NAG FL Interface
c06dcf (chebyshev)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

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: $\mathbf{lx}$ – Integer Input

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 $[x_{\min },x_{\max }]$. The Chebyshev series representation is in terms of the normalized variable $\overline{x}$, where

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

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

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

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: $\mathbf{n}$ – Integer Input

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

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

7: $\mathbf{s}$ – Integer Input

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) array Output

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

9: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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 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