NAG Library Function Document

nag_sum_cheby_series (c06dcc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{x}\left[\mathbf{lx}\right]$ – const doubleInput

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

Constraint: $\mathbf{xmin}\le \mathbf{x}\left[\mathit{i}-1\right]\le \mathbf{xmax}$, 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:    $\mathbf{xmin}$ – doubleInput

4:    $\mathbf{xmax}$ – doubleInput

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:    $\mathbf{c}\left[\mathbf{n}\right]$ – const doubleInput

On entry: $\mathbf{c}\left[\mathit{j}-1\right]$ 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:    $\mathbf{s}$ – Nag_SeriesInput

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

$\mathbf{s}=\mathrm{Nag\_SeriesGeneral}$

The series is general.

$\mathbf{s}=\mathrm{Nag\_SeriesEven}$

The series is even.

$\mathbf{s}=\mathrm{Nag\_SeriesOdd}$

The series is odd.

Constraint: $\mathbf{s}=\mathrm{Nag\_SeriesGeneral}$, $\mathrm{Nag\_SeriesEven}$ or $\mathrm{Nag\_SeriesOdd}$.

8:    $\mathbf{res}\left[\mathbf{lx}\right]$ – doubleOutput

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

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL_2

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

NE_REAL_3

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 $i$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c06dcce.c)

10.2

Program Data

Program Data (c06dcce.d)

10.3

Program Results

Program Results (c06dcce.r)