NAG FL Interface
s15atf (dawson_​vector)

1 Purpose

s15atf returns an array of values for Dawson's Integral, Fx.

2 Specification

Fortran Interface
Subroutine s15atf ( n, x, f, ifail)
Integer, Intent (In) :: n
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x(n)
Real (Kind=nag_wp), Intent (Out) :: f(n)
C Header Interface
#include <nag.h>
void  s15atf_ (const Integer *n, const double x[], double f[], Integer *ifail)
The routine may be called by the names s15atf or nagf_specfun_dawson_vector.

3 Description

s15atf evaluates approximations for Dawson's Integral
Fx = e-x2 0x et2 dt ,  
for an array of arguments xi, for i=1,2,,n.
The routine is based on two Chebyshev expansions:
For 0<x4,
Fx = x r=0 ar Tr t ,   where   t=2 x4 2 -1 .  
For x>4,
Fx = 1x r=0 br Tr t ,   where   t=2 4x 2 -1 .  
For x near zero, Fxx, and for x large, Fx12x. 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: xn Real (Kind=nag_wp) array Input
On entry: the argument xi of the function, for i=1,2,,n.
3: fn Real (Kind=nag_wp) array Output
On exit: Fxi, the function values.
4: ifail Integer Input/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 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 -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or -1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, n=value.
Constraint: n0.
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.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL 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 1-2xFx Fx δ.  
The following graph shows the behaviour of the error amplification factor x 1-2xFx Fx :
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

s15atf 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 (s15atfe.f90)

10.2 Program Data

Program Data (s15atfe.d)

10.3 Program Results

Program Results (s15atfe.r)