Opened 11 years ago

Last modified 5 years ago

# Access to beta function — at Version 13

Reported by: Owned by: kcrisman burcin major sage-5.0 symbolics special function, pynac, sd35.5 Cernay2012 benjaminfjones Karen T. Kohl, Burcin Erocal N/A

### Description (last modified by kcrisman)

Although Maxima has the beta function, Sage doesn't:

sage: a, b, c = var('a b c')
sage: assume(a > 0)
sage: assume(b > 0)
sage: x = var('x')
sage: beta_dist = x**(a-1) * (1 - x)**(b-1)
sage: c = integral(beta_dist, x, 0, 1)
sage: c
beta(a, b)
sage: c(a=.5,b=.5)
beta(0.500000000000000, 0.500000000000000)
sage: c(a=.5,b=.5).n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Users/karl-dietercrisman/<ipython console> in <module>()

/Users/karl-dietercrisman/Desktop/sage-4.4.2/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17042)()

TypeError: cannot evaluate symbolic expression numerically

This *is* is Ginac, though, and there is even room for defining it in symbolic/expression.pyx . It probably is also included in some of our other libraries, as a standard special function.

Apply

### comment:1 Changed 11 years ago by fredrik.johansson

For numerical evaluation, mpmath has beta and also the generalized incomplete beta function for complex arguments. But it's probably easy to do the complete beta function directly with Ginac.

Simplification for rational arguments (beta(0.5,0.5) = pi) would be nice.

Unless someone else wants to work on this, I might have a stab at it within a couple of days.

### comment:2 Changed 11 years ago by kcrisman

I wasn't suggesting which of the several packages in Sage should be used for numerical evaluation, though mpmath did come to mind :-)

I don't think that beta(0.5,0.5) would work, given that

sage: gamma(0.5)
1.77245385090552
sage: gamma(1/2)
sqrt(pi)

but beta(1/2,1/2) becoming pi should work fine once we have a symbolic wrapper (with or without Ginac):

sage: maxima_console()
Maxima 5.21.1 http://maxima.sourceforge.net
using Lisp ECL 10.4.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) beta(1/2,1/2);
(%o1)                                 %pi

Please do try to add this! We definitely often get email asking for various special functions both symbolically and numerically. Also, the more examples we have, the easier it is to finish off the rest of them by cut and paste.

### comment:3 follow-up: ↓ 4 Changed 11 years ago by burcin

GiNaC has a beta function, so this can probably be solved simply by wrapping that. See #8864 for an example.

Though I don't know why the beta() function in sage/symbolic/expression.pyx is commented. Maybe there is something I'm missing.

Fredrik, it would be great if you can do this. I'd be happy to answer questions if anything goes wrong.

### comment:4 in reply to: ↑ 3 ; follow-up: ↓ 5 Changed 11 years ago by kcrisman

Replying to burcin:

GiNaC has a beta function, so this can probably be solved simply by wrapping that. See #8864 for an example.

Though I don't know why the beta() function in sage/symbolic/expression.pyx is commented. Maybe there is something I'm missing.

I think the same reason the psi and psi2 ones are commented - when those were implemented, they didn't notice that they had been commented earlier. This was probably pretty early in the conversion, maybe when William was dealing with CLN (whatever that is)?

### comment:5 in reply to: ↑ 4 Changed 11 years ago by burcin

Replying to kcrisman:

Replying to burcin:

GiNaC has a beta function, so this can probably be solved simply by wrapping that. See #8864 for an example.

Though I don't know why the beta() function in sage/symbolic/expression.pyx is commented. Maybe there is something I'm missing.

I think the same reason the psi and psi2 ones are commented - when those were implemented, they didn't notice that they had been commented earlier. This was probably pretty early in the conversion, maybe when William was dealing with CLN (whatever that is)?

psi() and psi2() were commented because at the time there was no method defined to numerically evaluate those. This is not the case for beta() however. Here is the evalf method (from line 227 of ginac/inifcns_gamma.cpp):

if (is_exactly_a<numeric>(x) && is_exactly_a<numeric>(y)) {
try {
return exp(lgamma(ex_to<numeric>(x))+lgamma(ex_to<numeric>(y))-lgamma(ex_to<numeric>(x+y)));
} catch (const dunno &e) { }
}

We'll find out when someone tries this out I suppose.

### comment:6 Changed 11 years ago by burcin

• Keywords beginner added

### comment:7 Changed 11 years ago by ktkohl

• Status changed from new to needs_work

Added ginac wrapper for beta function. There is a problem when one argument is a float.

--Karen

sage: beta(3,2.0)

------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------

### Changed 10 years ago by burcin

fix segfault in py_float

### comment:8 Changed 10 years ago by burcin

• Authors set to Karen T. Kohl, Burcin Erocal
• Keywords beginner removed
• Milestone changed from sage-5.0 to sage-4.7.1

Hi Karen,

sorry for taking so long to look at this. It seems that I forgot to check for a NULL pointer in py_float(). attachment:trac_9130-py_float_segfault.patch fixes the segfault.

sage: from sage.functions.other import beta
sage: beta(3,2.0)
0.0833333333333333

Will you have time to finish the patch?

You need to add an import statement to sage/functions/all.py so beta is available at the command line. The documentation also needs some care. IIRC there should be an empty line after INPUT, OUTPUT and EXAMPLES. The statement

It is computed by various libraries within Sage, depending on
the input type.

is too vague. We should either remove it or explain how GiNaC evaluates this (see beta_eval() and beta_evalf() in inifcns_gamma.cpp).

### comment:9 Changed 9 years ago by ktkohl

• Keywords sd35.5 added

### comment:10 Changed 9 years ago by benjaminfjones

• Cc benjaminfjones added

### comment:11 Changed 9 years ago by ktkohl

• Status changed from needs_work to needs_review

### Changed 9 years ago by ktkohl

include beta in random_tests

### comment:12 Changed 9 years ago by ktkohl

Apply all patches in the order they were added:

• trac_9130_beta_function.patch
• trac_9130-py_float_segfault.patch
• trac_9130_beta_function.2.patch
• trac_9130_beta_function.3.patch

### comment:13 Changed 9 years ago by kcrisman

• Description modified (diff)
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