# sla_gbamv.f - Man Page

SRC/sla_gbamv.f

## Synopsis

### Functions/Subroutines

subroutine sla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
SLA_GBAMV performs a matrix-vector operation to calculate error bounds.

## Function/Subroutine Documentation

### subroutine sla_gbamv (integer trans, integer m, integer n, integer kl, integer ku, real alpha, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

SLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose:

``` SLA_GBAMV  performs one of the matrix-vector operations

y := alpha*abs(A)*abs(x) + beta*abs(y),
or   y := alpha*abs(A)**T*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.```
Parameters

TRANS

```          TRANS is 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**T)*abs(x) + beta*abs(y)
BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)

Unchanged on exit.```

M

```          M is INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.```

N

```          N is INTEGER
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.```

KL

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

KU

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

ALPHA

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

AB

```          AB is REAL array, dimension ( LDAB, n )
Before entry, the leading m by n part of the array AB must
contain the matrix of coefficients.
Unchanged on exit.```

LDAB

```          LDAB is INTEGER
On entry, LDA specifies the first dimension of AB as declared
in the calling (sub) program. LDAB must be at least
max( 1, m ).
Unchanged on exit.```

X

```          X is REAL array, dimension
( 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

```          INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.```

BETA

```          BETA is 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

```          Y is REAL array, dimension
( 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.
If either m or n is zero, then Y not referenced and the function
performs a quick return.```

INCY

```          INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.

Level 2 Blas routine.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 185 of file sla_gbamv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sla_gbamv(3) is an alias of sla_gbamv.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK