NAG Library Routine Document

D02UWF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, where the number of grid points for the input data is $n+1$.

Constraint: $\mathbf{N}>0$ and N is even.

2:     $\mathrm{NIP}$ – INTEGERInput

On entry: the number, $m$, of grid points in the uniform mesh $\hat{x}$ onto which function values are interpolated. If $\mathbf{NIP}=1$ then on successful exit from D02UWF, $\mathbf{FIP}\left(1\right)$ will contain the value $f\left(x_n\right)$.

Constraint: $\mathbf{NIP}>0$.

3:     $\mathrm{X}\left(\mathbf{N}+1\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: the grid points, $x_{\mathit{i}}$, for $\mathit{i}=0,1,\dots ,n$, at which the function is specified.

Usually this should be the array of Chebyshev Gauss–Lobatto points returned in D02UCF.

4:     $\mathrm{F}\left(\mathbf{N}+1\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: the function values, $f\left(x_{\mathit{i}}\right)$, for $\mathit{i}=0,1,\dots ,n$.

5:     $\mathrm{XIP}\left(\mathbf{NIP}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: the evenly-spaced grid points, ${\hat{x}}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,m$.

6:     $\mathrm{FIP}\left(\mathbf{NIP}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: the set of interpolated values $\hat{f}\left({\hat{x}}_{\mathit{j}}\right)$, for $\mathit{j}=1,2,\dots ,m$. Here $\hat{f}\left({\hat{x}}_{\mathit{j}}\right)\approx f\left(x={\hat{x}}_{\mathit{j}}\right)$.

7:     $\mathrm{IFAIL}$ – 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, $\mathbf{N}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{N}>0$.

On entry, $\mathbf{N}=〈\mathit{\text{value}}〉$.
Constraint: N is even.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{NIP}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{NIP}>0$.

$\mathbf{IFAIL}=-99$

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

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (d02uwfe.f90)

10.2  Program Data

Program Data (d02uwfe.d)

10.3  Program Results

Program Results (d02uwfe.r)