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.