Math Range Error: Overflow Error using numpy.power()

Question

I'm using Python 3 to use scipy's integrate.quad() function to integrate the expression (t^s / cosh^2(t)) for a given input s. I get the OverflowError: math range error.

My code looks like this:

from math import inf
from math import cosh
from scipy.integrate import quad
import numpy as np

def Integral_Expression(s):
    ans, err = quad(lambda t: (np.power(t,s))/(np.power(cosh(t),2)), 0, inf)
    return ans

I've seen other people who get the Math Range Error use numpy's exp() or power() methods to solve the problem, but it doesn't seem to be working. I also tried

and, err = decimal.Decimal(quad(lambda t: (power(t,s))/power(cosh(t),2), 0, inf))

with no success. Thanks for any help!

what range of s do you consider?

tstanisl
– tstanisl

2020-07-02 22:34:43 +00:00
Commented Jul 2, 2020 at 22:34 — tstanisl
– tstanisl, Commented Jul 2, 2020 at 22:34

tstanisl · Accepted Answer · 2020-07-03 08:41:43Z

1

You could use Integration by substitution. Try to change variable to something that does not grow so rapidly like cosh(x).

Try:

t = log(u)

Now:

cosh(t) = 0.5 *  (exp(t) + exp(-t)) = 0.5 * (u + 1/u)
dt = du / u

After the change, the old integral

Integral[(t**s)/cosh(t)**2, 0, Inf]

becomes

Integral[log(u)**s/((u+1/u)/2)**2/u, 1, inf]

Note that integral boundaries had changed as well.

The result:

s = 2
quad(lambda u: (log(u)**s)/((u+1/u)/2)**2/u, 1, inf)

returns (0.8224670334241126, 1.1430967283843074e-11).

This solution is slightly more precise than approach based on replacing infinity with a large number:

>>> quad(lambda t: (t**s)/cosh(t)**2, 0, 100)
(0.8224670334241144, 1.3879318674935893e-08)

edited Jul 3, 2020 at 8:41

answered Jul 2, 2020 at 22:36

tstanisl

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Comments

bousof · Accepted Answer · 2020-07-02 22:39:39Z

0

There is a great chance that the problem comes from the square of cosh(t) that behaves like an exponential for t close to infinity. Maybe you can stop the upper bound of the integral to 100 given that 1/cosh(100)**2=5e-87 you are already reaching the floating point precision.

Note that you'll get the same error if you simply try to evaluate cosh(1000) in your python code:

print(cosh(1000))

Output:

% python3 script.py
Traceback (most recent call last):
  File "script.py", line 11, in <module>
    print(cosh(1000))
OverflowError: math range error

answered Jul 2, 2020 at 22:39

bousof

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