Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	ivalid(n)
Real (Kind=nag_wp), Intent (In)	::	x(n)
Real (Kind=nag_wp), Intent (Out)	::	f(n)

C Header Interface

#include <nag.h>

void	s18crf_ (const Integer n, const double x[], double f[], Integer ivalid[], Integer ifail)

The routine may be called by the names s18crf or nagf_specfun_bessel_k1_scaled_vector.

3 Description

s18crf evaluates an approximation to

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

, where

K_{1}

is a modified Bessel function of the second kind for an array of arguments

x_{i}

, for

i = 1, 2, \dots, n

. The scaling factor

e^{x}

removes most of the variation in

K_{1} (x)

The routine uses the same Chebyshev expansions as s18arf, which returns an array of the unscaled values of

K_{1} (x)

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: $n$ – Integer Input

On entry:

n

, the number of points.

Constraint:

n \geq 0

2: $x (n)$ – Real (Kind=nag_wp) array Input

On entry: the argument

x_{i}

of the function, for

i = 1, 2, \dots, n

Constraint:

x (i) > 0.0

, for

i = 1, 2, \dots, n

3: $f (n)$ – Real (Kind=nag_wp) array Output

On exit:

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

, the function values.

4: $ivalid (n)$ – Integer array Output

On exit:

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 x02amf: there is a danger of causing overflow. $f (i)$ contains the reciprocal of the safe-range parameter.

5: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

- 1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

- 1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

- 1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, at least one value of x was invalid.
Check ivalid for more information.

$ifail = 2$: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further 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

s18crf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example reads values of x from a file, evaluates the function at each value of

x_{i}

and prints the results.

s18cr: FL CL CPP AD

NAG FL Interfaces18crf (bessel_​k1_​scaled_​vector)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
s18crf (bessel_k1_scaled_vector)