# la_geamv - Man Page

la_geamv: matrix-vector multiply |A| * |x|, general

## Synopsis

### Functions

subroutine cla_geamv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
CLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.
subroutine dla_geamv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
DLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.
subroutine sla_geamv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
SLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.
subroutine zla_geamv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

## Function Documentation

### subroutine cla_geamv (integer trans, integer m, integer n, real alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

CLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

Purpose:

``` CLA_GEAMV  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.```

ALPHA

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

A

```          A is COMPLEX array, 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

```          LDA is 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

```          X is COMPLEX 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 175 of file cla_geamv.f.

### subroutine dla_geamv (integer trans, integer m, integer n, double precision alpha, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

DLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

Purpose:

``` DLA_GEAMV  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.```

ALPHA

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

A

```          A is DOUBLE PRECISION array, 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

```          LDA is 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

```          X is 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

```          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 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.
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 174 of file dla_geamv.f.

### subroutine sla_geamv (integer trans, integer m, integer n, real alpha, real, dimension( lda, * ) a, integer lda, real, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

SLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

Purpose:

``` SLA_GEAMV  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.```

ALPHA

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

A

```          A is REAL array, 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

```          LDA is 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

```          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 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.
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 174 of file sla_geamv.f.

### subroutine zla_geamv (integer trans, integer m, integer n, double precision alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

ZLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

Purpose:

``` ZLA_GEAMV  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.```

ALPHA

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

A

```          A is COMPLEX*16 array, 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

```          LDA is 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

```          X is COMPLEX*16 array, 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

```          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.
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