void	f16zqc (Nag_OrderType order, Nag_RFP_Store transr, Nag_UploType uplo, Nag_TransType trans, Integer n, Integer k, double alpha, const Complex a[], Integer pda, double beta, Complex cr[], NagError *fail)

The function may be called by the names: f16zqc, nag_blast_zhfrk or nag_zhfrk.

3 Description

f16zqc performs one of the Hermitian rank-

k

update operations

C \leftarrow α A A^{H} + β C or C \leftarrow α A^{H} A + β C,

where

A

is a complex matrix,

C

is an

n \times n

complex Hermitian matrix stored in Rectangular Full Packed (RFP) format, and

α

and

β

are real scalars. The RFP storage format is described in Section 3.4.3 in the F07 Chapter Introduction.

n = 0

or if

β = 1.0

and either

k = 0

α = 0.0

then f16zqc returns immediately. If

β = 0.0

and either

k = 0

α = 0.0

then

C

is set to the zero matrix.

4 References

Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

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

Nag_ColMajor

2: $transr$ – Nag_RFP_Store Input

On entry: specifies whether the normal RFP representation of

C

or its conjugate transpose is stored.

$transr = Nag_RFP_Normal$: The matrix $C$ is stored in normal RFP format.
$transr = Nag_RFP_ConjTrans$: The conjugate transpose of the RFP representation of the matrix $C$ is stored.

Constraint:

transr = Nag_RFP_Normal

Nag_RFP_ConjTrans

3: $uplo$ – Nag_UploType Input

On entry: specifies whether the upper or lower triangular part of

C

is stored in RFP format.

$uplo = Nag_Upper$: The upper triangular part of $C$ is stored in RFP format.
$uplo = Nag_Lower$: The lower triangular part of $C$ is stored in RFP format.

Constraint:

uplo = Nag_Upper

Nag_Lower

4: $trans$ – Nag_TransType Input

On entry: specifies the operation to be performed.

$trans = Nag_NoTrans$: $C \leftarrow α A A^{H} + β C$ .
$trans = Nag_ConjTrans$: $C \leftarrow α A^{H} A + β C$ .

Constraint:

trans = Nag_NoTrans

Nag_ConjTrans

5: $n$ – Integer Input

On entry:

n

, the order of the matrix

C

Constraint:

n \geq 0

6: $k$ – Integer Input

On entry:

k

, the number of columns of

A

trans = Nag_NoTrans

, or the number of rows of

A

trans = Nag_ConjTrans

Constraint:

k \geq 0

7: $alpha$ – double Input

On entry: the scalar

α

8: $a [\dim]$ – const Complex Input

Note: the dimension, dim, of the array a must be at least

$\max (1, pda \times k)$ when $trans = Nag_NoTrans$ and $order = Nag_ColMajor$ ;
$\max (1, n \times pda)$ when $trans = Nag_NoTrans$ and $order = Nag_RowMajor$ ;
$\max (1, pda \times n)$ when $trans = Nag_ConjTrans$ and $order = Nag_ColMajor$ ;
$\max (1, k \times pda)$ when $trans = Nag_ConjTrans$ and $order = Nag_RowMajor$ .

On entry: the matrix

A

;

A

n \times k

trans = Nag_NoTrans

, or

k \times n

trans = Nag_ConjTrans

. If

alpha = 0.0

, a is not referenced.

9: $pda$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

Constraints:

if $order = Nag_ColMajor$ ,
- if $trans = Nag_NoTrans$ , $pda \geq \max (1, n)$ ;
- if $trans = Nag_ConjTrans$ , $pda \geq \max (1, k)$ ;
if $order = Nag_RowMajor$ ,
- if $trans = Nag_NoTrans$ , $pda \geq \max (1, k)$ ;
- if $trans = Nag_ConjTrans$ , $pda \geq \max (1, n)$ .

10: $beta$ – double Input

On entry: the scalar

β

11: $cr [n \times (n + 1) / 2]$ – Complex Input/Output

On entry: the upper or lower triangular part (as specified by uplo) of the

n \times n

Hermitian matrix

C

, stored in RFP format (as specified by transr). The storage format is described in detail in Section 3.4.3 in the F07 Chapter Introduction. If

β = 0.0

, cr need not be set on entry.

On exit: the updated matrix

C

, that is its upper or lower triangular part stored in RFP format.

12: $fail$ – 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_ENUM_INT_2: On entry, $trans = ⟨ value ⟩$ , $k = ⟨ value ⟩$ , $pda = ⟨ value ⟩$ .
Constraint: if $trans = Nag_ConjTrans$ , $pda \geq \max (1, k)$ .

On entry, $trans = ⟨ value ⟩$ , $k = ⟨ value ⟩$ , $pda = ⟨ value ⟩$ .
Constraint: if $trans = Nag_NoTrans$ , $pda \geq \max (1, k)$ .

On entry, $trans = ⟨ value ⟩$ , $n = ⟨ value ⟩$ , $pda = ⟨ value ⟩$ .
Constraint: if $trans = Nag_ConjTrans$ , $pda \geq \max (1, n)$ .

On entry, $trans = ⟨ value ⟩$ , $n = ⟨ value ⟩$ , $pda = ⟨ value ⟩$ .
Constraint: if $trans = Nag_NoTrans$ , $pda \geq \max (1, n)$ .
NE_INT: On entry, $k = ⟨ value ⟩$ .
Constraint: $k \geq 0$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
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

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

f16zqc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

None.

10 Example

This example reads in the lower triangular part of a symmetric matrix

C

which it converts to RFP format. It also reads in

α

β

and a

4 \times 3

matrix

A

and then performs the Hermitian rank-

3

update

C \leftarrow α A A^{H} + β C

f16zq: FL CL CPP AD PY MB

NAG CL Interfacef16zqc (zhfrk)

▸▿ 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

NAG CL Interface
f16zqc (zhfrk)