NAG Library Function Document

nag_zhfrk (f16zqc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

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 3.3.1.3 in How to Use the NAG Library and its Documentation 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_StoreInput

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_UploTypeInput

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_TransTypeInput

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:    $\mathbf{n}$ – IntegerInput

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

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

6:    $\mathbf{k}$ – IntegerInput

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:    $\mathbf{alpha}$ – doubleInput

On entry: the scalar $\alpha$.

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

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:    $\mathbf{pda}$ – IntegerInput

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:  $\mathbf{beta}$ – doubleInput

On entry: the scalar $\beta$.

11:  $\mathbf{cr}\left[\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right]$ – ComplexInput/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 3.3.3 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 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f16zqce.c)

10.2

Program Data

Program Data (f16zqce.d)

10.3

Program Results

Program Results (f16zqce.r)