SYNOPSIS

SUBROUTINE SLA_GBAMV(

TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY )

    

IMPLICIT NONE

    

REAL ALPHA, BETA

    

INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS

    

REAL AB( LDAB, * ), X( * ), Y( * )

PURPOSE

SLA_GEAMV performs one of the matrix-vector operations
   or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices,
"symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

ARGUMENTS

TRANS - INTEGER

On entry, TRANS specifies the operation to be performed as follows:

BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)

BLAS_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y)
BLAS_CONJ_TRANS y := alpha*abs(A')*abs(x) + beta*abs(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

The number of subdiagonals within the band of A. KL >= 0.

KU - INTEGER

The number of superdiagonals within the band of A. KU >= 0.

ALPHA - REAL

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A - REAL array of DIMENSION ( LDA, n )

Before entry, the leading m by n part of the array A must contain the matrix of coefficients. 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 max( 1, m ). 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 with BETA non-zero, 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.