NAG CL Interface
s18crc (bessel_​k1_​scaled_​vector)

1 Purpose

s18crc returns an array of values of the scaled modified Bessel function exK1x.

2 Specification

#include <nag.h>
void  s18crc (Integer n, const double x[], double f[], Integer ivalid[], NagError *fail)
The function may be called by the names: s18crc, nag_specfun_bessel_k1_scaled_vector or nag_bessel_k1_scaled_vector.

3 Description

s18crc 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 function uses the same Chebyshev expansions as s18arc, which returns an array of the unscaled values of K1x.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: n Integer Input
On entry: n, the number of points.
Constraint: n0.
2: x[n] const double Input
On entry: the argument xi of the function, for i=1,2,,n.
Constraint: x[i-1]>0.0, for i=1,2,,n.
3: f[n] double Output
On exit: exiK1xi, the function values.
4: ivalid[n] Integer Output
On exit: ivalid[i-1] contains the error code for xi, for i=1,2,,n.
No error.
On entry, xi0.0, K1xi is undefined. f[i-1] contains 0.0.
xi is too close to zero, as determined by the value of the safe-range parameter X02AMC: there is a danger of causing overflow. f[i-1] contains the reciprocal of the safe-range parameter.
5: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
On entry, at least one value of x was invalid.
Check ivalid for more 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

s18crc is not threaded in any implementation.

9 Further Comments


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 (s18crce.c)

10.2 Program Data

Program Data (s18crce.d)

10.3 Program Results

Program Results (s18crce.r)