# dsbmv

```DSBMV(l)                         BLAS routine                         DSBMV(l)

NAME
DSBMV - perform the matrix-vector 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 matrix-vector  operation

where alpha and beta are scalars, x and y are n element vectors and A
is an n by n symmetric band matrix, with k super-diagonals.

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 super-diagonals 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 super-diagonal 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
sub-diagonal 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 22-October-1986.  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)```