SYNOPSIS
 SUBROUTINE DSBMV
 ( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
 DOUBLE PRECISION ALPHA, BETA
 INTEGER INCX, INCY, K, LDA, N
 CHARACTER*1 UPLO
 DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
PURPOSE
DSBMV performs the matrixvector operationwhere alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k superdiagonals.
PARAMETERS
 UPLO  CHARACTER*1.

On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being supplied as
follows:
UPLO = 'U' or 'u' The upper triangular part of A is being supplied.
UPLO = 'L' or 'l' The lower triangular part of A is being supplied.
Unchanged on exit.
 N  INTEGER.
 On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
 K  INTEGER.
 On entry, K specifies the number of superdiagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit.
 ALPHA  DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
 A  DOUBLE PRECISION array of DIMENSION ( LDA, n ).

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the symmetric matrix, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first superdiagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer the upper
triangular part of a symmetric band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N M = K + 1  J DO 10, I = MAX( 1, J  K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE
Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first subdiagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a symmetric band matrix from conventional full matrix storage to band storage:
DO 20, J = 1, N M = 1  J DO 10, I = J, MIN( N, J + K ) A( M + 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 ( k + 1 ). Unchanged on exit.
 X  DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( n  1 )*abs( INCX ) ). 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  DOUBLE PRECISION.
 On entry, BETA specifies the scalar beta. Unchanged on exit.
 Y  DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( n  1 )*abs( INCY ) ). 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.