python - 用numba计算内积的正确方法

Question

我正在尝试计算两个大矩阵的内积。似乎 numpy 在尝试计算点积时创建了矩阵的副本，这导致了一些内存问题。谷歌搜索后，我发现 numba 包很有前途。但是我不能让它正常工作。这是我的代码:

import numpy as np
from numba import jit
import time, contextlib



@contextlib.contextmanager
def timeit():
    t=time.time()
    yield
    print(time.time()-t,"sec")


def dot1(a,b):
    return np.dot(a,b)

@jit(nopython=True)
def dot2(a,b):
    n = a.shape[0]
    m = b.shape[1]
    K = b.shape[0]
    c = np.zeros((n,m))
    for i in xrange(n):
        for j in xrange(m):
            for k in range(K):
                c[i,j] += a[i,k]*b[k,j]

    return c



def main():
    a = np.random.random((200,1000))
    b = np.random.random((1000,400))

    with timeit():
        c1 = dot1(a,b)
    with timeit():
        c2 = dot2(a,b)

运行时间如下:

dot1:
(0.034691810607910156, 'sec')

dot2:
(0.9215810298919678, 'sec')

谁能告诉我我在这里缺少什么？

Answer 1

您的算法是朴素算法。 BLAS 实现了一个更快的。

引用维基百科的 matrix multiplication页:

Nevertheless, it appears in several libraries, such as BLAS, where it is significantly more efficient for matrices with dimensions n > 100