A standard mathematical process is integrating an equation. SciPy accomplishes this using a callback function to iteratively calculate out the integration of your function. For example, suppose that we wanted to determine the integral of the following equation:

We would use a script like the following. We are using the definition of pi from the standard math package.

from scipy.integrate import quad
import math

def integrand(x, a, b):
    return a*math.pi + b

a = 2
b = 1
quad(integrand, 0, 1, args=(a,b))

Again, this coding is very clean and simple, yet almost impossible to do in many languages. Running this script in Jupyter we see the results quickly:

I was curious how the integrand function is used during the execution. I am using this to exercise a call back function. To see this work, I added some debugging information to the script where we count how many iterations occur and what display the values called each time:

from scipy.integrate import quad
import math

counter = 0
def integrand(x, a, b):
    global counter
    counter = counter + 1
    print ('called with x=',x,'a = ',a,'b = ', b)
    return a*math.pi + b

a = 2
b = 1
print(quad(integrand, 0, 1, args=(a,b)))
print(counter)

We are using a counter at the global level, hence when referencing inside the integrand function we use the global keyword. Otherwise, Python assumes it is a local variable to the function.

The results are as follows:

The function was called 21 times to narrow down the solution.