Bessel library function in Java

Question

I'm looking for a bessel function in Java that matches the Excel function BESSELI, description provided:

Returns the modified Bessel function, which is equivalent to the Bessel function evaluated for purely imaginary arguments.

Syntax BESSELI(x,n)

X is the value at which to evaluate the function.

N is the order of the Bessel function. If n is not an integer, it is truncated.

I have found things that look close, but there are many different types of bessel function...

My other option is to try and derive an approximation but that sounds quite tough. Can anyone give me any good advice on how to represent that excel function in Java?

I think there's only one 'type' of Bessel functions (http://en.wikipedia.org/wiki/Bessel_function), different orders though, but anything you find should work. — falstro, Jul 28 '09 at 09:54
No, not true. There's J and Y, I and K, ber and bei, ker and kei, etc. all of order n. — duffymo, Jul 28 '09 at 10:01
right, I vaguely remember it now.. sorry. Although I suppose most libraries dealing with bessel functions will probably support whatever you might need. — falstro, Jul 28 '09 at 10:05

score 5 · Answer 1 · answered Jul 28 '09 at 09:58

5

I image that you should be able to port one of these quite easily:

http://www.astro.rug.nl/~gipsy/sub/bessel.c

answered Jul 28 '09 at 09:58

Amos Robinson

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Look for bessk0, bessk1, bessk. – Vinay Sajip Jul 28 '09 at 10:11
Just looking at the source code now... looks promising. thanks. – David Turner Jul 28 '09 at 10:18

score 1 · Answer 2 · answered Jul 28 '09 at 09:53

1

JScience provides a class SpecialMathsUtils with modified Bessel functions.

If the Excel function is particularly important to you in it's current form/implementation, you could use Excel directly by starting up an Excel COM object, and invoking the method within Excel. I've done this before using JACOB and it works ok.

However it does depend on your use case, performance criteria and deployment scenario.

answered Jul 28 '09 at 09:53

Brian Agnew

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I am currently trying to move away from excel models for various reasons (including performance) but thanks for your suggestion. – David Turner Jul 28 '09 at 09:55
Fair enough. Just modified the above re. the JScience stuff – Brian Agnew Jul 28 '09 at 09:57
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The JScience library only appears to offer modified Bessel functions of order 0 and 1, not N as asked for in the question. – Vinay Sajip Jul 28 '09 at 10:07

score 1 · Answer 3 · edited Feb 04 '13 at 17:47

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Dig out a copy of Numerical Recipes, which you'll find in Fortran, C and C++ flavours (or, if your library is very good, also in Basic and Pascal) and translate. By the usual standards of exotic functions Bessel functions are quite 'easy'. for further info, you could start at http://mathworld.wolfram.com/BesselFunction.html

edited Feb 04 '13 at 17:47

user229044

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answered Jul 28 '09 at 09:58

High Performance Mark

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score 1 · Answer 4 · answered Jul 18 '15 at 00:09

You could use the Digital Library of Mathematical Functions:

http://dlmf.nist.gov/

Here are few short things about programming in Java and calculating special functions which I have learned from experience.

If you have the CPU power to do so, use BigDecimal as much as possible. At the moment (July 2015), Microsoft seems not to have an in-house arbitrary numerical precision library in the .NET framework. This makes scientific computing tricky. How they achieved the precision they did in VB6/VBA for Excel eludes me.

BigDecimal, on the other hand, is relatively easy to use. I was introduced to BigDecimal by a friend and read about it in a Murach book on Java 5. I'd highly suggest the Oracle documentation:

http://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html

Secondly, there is a difference, as you have probably observed, between floating-point error and the mathematical-numerical error introduced in an approximation to a special function. Both the mathematical-numerical error and the floating-point error conspire to make things difficult for application development. Use a lot of different programs to check yourself and your calculation.

Thirdly, string constructors for BigDecimal are preferable to the double constructor in many cases. See the Oracle documentation above.

Fourthly, be very careful in using BigDecimal with the unlimited precision of MathContext. Be aware that you will probably have to use setScale to introduce how many decimal places you will need for your application to avoid infinitely repeating decimal expressions and the exceptions thrown to you by the JVM.

Fifthly, try to check integer arguments for the first-kind modified Bessel function first. Also, you can calculate Bessel functions either from the recursion relations available to you or from their definitions as degenerate hypergeometric functions.

Finally,

Good luck!

score 0 · Answer 5 · answered Jul 28 '09 at 10:02

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Or refer to Abramowitz and Stegun. They have very good representations of all these functions. Easy to program.

answered Jul 28 '09 at 10:02

duffymo

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Bessel library function in Java

5 Answers5