Creating a matrix of arbitrary size where rows sum to 1?

Question

My task is to create a program that simulates a discrete time Markov Chain, for an arbitrary number of events. However, right now the part I'm struggling with is creating the right stochastic matrix that will represent the probabilities. A right stochastic matrix is a matrix that has row entries that sum to 1. And for a given size, I kind of know how to write the matrix that does that, however, the problem is that I don't know how to do that for an arbitrary size.

For example: here is my code for a 3x3 matrix, along with example of the output I was getting.

http://pastebin.com/4GXpAYTM

However, my code doesn't work every time -- there are certain times when the third entry in the row is negative because the first two are too large. And I don't know how to get around that, as far as I know, there isn't a function in Python that makes it so that you can generate random numbers that sum to something in particular.

Any help is appreciated.

(Note that this isn't a homework problem, it's only for extra credit in my Math class and the professor doesn't mind the use of outside sources.)

Answer 1

Using @MBo's idea:

In [16]: matrix = np.random.rand(3,3)

In [17]: matrix/matrix.sum(axis=1)[:,None]
Out[17]:
array([[ 0.25429337,  0.22502947,  0.52067716],
       [ 0.17744651,  0.42358254,  0.39897096],
       [ 0.36179247,  0.28707039,  0.35113714]])

In [18]: