#18210: numerical bug in incomplete gamma function
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Reporter: VivianePons | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.7
Component: symbolics | Resolution:
Keywords: sd67 | Merged in:
Authors: | Reviewers:
Report Upstream: Reported upstream. Developers | Work issues:
acknowledge bug. |
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by slelievre):
This ticket seems to be solved now in Sage 7.3.beta9.
Trying the code from the ticket description...
{{{
$ ./sage -v
SageMath version 7.3.beta9, Release Date: 2016-07-22
$ ./sage -q
sage: gamma(60, 30).numerical_approx()
1.38682990237888e80
}}}
{{{
sage: %gp
--> Switching to PARI/GP interpreter <--
pari: \p 50
realprecision = 57 significant digits (50 digits displayed)
pari: incgam(60,30)
1.3868299023788801161747839921239559320835799009004 E80
pari: \p 30
realprecision = 38 significant digits (30 digits displayed)
pari: incgam(60,30)
1.38682990237888011617478399212 E80
pari: <ctrl-D>
--> Exiting back to Sage <--
}}}
{{{
sage: _ = var('R k')
sage: integrated = -(gamma(1/2*k, 1/2*R*k) - gamma(1/2*k))/gamma(1/2*k)
sage: plot(integrated.subs(k=41), (R,0,6))
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: integrated = -(gamma(1/2*k, 1/2*R*k) - gamma(1/2*k))/gamma(1/2*k)
sage: plot(integrated.subs(k=41.), (R,0,6))
Launched png viewer for Graphics object consisting of 2 graphics
primitives
}}}
{{{
sage: from sage.libs.mpmath import utils as mpmath_utils
sage: import mpmath
sage: mpmath_utils.call(mpmath.gammainc, 60, 0, 30)
1.28307801824120e74
}}}
Replying to [comment:37 buck]:
> I was finally able to integrate pari master-branch with sage, and while
the problem is much improved, it's not fixed.
> Here's the graph from the original bug report, using newest pari:
Trying that now seems to work for me, I get nice graphs with no spikes.
{{{
sage: sum(
....: plot(
....: integrated(k=k),
....: (x, 0, 2.5),
....: ymax=1.6,
....: color=color,
....: legend_label='k=%i' % k,
....: figsize=6,
....: aspect_ratio=1.0,
....: )
....: for k, color in zip(
....: [21, 22, 23, 26, 31, 41],
....: ['blue', 'brown', 'red', 'green', 'black', 'yellow',
'orange'],
....: )
....: )
Launched png viewer for Graphics object consisting of 6 graphics
primitives
}}}
> Those discontinuities are false. An example bad value:
> {{{
> sage: gamma(100, 7.01)
> -2.71843697211100e151
> }}}
> I will report this upstream, and attach a worksheet showing more detail.
What is the correct value? I get the following in Sage 7.3.beta9.
{{{
sage: gamma(100, 7.01)
9.33262154439442e155
}}}
--
Ticket URL: <https://trac.sagemath.org/ticket/18210#comment:38>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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