Python Numpy Outer Product Apply List Of Functions To List Of Arguments Without For Loops

Question

I have an array of numbers, and a list of functions.

I want to run every function on every number to get back a matrix.

Is there a way to do it without slow python for looping / mapping?

import numpy
    arr = numpy.array([1,2,3,4,5])
    fns = [numpy.sin, numpy.cos, numpy.exp]
    results = numpy.zeros(shape=( len(fns), len(arr) ))
    for i, fn in enumerate(fns):
        for j, val in enumerate(arr):
            results[i][j] = fn(val)
    print ('results', results)

I can get rid of one loop with function broadcasting:

results2 = numpy.zeros(shape=( len(fns), len(arr) ))
    for i, fn in enumerate(fns):
        results2[i] = fn(arr)
    print ('results2', results2)

Is there some clever pythonic numpy-ish way to get rid of my second loop?

Perhaps some built in outer-product-ish interaction which is difficult to google?

results3 = numpy.function_outer( fns, arr)

Numpy does not know how to vectorize fns. You could create a lambda function and use numpy's frompyfunc or apply_along_axis, but this will just marginally slow things down. — Kevin
– Kevin, Commented May 4, 2021 at 9:21
I found this link stackoverflow.com/questions/44614254/… that is related to your question. — RandomGuy
– RandomGuy, Commented May 4, 2021 at 9:23

quantummind · Accepted Answer · 2021-05-04 08:33:46Z

1

You can use a list comprehension and transform it back to a numpy array like this:

results3 = numpy.array([ fn(arr) for fn in fns])

answered May 4, 2021 at 8:33

quantummind

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6 Comments

RandomGuy Over a year ago

This is cleaner to write, but not faster as it's still a for loop.

quantummind Over a year ago

I cannot agree, since this is a pythonic way, as it was requested.

RandomGuy Over a year ago

"Is there a way to do it without slow python for looping / mapping?"

quantummind Over a year ago

@RandomGuy It depends on what you mean by slow. By my measurement the solution int the answer takes 5.84 µs ± 257 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each). It is a less than half the time compared to the solution with classical loop.

RandomGuy Over a year ago

The author expected a numpy function like apply_along_axis to do so, but after some researchs it seems it is simply not possible. Moreover I tried your solution but I did not measure any significant difference between the two execution times, could you please provide a piece of your code so I can compare?

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