NAG Library Routine Document

s18csf  (bessel_i0_scaled_vector)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

s18csf returns an array of values of the scaled modified Bessel function e-xI0x.

2
Specification

Fortran Interface
Subroutine s18csf ( 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 nagmk26.h
void  s18csf_ ( const Integer *n, const double x[], double f[], Integer *ifail)

3
Description

s18csf evaluates an approximation to e-xiI0xi, where I0 is a modified Bessel function of the first kind for an array of arguments xi, for i=1,2,,n. The scaling factor e-x removes most of the variation in I0x.
The routine uses the same Chebyshev expansions as s18asf, which returns an array of the unscaled values of I0x.

4
References

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

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.
3:     fn – Real (Kind=nag_wp) arrayOutput
On exit: e-xiI0xi, the function values.
4:     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, 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

s18csf 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 (s18csfe.f90)

10.2
Program Data

Program Data (s18csfe.d)

10.3
Program Results

Program Results (s18csfe.r)

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