NAG Library Routine Document

c06pwf (fft_hermitian_2d)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the first dimension of the transform.

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

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the second dimension of the transform.

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

3:     $\mathbf{y}\left(\left(\mathbf{m}/2+1\right)\times \mathbf{n}\right)$ – Complex (Kind=nag_wp) arrayInput

On entry: the Hermitian sequence of complex input dataset $z$, where $z_{j_1{j}_2}$ is stored in $\mathbf{y}\left(j_2\times \left(m/2+1\right)+j_1\right)$, for $j_1=0,1,\dots ,m/2$ and $j_2=0,1,\dots ,n-1$. That is, if y is regarded as a two-dimensional array of dimension $\left(0:\mathbf{m}/2,0:\mathbf{n}-1\right)$, $\mathbf{y}\left(j_1,j_2\right)$ must contain $z_{j_1{j}_2}$.

4:     $\mathbf{x}\left(\mathbf{m}\times \mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the real output dataset $\hat{x}$, where ${\hat{x}}_{k_1{k}_2}$ is stored in $\mathbf{x}\left(k_2\times m+k_1\right)$, for $k_1=0,1,\dots ,m-1$ and $k_2=0,1,\dots ,n-1$. That is, if x is regarded as a two-dimensional array of dimension $\left(0:\mathbf{m}-1,0:\mathbf{n}-1\right)$, $\mathbf{x}\left(k_1,k_2\right)$ contains ${\hat{x}}_{k_1{k}_2}$.

5:     $\mathbf{ifail}$ – IntegerInput/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 3.4 in How to Use the NAG Library and its Documentation 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, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

$\mathbf{ifail}=2$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=3$

An internal error has occurred in this routine. Check the routine call and any array sizes. If the call is correct then please contact NAG for assistance.

$\mathbf{ifail}=-99$

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

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example