^{Introductory notes: trying to accelerate Python+Numpy code with Cython is a common problem and this question is an attempt to create a canonical question about what types of operation you can accelerate effectively. Although I try to illustrate with a specific example, it is meant as an illustration - please don't focus too much on the fairly meaningless example.}

^{Also, I've contributed enough to Cython that I should declare an affiliation (given that I'm bringing the topic up)}

Actual question

Suppose I have a function that tries to do numeric calculations on Numpy arrays. It uses fairly typical operations:

• a loop over array elements that can't easily be vectorized
• calls to Numpy/Scipy functions (in this case np.sin).
• Mathematical operations on the whole array (a-b)

import numpy as np

def some_func(a, b):
    """
    a and b are 1D arrays

    This is intended to be illustrative! Please don't focus on what it
    actually does!
    """
    transformed_a = np.zeros_like(a)
    last = 0
    for n in range(1, a.shape[0]):
        an = a[n]
        if an > 0:
            delta = an - a[n-1]
            transformed_a[n] = delta*last
        else:
            last = np.sin(an)
    return transformed_a * b

a = np.random.randn(100)
b = np.linspace(0, 100, a.shape[0])

print(some_func(a, b))

Can I speed this up with Cython, and which parts would I expect to be able to speed up?