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Technical Reference: Base Operating System and Extensions , Volume 2
Performs matrixvector operations
using symmetric band matrix.
BLAS Library
(libblas.a)
SUBROUTINE SSBMV(UPLO, N, K, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
REAL ALPHA, BETA
INTEGER INCX, INCY, K, LDA, N
CHARACTER*1 UPLO
REAL A(LDA,*), X(*), Y(*)
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(*)
The SSBMV or
DSBMV subroutine performs the matrixvector operation:
y := alpha
* A * x + beta * y
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
superdiagonals.
UPLO
 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
 On entry, N specifies the order of the matrix
A; N must be at least 0; unchanged on exit.

K
 On entry, K specifies the number of superdiagonals of the
matrix A; K must satisfy 0 .le.
K; unchanged on exit.

ALPHA
 On entry, ALPHA specifies the scalar alpha; unchanged on
exit.

A
 An array of dimension ( LDA, N ); on 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
transfers 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
On 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 transfers 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
 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
 A vector of dimension at least (1 + (N1) * abs(
INCX ) ); on entry, the incremented array X must
contain the vector x; unchanged on exit.

INCX
 On entry, INCX specifies the increment for the elements of
X; INCX must not be 0; unchanged on
exit.

BETA
 On entry, BETA specifies the scalar beta; unchanged on
exit.

Y
 A vector of dimension at least (1 + (N1) * abs(
INCY ) ); on entry, the incremented array Y must
contain the vector y; on exit, Y is overwritten by the updated
vector y.

INCY
 On entry, INCY specifies the increment for the elements of
Y; INCY must not be 0; unchanged on
exit.

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