NAG Library Routine Document

F06ZRF (ZHER2K)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{UPLO}$ – CHARACTER(1)Input

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

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

The upper triangular part of $C$ is stored.

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

The lower triangular part of $C$ is stored.

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

2:     $\mathrm{TRANS}$ – CHARACTER(1)Input

On entry: specifies the operation to be performed.

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

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

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

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

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

3:     $\mathrm{N}$ – INTEGERInput

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

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

4:     $\mathrm{K}$ – 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: $\mathbf{K}\ge 0$.

5:     $\mathrm{ALPHA}$ – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

6:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – 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 $\mathbf{TRANS}=\text{'C'}$.

7:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06ZRF (ZHER2K) is called.

Constraints:

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

8:     $\mathrm{B}\left(\mathbf{LDB},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array B 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 $B$; $B$ is $n$ by $k$ if $\mathbf{TRANS}=\text{'N'}$, or $k$ by $n$ if $\mathbf{TRANS}=\text{'C'}$.

9:     $\mathrm{LDB}$ – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F06ZRF (ZHER2K) is called.

Constraints:

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

10:   $\mathrm{BETA}$ – REAL (KIND=nag_wp)Input

On entry: the scalar $\beta$.

11:   $\mathrm{C}\left(\mathbf{LDC},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array C must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the $n$ by $n$ Hermitian matrix $C$.

• If $\mathbf{UPLO}=\text{'U'}$, the upper triangular part of $C$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, the lower triangular part of $C$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: the updated matrix $C$. The imaginary parts of the diagonal elements are set to zero.

12:   $\mathrm{LDC}$ – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F06ZRF (ZHER2K) is called.

Constraint: $\mathbf{LDC}\ge \max \left(1,\mathbf{N}\right)$.

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example