NAG Library Routine Document

c06dcf  (chebyshev)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{x}\left(\mathbf{lx}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $x\in X$, the set of arguments of the series.

Constraint: $\mathbf{xmin}\le \mathbf{x}\left(\mathit{i}\right)\le \mathbf{xmax}$, for $\mathit{i}=1,2,\dots ,\mathbf{lx}$.

2:     $\mathbf{lx}$ – IntegerInput

On entry: the number of evaluation points in $X$.

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

3:     $\mathbf{xmin}$ – Real (Kind=nag_wp)Input

4:     $\mathbf{xmax}$ – Real (Kind=nag_wp)Input

On entry: the lower and upper end points respectively of the interval $\left[x_{\min },x_{\max }\right]$. The Chebyshev series representation is in terms of the normalized variable $\stackrel{-}{x}$, where

$$\stackrel{-}{x}=\frac{2x-\left(x_{\max }+x_{\min }\right)}{x_{\max }-x_{\min }}\text{.}$$

Constraint: $\mathbf{xmin}<\mathbf{xmax}$.

5:     $\mathbf{c}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{c}\left(\mathit{j}\right)$ must contain the coefficient $c_{\mathit{j}}$ of the Chebyshev series, for $\mathit{j}=1,2,\dots ,n$.

6:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of terms in the series.

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

7:     $\mathbf{s}$ – IntegerInput

On entry: determines the series (see Section 3).

$\mathbf{s}=1$

The series is general.

$\mathbf{s}=2$

The series is even.

$\mathbf{s}=3$

The series is odd.

Constraint: $\mathbf{s}=1$, $2$ or $3$.

8:     $\mathbf{res}\left(\mathbf{lx}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the Chebyshev series evaluated at the set of points $X$.

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

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

On entry, $\mathbf{s}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{s}=1$, $2$ or $3$.

$\mathbf{ifail}=4$

On entry, $\mathbf{xmax}=〈\mathit{\text{value}}〉$ and $\mathbf{xmin}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{xmin}<\mathbf{xmax}$.

$\mathbf{ifail}=5$

On entry, element $\mathbf{x}\left(〈\mathit{\text{value}}〉\right)=〈\mathit{\text{value}}〉$, $\mathbf{xmin}=〈\mathit{\text{value}}〉$ and $\mathbf{xmax}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{xmin}\le \mathbf{x}\left(i\right)\le \mathbf{xmax}$, for all $i$.

$\mathbf{ifail}=-99$

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

10.1

Program Text

Program Text (c06dcfe.f90)

10.2

Program Data

Program Data (c06dcfe.d)

10.3

Program Results

Program Results (c06dcfe.r)