CODEWITHSUNDEEP
pythonpython-3.xnumpymachine-learning
J.Do
J.Do

Reputation: 428

How to express the following piecewise function in python?

How can I implement with numpy the following piecewise function and its derivative?:

enter image description here

I tried to:

def func(n):
    return beta * ((0 < n) * n + (n <= 0) * (k * np.exp(n) - alpha))

with its derivative (back propagation):

def func_prime(n)
    return (n <= 0) * np.multiply(beta ,k, np.exp(n)) + (beta)

However its not working. Thus, how can I implement the above function with numpy (note that n is an array).

Upvotes: 1

Views: 630

Answers (2)

jimidime
jimidime

Reputation: 552

To compute the function and its derivative you can follow below procedure:

fun = np.where(n<=0, beta*K*(np.exp(n)-1), beta*n)
derivativ = np.where(n<=0, beta*K*(np.exp(n)), beta)

you can also use scipy.misc.derivative.https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.misc.derivative.html

Upvotes: 1

Timofey Chernousov
Timofey Chernousov

Reputation: 1294

Probably you need numpy.where for you goal. Also keep in mind, numpy arrays could be used for vector operations directly (most times).

Sample code below:

In [1]: import numpy as np

In [2]: n = np.random.random(10)-0.5

In [3]: n
Out[3]:
array([ 0.15714377, -0.30756307,  0.02925383, -0.05156817, -0.32182295,
       -0.32772489,  0.15692736, -0.24274195, -0.19055825,  0.25264444])

In [4]: beta=1.0

In [5]: K=2.0

In [6]: np.where(n<=0, beta*K*(np.exp(n)-1), beta*n)
Out[6]:
array([ 0.15714377, -0.52952701,  0.02925383, -0.10052219, -0.55034698,
       -0.55887755,  0.15692736, -0.43105215, -0.34700477,  0.25264444])

In [7]:

From numpy.where manual:

numpy.where(condition[, x, y])

Return elements, either from x or y, depending on condition.

Upvotes: 1

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