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ID Category Severity Reproducibility Date Submitted Last Update
0000010 [ALGLIB] Spec.functions major always 2009-03-10 21:02 2009-07-23 12:42
Reporter SergeyB View Status public  
Assigned To SergeyB
Priority normal Resolution fixed Platform
Status resolved   OS
Projection none   OS Version
ETA none Fixed in Version 2.0 Product Version
  Target Version 2.0 Product Build
Summary 0000010: FIXED: modified Besel function returns incorrect results
Description From: Kors van der Werf < korsvanderwerf@yahoo.com >

Hi,

Very nice, ythis ALGLib. I use the VB version for now, and it seems the Modified BesselI funtion for orders of negative half integers do not give proper results, can you have a look?

Already order = -0.5 fails, and can be compared to the well known sqrt(2/(PI x)) cosh(x)

For x=1 it should be 1.2312, I get 0.293525.

Could you ahve a look please.
Steps To Reproduce
Additional Information
Programming language All
Attached Files

- Relationships

-  Notes
(0000006)
SergeyB (administrator)
2009-03-11 10:21

 Confirmed: should be 1.2312, returns 0.2935
(0000007)
SergeyB (administrator)
2009-03-11 12:15
edited on: 2009-03-11 14:12

 Fixed.

There was an error in original Cephes code when calculating 1F1(v,2*v,2*x) with v=0. Straightforward formula for 1F1 may return 1.0 or NAN (depending on implementation, 1.0 in Cephes), more elaborate calculations gives us 0.5*(1+exp(2*x)).

This error can only happen when v=-0.5, should be OK with other values of v.
(0000008)
SergeyB (administrator)
2009-03-11 23:36

 Other negative half-integer values should be fixed also...
(0000010)
SergeyB (administrator)
2009-04-19 11:07

 Looks like that this subroutine can't calculate modified Bessel functions of negative orders. It is not a bug - it is a limitation of formula used.

I've modified documentation...

- Issue History
Date Modified Username Field Change
2009-03-10 21:02 SergeyB New Issue
2009-03-10 21:02 SergeyB Programming language => VBA
2009-03-10 21:50 SergeyB Status new => assigned
2009-03-10 21:50 SergeyB Assigned To => SergeyB
2009-03-10 21:54 SergeyB Assigned To SergeyB =>
2009-03-10 21:55 SergeyB Status assigned => new
2009-03-11 10:20 SergeyB Status new => assigned
2009-03-11 10:20 SergeyB Assigned To => SergeyB
2009-03-11 10:21 SergeyB Note Added: 0000006
2009-03-11 10:21 SergeyB Status assigned => confirmed
2009-03-11 10:21 SergeyB Reproducibility have not tried => always
2009-03-11 12:04 SergeyB Programming language VBA => All
2009-03-11 12:15 SergeyB Note Added: 0000007
2009-03-11 12:15 SergeyB Status confirmed => resolved
2009-03-11 12:15 SergeyB Fixed in Version => Next minor release
2009-03-11 12:15 SergeyB Resolution open => fixed
2009-03-11 12:17 SergeyB Note Edited: 0000007
2009-03-11 14:12 SergeyB Note Edited: 0000007
2009-03-11 23:36 SergeyB Note Added: 0000008
2009-03-11 23:36 SergeyB Status resolved => feedback
2009-03-11 23:36 SergeyB Resolution fixed => reopened
2009-04-19 11:07 SergeyB Note Added: 0000010
2009-04-19 11:07 SergeyB Status feedback => resolved
2009-04-19 11:07 SergeyB Resolution reopened => fixed
2009-04-20 09:42 SergeyB Summary modified Besel function returns incorrect results => FIXED: modified Besel function returns incorrect results
2009-04-20 09:47 SergeyB Target Version => Upcoming release
2009-07-23 12:42 SergeyB Category => Special functions

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