NAG FL Interface
f01rkf (complex_​gen_​rq_​formq)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

On entry: indicates where the elements of $\theta$ are to be found.

$\mathbf{wheret}=\text{'I'}$ (In a)

The elements of $\theta$ are in a.

$\mathbf{wheret}=\text{'S'}$ (Separate)

The elements of $\theta$ are separate from a, in theta.

Constraint: $\mathbf{wheret}=\text{'I'}$ or $\text{'S'}$.

2: $\mathbf{m}$ – Integer Input

On entry: $m$, the number of rows of the matrix $A$.

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

3: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of columns of the matrix $A$.

Constraint: $\mathbf{n}\ge \mathbf{m}$.

4: $\mathbf{nrowp}$ – Integer Input

On entry: $\ell$, the required number of rows of $P$.

If $\mathbf{nrowp}=0$, an immediate return is effected.

Constraint: $0\le \mathbf{nrowp}\le \mathbf{n}$.

5: $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) array Input/Output

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

On entry: the leading $m$ by $m$ strictly lower triangular part of the array a, and the $m$ by $\left(n-m\right)$ rectangular part of a with top left-hand corner at element $\mathbf{a}\left(1,\mathbf{m}+1\right)$ must contain details of the matrix $P$. In addition, if $\mathbf{wheret}=\text{'I'}$, the diagonal elements of a must contain the elements of $\theta$.

On exit: the first nrowp rows of the array a are overwritten by the first nrowp rows of the $n$ by $n$ unitary matrix $P^{\mathrm{H}}$.

6: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01rkf is called.

Constraint: $\mathbf{lda}\ge \max \left(1,\mathbf{m},\mathbf{nrowp}\right)$.

7: $\mathbf{theta}\left(*\right)$ – Complex (Kind=nag_wp) array Input

Note: the dimension of the array theta must be at least $\max \left(1,\mathbf{m}\right)$ if $\mathbf{wheret}=\text{'S'}$, and at least $1$ otherwise.

On entry: if $\mathbf{wheret}=\text{'S'}$, the array theta must contain the elements of $\theta$. If $\mathbf{theta}\left(k\right)=0.0$, $P_k$ is assumed to be $I$, if $\mathbf{theta}\left(k\right)=\alpha$ and $\mathrm{Re}\left(\alpha \right)<0.0$, $P_k$ is assumed to be of the form

$$P_k=\left(\begin{array}{lll}I& 0& 0\\ 0& \alpha & 0\\ 0& 0& I\end{array}\right)\text{,}$$

otherwise $\mathbf{theta}\left(k\right)$ is assumed to contain ${\theta }_k$ given by

$${\theta }_k=\left({\zeta }_k,\mathrm{Im}\left({\gamma }_k\right)\right)\text{.}$$

If $\mathbf{wheret}=\text{'I'}$, the array theta is not referenced.

8: $\mathbf{work}\left(\max \left(\mathbf{m}-1,\mathbf{nrowp}-\mathbf{m},1\right)\right)$ – Complex (Kind=nag_wp) array Workspace

9: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=-1$

On entry, $\mathbf{lda}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{nrowp}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lda}\ge \max \left(\mathbf{m},\mathbf{nrowp}\right)$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge \mathbf{m}$.

On entry, $\mathbf{nrowp}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrowp}\ge 0$ and $\mathbf{nrowp}\le \mathbf{n}$.

On entry, $\mathbf{wheret}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{wheret}=\text{'I'}$ or $\text{'S'}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results