NAG Library Routine Document

s18cdf  (bessel_k1_scaled)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

s18cdf returns a value of the scaled modified Bessel function exK1x via the function name.

2
Specification

Fortran Interface
Function s18cdf ( x, ifail)
Real (Kind=nag_wp):: s18cdf
Integer, Intent (Inout):: ifail
Real (Kind=nag_wp), Intent (In):: x
C Header Interface
#include nagmk26.h
double  s18cdf_ ( const double *x, Integer *ifail)

3
Description

s18cdf evaluates an approximation to exK1x, where K1 is a modified Bessel function of the second kind. The scaling factor ex removes most of the variation in K1x.
The routine uses the same Chebyshev expansions as s18adf, which returns the unscaled value of K1x.

4
References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5
Arguments

1:     x – Real (Kind=nag_wp)Input
On entry: the argument x of the function.
Constraint: x>0.0.
2:     ifail – IntegerInput/Output
On entry: ifail must be set to 0, -1​ 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​ 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:
ifail=1
On entry, x0.0: K1 is undefined. On soft failure s18cdf returns zero.
ifail=2
On entry, x is too close to zero, as determined by the value of the safe-range parameter x02amf: there is a danger of causing overflow. On soft failure, s18cdf returns the reciprocal of the safe-range parameter.
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.
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.
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

Relative errors in the argument are attenuated when propagated into the function value. When the accuracy of the argument is essentially limited by the machine precision, the accuracy of the function value will be similarly limited by at most a small multiple of the machine precision.

8
Parallelism and Performance

s18cdf is not threaded in any implementation.

9
Further Comments

None.

10
Example

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

10.1
Program Text

Program Text (s18cdfe.f90)

10.2
Program Data

Program Data (s18cdfe.d)

10.3
Program Results

Program Results (s18cdfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017