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NAME
SSBMV - perform the matrix-vector operation y := alpha*A*x
+ beta*y,
SYNOPSIS
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( * )
PURPOSE
SSBMV performs the matrix-vector operation
where alpha and beta are scalars, x and y are n element vec-
tors 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 sup-
plied 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 - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL 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, sup-
plied 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, sup-
plied 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 - REAL 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 ele-
ments of X. INCX must not be zero. Unchanged on
exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. Unchanged
on exit.
Y - REAL 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 ele-
ments 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.