S18CRF (PDF version)
S Chapter Contents
S Chapter Introduction
NAG Library Manual

NAG Library Routine Document


Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

S18CRF returns an array of values of the scaled modified Bessel function exK1x.

2  Specification

REAL (KIND=nag_wp)  X(N), F(N)

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

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

5  Parameters

1:     N – INTEGERInput
On entry: n, the number of points.
Constraint: N0.
2:     X(N) – 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:     F(N) – REAL (KIND=nag_wp) arrayOutput
On exit: exiK1xi, the function values.
4:     IVALID(N) – INTEGER arrayOutput
On exit: IVALIDi contains the error code for xi, for i=1,2,,N.
No error.
On entry,xi0.0, K1xi is undefined. Fi contains 0.0.
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 parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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, at least one value of X was invalid.
Check IVALID for more information.
On entry, N=value.
Constraint: N0.

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  Further Comments


9  Example

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

9.1  Program Text

Program Text (s18crfe.f90)

9.2  Program Data

Program Data (s18crfe.d)

9.3  Program Results

Program Results (s18crfe.r)

S18CRF (PDF version)
S Chapter Contents
S Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012