Numpy RuntimeWarning: divide by zero encountered in log10

Question

From this post I understand that the log10() evaluates before the where is evaluated. Put simply I dont understand the answer provided in that question. Also why would the log10() be evaluated first, surely that just results in unnecessary computations?

merge_y = np.where(n <= 1, 1, n * np.log10(n))

import matplotlib.pyplot as plt
import numpy as np

n = np.arange(0, 10, 0.0001)

merge_y = np.where(n <= 1, 1, n * np.log10(n))
insertion_y = n*n

plt.plot(n, merge_y,'g')
plt.plot(n,insertion_y,'r')
plt.grid(True)
plt.xlabel('n')
plt.ylabel('T(n)')
plt.title('Time complexities of merge and insertion sort w/ input size n')
plt.show()

Answer 1

You have to understand that np.where is working based on logical indexing, you are thinking about it like a loop. What np.where does is

np.where(return_this_logical_indexes, From_this_array_if_true, From_this_array_if_false)

But in order to to do this, those arrays must exist, if it's a function, then it will evaluate it in order to obtain an array and then index it with the logical array created by the condition.

You are thinking it more like a list comprenhension, like:

merge_y = [x*np.log10(x) if x>=1 else 1 for x in n]