NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18cf: FL CL CPP AD PY MB

NAG CL Interface
s18cfc (bessel_i1_scaled)

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NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18cf: FL CL CPP AD PY MB

▸▿ 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. 2024

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

1 Purpose

s18cfc returns a value of the scaled modified Bessel function

e^{- | x |} I_{1} (x)

.

2 Specification

#include <nag.h>

double

s18cfc (double x)

The function may be called by the names: s18cfc, nag_specfun_bessel_i1_scaled or nag_bessel_i1_scaled.

3 Description

s18cfc evaluates an approximation to

e^{- | x |} I_{1} (x)

, where

I_{1}

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

e^{- | x |}

removes most of the variation in

I_{1} (x)

.

The function uses the same Chebyshev expansions as s18afc, which returns the unscaled value of

I_{1} (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

Background information to multithreading can be found in the Multithreading documentation.

s18cfc 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 (s18cfce.c)

10.2 Program Data

Program Data (s18cfce.d)

10.3 Program Results

Program Results (s18cfce.r)

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG CL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s18cf: FL CL CPP AD PY MB

© The Numerical Algorithms Group Ltd. 2024