#10075 closed enhancement (fixed)
Make log gamma symbolic
Reported by: | kcrisman | Owned by: | burcin |
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Priority: | major | Milestone: | sage-5.0 |
Component: | symbolics | Keywords: | sd35.5 |
Cc: | ktkohl, benjaminfjones | Merged in: | sage-5.0.beta7 |
Authors: | Karen Kohl, Karl-Dieter Crisman | Reviewers: | Karl-Dieter Crisman, Benjamin Jones |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #12507, #9130 | Stopgaps: |
Description (last modified by )
Currently, there is no way to send log_gamma
to Maxima, for instance. This can be fixed by following the models in the functions/ directory; it should be possible to make it a GinacFunction. Before doing so, though, one will have to resolve #10072, since the evaluation will be wrong (?) otherwise.
Apply only trac_10075.patch.
Attachments (3)
Change History (23)
comment:1 Changed 11 years ago by
Cc: | ktkohl added |
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Keywords: | sd35.5 added |
comment:2 Changed 11 years ago by
Cc: | benjaminfjones added |
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comment:3 Changed 11 years ago by
comment:4 Changed 11 years ago by
More precisely,
class Function_log_gamma(GinacFunction): def __init__(self): GinacFunction.__init__(self, "log_gamma", latex_name=r'\log\Gamma', ginac_name='lgamma', conversions={'mathematica':'LogGamma','maxima':'log_gamma'}) log_gamma = Function_log_gamma()
causes this failure.
comment:5 Changed 11 years ago by
Milestone: | sage-4.8 → sage-5.0 |
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It works if you drop the ginac_name
argument. The function is named log_gamma
in pynac.
comment:6 Changed 11 years ago by
Weird. So what about things like
unsigned lgamma_serial "GiNaC::lgamma_SERIAL::serial" # logarithm of gamma function
?
Changed 11 years ago by
Attachment: | trac_10075_log_gamma.patch added |
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symbolic log_gamma (with modification of functions.rst in case merged before #9130)
Changed 11 years ago by
Attachment: | trac_10075_log_gamma_without_functions.rst.patch added |
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symbolic log_gamma (with modification of functions.rst in case merged after #9130)
comment:7 Changed 11 years ago by
Authors: | → Karen T. Kohl |
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Status: | new → needs_review |
Load one of the above two patches depending on whether the functions.rst documentation file has been modified already (as in the combined patch for #9130).
The second patch file above (without functions.rst) was edited by hand from the first.
comment:8 Changed 11 years ago by
Burcin points out that
sage: log_gamma(-2.1) NaN
is not good. Sage itself does
sage: log(gamma(-2.1)) 1.53171380819509 + 3.14159265358979*I
but Wolfram Alpha says
1.53171... - 9.42478... i
so the branches seem to differ even there.
comment:9 follow-up: 10 Changed 11 years ago by
Description: | modified (diff) |
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Since #9130 has positive review: Apply only trac_10075_log_gamma_without_functions.rst.patch.
One might think that Burcin's comment about -2.1
makes this 'needs work', but that is actually the current Sage behavior as well, so in principle that would be a different ticket, since making log_gamma
symbolic would not introduce a regression...
In fact,
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: get_systems('log_gamma(2.1)') ['MPFR']
Apparently this is how MPFR deals with this function. So maybe all is well?
comment:10 Changed 11 years ago by
Apparently this is how MPFR deals with this function. So maybe all is well?
I mean, for this ticket. Though we should not claim that it is evaluated by Ginac, because it isn't (all the above is in Sage with or without this patch).
Believe it or not:
Not any negative value, but in lngamma.c: /* if x < 0 and -2k-1 <= x <= -2k, then lngamma(x) = NaN */ probably because the gamma value is negative. This is because MPFR defines lngamma as log(gamma(x)) while the C standard defines it as log|gamma(x)|. I wonder if this should be regarded as a bug or if a new function (say, mpfr_lgamma) should be defined in MPFR (in which case, not before 2.3.0). Do other standards (other languages) define such a function, either as log(gamma(x)) or as log|gamma(x)|?
I'm cc:ing Paul Z. just to confirm that this is intended MPFR behavior. We should then open another ticket to make sure to use mpmath or ginac or something to get complex answers. We currently somehow use PARI to get the complex versions.
sage: log_gamma(CC(-2.1)) 1.53171380819509 + 3.14159265358979*I sage: from sage.misc.citation import get_systems sage: get_systems('log_gamma(CC(-2.1))') ['PARI', 'MPFR']
comment:11 Changed 11 years ago by
Reviewers: | → Karl-Dieter Crisman |
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Ok, here we go.
sage: log_gamma(-21/10).n() NaN sage: get_systems('log_gamma(-21/10).n()') ['ginac']
So both give NaN
, but we end up using RR.log_gamma()
as in the GinacFunction
code.
sage: log_gamma(-31/10).n() 0.400311696703985 sage: log_gamma(-3.1) 0.400311696703985 sage: a = RR(5) sage: a.log_gamma() 3.17805383034795
I don't see anything holding this up except cosmetics. I'll try to make a refreshed patch momentarily.
comment:12 Changed 11 years ago by
Okay, I've been messing with this for too long today.
sage: get_systems('log_gamma(SR(6))') ['ginac', 'GMP'] sage: get_systems('log_gamma(RR(6))') [] sage: get_systems('log_gamma(CC(6))') ['PARI', 'MPFR'] sage: get_systems('log_gamma(6.)') ['MPFR']
See also #10072, where a lot of the numerical evaluation was fixed. Anyway, updated patch with more explanation and other information coming up. It needs light review; no code was changed, only doctests.
I'm not sure I like the last doctest either
sage: conjugate(log_gamma(-2)) conjugate(+Infinity)
What is the conjugate of plus infinity? But I'll leave it for now, just to document it, unless someone has an objection, since we have in vanilla Sage
sage: conjugate(+Infinity) conjugate(+Infinity)
I've opened #12521 for the evaluation at negative input with even ceiling function issue (i.e., log_gamma(-2.1)
).
comment:13 Changed 11 years ago by
Authors: | Karen T. Kohl → Karen T. Kohl, Karl-Dieter Crisman |
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Dependencies: | → #12507, #9130 |
I'm marking this as 'needs review', because I did change a fair number of tests. This definitely depends on #9130 because of some doc fixes. Also, I am marking this as depending on #12507, because I don't want to bother fixing that doctest if no one else is either. However, I don't really care either way.
comment:14 Changed 11 years ago by
Reviewers: | Karl-Dieter Crisman → Karl-Dieter Crisman, Benjamin Jones |
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The latest patch trac_10075.patch failed to apply on top of 5.0.beta4 with this patch queue:
trac_12507_v2.patch trac_9130-beta_function.2.patch trac_9130-py_float_segfault.take2.patch trac_9130-reviewer.patch
the failure seems to be in all.py
~/sage/latest/devel/sage> hg qpush -v applying trac_10075.patch patching file sage/functions/all.py Hunk #1 FAILED at 15 1 out of 2 hunks FAILED -- saving rejects to file sage/functions/all.py.rej
Here is sage/functions/all.py.rej
--- all.py +++ all.py @@ -16,7 +16,7 @@ from other import ( ceil, floor, gamma, psi, factorial, - abs_symbolic, erf, sqrt, + abs_symbolic, erf, sqrt, log_gamma, gamma_inc, incomplete_gamma, arg, real_part, real, imag_part, imag, imaginary, conjugate)
comment:15 Changed 11 years ago by
Makes sense, since beta is in that list now. I was not careful enough about the dependencies, I guess. Coming up.
comment:16 Changed 11 years ago by
Description: | modified (diff) |
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Okay, all should be well now? Sorry about that.
comment:17 Changed 11 years ago by
Status: | needs_review → positive_review |
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OK! All looks good now.
The patch now applies cleanly to 5.0.beta4 on top of the patch queue in my last comment. I've tested everything in sage/functions
and sage/symbolic
and running all tests now (I don't expect any problems). The docs look good too. Positive review.
comment:18 Changed 11 years ago by
Actually, one test did fail, but I don't think it's due to this patch (right?)
File "/home/jonesbe/sage/sage-5.0.beta4/devel/sage/sage/misc/trace.py", line 61: sage: print s.before[s.before.find('-'):] Expected: ---... ipdb> c 2 * 5 Got: ---------------------------------------------------------------------- | Sage Version 5.0.beta4, Release Date: 2012-02-14 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- ********************************************************************** * * * Warning: this is a prerelease version, and it may be unstable. * * * ********************************************************************** trace('print factor(10)'); print 3+97 s c Loading Sage library. Current Mercurial branch is: ********************************************************************** 1 items had failures: 1 of 11 in __main__.example_1 ***Test Failed*** 1 failures. For whitespace errors, see the file /home/jonesbe/.sage//tmp/trace_30044.py [2.2 s]
I haven't seen that failure before.
comment:19 Changed 11 years ago by
Merged in: | → sage-5.0.beta7 |
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Resolution: | → fixed |
Status: | positive_review → closed |
comment:20 Changed 7 years ago by
Authors: | Karen T. Kohl, Karl-Dieter Crisman → Karen Kohl, Karl-Dieter Crisman |
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Sage gives this error message on startup:
with this change in functions/other.py: