Man page - la_heamv(3)

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Manual

la_heamv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cla_heamv (integer uplo, integer n, real alpha, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integerincx, real beta, real, dimension( * ) y, integer incy)
subroutine cla_syamv (integer uplo, integer n, real alpha, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integerincx, real beta, real, dimension( * ) y, integer incy)
subroutine dla_syamv (integer uplo, integer n, double precision alpha,double precision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) x, integer incx, double precision beta, doubleprecision, dimension( * ) y, integer incy)
subroutine sla_syamv (integer uplo, integer n, real alpha, real, dimension(lda, * ) a, integer lda, real, dimension( * ) x, integer incx, realbeta, real, dimension( * ) y, integer incy)
subroutine zla_heamv (integer uplo, 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)
subroutine zla_syamv (integer uplo, 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)
Author

NAME

la_heamv - la_heamv: matrix-vector multiply |A| * |x|, Hermitian/symmetric

SYNOPSIS

Functions

subroutine cla_heamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.
subroutine cla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
CLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.
subroutine dla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
DLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.
subroutine sla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
SLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.
subroutine zla_heamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
ZLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.
subroutine zla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

Detailed Description

Function Documentation

subroutine cla_heamv (integer uplo, integer n, real alpha, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integerincx, real beta, real, dimension( * ) y, integer incy)

CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

Purpose:

CLA_SYAMV performs the matrix-vector operation

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors and A is an
n by n symmetric 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

UPLO

UPLO is INTEGER
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:

UPLO = BLAS_UPPER Only the upper triangular part of A
is to be referenced.

UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced.

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, n ).
Unchanged on exit.

X

X is COMPLEX array, dimension
( 1 + ( n - 1 )*abs( INCX ) )
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 + ( n - 1 )*abs( INCY ) )
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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley

subroutine cla_syamv (integer uplo, integer n, real alpha, complex,dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integerincx, real beta, real, dimension( * ) y, integer incy)

CLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

Purpose:

CLA_SYAMV performs the matrix-vector operation

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors and A is an
n by n symmetric 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

UPLO

UPLO is INTEGER
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:

UPLO = BLAS_UPPER Only the upper triangular part of A
is to be referenced.

UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced.

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, n ).
Unchanged on exit.

X

X is COMPLEX array, dimension
( 1 + ( n - 1 )*abs( INCX ) )
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 + ( n - 1 )*abs( INCY ) )
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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley

subroutine dla_syamv (integer uplo, integer n, double precision alpha,double precision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) x, integer incx, double precision beta, doubleprecision, dimension( * ) y, integer incy)

DLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

Purpose:

DLA_SYAMV performs the matrix-vector operation

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors and A is an
n by n symmetric 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

UPLO

UPLO is INTEGER
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:

UPLO = BLAS_UPPER Only the upper triangular part of A
is to be referenced.

UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced.

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, n ).
Unchanged on exit.

X

X is DOUBLE PRECISION array, dimension
( 1 + ( n - 1 )*abs( INCX ) )
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 + ( n - 1 )*abs( INCY ) )
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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley

subroutine sla_syamv (integer uplo, integer n, real alpha, real, dimension(lda, * ) a, integer lda, real, dimension( * ) x, integer incx, realbeta, real, dimension( * ) y, integer incy)

SLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

Purpose:

SLA_SYAMV performs the matrix-vector operation

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors and A is an
n by n symmetric 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

UPLO

UPLO is INTEGER
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:

UPLO = BLAS_UPPER Only the upper triangular part of A
is to be referenced.

UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced.

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, n ).
Unchanged on exit.

X

X is REAL array, dimension
( 1 + ( n - 1 )*abs( INCX ) )
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 + ( n - 1 )*abs( INCY ) )
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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley

subroutine zla_heamv (integer uplo, 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_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

Purpose:

ZLA_SYAMV performs the matrix-vector operation

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors and A is an
n by n symmetric 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

UPLO

UPLO is INTEGER
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:

UPLO = BLAS_UPPER Only the upper triangular part of A
is to be referenced.

UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced.

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, n ).
Unchanged on exit.

X

X is COMPLEX*16 array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) )
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 + ( n - 1 )*abs( INCY ) )
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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley

subroutine zla_syamv (integer uplo, 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_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

Purpose:

ZLA_SYAMV performs the matrix-vector operation

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors and A is an
n by n symmetric 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

UPLO

UPLO is INTEGER
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:

UPLO = BLAS_UPPER Only the upper triangular part of A
is to be referenced.

UPLO = BLAS_LOWER Only the lower triangular part of A
is to be referenced.

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, n ).
Unchanged on exit.

X

X is COMPLEX*16 array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) )
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 + ( n - 1 )*abs( INCY ) )
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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
-- Modified for the absolute-value product, April 2006
Jason Riedy, UC Berkeley

Author

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