SYNOPSIS
 SUBROUTINE SGBMV
 ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
 REAL ALPHA, BETA
 INTEGER INCX, INCY, KL, KU, LDA, M, N
 CHARACTER*1 TRANS
 REAL A( LDA, * ), X( * ), Y( * )
PURPOSE
SGBMV performs one of the matrixvector operationswhere alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl subdiagonals and ku superdiagonals.
PARAMETERS
 TRANS  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'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
Unchanged on exit.
 M  INTEGER.
 On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
 N  INTEGER.
 On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
 KL  INTEGER.
 On entry, KL specifies the number of subdiagonals of the matrix A. KL must satisfy 0 .le. KL. Unchanged on exit.
 KU  INTEGER.
 On entry, KU specifies the number of superdiagonals of the matrix A. KU must satisfy 0 .le. KU. Unchanged on exit.
 ALPHA  REAL .
 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
 A  REAL array of 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 superdiagonal
starting at position 2 in row ku, the first subdiagonal
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
Unchanged on exit.
 LDA  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 ). Unchanged on exit.
 X  REAL array of 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. Unchanged on exit.
 INCX  INTEGER.
 On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
 BETA  REAL .
 On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.
 Y  REAL array of 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.
 INCY  INTEGER.

On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.
 Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.