与CPython相比，Numba和Cython没有提高性能，也许我使用不正确？

Question

BIG EDIT:

================

For the sake of clarity, I am removing the old results and replace it by the more recent results. The question is still the same: Am I using both Cython and Numba correctly, and what improvements to the code can be made? (I have a newer and more bare-bones temporary IPython notebook with all the code and results here )

1)

I think I figured out why there was initially no difference between Cython, Numba, and CPython: It was because I fed them

numpy arrays as input:

x = np.asarray([x_i*np.random.randint(8,12)/10 for x_i in range(n)])

instead of lists:

x = [x_i*random.randint(8,12)/10 for x_i in range(n)]

Benchmark using Numpy arrays as data input

Benchmark using Python lists as input

2)

I replaced the zip() function by explicit loops, however, it didn't make much of a difference. The code would be:

CPython

def py_lstsqr(x, y):
    """ Computes the least-squares solution to a linear matrix equation. """
    len_x = len(x)
    x_avg = sum(x)/len_x
    y_avg = sum(y)/len(y)
    var_x = 0
    cov_xy = 0
    for i in range(len_x):
        temp = (x[i] - x_avg)
        var_x += temp**2
        cov_xy += temp*(y[i] - y_avg)
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg
    return (slope, y_interc) 

Cython

%load_ext cythonmagic

%%cython
def cy_lstsqr(x, y):
    """ Computes the least-squares solution to a linear matrix equation. """
    cdef double x_avg, y_avg, var_x, cov_xy,\
         slope, y_interc, x_i, y_i
    cdef int len_x
    len_x = len(x)
    x_avg = sum(x)/len_x
    y_avg = sum(y)/len(y)
    var_x = 0
    cov_xy = 0
    for i in range(len_x):
        temp = (x[i] - x_avg)
        var_x += temp**2
        cov_xy += temp*(y[i] - y_avg)
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg
    return (slope, y_interc)

Numba

from numba import jit

@jit
def numba_lstsqr(x, y):
    """ Computes the least-squares solution to a linear matrix equation. """
    len_x = len(x)
    x_avg = sum(x)/len_x
    y_avg = sum(y)/len(y)
    var_x = 0
    cov_xy = 0
    for i in range(len_x):
        temp = (x[i] - x_avg)
        var_x += temp**2
        cov_xy += temp*(y[i] - y_avg)
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg
    return (slope, y_interc)

Answer 1

Here's what I think is happening with Numba:

Numba works on Numpy arrays. Nothing else. Everything else has nothing to do with Numba .

zip returns an iterator of arbitrary items, which Numba cannot see into. Thus Numba cannot do much compiling.

Looping over the indexes with a for i in range(...) is likely to produce a much better result and allow much stronger type inference.

Answer 2

Using the builtin sum() could be causing problems.

Here's linear regression code that will run faster in Numba:

@numba.jit
def ols(x, y):
    """Simple OLS for two data sets."""
    M = x.size

    x_sum = 0.
    y_sum = 0.
    x_sq_sum = 0.
    x_y_sum = 0.

    for i in range(M):
        x_sum += x[i]
        y_sum += y[i]
        x_sq_sum += x[i] ** 2
        x_y_sum += x[i] * y[i]

    slope = (M * x_y_sum - x_sum * y_sum) / (M * x_sq_sum - x_sum**2)
    intercept = (y_sum - slope * x_sum) / M

    return slope, intercept