#12521: evaluate log gamma for complex input
-------------------------------------+-------------------------------------
Reporter: kcrisman | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: critical | Milestone: sage-6.4
Component: basic arithmetic | Resolution:
Keywords: lgamma log_gamma | Merged in:
Authors: Eviatar Bach | Reviewers: Burcin Erocal, Ralf
Report Upstream: N/A | Stephan
Branch: | Work issues: speedup
u/rws/evaluate_log_gamma_for_complex_input| Commit:
Dependencies: | bacd2349b07fd6296737d56b6f430c08fe28c767
| Stopgaps:
-------------------------------------+-------------------------------------
Description changed by rws:
Old description:
> Currently, we use MPFR or Ginac to evaluate `log_gamma`, but this returns
> `NaN` for negative input with even ceiling.
> {{{
> sage: log_gamma(-2.1)
> NaN
> sage: log_gamma(-3.1)
> 0.400311696703985
> sage: log_gamma(-4.1)
> NaN
> sage: log_gamma(-5.1)
> -2.63991581673655
> sage: log_gamma(-21/10).n()
> NaN
> sage: get_systems('log_gamma(-21/10).n()')
> ['ginac']
> sage: log_gamma(CC(-2.1))
> 1.53171380819509 + 3.14159265358979*I
> }}}
> We can use mpmath or something other trick to get this to work, now that
> #10075 has a nice symbolic function available. See #10072 for where we
> originally got better numerical evaluation.
> {{{
> sage: mpmath.loggamma(-2.1)
> mpc(real='1.5317138081950856', imag='-9.4247779607693793')
> }}}
> Putting as defect because there is a log gamma for negative numbers,
> though we should talk about branches...
>
> Apply: [attachment:trac_12521_3.patch]
New description:
Currently, we use MPFR or Ginac to evaluate `log_gamma`, but this returns
`NaN` for negative input with even ceiling.
{{{
sage: log_gamma(-2.1)
NaN
sage: log_gamma(-3.1)
0.400311696703985
sage: log_gamma(-4.1)
NaN
sage: log_gamma(-5.1)
-2.63991581673655
sage: log_gamma(-21/10).n()
NaN
sage: get_systems('log_gamma(-21/10).n()')
['ginac']
sage: log_gamma(CC(-2.1))
1.53171380819509 + 3.14159265358979*I
}}}
We can use mpmath or something other trick to get this to work, now that
#10075 has a nice symbolic function available. See #10072 for where we
originally got better numerical evaluation.
{{{
sage: mpmath.loggamma(-2.1)
mpc(real='1.5317138081950856', imag='-9.4247779607693793')
}}}
Putting as defect because there is a log gamma for negative numbers,
though we should talk about branches...
Apply: [attachment:trac_12521_3.patch]
There is now also the arb option:
{{{
sage: x=ComplexBallField(53)(-2.1)
sage: %timeit _ = x.log_gamma()
The slowest run took 8.11 times longer than the fastest. This could mean
that an intermediate result is being cached.
100000 loops, best of 3: 8.15 µs per loop
sage: x.log_gamma()
[1.53171380819509 +/- 5.52e-15] + [-9.42477796076938 +/- 2.48e-15]*I
}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/12521#comment:30>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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