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NAG Toolbox: nag_specfun_bessel_k1_scaled_vector (s18cr)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_specfun_bessel_k1_scaled_vector (s18cr) returns an array of values of the scaled modified Bessel function exK1x.

Syntax

[f, ivalid, ifail] = s18cr(x, 'n', n)
[f, ivalid, ifail] = nag_specfun_bessel_k1_scaled_vector(x, 'n', n)

Description

nag_specfun_bessel_k1_scaled_vector (s18cr) 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_specfun_bessel_k1_real_vector (s18ar), which returns an array of the unscaled values of K1x.

References

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

Parameters

Compulsory Input Parameters

1:     xn – double array
The argument xi of the function, for i=1,2,,n.
Constraint: xi>0.0, for i=1,2,,n.

Optional Input Parameters

1:     n int64int32nag_int scalar
Default: the dimension of the array x.
n, the number of points.
Constraint: n0.

Output Parameters

1:     fn – double array
exiK1xi, the function values.
2:     ivalidn int64int32nag_int array
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 nag_machine_real_safe (x02am): there is a danger of causing overflow. fi contains the reciprocal of the safe-range parameter.
3:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W  ifail=1
On entry, at least one value of x was invalid.
Check ivalid for more information.
   ifail=2
Constraint: n0.
   ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
   ifail=-399
Your licence key may have expired or may not have been installed correctly.
   ifail=-999
Dynamic memory allocation failed.

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.

Further Comments

None.

Example

This example reads values of x from a file, evaluates the function at each value of xi and prints the results.
function s18cr_example


fprintf('s18cr example results\n\n');

x = [0.4; 0.6; 1.4; 2.5; 10; 1000];

[f, ivalid, ifail] = s18cr(x);

fprintf('     x         e^xK_1(x)   ivalid\n');
for i=1:numel(x)
  fprintf('%12.3e%12.3e%5d\n', x(i), f(i), ivalid(i));
end

s18cr example results

     x         e^xK_1(x)   ivalid
   4.000e-01   3.259e+00    0
   6.000e-01   2.374e+00    0
   1.400e+00   1.301e+00    0
   2.500e+00   9.002e-01    0
   1.000e+01   4.108e-01    0
   1.000e+03   3.965e-02    0

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
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