python - How to apply numpy random.choice to a matrix of probability values (Vectorized solution)

Question

The problem I have is as follows

I have a 1-D list of integers (or np.array) with 3 values

l = [0,1,2]

I have a 2-D list of probabilities (for simplicity, we'll use two rows)

P = 
[[0.8, 0.1, 0.1],
 [0.3, 0.3, 0.4]]

What I want is numpy.random.choice(a=l, p=P), where each row in P (probability distribution) is applied to l. So, I want a random sample to be drawn from [0,1,2] with prob. dist. [0.8, 0.1, 0.1] first, then with prob. dist. [0.3, 0.3, 0.4] next, to give me two outputs.

===== Update ======

I can use for loops or list comprehension, but I am looking for a fast/vectorized solution.

Answer 1

Here's one way.

Here's the array of probabilities:

In [161]: p
Out[161]: 
array([[ 0.8 ,  0.1 ,  0.1 ],
       [ 0.3 ,  0.3 ,  0.4 ],
       [ 0.25,  0.5 ,  0.25]])

c holds the cumulative distributions:

In [162]: c = p.cumsum(axis=1)

Generate a set of uniformly distributed samples...

In [163]: u = np.random.rand(len(c), 1)

...and then see where they "fit" in c:

In [164]: choices = (u < c).argmax(axis=1)

In [165]: choices
Out[165]: array([1, 2, 2])