NAG Library Routine Document

F06WQF (ZHFRK)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     TRANSR – CHARACTER(1)Input

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

$\mathbf{TRANSR}=\text{'N'}$

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

$\mathbf{TRANSR}=\text{'C'}$

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

Constraint: $\mathbf{TRANSR}=\text{'N'}$ or $\text{'C'}$.

2:     UPLO – CHARACTER(1)Input

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

$\mathbf{UPLO}=\text{'U'}$

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

$\mathbf{UPLO}=\text{'L'}$

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

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

3:     TRANS – CHARACTER(1)Input

On entry: specifies the operation to be performed.

$\mathbf{TRANS}=\text{'N'}$

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

$\mathbf{TRANS}=\text{'C'}$

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

Constraint: $\mathbf{TRANS}=\text{'N'}$ or $\text{'C'}$.

4:     N – INTEGERInput

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

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

5:     K – INTEGERInput

On entry: $k$, the number of columns of $A$ if $\mathbf{TRANS}=\text{'N'}$, or the number of rows of $A$ if $\mathbf{TRANS}=\text{'C'}$.

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

6:     ALPHA – REAL (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

7:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{K}\right)$ if $\mathbf{TRANS}=\text{'N'}$ and at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{TRANS}=\text{'C'}$.

On entry: the matrix $A$; $A$ is $n$ by $k$ if $\mathbf{TRANS}=\text{'N'}$, or $k$ by $n$ if $\mathbf{TRANS}=\text{'C'}$.

8:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06WQF (ZHFRK) is called.

Constraints:

• if $\mathbf{TRANS}=\text{'N'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$;
• if $\mathbf{TRANS}=\text{'C'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{K}\right)$.

9:     BETA – REAL (KIND=nag_wp)Input

On entry: the scalar $\beta$.

10:   C($\mathbf{N}\times \left(\mathbf{N}+1\right)/2$) – COMPLEX (KIND=nag_wp) arrayInput/Output

On entry: the upper or lower triangular part (as specified by UPLO) of the $n$ by $n$ symmetric matrix $C$, stored in RFP format, as described in Section 3.3.3 in the F07 Chapter Introduction.

On exit: the updated matrix $C$, that is its upper or lower triangular part stored in RFP format.

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f06wqfe.f90)

9.2  Program Data

Program Data (f06wqfe.d)

9.3  Program Results

Program Results (f06wqfe.r)