nag_bessel_k1_scaled_vector (s18crc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_bessel_k1_scaled_vector (s18crc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_bessel_k1_scaled_vector (s18crc) returns an array of values of the scaled modified Bessel function exK1x.

2  Specification

#include <nag.h>
#include <nags.h>
void  nag_bessel_k1_scaled_vector (Integer n, const double x[], double f[], Integer ivalid[], NagError *fail)

3  Description

nag_bessel_k1_scaled_vector (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 nag_bessel_k1_vector (s18arc), 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  Arguments

1:     nIntegerInput
On entry: n, the number of points.
Constraint: n0.
2:     x[n]const doubleInput
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]doubleOutput
On exit: exiK1xi, the function values.
4:     ivalid[n]IntegerOutput
On exit: ivalid[i-1] contains the error code for xi, for i=1,2,,n.
ivalid[i-1]=0
No error.
ivalid[i-1]=1
On entry,xi0.0, K1xi is undefined. f[i-1] contains 0.0.
ivalid[i-1]=2
xi is too close to zero, as determined by the value of the safe-range parameter nag_real_safe_small_number (X02AMC): there is a danger of causing overflow. f[i-1] contains the reciprocal of the safe-range parameter.
5:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
NE_INTERNAL_ERROR
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.
NW_IVALID
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  Further Comments

None.

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 (s18crce.c)

9.2  Program Data

Program Data (s18crce.d)

9.3  Program Results

Program Results (s18crce.r)


nag_bessel_k1_scaled_vector (s18crc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

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