优化numpy数组乘法：*比numpy.dot？

Question

问题：

1）当使用BLAS时，numpy.dot()怎么比下面示例代码中的*慢？在

2）在这种情况下，是否有一种方法可以实现numpy.dot()，而不是{}，以实现更快的数组乘法？我认为这是一个关键的问题，至少我认为这不是一个快速的问题。在

详情如下。提前感谢您的回答和帮助。在

详细信息：

我正在编写一个程序，它使用Python2.7（64位）、Numpy1.11.2、Windows7上的Anaconda2来解决耦合的PDE。为了提高程序输出的精度，我需要使用大数组（shape（2，2^14）和较小的积分步骤，从而导致每个模拟的数组乘法运算数量巨大，我需要对其速度进行优化。在

有了looked around，似乎只要安装BLAS并使用numpy，numpy.dot()就应该用于相对于*更快的数组乘法。这是经常推荐的。但是，当我使用下面的计时器脚本时，*比numpy.dot()快至少7倍。在某些情况下，这会增加到系数>1000：

from __future__ import division
import numpy as np
import timeit

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

def timeser(a, b):
    return a*b

def wrapper(func, a, b):
    def wrapped():
        return func(a, b)
    return wrapped

size = 100
num = int(3e5)

a = np.random.random_sample((size, size))
b = np.random.random_sample((size, size))

wrapped = wrapper(dotter, a, b)
dotTime = timeit.timeit(wrapped, number=num)/num
print "\nTime for np.dot: ", dotTime

wrapped = wrapper(timeser, a, b)
starTime = timeit.timeit(wrapped, number=num)/num
print "\nTime for *: ", starTime

print "dotTime / starTime: ", dotTime/starTime

该输出：

^{pr2}$

numpy.dot()和{}都分布在多个核心上，我认为这表明BLAS在某种程度上起作用，至少：

看看numpy.__config__.show()我似乎在使用BLAS和lapack（尽管不是openblas_lapack？）公司名称：

lapack_opt_info:
    libraries = ['mkl_lapack95_lp64', 'mkl_blas95_lp64', 'mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'libiomp5md', 'libifportmd']
    library_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/lib/intel64']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/include']
blas_opt_info:
    libraries = ['mkl_lapack95_lp64', 'mkl_blas95_lp64', 'mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'libiomp5md', 'libifportmd']
    library_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/lib/intel64']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/include']
openblas_lapack_info:
  NOT AVAILABLE
lapack_mkl_info:
    libraries = ['mkl_lapack95_lp64', 'mkl_blas95_lp64', 'mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'libiomp5md', 'libifportmd']
    library_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/lib/intel64']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/include']
blas_mkl_info:
    libraries = ['mkl_lapack95_lp64', 'mkl_blas95_lp64', 'mkl_intel_lp64', 'mkl_intel_thread', 'mkl_core', 'libiomp5md', 'libifportmd']
    library_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/lib/intel64']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:/Program Files (x86)/Intel/Composer XE/mkl/include']

Answer 1

np.dot调用矩阵矩阵乘法，而*是元素乘法。对于python3.5+，矩阵矩阵乘法的符号是@。在