Quad function returning different values in python

Question

I faced an issue when trying to use quad to integrate a function. Essentially, I have two versions of code where I define t(a) in different places. Both codes looks the same to me but the result I am getting is slightly different.

I am guessing that it is due to the error associated with using the quad method, but am not too sure. Would appreciate any help!

import numpy as np
from scipy.integrate import quad

s = 0.05

# Version 1
def POi1(w):
    def t(a):
        return (1/(0.27*a**(-1)+(1-0.27)*a**(-3*w-1))**(1/2))
    return (np.exp(-((1+w)**2)/(2*s**2))*(1/(quad(t, 0, 1)[0]+((2/3)*(1/(np.abs(1+w)*1*(1-0.27)**2))))))

PO1 = quad(POi1, -np.inf, -1)[0]
print(PO1)

#Version 2
def t(a):
    return (1/(0.27*a**(-1)+(1-0.27)*a**(-3*w-1))**(1/2))

def POi1(w):
    return (np.exp(-((1+w)**2)/(2*s**2))*(1/(quad(t, 0, 1)[0]+((2/3)*(1/(np.abs(1+w)*1*(1-0.27)**2))))))

PO1 = quad(POi1, -np.inf, -1)[0]
print(PO1)

Answer 1

your current code doesn't work (version 2) because the function t will take as parameter a, only one parameter, but you can see that requires 2 params, a and w, it may work if you have a variable w already defined (maybe you work in jupyter notebook) and this it may be the cause of your different results

to make your code work and have the same result for your version 2 you can use:

def get_t(w):
    def t(a):
        return (1/(0.27*a**(-1)+(1-0.27)*a**(-3*w-1))**(1/2))
    
    return t

def POi1(w):
    t = get_t(w)
    return (np.exp(-((1+w)**2)/(2*s**2))*(1/(quad(t, 0, 1)[0]+((2/3)*(1/(np.abs(1+w)*1*(1-0.27)**2))))))

PO1 = quad(POi1, -np.inf, -1)[0]
print(PO1)

in this example a closure it is used to pass the w variable, you will get the same results