NAG Library Routine Document

C06PRF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     DIRECT – CHARACTER(1)Input

On entry: if the forward transform as defined in Section 3 is to be computed, then DIRECT must be set equal to 'F'.

If the backward transform is to be computed then DIRECT must be set equal to 'B'.

Constraint: $\mathbf{DIRECT}=\text{'F'}$ or $\text{'B'}$.

2:     M – INTEGERInput

On entry: $m$, the number of sequences to be transformed.

Constraint: $\mathbf{M}\ge 1$.

3:     N – INTEGERInput

On entry: $n$, the number of complex values in each sequence.

Constraint: $\mathbf{N}\ge 1$.

4:     X($\mathbf{M}\times \mathbf{N}$) – COMPLEX (KIND=nag_wp) arrayInput/Output

On entry: the complex data must be stored in X as if in a two-dimensional array of dimension $\left(1:\mathbf{M},0:\mathbf{N}-1\right)$; each of the $m$ sequences is stored in a row of each array. In other words, if the elements of the $p$th sequence to be transformed are denoted by $z_{\mathit{j}}^p$, for $\mathit{j}=0,1,\dots ,n-1$, then $\mathbf{X}\left(j\times \mathbf{M}+p\right)$ must contain $z_j^p$.

On exit: is overwritten by the complex transforms.

5:     WORK($*$) – COMPLEX (KIND=nag_wp) arrayWorkspace

Note: the dimension of the array WORK must be at least $\mathbf{M}\times \mathbf{N}+2\times \mathbf{N}+15$.

The workspace requirements as documented for C06PRF may be an overestimate in some implementations.

On exit: the real part of $\mathbf{WORK}\left(1\right)$ contains the minimum workspace required for the current values of M and N with this implementation.

6:     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,

$\mathbf{M}<1$.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{N}<1$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{DIRECT}\ne \text{'F'}$ or $\text{'B'}$.

$\mathbf{IFAIL}=4$

On entry,

N has more than $30$ prime factors.

$\mathbf{IFAIL}=5$

An unexpected error has occurred in an internal call. Check all subroutine calls and array dimensions. Seek expert help.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (c06prfe.f90)

9.2  Program Data

Program Data (c06prfe.d)

9.3  Program Results

Program Results (c06prfe.r)