Theano：将theano.scan与theano.scan_module.until一起使用

Question

I'm new to using theano.scan and theano.scan_module.until . From the docs here , I'm not sure how to set variables in my while loop, and I'm uncertain how to adapt this post here to use theano.scan_module.until .

This is the code I'd like to translate to equivalent theano. Someone wanna take a shot in translating this? (And perhaps explaining the translated code.)

# Code to perform a random walk using a row stochastic matrix M.
for i in range(100):
    r_last = r
    r = r.dot(M)
    err = np.linalg.norm(r - r_last, ord=1).sum()
    if err < N * tol:
        break

I see three assignment operations here, and one if-statement. But I don't know how to translate this to theano.

And if you were curious, you could paste this code above to set the variables

import numpy as np

N = 3
tol = 1.0e-6
M = np.random.rand(N, N)
M = M / M.sum(axis=1).reshape(-1, 1)

r = np.ones(N, dtype=np.float) / N

Answer 1

Given:

N = 3
tol = 1.0e-6

You can define your symbolic function like this:

r_init = T.vector()
W = T.matrix()

def step(r):
    r_prime = T.dot(r, W)
    delta = (r_prime - r).norm(1)
    condition = T.lt(delta, N * tol)
    return r_prime, theano.scan_module.until(condition)

outputs, updates = theano.scan(step, outputs_info=[r_init], n_steps=1024)
r_final = outputs[-1]

solve = theano.function(inputs=[r_init, W], outputs=r_final)

And then use it like this:

M = np.random.rand(N, N)
M /= M.sum(axis=1).reshape((-1, 1))

r = np.ones(N, dtype=np.float) / N

print solve(r, M)

By the way, you are not performing a "random walk." You are solving for r such that rW = r, typically called the stationary distribution of the Markov chain.