Man page - la_gbamv(3)

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Manual

la_gbamv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cla_gbamv (integer trans, integer m, integer n, integer kl,integer ku, real alpha, complex, dimension( ldab, * ) ab, integer ldab,complex, dimension( * ) x, integer incx, real beta, real, dimension( *) y, integer incy)
subroutine dla_gbamv (integer trans, integer m, integer n, integer kl,integer ku, double precision alpha, double precision, dimension( ldab,* ) ab, integer ldab, double precision, dimension( * ) x, integer incx,double precision beta, double precision, dimension( * ) y, integerincy)
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)
subroutine zla_gbamv (integer trans, integer m, integer n, integer kl,integer ku, double precision alpha, complex*16, dimension( ldab, * )ab, integer ldab, complex*16, dimension( * ) x, integer incx, doubleprecision beta, double precision, dimension( * ) y, integer incy)
Author

NAME

la_gbamv - la_gbamv: matrix-vector multiply |A| * |x|, general banded

SYNOPSIS

Functions

subroutine cla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
CLA_GBAMV performs a matrix-vector operation to calculate error bounds.
subroutine dla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
DLA_GBAMV performs a matrix-vector operation to calculate error bounds.
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.
subroutine zla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Detailed Description

Function Documentation

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

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

Purpose:

CLA_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 COMPLEX 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, 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 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

Univ. of Colorado Denver

NAG Ltd.

subroutine dla_gbamv (integer trans, integer m, integer n, integer kl,integer ku, double precision alpha, double precision, dimension( ldab,* ) ab, integer ldab, double precision, dimension( * ) x, integer incx,double precision beta, double precision, dimension( * ) y, integerincy)

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

Purpose:

DLA_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 DOUBLE PRECISION 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 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
( 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

Univ. of Colorado Denver

NAG Ltd.

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

Univ. of Colorado Denver

NAG Ltd.

subroutine zla_gbamv (integer trans, integer m, integer n, integer kl,integer ku, double precision alpha, complex*16, dimension( ldab, * )ab, integer ldab, complex*16, dimension( * ) x, integer incx, doubleprecision beta, double precision, dimension( * ) y, integer incy)

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, 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.
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

Univ. of Colorado Denver

NAG Ltd.

Author

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