NAG Library Routine Document

C06RAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

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

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

2:     N – INTEGERInput

On entry: one more than the number of real values in each sequence, i.e., the number of values in each sequence is $n-1$.

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

3:     X($\mathbf{M}\times \left(\mathbf{N}+2\right)$) – REAL (KIND=nag_wp) arrayInput/Output

On entry: the data must be stored in X as if in a two-dimensional array of dimension $\left(1:\mathbf{M},1:\mathbf{N}+2\right)$; each of the $m$ sequences is stored in a row of the array. In other words, if the $n-1$ data values of the $\mathit{p}$th sequence to be transformed are denoted by $x_{\mathit{j}}^{\mathit{p}}$, for $\mathit{j}=1,2,\dots ,n-1$ and $\mathit{p}=1,2,\dots ,m$, then the first $m\left(n-1\right)$ elements of the array X must contain the values

$$x_1^1,x_1^2,\dots ,x_1^m,x_2^1,x_2^2,\dots ,x_2^m,\dots ,x_{n-1}^1,x_{n-1}^2,\dots ,x_{n-1}^m\text{.}$$

The $n$th to $\left(n+2\right)$th elements of each row $x_n^{\mathit{p}},\dots ,x_{n+2}^{\mathit{p}}$, for $\mathit{p}=1,2,\dots ,m$, are required as workspace. These $3m$ elements may contain arbitrary values as they are set to zero by the routine.

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

$${\hat{x}}_1^1,{\hat{x}}_1^2,\dots ,{\hat{x}}_1^m,{\hat{x}}_2^1,{\hat{x}}_2^2,\dots ,{\hat{x}}_2^m,\dots ,{\hat{x}}_{n-1}^1,{\hat{x}}_{n-1}^2,\dots ,{\hat{x}}_{n-1}^m,0,0,\dots ,0\left(3m\text{ times}\right)\text{.}$$

4:     WORK($*$) – REAL (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 C06RAF 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.

5:     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,

$\mathbf{N}<1$.

$\mathbf{IFAIL}=3$

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 (c06rafe.f90)

9.2  Program Data

Program Data (c06rafe.d)

9.3  Program Results

Program Results (c06rafe.r)