1: $result$ – double scalar: The result of the function.
2: $ifail$ – 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:

$ifail = 1$: On entry, $x \leq 0.0$ : $K_{1}$ is undefined. On soft failure nag_specfun_bessel_k1_scaled (s18cd) returns zero.

$ifail = 2$: On entry, x 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. On soft failure, nag_specfun_bessel_k1_scaled (s18cd) returns the reciprocal of the safe-range parameter.

$ifail = - 99$: 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 the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

Open in the MATLAB editor: s18cd_example

function s18cd_example


fprintf('s18cd example results\n\n');

x = [0.4  0.6  1.4  2.5  10  1000];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s18cd(x(j));
end

disp('      x        e^xK_1(x)');
fprintf('%12.3e%12.3e\n',[x; result]);

s18cd example results

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

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox