How do I vectorize a function in numpy with some fixed parameters?

Question

I have written a code for approximating a function with the Bernstein polynomials ( https://en.wikipedia.org/wiki/Bernstein_polynomial )

at

https://github.com/pdenapo/metodos-numericos/blob/master/python/bernstein.py

I have a function that gives the polynomial approximating f as bernstein(f, n, p) (where f is the function that I want to approximate, n is the degree and p the point where it is evaluated.

def bernstein(f, n, p):
    return np.sum(
        [f(k / n) * st.binom.pmf(k, n, p) for k in np.arange(0, n + 1)])

Now I want to generate a plot of this function where f and n es fixed, and p runs though a vector generated by np.arrange So I am vectorizing the function in the following way:

 bernstein3 = lambda x: bernstein(f, 3, x)
 bernstein3 = np.vectorize(bernstein3)
 y3 = bernstein3(x)
 plt.plot(x, y3, 'green', label='$B_3$')

It works. But I guess there must be some more elegant, or perhaps more pythonic way of doing this. Any suggestions? Many thanks

Please post the bernstein function within the question, as the answer depends on how it is implemented. Also, I suppose it could be assumed that f is a vectorized function in the first place, otherwise it would be difficult to work around that. — javidcf
– javidcf, Commented Mar 4, 2020 at 19:05

javidcf · Accepted Answer · 2020-03-04 19:36:58Z

1

Since SciPy statistic functions are vectorized, your bernstein function can be modified in a straightforward manner to work that way:

import numpy as np
import scipy.stats

def bernstein(f, n, p):
    # Vector of k values
    k = np.arange(n + 1)
    # Add a broadcasting dimension to p
    pd = np.expand_dims(p, -1)
    # Compute approximation
    return np.sum(f(k / n) * scipy.stats.binom.pmf(k, n, pd), -1)

It would be used simply as this:

import numpy as np
import matplotlib.pyplot as plt

def f(x):
    return np.abs(1 / 2 - x)

x = np.linspace(0, 1, 100)
y = f(x)
plt.plot(x, y, 'blue', label='f(x)')
y_approx = bernstein(f, 10, x)
plt.plot(x, y_approx, 'orange', label='f_approx(x)')
plt.show()

answered Mar 4, 2020 at 19:36

javidcf

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2 Comments

Pablo De Napoli Over a year ago

Many thanks but I don't undersand the line pd = np.expand_dims(p, -1) What is supposed to do?

javidcf Over a year ago

@PabloDeNapoli It adds an extra dimension at the end of the shape of p, so whatever shape it has the computations of the polynomials are broadcasted along that dimension (see NumPy's broadcasting rules). Then np.sum reduces that dimension, so the output has the same shape as the input.

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