!>
!> SGBMV  performs one of the matrix-vector operations
!>
!>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*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.
!> 

TRANS

!>          TRANS is 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**T*x + beta*y.
!>
!>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
!> 

M

!>          M is INTEGER
!>           On entry, M specifies the number of rows of the matrix A.
!>           M must be at least zero.
!> 

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix A.
!>           N must be at least zero.
!> 

KL

!>          KL is INTEGER
!>           On entry, KL specifies the number of sub-diagonals of the
!>           matrix A. KL must satisfy  0 .le. KL.
!> 

KU

!>          KU is INTEGER
!>           On entry, KU specifies the number of super-diagonals of the
!>           matrix A. KU must satisfy  0 .le. KU.
!> 

ALPHA

!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!> 

A

!>          A is REAL array, 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
!> 

LDA

!>          LDA is 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 ).
!> 

X

!>          X is REAL array, 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.
!> 

INCX

!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!> 

BETA

!>          BETA is REAL
!>           On entry, BETA specifies the scalar beta. When BETA is
!>           supplied as zero then Y need not be set on input.
!> 

Y

!>          Y is REAL array, 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.
!>           If either m or n is zero, then Y not referenced and the function
!>           performs a quick return.
!> 

INCY

!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  Level 2 Blas routine.
!>  The vector and matrix arguments are not referenced when N = 0, or M = 0
!>
!>  -- 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.
!>