NAME
SGBMV - perform one of the matrix-vector operations y := alpha*A*x +
beta*y, or y := alpha*A’*x + beta*y,
SYNOPSIS
SUBROUTINE SGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA,
Y, INCY )
REAL ALPHA, BETA
INTEGER INCX, INCY, KL, KU, LDA, M, N
CHARACTER*1 TRANS
REAL A( LDA, * ), X( * ), Y( * )
PURPOSE
SGBMV performs one of the matrix-vector operations
where alpha and beta are scalars, x and y are vectors and A is an m by
n band matrix, with kl sub-diagonals and ku super-diagonals.
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 sub-diagonals of the matrix
A. KL must satisfy 0 .le. KL. Unchanged on exit.
KU - INTEGER.
On entry, KU specifies the number of super-diagonals of the
matrix A. KU must satisfy 0 .le. KU. Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A - REAL 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 super-diagonal starting at position 2
in row ku, the first sub-diagonal 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 - REAL 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 - REAL .
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 - REAL 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 22-October-1986. Jack Dongarra, Argonne National
Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
Central Office. Richard Hanson, Sandia National Labs.