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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: performs one of the matrix-vector operations y := alpha*abs(A)*abs(x) + beta*abs(y),

```NAME
LAPACK-3  -  performs  one  of  the  matrix-vector  operations    y  :=
alpha*abs(A)*abs(x) + beta*abs(y),

SYNOPSIS
SUBROUTINE ZLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB,  LDAB,  X,  INCX,
BETA, Y, INCY )

IMPLICIT          NONE

DOUBLE            PRECISION ALPHA, BETA

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

COMPLEX*16        AB( LDAB, * ), X( * )

DOUBLE            PRECISION Y( * )

PURPOSE
DLA_GBAMV  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   (input) 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       (input) INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.

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

KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.

KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.

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

A      - DOUBLE PRECISION   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     (input) 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       (input) DOUBLE PRECISION 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    (input) INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.

BETA   - 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       (input/output) 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    (input) INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Level 2 Blas routine.

LAPACK routine (version 3.2.2)March 2011                       LAPACK-3(3)
```