NAG Library Routine Document

F01RKF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     M – INTEGERInput

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

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

3:     N – INTEGERInput

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

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

4:     NROWP – INTEGERInput

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:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/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:     LDA – INTEGERInput

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:     THETA($*$) – COMPLEX (KIND=nag_wp) arrayInput

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:     WORK($\max \left(\mathbf{M}-1,\mathbf{NROWP}-\mathbf{M},1\right)$) – COMPLEX (KIND=nag_wp) arrayWorkspace

9:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,	$\mathbf{WHERET}\ne \text{'I'}$ or $\text{'S'}$,
or	$\mathbf{M}<0$,
or	$\mathbf{N}<\mathbf{M}$,
or	$\mathbf{NROWP}<0$ or $\mathbf{NROWP}>\mathbf{N}$,
or	$\mathbf{LDA}<\max \left(1,\mathbf{M},\mathbf{NROWP}\right)$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f01rkfe.f90)

9.2  Program Data

Program Data (f01rkfe.d)

9.3  Program Results

Program Results (f01rkfe.r)