I was trying to compute the expected value of log(x) under the gamma
distribution, but sympy hangs using 100% CPU, and appears to be inside a
recursion loop:
....
File "/home/keir/wrk/sympy/sympy/polys/densebasic.py", line 296, in
dmp_zero_p
return dmp_zero_p(f[0], u-1)
File "/home/keir/wrk/sympy/sympy/polys/densebasic.py", line 296, in
dmp_zero_p
return dmp_zero_p(f[0], u-1)
File "/home/keir/wrk/sympy/sympy/polys/densebasic.py", line 296, in
dmp_zero_p
return dmp_zero_p(f[0], u-1)
File "/home/keir/wrk/sympy/sympy/polys/densebasic.py", line 296, in
dmp_zero_p
return dmp_zero_p(f[0], u-1)
File "/home/keir/wrk/sympy/sympy/polys/densebasic.py", line 296, in
dmp_zero_p
return dmp_zero_p(f[0], u-1)
....
Here's the code:
import sympy
from sympy import exp, log, var, integrate, oo
from sympy.functions.special.gamma_functions import gamma
x, k = var('x k')
# Compute the expected value of log(x) under a gamma distribution with theta
= 1
gamma_pdf = x**(k-1) * exp(-x) / gamma(k)
print integrate(log(x) * gamma_pdf, (x, 0, oo))
Compare with wolfram alpha:
http://integrals.wolfram.com/index.jsp?expr=log(x)x^(k-1)Exp[-x]/Gamma[k]
Any tips on how to get sympy to solve this sort of problem?
Thanks,
Keir
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