running sage from a Python script
I'm using sage 5.5 on ubuntu 12.04. I'm trying to run sage via the following script
#!/usr/bin/env sage -python
import sys
from sage.all import *
sigma = 10
z = var('z')
m0 = 128
P = exp(-(1/2)*z**2/sigma**2)/(sqrt(2*pi)*sigma)
m = m0*exp(-(1/2)*z**2)
mb = m0/sqrt(1+sigma**2)
f = lambda u: 1-2*(numerical_integral(u*P*m**2/(mb*(u*mb+(1-u)*m)), 0, Infinity))[0]
print find_root(f, 0.1, 1, rtol=0.01)
I run this from the command line with
sage -python runDispK1.py
and I get the following error
Warning: invalid value encountered in absolute
Warning: invalid value encountered in absolute
Warning: invalid value encountered in absolute
Warning: invalid value encountered in absolute
Warning: invalid value encountered in absolute
Traceback (most recent call last):
File "runDispK1.py", line 16, in <module>
print find_root(f, 0.1, 1, rtol=0.01)
File "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/numerical/optimize.py", line 108, in find_root
raise RuntimeError, "f appears to have no zero on the interval"
RuntimeError: f appears to have no zero on the interval
Whereas if I run the exact same code within sage, e.g. I have a file called run.sage with this text in it:
sigma = 10
z = var('z')
m0 = 128
P = exp(-(1/2)*z**2/sigma**2)/(sqrt(2*pi)*sigma)
m = m0*exp(-(1/2)*z**2)
mb = m0/sqrt(1+sigma**2)
f = lambda u: 1-2*(numerical_integral(u*P*m**2/(mb*(u*mb+(1-u)*m)), 0, Infinity))[0]
print find_root(f, 0.1, 1, rtol=0.01)
then sage gives me the correct answer
sage: load("run.sage")
0.550279773862
Is there something I'm missing here? I'm new to sage and python scripting but it seems the numerical_integral function is returning nothing useful, so I are these functions created incorrectly?
Thanks