
DGBMV(l) BLAS routine DGBMV(l)
NAME
DGBMV  perform one of the matrixvector operations y := alpha*A*x + beta*y, or y :=
alpha*A'*x + beta*y,
SYNOPSIS
SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, KL, KU, LDA, M, N
CHARACTER*1 TRANS
DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
PURPOSE
DGBMV performs one of the matrixvector operations
where 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 sat
isfy 0 .le. KU. 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, 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 posi
tion 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  DOUBLE PRECISION 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  DOUBLE PRECISION.
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  DOUBLE PRECISION 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.
BLAS routine 16 October 1992 DGBMV(l) 
