Numpy vectorized function assignment with a boolean statement

Question

I would like to assign a function that has a boolean evaluation in it, using a fast way. Here is a simple example. I want the following function to be evaluated for arbitrary a and b:

a = 0.5
b = 0.6
def func(x):
    x=max(x,a)
    if x>b:
        return x**2
    else:
        return x**3

and then I want to assign the function values into an array in a vectorized manner (for speed):

xRange = np.arange(0, 1, 0.1)
arr_func = func(xRange)

But I get the error:

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

Now, I know I can assign the values in a loop. But that will be slow compared to the vectorized equivalent. Can I bypass this exception and still assign the values in a vectorized manner?

I think you could use docs.scipy.org/doc/numpy-1.10.0/reference/generated/… — Lukisn
– Lukisn, Commented Aug 16, 2017 at 11:44
@Lukisn, you should consider deleting your comment since it got an upvote and is misleading, see your answer. — Ulrich Stern
– Ulrich Stern, Commented Dec 18, 2018 at 21:19

mgilson · Accepted Answer · 2017-08-16 11:41:00Z

4

If I'm reading your code correctly, the vectorized version of this would be to use a couple np.where:

def func(x):
    x = np.where(a > x, a, x)
    return np.where(x > b, x**2, x**3)

answered Aug 16, 2017 at 11:41

mgilson

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2 Comments

mgilson Over a year ago

@DanielF -- Yes, you're probably right. However, that would modify the argument (xRange in the case of OP's example). That may not be desirable. Numpy is already making a bunch of copies in both cases -- the (frequently correct) assumption that is usually made when writing numpy code is that the overhead of the copies is small compared to the overhead of python loops.

Daniel F Over a year ago

True - I'm surprised pass by reference doesn't trip me up more considering how often I forget it :) Deleted the comment to prevent confusion

Daniel F · Accepted Answer · 2017-08-16 12:17:04Z

1

It's also possible to use np.select - it's a little wordier than necessary in this case, but is extensible to many conditions

def func(x):
    condlist =   [
                  x < a, 
                  (x >= a) & (x <= b), 
                  x > b
                 ]
    choicelist = [
                  a**3, 
                  x**3, 
                  x**2
                 ]
    return np.select(condlist, choicelist)

or

def func(x):
    condlist =   [
                  x < a,  
                  x > b
                 ]
    choicelist = [
                  a**3, 
                  x**2
                 ]
    return np.select(condlist, choicelist, default = x**3)

edited Aug 16, 2017 at 12:17

answered Aug 16, 2017 at 12:03

Daniel F

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Comments

Lukisn · Accepted Answer · 2017-08-16 13:45:37Z

0

If you want (or have) to keep your original function, you could use numpy's vectorize function to create the "vectorized" version that accepts a numpy array as an input.

Note that this function is only for convenience and offers no performance improvements since it internally only implements a for loop. So there is no "real" vectorization!

import numpy as np

def func(x, a=0.5, b=0.6):
    x = max(x, a)
    if x > b:
        return x**2
    else:
        return x**3

vfunc = np.vectorize(func)  # this is it!

xRange = np.arange(0, 1, 0.1)
arr_func = vfunc(xRange)

print(arr_func)

The above code works and produces the following output:

[ 0.125  0.125  0.125  0.125  0.125  0.125  0.36   0.49   0.64   0.81 ]

edited Aug 16, 2017 at 13:45

answered Aug 16, 2017 at 12:01

Lukisn

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2 Comments

Nils Werner Over a year ago

This is a bad idea. You may want to read the "Notes" section of the vectorize documentation page.

Lukisn Over a year ago

Thanks for pointing that out. I edited my answer to make this clear.

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