Most pythonic way of weighted random selection

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Dear list,

who's got aesthetic advice for the following problem? I've got some joint probabilities of two distinct events Pr(X=x, Y=y), stored in a list of lists of floats, where every row represents a possible outcome of X and every float in a row a possible outcome of Y (which I will now call my matrix, altough I can't use numpy or numeric for this), so e.g. m = [[0.2, 0.4, 0.05], [0.1, 0.05, 0.2]]. All lists in the list are equally long and the values of the flattened list add up to 1.0, i.e. sum([sum(row) for row in m]) == 1. In practice, this 'matrix' is about 20x40, i.e. a list with 20 lists á 40 floats each.

Now the task is to select one outcome for X and Y based on the joint probabilites, and afterwards check that the outcomes fullfill certain criteria. If it doesn't fulfill some criteria a new pair of outcomes has to be selected, for other criteria it will still be selected with a certain probability. My approach was to choose a random number, and then walk through the list adding the values together until the accumulated sum is greater than my random threshold:

import random
r = random.random()
s = 0.0
p = 0.2 # probability of selecting outcome if it doesn't fulfill criterion 2
break_loop = False
while not break_loop:
for row_index in range(len(m)):
for col_index in range(len(row)):
s += m[row_index][col_index]
if s >= r:
if not fulfills_criterion_a(row_index, col_index):
break_loop = True
elif not fulfills_criterion_b(row_index, col_index):
if random.random() <= p:
return row_index, col_index
else:
break_loop = True
else:
return row_index, col_index
if break_loop: break
if break_loop: break
break_loop = False


Now that looks plain ugly, and I wonder whether you might find a slightly more elegant way of doing it without using numpy and the like.

Bests,
Manuel
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