NAG Library Routine Document

s18crf (bessel_k1_scaled_vector)

1
Purpose

s18crf returns an array of values of the scaled modified Bessel function exK1x.

2
Specification

Fortran Interface
Subroutine s18crf ( n, x, f, ivalid, ifail)
Integer, Intent (In):: n
Integer, Intent (Inout):: ifail
Integer, Intent (Out):: ivalid(n)
Real (Kind=nag_wp), Intent (In):: x(n)
Real (Kind=nag_wp), Intent (Out):: f(n)
C Header Interface
#include <nagmk26.h>
void  s18crf_ (const Integer *n, const double x[], double f[], Integer ivalid[], Integer *ifail)

3
Description

s18crf evaluates an approximation to exiK1xi, where K1 is a modified Bessel function of the second kind for an array of arguments xi, for i=1,2,,n. The scaling factor ex removes most of the variation in K1x.
The routine uses the same Chebyshev expansions as s18arf, which returns an array of the unscaled values of K1x.

4
References

NIST Digital Library of Mathematical Functions

5
Arguments

1:     n – IntegerInput
On entry: n, the number of points.
Constraint: n0.
2:     xn – Real (Kind=nag_wp) arrayInput
On entry: the argument xi of the function, for i=1,2,,n.
Constraint: xi>0.0, for i=1,2,,n.
3:     fn – Real (Kind=nag_wp) arrayOutput
On exit: exiK1xi, the function values.
4:     ivalidn – Integer arrayOutput
On exit: ivalidi contains the error code for xi, for i=1,2,,n.
ivalidi=0
No error.
ivalidi=1
On entry,xi0.0, K1xi is undefined. fi contains 0.0.
ivalidi=2
xi is too close to zero, as determined by the value of the safe-range parameter x02amf: there is a danger of causing overflow. fi contains the reciprocal of the safe-range parameter.
5:     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, at least one value of x was invalid.
Check ivalid for more information.
ifail=2
On entry, n=value.
Constraint: n0.
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

s18crf is not threaded in any implementation.

9
Further Comments

None.

10
Example

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

10.1
Program Text

Program Text (s18crfe.f90)

10.2
Program Data

Program Data (s18crfe.d)

10.3
Program Results

Program Results (s18crfe.r)