Most efficient way to map function over numpy array

What is the most efficient way to map a function over a numpy array? The way I've been doing it in my current project is as follows:

import numpy as np 

x = np.array([1, 2, 3, 4, 5])

# Obtain array of square of each element in x
squarer = lambda t: t ** 2
squares = np.array([squarer(xi) for xi in x])

However, this seems like it is probably very inefficient, since I am using a list comprehension to construct the new array as a Python list before converting it back to a numpy array.

Can we do better?

I've tested all suggested methods plus np.array(map(f, x)) with perfplot (a small project of mine).

Message #1: If you can use numpy's native functions, do that.

If the function you're trying to vectorize already is vectorized (like the x**2 example in the original post), using that is much faster than anything else (note the log scale):

If you actually need vectorization, it doesn't really matter much which variant you use.

Code to reproduce the plots:

import numpy as np
import perfplot
import math


def f(x):
    # return math.sqrt(x)
    return np.sqrt(x)


vf = np.vectorize(f)


def array_for(x):
    return np.array([f(xi) for xi in x])


def array_map(x):
    return np.array(list(map(f, x)))


def fromiter(x):
    return np.fromiter((f(xi) for xi in x), x.dtype)


def vectorize(x):
    return np.vectorize(f)(x)


def vectorize_without_init(x):
    return vf(x)


b = perfplot.bench(
    setup=np.random.rand,
    n_range=[2 ** k for k in range(20)],
    kernels=[
        f,
        array_for,
        array_map,
        fromiter,
        vectorize,
        vectorize_without_init,
    ],
    xlabel="len(x)",
)
b.save("out1.svg")
b.show()

How about using numpy.vectorize.

import numpy as np
x = np.array([1, 2, 3, 4, 5])
squarer = lambda t: t ** 2
vfunc = np.vectorize(squarer)
vfunc(x)
# Output : array([ 1,  4,  9, 16, 25])