NAG Library Manual, Mark 28.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18ce: FL CL CPP AD

NAG CL Interface
s18cec (bessel_i0_scaled)

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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

s18ce: 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

s18cec returns a value of the scaled modified Bessel function

e^{- | x |} I_{0} (x)

.

2 Specification

#include <nag.h>

double

s18cec (double x)

The function may be called by the names: s18cec, nag_specfun_bessel_i0_scaled or nag_bessel_i0_scaled.

3 Description

s18cec evaluates an approximation to

e^{- | x |} I_{0} (x)

, where

I_{0}

is a modified Bessel function of the first kind. The scaling factor

e^{- | x |}

removes most of the variation in

I_{0} (x)

.

The function uses the same Chebyshev expansions as s18aec, which returns the unscaled value of

I_{0} (x)

.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: $x$ – double Input: On entry: the argument $x$ of the function.

6 Error Indicators and Warnings

None.

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

s18cec is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

10.1 Program Text

Program Text (s18cece.c)

10.2 Program Data

Program Data (s18cece.d)

10.3 Program Results

Program Results (s18cece.r)

NAG Library Manual, Mark 28.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18ce: FL CL CPP AD

© The Numerical Algorithms Group Ltd. 2022