hyperg is wrong for large negative x (Trac #659)

[scipy-gitbot]

Original ticket http://projects.scipy.org/scipy/ticket/659 on 2008-04-29 by trac user helias, assigned to unknown.

=== problem ===
The evaluation of hyperg (hyp1f1, real arguments) yields wrong results for large negative x=-30.
The problem appeared with changeset 3012, where Kahan's summation formula was applied. The problem seems to be a too optimistic error estimate in Kahan's summation: The error estimation of hy1f1p (special/cehpes/hyperg.c) is always in the range of machine resolution, but the actual error is much larger due to cancelation in the strongly alternating series (for negative x). Hence, hyperg always returns the result of hy1f1p, even, if hy1f1a would be better (as for large negative x).[[BR]]
Restoring the old error estimation based on the maximum term yields a too high error estimates.

=== possible solution ===
Resorting to the fortran function chgm in specfun/specfun.f also works for negative x=-30.

[scipy-gitbot]

Attachment added by trac user helias on 2008-04-29: hyp1f1_ticket.py

[scipy-gitbot]

trac user helias wrote on 2008-05-29

Here is a patch based on revision 4393 made from the scipy root directory (scipy_4393_hyp1f1_chgm.patch).[[BR]]

It replaces the implementation hyperg in special/cephes/hyperg.c with the implementation chgm in special/specfun/specfun.f for the function hyp1f1 (real arguments).

[scipy-gitbot]

Attachment added by trac user helias on 2008-05-29: scipy_4393_hyp1f1_chgm.patch

[scipy-gitbot]

Attachment added by trac user helias on 2008-05-29: test_hyp1f1.nb

[scipy-gitbot]

Attachment added by trac user helias on 2008-05-29: hyp1f1_test.py

[scipy-gitbot]

@wnbell wrote on 2008-06-24

added in 55c40c5

I found that the maximum relative error was about 5e-5, does that match your expectations?