanged on exit.
C
C  N      - INTEGER.
C           On entry, N specifies the number of columns of the matrix A.
C           N must be at least zero.
C           Unchanged on exit.
C
C  KL     - INTEGER.
C           On entry, KL specifies the number of sub-diagonals of the
C           matrix A. KL must satisfy  0 .le. KL.
C           Unchanged on exit.
C
C  KU     - INTEGER.
C           On entry, KU specifies the number of super-diagonals of the
C           matrix A. KU must satisfy  0 .le. KU.
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, the leading ( kl + ku + 1 ) by n part of the
C           array A must contain the matrix of coefficients, supplied
C           column by column, with the leading diagonal of the matrix in
C           row ( ku + 1 ) of the array, the first super-diagonal
C           starting at position 2 in row ku, the first sub-diagonal
C           starting at position 1 in row ( ku + 2 ), and so on.
C           Elements in the array A that do not correspond to elements
C           in the band matrix (such as the top left ku by ku triangle)
C           are not referenced.
C           The following program segment will transfer a band matrix
C           from conventional full matrix storage to band storage:
C
C                 DO 20, J = 1, N
C                    K = KU + 1 - J
C                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
C                       A( K + 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           ( kl + ku + 1 ).
C           Unchanged on exit.
C
C  X      - REAL             array of DIMENSION at least
C           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
C           and at least
C           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
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. When BETA is
C           supplied as zero then Y need not be set on input.
C           Unchanged on exit.
C
C  Y      - REAL             array of DIMENSION at least
C           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
C           and at least
C           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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  SGBMV