# zla_gbamv.f man page

zla_gbamv.f —

## Synopsis

### Functions/Subroutines

subroutinezla_gbamv(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY)ZLA_GBAMVperforms a matrix-vector operation to calculate error bounds.

## Function/Subroutine Documentation

### subroutine zla_gbamv (integerTRANS, integerM, integerN, integerKL, integerKU, double precisionALPHA, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( * )X, integerINCX, double precisionBETA, double precision, dimension( * )Y, integerINCY)

**ZLA_GBAMV** performs a matrix-vector operation to calculate error bounds.

**Purpose:**

```
ZLA_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 DOUBLE PRECISION
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
```

*AB*

```
AB is COMPLEX*16 array of 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, LDAB 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 COMPLEX*16 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 DOUBLE PRECISION
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 DOUBLE PRECISION 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.
```

*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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 186 of file zla_gbamv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zla_gbamv(3) is an alias of zla_gbamv.f(3).