On Mon, Oct 27, 2008 at 2:37 PM, Neal Becker <[EMAIL PROTECTED]> wrote:
>
> On Friday 24 October 2008, Fredrik Johansson wrote:
>> On Fri, Oct 24, 2008 at 3:53 PM, Neal Becker <[EMAIL PROTECTED]> wrote:
>> > I'm a noob to sympy. I need something to replace ive from cephes. iv is
>> > the modified bessel function of order v, while ive is the exponentially
>> > scaled version: exp(-|x|) I(v,x)
>> >
>> > Any suggestions?
>>
>> Replace how? What features do you need?
>>
>> Fredrik
>>
> Sorry, I'll try to describe better.
>
> I have a calculation of probability which involves things like factorial,
> exponential, and also Ive. It was working fine using scipy. Now I need to
> extend it to larger parameter values, and the calculation blows up (involves
> things like 512!). I thought, why not try using sympy? It has extended
> precision. I noticed that sympy has some bessel functions, but not the ones I
> need.
Well, mpmath handles big floating-point factorials without trouble:
>>> from mpmath import *
>>> fac(512)
mpf('3.4772897931326054e+1166')
Mpmath doesn't have the Bessel I function, but it's not too hard to
write a basic implementation:
from mpmath import *
from mpmath.functions import funcwrapper
@funcwrapper
def ive(v,z):
s = hyp1f1(v+0.5, 2*v+1, 2*z)
c = z**v / (2**v * exp(z) * gamma(v+1))
return exp(-abs(z)) * s*c
>>> mp.dps = 50
>>> print ive(3, 0.5)
0.0016043415075654608433293663669854375123123266820256
>>>
>>> from scipy.special import ive
>>> ive(3, 0.5)
0.0016043415075654604
(However, this implementation will not be fast for very large z. You'd
have to use an asymptotic series for that.)
Fredrik
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