NAG Library Manual, Mark 28.7
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NAG CL Interface
f16spc (zher)
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Contents
1
Purpose
2
Specification
3
Description
4
References
5
Arguments
6
Error Indicators and Warnings
7
Accuracy
8
Parallelism and Performance
9
Further Comments
▸
▿
10
Example
10.1
Program Text
10.2
Program Data
10.3
Program Results
© The Numerical Algorithms Group Ltd. 2022
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1
Purpose
f16spc
performs a Hermitian rank-1 update on a complex Hermitian matrix.
2
Specification
copy
#include <nag.h>
void
f16spc
(
Nag_OrderType
order
,
Nag_UploType
uplo
,
Integer
n
,
double
alpha
,
const Complex
x
[],
Integer
incx
,
double
beta
,
Complex
a
[],
Integer
pda
,
NagError *
fail
)
The function may be called by the names:
f16spc
,
nag_blast_zher
or
nag_zher
.
3
Description
f16spc
performs the Hermitian rank-1 update operation
A
←
α
x
x
H
+
β
A
,
where
A
is an
n
×
n
complex Hermitian matrix,
x
is an
n
-element complex vector, while
α
and
β
are real scalars.
4
References
Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)
Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard
University of Tennessee, Knoxville, Tennessee
https://www.netlib.org/blas/blast-forum/blas-report.pdf
5
Arguments
1:
order
–
Nag_OrderType
Input
On entry
: the
order
argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by
order
=
Nag_RowMajor
. See
Section 3.1.3
in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint
:
order
=
Nag_RowMajor
or
Nag_ColMajor
.
2:
uplo
–
Nag_UploType
Input
On entry
: specifies whether the upper or lower triangular part of
A
is stored.
uplo
=
Nag_Upper
The upper triangular part of
A
is stored.
uplo
=
Nag_Lower
The lower triangular part of
A
is stored.
Constraint
:
uplo
=
Nag_Upper
or
Nag_Lower
.
3:
n
–
Integer
Input
On entry
:
n
, the order of the matrix
A
.
Constraint
:
n
≥
0
.
4:
alpha
–
double
Input
On entry
: the scalar
α
.
5:
x
[
dim
]
–
const Complex
Input
Note:
the dimension,
dim
, of the array
x
must be at least
max
(
1
,
1
+
(
n
-
1
)
|
incx
|
)
.
On entry
: the
n
-element vector
x
.
If
incx
>
0
,
x
i
must be stored in
x
[
(
i
-
1
)
×
incx
]
, for
i
=
1
,
2
,
…
,
n
.
If
incx
<
0
,
x
i
must be stored in
x
[
(
n
-
i
)
×
|
incx
|
]
, for
i
=
1
,
2
,
…
,
n
.
Intermediate elements of
x
are not referenced. If
n
=
0
,
x
is not referenced and may be
NULL
.
6:
incx
–
Integer
Input
On entry
: the increment in the subscripts of
x
between successive elements of
x
.
Constraint
:
incx
≠
0
.
7:
beta
–
double
Input
On entry
: the scalar
β
.
8:
a
[
dim
]
–
Complex
Input/Output
Note:
the dimension,
dim
, of the array
a
must be at least
max
(
1
,
pda
×
n
)
.
On entry
: the
n
×
n
Hermitian matrix
A
.
If
order
=
Nag_ColMajor
,
A
i
j
is stored in
a
[
(
j
-
1
)
×
pda
+
i
-
1
]
.
If
order
=
Nag_RowMajor
,
A
i
j
is stored in
a
[
(
i
-
1
)
×
pda
+
j
-
1
]
.
If
uplo
=
Nag_Upper
, the upper triangular part of
A
must be stored and the elements of the array below the diagonal are not referenced.
If
uplo
=
Nag_Lower
, the lower triangular part of
A
must be stored and the elements of the array above the diagonal are not referenced.
On exit
: the updated matrix
A
. The imaginary parts of the diagonal elements are set to zero.
9:
pda
–
Integer
Input
On entry
: the stride separating row or column elements (depending on the value of
order
) of the matrix
A
in the array
a
.
Constraint
:
pda
≥
max
(
1
,
n
)
.
10:
fail
–
NagError *
Input/Output
The NAG error argument (see
Section 7
in the Introduction to the NAG Library CL Interface).
6
Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See
Section 3.1.2
in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument
⟨
value
⟩
had an illegal value.
NE_INT
On entry,
incx
=
⟨
value
⟩
.
Constraint:
incx
≠
0
.
On entry,
n
=
⟨
value
⟩
.
Constraint:
n
≥
0
.
NE_INT_2
On entry,
pda
=
⟨
value
⟩
,
n
=
⟨
value
⟩
.
Constraint:
pda
≥
max
(
1
,
n
)
.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See
Section 8
in the Introduction to the NAG Library CL Interface for further information.
7
Accuracy
The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of
Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)
).
8
Parallelism and Performance
Background information to multithreading can be found in the
Multithreading
documentation.
f16spc
is not threaded in any implementation.
9
Further Comments
None.
10
Example
Perform rank-1 update of complex Hermitian matrix
A
using vector
x
:
A
←
A
-
x
x
H
,
where
A
is the
4
×
4
Hermitian matrix given by
A
=
(
4.0
+
0.0
i
7.0
-
4.0
i
-
0.6
0
+
2.2
i
-
4.0
+
3.0
i
7.0
+
4.0
i
14.0
+
0.0
i
0.3
0
+
1.2
i
-
4.7
+
2.1
i
-
0.6
-
2.2
i
0.3
-
1.2
i
2.04
+
0.0
i
-
5.9
-
0.1
i
-
4.0
-
3.0
i
-
4.7
+
2.1
i
-
5.9
0
+
0.1
i
6.0
+
0.0
i
)
and
x
=
(
2.0
+
1.0
i
2.0
+
3.0
i
0.2
-
1.0
i
-
1.0
-
2.0
i
)
.
10.1
Program Text
Program Text (f16spce.c)
10.2
Program Data
Program Data (f16spce.d)
10.3
Program Results
Program Results (f16spce.r)
NAG Library Manual, Mark 28.7
Interfaces:
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NAG CL Interface Introduction
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F16 (Blast) Chapter Introduction
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© The Numerical Algorithms Group Ltd. 2022