NAG Library Manual, Mark 28.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

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S (Specfun) Chapter Introduction

s18cq: FL CL CPP AD

NAG CL Interface
s18cqc (bessel_k0_scaled_vector)

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NAG Library Manual, Mark 28.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18cq: FL CL CPP AD

▸▿ Contents

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

© The Numerical Algorithms Group Ltd. 2022

CL Name Style:
Short (a00aac)
Long (impl_details)
Full (nag_info_impl_details)

1 Purpose

s18cqc returns an array of values of the scaled modified Bessel function

e^{x} K_{0} (x)

.

2 Specification

#include <nag.h>

void	s18cqc (Integer n, const double x[], double f[], Integer ivalid[], NagError *fail)

The function may be called by the names: s18cqc, nag_specfun_bessel_k0_scaled_vector or nag_bessel_k0_scaled_vector.

3 Description

s18cqc evaluates an approximation to

e^{x_{i}} K_{0} (x_{i})

, where

K_{0}

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_{0} (x)

.

The function uses the same Chebyshev expansions as s18aqc, which returns an array of the unscaled values of

K_{0} (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: $x [n]$ – const double Input

On entry: the argument

x_{i}

of the function, for

i = 1, 2, \dots, n

.

Constraint:

x [i - 1] > 0.0

, for

i = 1, 2, \dots, n

.

3: $f [n]$ – double Output

On exit:

e^{x_{i}} K_{0} (x_{i})

, the function values.

4: $ivalid [n]$ – Integer Output

On exit:

ivalid [i - 1]

contains the error code for

x_{i}

, for

i = 1, 2, \dots, n

.

$ivalid [i - 1] = 0$: No error.
$ivalid [i - 1] = 1$: On entry, $x_{i} \leq 0.0$ , $K_{0} (x_{i})$ is undefined. $f [i - 1]$ contains $0.0$ .

5: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
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 Parallelism and Performance

s18cqc 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.

10.1 Program Text

Program Text (s18cqce.c)

10.2 Program Data

Program Data (s18cqce.d)

10.3 Program Results

Program Results (s18cqce.r)

NAG Library Manual, Mark 28.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18cq: FL CL CPP AD

© The Numerical Algorithms Group Ltd. 2022