NAG Library Routine Document

e02akf  (dim1_cheb_eval2)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{np1}$ – IntegerInput

On entry: $n+1$, where $n$ is the degree of the given polynomial $p\left(\stackrel{-}{x}\right)$.

Constraint: $\mathbf{np1}\ge 1$.

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

3:     $\mathbf{xmax}$ – 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: $\mathbf{xmin}<\mathbf{xmax}$.

4:     $\mathbf{a}\left(\mathbf{la}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the Chebyshev coefficients of the polynomial $p\left(\stackrel{-}{x}\right)$. Specifically, element $\mathit{i}\times \mathbf{ia1}+1$ must contain the coefficient $a_{\mathit{i}}$, for $\mathit{i}=0,1,\dots ,n$. Only these $n+1$ elements will be accessed.

5:     $\mathbf{ia1}$ – IntegerInput

On entry: the index increment of a. Most frequently, the Chebyshev coefficients are stored in adjacent elements of a, and ia1 must be set to $1$. However, if, for example, they are stored in $\mathbf{a}\left(1\right),\mathbf{a}\left(4\right),\mathbf{a}\left(7\right),\dots$, the value of ia1 must be $3$.

Constraint: $\mathbf{ia1}\ge 1$.

6:     $\mathbf{la}$ – IntegerInput

On entry: the dimension of the array a as declared in the (sub)program from which e02akf is called.

Constraint: $\mathbf{la}\ge \left(\mathbf{np1}-1\right)\times \mathbf{ia1}+1$.

7:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: the argument $x$ at which the polynomial is to be evaluated.

Constraint: $\mathbf{xmin}\le \mathbf{x}\le \mathbf{xmax}$.

8:     $\mathbf{result}$ – Real (Kind=nag_wp)Output

On exit: the value of the polynomial $p\left(\stackrel{-}{x}\right)$.

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,	$\mathbf{np1}<1$,
or	$\mathbf{ia1}<1$,
or	$\mathbf{la}\le \left(\mathbf{np1}-1\right)\times \mathbf{ia1}$,
or	$\mathbf{xmin}\ge \mathbf{xmax}$.

$\mathbf{ifail}=2$

x does not satisfy the restriction $\mathbf{xmin}\le \mathbf{x}\le \mathbf{xmax}$.

$\mathbf{ifail}=-99$

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 (e02akfe.f90)

10.2

Program Data

10.3

Program Results

Program Results (e02akfe.r)