Vectorization

Efficient computation via vectorization in the numpy library

Note: This is more of an advanced topic, something to be aware of if you are running slow code but not totally necessary. In a previous challenge, you may have created a program to estimate $\pi$ via a simple Monte Carlo simulation. A simple loop in python is not efficient if one wants to evaluate millions or billions of operations! Vectorization implemented in numpy allows more efficient computations to be carried using very efficient linear algebra implementations in programming languages like C or Fortran. Here is an example code for estimating $\pi$ using numpy (installed with mamba install numpy if needed):

import numpy as np

Nsteps  = int(1e8)
Ncircle = 0

# allocate initial random numbers
x_array = np.random.uniform(-1.,1.,Nsteps)
y_array = np.random.uniform(-1.,1.,Nsteps)
ones    = np.ones(Nsteps)

# do the calculation
start = time.time()
x_squared = np.square(x_array)
y_squared = np.square(y_array)
r_squared = np.add(x_squared, y_squared)
lessthan_one = np.greater(ones, r_squared)
Ncircle = np.sum(lessthan_one)
pi = 4.*(Ncircle/Nsteps)
print('%.16f'%pi)