la_heamv - Man Page

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.

Function Documentation

subroutine cla_heamv (integer uplo, integer n, real alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, 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```

Definition at line 176 of file cla_heamv.f.

subroutine cla_syamv (integer uplo, integer n, real alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, 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```

Definition at line 177 of file cla_syamv.f.

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, double precision, 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```

Definition at line 175 of file dla_syamv.f.

subroutine sla_syamv (integer uplo, integer n, real alpha, real, dimension( lda, * ) a, integer lda, real, dimension( * ) x, integer incx, real beta, 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```

Definition at line 175 of file sla_syamv.f.

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```

Definition at line 176 of file zla_heamv.f.

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```

Definition at line 177 of file zla_syamv.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK