1: $x (n)$ – double array: The argument $x_{i}$ of the function, for $i = 1, 2, \dots, n$ .

Constraint: $x (i) > 0.0$ , for $i = 1, 2, \dots, n$ .

Optional Input Parameters

1: $n$ – int64int32nag_int scalar: Default: the dimension of the array x.
$n$ , the number of points.

Constraint: $n \geq 0$ .

Output Parameters

1: $f (n)$ – double array

e^{x_{i}} K_{1} (x_{i})

, the function values.

2: $ivalid (n)$ – int64int32nag_int array

ivalid (i)

contains the error code for

x_{i}

, for

i = 1, 2, \dots, n

$ivalid (i) = 0$

No error.

$ivalid (i) = 1$

On entry,

x_{i} \leq 0.0

K_{1} (x_{i})

is undefined.

f (i)

contains

0.0

$ivalid (i) = 2$

x_{i}

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.

f (i)

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: $n \geq 0$ .

$ifail = - 99$: 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

x_{i}

and prints the results.

Open in the MATLAB editor: s18cr_example

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

NAG Toolbox