
DSBMV(l) BLAS routine DSBMV(l)
NAME
DSBMV  perform the matrixvector operation y := alpha*A*x + beta*y,
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 operation
where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmet
ric 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 col
umn 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 seg
ment will transfer the upper triangular part of a symmetric band matrix from con
ventional 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 col
umn 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.
BLAS routine 16 October 1992 DSBMV(l) 
