NAG Library Routine Document

F06ZPF (ZHERK)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     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 $\text{'C'}$.

3:     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 $\mathbf{TRANS}=\text{'T'}$ or $\text{'C'}$.

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

4:     K – INTEGERInput

On entry: $k$, the number of columns of $A$ if $\mathbf{TRANS}=\text{'N'}$, or the number of rows of $A$ if $\mathbf{TRANS}=\text{'T'}$ or $\text{'C'}$.

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

5:     ALPHA – REAL (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

6:     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 $\mathbf{TRANS}=\text{'T'}$ or $\text{'C'}$.

On entry: the matrix $A$; $A$ is $n$ by $k$ if $\mathbf{TRANS}=\text{'N'}$, or $k$ by $n$ if $\mathbf{TRANS}=\text{'T'}$ or $\text{'C'}$.

7:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06ZPF (ZHERK) is called.

Constraints:

• if $\mathbf{TRANS}=\text{'N'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$;
• if $\mathbf{TRANS}=\text{'T'}$ or $\text{'C'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{K}\right)$.

8:     BETA – REAL (KIND=nag_wp)Input

On entry: the scalar $\beta$.

9:     C(LDC,$*$) – 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.

10:   LDC – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F06ZPF (ZHERK) is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example