NAG Library Routine Document

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.

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

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

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

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

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

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

On entry: the scalar $\alpha$.

6:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – 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:     $\mathbf{lda}$ – 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:     $\mathbf{b}\left(\mathbf{ldb},*\right)$ – 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:     $\mathbf{ldb}$ – 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:   $\mathbf{beta}$ – Real (Kind=nag_wp)Input

On entry: the scalar $\beta$.

11:   $\mathbf{c}\left(\mathbf{ldc},*\right)$ – 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:   $\mathbf{ldc}$ – 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