How to return array from element-wise custom calculation on other numpy arrays?

Question

I would like to obtain a numpy array from element-wise calculation on different numpy arrays. As of now, I am using a lambda function to return a value, repeat that for all values, create a list therefrom, and convert to numpy array:

import math
import numpy as np 
def weightAdjLoads(loadsX, loadsY, angles, g):
        adjust = lambda x, y, a: math.sqrt((abs(x) - math.sin(a)*g)**2 + (abs(y) - math.cos(a)*g)**2)
        return np.array([adjust(x, y, a) for x, y, a in zip (loadsX, loadsY, angles)])

This seems to me like too much overhead. Are there any numpy routines which could do just that?

I am aware of methods such as numpy.sqrt(A**2 + B**2), where A and B are numpy arrays. However, those only allow to apply predefined formulas. How can I apply custom formulas on numpy arrays?

"However, those only allow to apply predefined formulas. How can I apply custom formulas on numpy arrays?" - what do you mean, only predefined formulas? Write your custom formulas in such a way that they apply to NumPy arrays naturally. — user2357112
– user2357112, Commented Jul 20, 2017 at 16:26

hpaulj · Accepted Answer · 2017-07-20 16:30:24Z

numpy.sqrt(A**2 + B**2) is parsed by the Python interpreter into calls roughly as follows:

 tmp1 = A**2  # A.__pow__(2)
 tmp2 = B**2  #
 tmp3 = tmp1 + tmp2  # tmp1.__add__(tmp2)
 tmp4 = np.sqrt(tmp3)

That is, there are defined numpy functions and methods for power, addition, sqrt etc.

Your lambda works with scalars, not numpy arrays:

math.sqrt((abs(x) - math.sin(a)*g)**2 + (abs(y) - math.cos(a)*g)**2)

Specifically it's the math trig functions that require scalars. abs works with arrays:

abs(A) => A.__abs__()

numpy provides a full set of trig functions, so this function should work with array, or scalar, arguments:

def foo(x, y, a):
    return np.sqrt((abs(x) - np.sin(a)*g)**2 + (abs(y) - np.cos(a)*g)**2)

There are ways of wrapping your scalar adjust into a numpy function, but the speed savings relative to your list comprehension are minor.

f = np.vectorize(adjust)
f = np.frompyfunc(adjust, 3, 1)

Mainly they make it easier to broadcast arrays to a scalar functions. But to gain compiled speed you have to make a conversion such as in my foo, or use a third party package like cython, numba, or numexpr.

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