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NAG CL Interface
s18gdc (struve_​i1ml1)

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
s18gd:  FL   CL   CPP   AD   PY   MB 

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© The Numerical Algorithms Group Ltd. 2024
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1 Purpose

s18gdc returns the value of I1(x)-L1(x) where I1(x) is the modified Bessel function of the first kind of order 1, and L1(x) is the modified Struve function of order 1.

2 Specification

#include <nag.h>
double  s18gdc (double x, NagError *fail)
The function may be called by the names: s18gdc, nag_specfun_struve_i1ml1 or nag_struve_i1ml1.

3 Description

s18gdc evaluates an approximation to I1(x)-L1(x).
Please consult the NIST Digital Library of Mathematical Functions for a detailed discussion of the Struve function including special cases, transformations, relations and asymptotic approximations.
The approximation method used by this function is based on Chebyshev expansions.

4 References

NIST Digital Library of Mathematical Functions
MacLeod A J (1996) MISCFUN, a software package to compute uncommon special functions ACM Trans. Math. Software (TOMS) 22(3) 288–301

5 Arguments

1: x – double Input
On entry: the argument x of the function.
Constraint: x≥ 0.0.
2: 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_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.
NE_REAL
On entry, x=⟨value⟩.
Constraint: x≥0.0.

7 Accuracy

The Chebyshev coefficients used by this function are internally represented to 20 digits of precision. Calling the number of digits of precision in the floating-point arithmetic being used t, then clearly the maximum number of correct digits in the results obtained is limited by p=min(t,20).
Apart from this, rounding errors in internal arithmetic may result in a slight loss of accuracy, but it is reasonable to assume that the result is accurate to within a small multiple of the machine precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s18gdc 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 (s18gdce.c)

10.2 Program Data

Program Data (s18gdce.d)

10.3 Program Results

Program Results (s18gdce.r)
GnuplotProduced by GNUPLOT 5.4 patchlevel 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 1 2 3 4 5 6 7 8 9 10 I1(x)-L1(x) x "s18gdfe.r" Example Program Returns values for the Bessel Function - the modified Struve Function I1(x)-L1(x)
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
s18gd:  FL   CL   CPP   AD   PY   MB 
© The Numerical Algorithms Group Ltd. 2024