NAG FL Interface
f06zrf (zher2k)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{uplo}$ – 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: $\mathbf{trans}$ – Character(1) Input

On entry: specifies the operation to be performed.

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

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

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

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

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

3: $\mathbf{n}$ – Integer Input

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: $\mathbf{k}$ – Integer Input

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: $\mathbf{alpha}$ – Complex (Kind=nag_wp) Input

On entry: the scalar $\alpha$.

6: $\mathbf{a}(\mathbf{lda},*)$ – Complex (Kind=nag_wp) array Input

Note: the second dimension of the array a must be at least $\max (1,\mathbf{k})$ if $\mathbf{trans}=\text{'N'}$ and at least $\max (1,\mathbf{n})$ if $\mathbf{trans}=\text{'C'}$.

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

7: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f06zrf is called.

Constraints:

• if $\mathbf{trans}=\text{'N'}$, $\mathbf{lda}\ge \max (1,\mathbf{n})$;
• if $\mathbf{trans}=\text{'C'}$, $\mathbf{lda}\ge \max (1,\mathbf{k})$.

8: $\mathbf{b}(\mathbf{ldb},*)$ – Complex (Kind=nag_wp) array Input

Note: the second dimension of the array b must be at least $\max (1,\mathbf{k})$ if $\mathbf{trans}=\text{'N'}$ and at least $\max (1,\mathbf{n})$ if $\mathbf{trans}=\text{'C'}$.

On entry: the matrix $B$; $B$ is $n\times k$ if $\mathbf{trans}=\text{'N'}$, or $k\times n$ if $\mathbf{trans}=\text{'C'}$.

9: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f06zrf is called.

Constraints:

• if $\mathbf{trans}=\text{'N'}$, $\mathbf{ldb}\ge \max (1,\mathbf{n})$;
• if $\mathbf{trans}=\text{'C'}$, $\mathbf{ldb}\ge \max (1,\mathbf{k})$.

10: $\mathbf{beta}$ – Real (Kind=nag_wp) Input

On entry: the scalar $\beta$.

11: $\mathbf{c}(\mathbf{ldc},*)$ – Complex (Kind=nag_wp) array Input/Output

Note: the second dimension of the array c must be at least $\max (1,\mathbf{n})$.

On entry: the $n\times n$ 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: $\mathbf{ldc}$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which f06zrf is called.

Constraint: $\mathbf{ldc}\ge \max (1,\mathbf{n})$.

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example