Python，for循环中的随机向量与随机数

Question

I am trying to solve some stochastic differential equations , with Gaussian noise . I wonder if is better to use a Noise Vector :

eta = np.random.normal(size=N)*sqrtdt
q = []
p = []
q.append(1.0)
p.append(1.0)
for i in range(N):
    q.append(f(q[i],p[i],eta[i])
    p.append(g(q[i],p[i],eta[i])

with f and g well behaved functions, or if I should create the random number in each iteration:

q = []
p = []
q.append(1.0)
p.append(1.0)
for i in range(N):
    eta = np.random.normal()*sqrtdt
    q.append(f(q[i],p[i],eta)
    p.append(g(q[i],p[i],eta)

This code should be put into another for loop and run for several values of N , which varies from 10^4 to 10^9. I am also open to another way to write this, I know for loops are not the closest to Python mindset .

Answer 1

There is no clear-cut reply to your problem in general and assuming that "ok" performance is enough. There are actually three such strategies that I would consider here.

1. Generate all random values at the start. Pro: reduces call overhead during loop. Con: Requires a lot of memory.
2. Use an outer and an inner loop, where you generate the random values for the number of iterations of the inner loop only.
3. Do all the work in the inner loop. Pro: needs less memory. Con: Maximum call overhead.

An interesting advantage of approach "2" is that you can accelerate the inner-loop with Cython (for instance) without changing the random number generator.

You can store the current values of q and p to avoid fetching them from the list. You would append via q.append(q_loop) and p.append(p_loop) .

Anyway, if performance is a concern you should benchmark the difference strategies and consider, in a second time, the use of "acceleration" (ie Cython, Numba, etc). Time resolution of stochastic equations do not vectorize well, so NumPy strategies could not apply to you.