NAG FL Interface
c06rdf (fft_​real_​qtrcosine_​simple)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

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

If the backward transform is to be computed, direct must be set equal to 'B'.

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

2: $\mathbf{m}$ – Integer Input

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

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

3: $\mathbf{n}$ – Integer Input

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

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

4: $\mathbf{x}\left(\mathbf{m}\times \left(\mathbf{n}+2\right)\right)$ – Real (Kind=nag_wp) array Input/Output

On entry: the 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 the array. In other words, if the data values of the $\mathit{p}$th sequence to be transformed are denoted by $x_{\mathit{j}}^{\mathit{p}}$, for $\mathit{j}=0,1,\dots ,n-1$ and $\mathit{p}=1,2,\dots ,m$, the first $mn$ elements of the array x must contain the values

$$x_0^1,x_0^2,\dots ,x_0^m,x_1^1,x_1^2,\dots ,x_1^m,\dots ,x_{n-1}^1,x_{n-1}^2,\dots ,x_{n-1}^m\text{.}$$

The $\left(n+1\right)$th and $\left(n+2\right)$th elements of each row $x_n^{\mathit{p}},x_{n+1}^{\mathit{p}}$, for $\mathit{p}=1,2,\dots ,m$, are required as workspace. These $2m$ elements may contain arbitrary values as they are set to zero by the routine.

On exit: the $m$ quarter-wave cosine transforms stored as if in a two-dimensional array of dimension $\left(1:\mathbf{m},0:\mathbf{n}+1\right)$. Each of the $m$ transforms is stored in a row of the array, overwriting the corresponding original sequence. If the $n$ components of the $\mathit{p}$th quarter-wave cosine transform are denoted by ${\hat{x}}_{\mathit{k}}^{\mathit{p}}$, for $\mathit{k}=0,1,\dots ,n-1$ and $\mathit{p}=1,2,\dots ,m$, the $m\left(n+2\right)$ elements of the array x contain the values

$${\hat{x}}_0^1,{\hat{x}}_0^2,\dots ,{\hat{x}}_0^m,{\hat{x}}_1^1,{\hat{x}}_1^2,\dots ,{\hat{x}}_1^m,\dots ,{\hat{x}}_{n-1}^1,{\hat{x}}_{n-1}^2,\dots ,{\hat{x}}_{n-1}^m,0,0,\dots ,0\left(2m\text{ times}\right)\text{.}$$

5: $\mathbf{work}\left(*\right)$ – Real (Kind=nag_wp) array Workspace

Note: the dimension of the array work must be at least $\mathbf{m}\times \mathbf{n}+2\times \mathbf{n}+2\times \mathbf{m}+15$.

The workspace requirements as documented for c06rdf may be an overestimate in some implementations.

On exit: $\mathbf{work}\left(1\right)$ contains the minimum workspace required for the current values of m and n with this implementation.

6: $\mathbf{ifail}$ – 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, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

On entry, $\mathbf{direct}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{direct}=\text{'F'}$ or $\text{'B'}$.

$\mathbf{ifail}=4$

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 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