NAG CL Interface
s15atc (dawson_​vector)

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1 Purpose

s15atc returns an array of values for Dawson's Integral, F(x).

2 Specification

#include <nag.h>
void  s15atc (Integer n, const double x[], double f[], NagError *fail)
The function may be called by the names: s15atc, nag_specfun_dawson_vector or nag_dawson_vector.

3 Description

s15atc evaluates approximations for Dawson's Integral
F(x) = e-x2 0x et2 dt ,  
for an array of arguments xi, for i=1,2,,n.
The function is based on two Chebyshev expansions:
For 0<|x|4,
F(x) = x r=0 ar Tr (t) ,   where   t=2 (x4) 2 -1 .  
For |x|>4,
F(x) = 1x r=0 br Tr (t) ,   where   t=2 (4x) 2 -1 .  
For |x| near zero, F(x)x, and for |x| large, F(x)12x. These approximations are used for those values of x for which the result is correct to machine precision.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: n Integer Input
On entry: n, the number of points.
Constraint: n0.
2: x[n] const double Input
On entry: the argument xi of the function, for i=1,2,,n.
3: f[n] double Output
On exit: F(xi), the function values.
4: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
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 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

Let δ and ε be the relative errors in the argument and result respectively.
If δ is considerably greater than the machine precision (i.e., if δ is due to data errors etc.), then ε and δ are approximately related by:
ε | x (1-2xF(x)) F(x) | δ.  
The following graph shows the behaviour of the error amplification factor | x (1-2xF(x)) F(x) | :
Figure 1
Figure 1
However, if δ is of the same order as machine precision, then rounding errors could make ε somewhat larger than the above relation indicates. In fact ε will be largely independent of x or δ, but will be of the order of a few times the machine precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s15atc is not threaded in any implementation.

9 Further Comments


10 Example

This example reads values of the argument x from a file, evaluates the function at each value of xi and prints the results.

10.1 Program Text

Program Text (s15atce.c)

10.2 Program Data

Program Data (s15atce.d)

10.3 Program Results

Program Results (s15atce.r)