NAG CL Interface
f16zqc (zhfrk)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – 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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$. 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: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2: $\mathbf{transr}$ – Nag_RFP_Store Input

On entry: specifies whether the normal RFP representation of $C$ or its conjugate transpose is stored.

$\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$

The matrix $C$ is stored in normal RFP format.

$\mathbf{transr}=\mathrm{Nag\_RFP\_ConjTrans}$

The conjugate transpose of the RFP representation of the matrix $C$ is stored.

Constraint: $\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$ or $\mathrm{Nag\_RFP\_ConjTrans}$.

3: $\mathbf{uplo}$ – Nag_UploType Input

On entry: specifies whether the upper or lower triangular part of $C$ is stored in RFP format.

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

The upper triangular part of $C$ is stored in RFP format.

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

The lower triangular part of $C$ is stored in RFP format.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

4: $\mathbf{trans}$ – Nag_TransType Input

On entry: specifies the operation to be performed.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

$C\leftarrow \alpha A{A}^{\mathrm{H}}+\beta C$.

$\mathbf{trans}=\mathrm{Nag\_ConjTrans}$

$C\leftarrow \alpha A^{\mathrm{H}}A+\beta C$.

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ or $\mathrm{Nag\_ConjTrans}$.

5: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the matrix $C$.

Constraint: $\mathbf{n}\ge 0$.

6: $\mathbf{k}$ – Integer Input

On entry: $k$, the number of columns of $A$ if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, or the number of rows of $A$ if $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$.

Constraint: $\mathbf{k}\ge 0$.

7: $\mathbf{alpha}$ – double Input

On entry: the scalar $\alpha$.

8: $\mathbf{a}\left[\mathit{dim}\right]$ – const Complex Input

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

• $\max \left(1,\mathbf{pda}\times \mathbf{k}\right)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pda}\right)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$;
• $\max \left(1,\mathbf{pda}\times \mathbf{n}\right)$ when $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{k}\times \mathbf{pda}\right)$ when $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the matrix $A$; $A$ is $n$ by $k$ if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, or $k$ by $n$ if $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$. If $\mathbf{alpha}=0.0$, a is not referenced.

9: $\mathbf{pda}$ – Integer Input

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$,
  • if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$;
  • if $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$,
  • if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$;
  • if $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

10: $\mathbf{beta}$ – double Input

On entry: the scalar $\beta$.

11: $\mathbf{cr}\left[\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right]$ – Complex Input/Output

On entry: the upper or lower triangular part (as specified by uplo) of the $n$ by $n$ 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 $\beta =0.0$, 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: $\mathbf{fail}$ – 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 $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_INT_2

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_ConjTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{trans}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

NE_INT

On entry, $\mathbf{k}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{k}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

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

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results