How to implement step-like function in python

Question

I am frequently using the following construct to implement the Heaviside step function

def f(x,xm):   
   1 * (xm > c)

I used the same to implement the CDF of the Pareto distribution.

def pareto_cum(x,xm,a):
     return (1.-(xm/x)**a) * (x > xm)

Unfortunately this produces an error message in python 3. I don't understand why division by zero is a problem here, since always xm>0. That is, x > 0 should be guaranteed by default.

import numpy as np
import matplotlib.pyplot as plt


x=np.linspace(0,10,100000)
def pareto_cum(x,xm,a):
     return (1.-(xm/x)**a) * (x > xm)

plt.plot(x,pareto_cum(x,2,3))
__main__:2: RuntimeWarning: divide by zero encountered in true_divide
__main__:2: RuntimeWarning: invalid value encountered in multiply
[<matplotlib.lines.Line2D object at 0x7fdf026770b8>]

CDF of the Pareto distribution https://en.wikipedia.org/wiki/Pareto_distribution

Why would it be "guaranteed by default"? You never check to make sure it's non-zero. — Carcigenicate
– Carcigenicate, Commented May 27, 2017 at 18:44
Perhaps I misunderstand something, but shouldn't (x > xm) be taking care of it? I would expect that the if condition is evaluated first. — Alexander Cska
– Alexander Cska, Commented May 27, 2017 at 18:46
I don't see any ifs in your code. I don't have numpy experience, but x > xm will evaluate to a boolean value, then it's cast to a number since you're multiplying it. All it will do is force everything to either evaluate to 0 (if x is less than xm), or do nothing otherwise. — Carcigenicate
– Carcigenicate, Commented May 27, 2017 at 18:50
Deleted my answer since I was over my head. Hopefully Importance's answer can help you. — Carcigenicate
– Carcigenicate, Commented May 27, 2017 at 19:07

ImportanceOfBeingErnest · Accepted Answer · 2017-05-27 19:02:28Z

1

It's not an error message, it's a warning. So you can ignore it if you like. The only effect this has it that the first point of the result is nan. The code runs fine otherwise.

import numpy as np
import matplotlib.pyplot as plt

x=np.linspace(0,10,100000)
def pareto_cum(x,xm,a):
     return (1.-(xm/x)**a) * (x > xm)

plt.plot(x,pareto_cum(x,2,3))
plt.show()

produces as expected:

You can get rid of the warning by not letting 0 be part of the array, e.g.

x=np.linspace(0,10,100000)
x[0] = 1e-12

You can also check inside the function

def pareto_cum(x,xm,a):
     x[x==0] = 1e-12
     return (1.-(xm/x)**a) * (x > xm)

answered May 27, 2017 at 19:02

ImportanceOfBeingErnest

342k61 gold badges737 silver badges771 bronze badges

Sign up to request clarification or add additional context in comments.

4 Comments

Alexander Cska Over a year ago

x[x==0] = 1e-12 is passed by value I guess. i.e. this will not change the actual data.

ImportanceOfBeingErnest Over a year ago

Of course it will change the data. Every item in x that is equal to zero will afterwards be 1e-12. But of course we only change the local variable x here. The global x outside the function has nothing do do with it (they just have the same name but python wouldn't know about that anyways).

Alexander Cska Over a year ago

OK, pass by value it is.

ImportanceOfBeingErnest Over a year ago

Well, python does not have the concept of pass-by-value, but the behaviour as seen by the programmer is mostly the same.

Collectives™ on Stack Overflow

How to implement step-like function in python

1 Answer 1

4 Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

4 Comments

Your Answer

Sign up or log in

Post as a guest

Related