python - Using a function to populate a numpy array

Question

I have made a function that performs a random walk simulation (random_path) and returns a 1D array (of length num_steps +1). I would like to perform a large number of simulations (n_sims) using this function and then examine my results. I can do this using lists and for loops as:

simulations = [] 
for i in range(0, n_sims):
    current_sim = random_path(x, y, sigma, T, num_steps)
    simulations.append(current_sim)

This works fine. I am wondering if there is a more pythonic way of doing this though? Is it possible to do this using only numpy arrays? That is, instead of setting up simulations as an empty list and then creating a list of arrays with a for loop, can I directly initialise simulations using the function random_path to create an array that I guess ultimately would be of shape (n_sims, num_steps + 1)?

Answer 1

Let's assume that you generate your random walk something like this (and if you don't, you probably should be):

walk = np.r_[0, np.random.normal(scale=sigma, size=N).cumsum()]

To make M simulations, just generate the appropriate number of data points and sum over the correct axis:

walks = np.concatenate((np.zeros((M, 1)), np.random.normal(scale=sigma, size=(M, N)).cumsum(axis=-1)), axis=-1)