python - python中数学函数的优化和加速

Question

这个数学函数的目的是使用二面角计算两个(或更多)蛋白质结构之间的距离:

例如，它在结构生物学中非常有用。我已经使用 numpy 在 python 中编写了这个函数，但目标是实现更快。作为计算时间引用，我使用 scikit-learn 包中提供的欧氏距离函数。

这里是我目前的代码:

import numpy as np
import numexpr as ne
from sklearn.metrics.pairwise import euclidean_distances

# We have 10000 structures with 100 dihedral angles
n = 10000
m = 100

# Generate some random data
c = np.random.rand(n,m)
# Generate random int number
x = np.random.randint(c.shape[0])

print c.shape, x

# First version with numpy of the dihedral_distances function
def dihedral_distances(a, b):
    l = 1./a.shape[0]
    return np.sqrt(l* np.sum((0.5)*(1. - np.cos(a-b)), axis=1))

# Accelerated version with numexpr
def dihedral_distances_ne(a, b):
    l = 1./a.shape[0]
    tmp = ne.evaluate('sum((0.5)*(1. - cos(a-b)), axis=1)')
    return ne.evaluate('sqrt(l* tmp)')

# The function of reference I try to be close as possible 
# in term of computation time
%timeit euclidean_distances(c[x,:], c)[0]
1000 loops, best of 3: 1.07 ms per loop

# Computation time of the first version of the dihedral_distances function
# We choose randomly 1 structure among the 10000 structures.
# And we compute the dihedral distance between this one and the others
%timeit dihedral_distances(c[x,:], c)
10 loops, best of 3: 21.5 ms per loop

# Computation time of the accelerated function with numexpr
%timeit dihedral_distances_ne(c[x,:], c)
100 loops, best of 3: 9.44 ms per loop

9.44 ms 它非常快，但是如果你需要运行它一百万次它就非常慢了。现在的问题是，如何做到这一点？你下一步怎么做？赛通？ PyOpenCL？我有一些使用 PyOpenCL 的经验，但是我从来没有编写过像这个这样复杂的东西。我不知道是否可以像我使用 numpy 那样在 GPU 上一步计算二面角距离以及如何继续。

谢谢你帮助我!

编辑: 感谢你们!我目前正在研究完整的解决方案，完成后我会将代码放在这里。

赛通版本:

%load_ext cython
import numpy as np

np.random.seed(1234)

n = 10000
m = 100

c = np.random.rand(n,m)
x = np.random.randint(c.shape[0])

print c.shape, x

%%cython --compile-args=-fopenmp --link-args=-fopenmp --force

import numpy as np
cimport numpy as np
from libc.math cimport sqrt, cos
cimport cython
from cython.parallel cimport parallel, prange

# Define a function pointer to a metric
ctypedef double (*metric)(double[: ,::1], np.intp_t, np.intp_t)

cdef extern from "math.h" nogil:
    double cos(double x)
    double sqrt(double x)

@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef double dihedral_distances(double[:, ::1] a, np.intp_t i1, np.intp_t i2):
    cdef double res
    cdef int m
    cdef int j

    res = 0.
    m = a.shape[1]

    for j in range(m):
        res += 1. - cos(a[i1, j] - a[i2, j])

    res /= 2.*m

    return sqrt(res)

@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef double dihedral_distances_p(double[:, ::1] a, np.intp_t i1, np.intp_t i2):
    cdef double res
    cdef int m
    cdef int j

    res = 0.
    m = a.shape[1]

    with nogil, parallel(num_threads=2):
        for j in prange(m, schedule='dynamic'):
            res += 1. - cos(a[i1, j] - a[i2, j])

    res /= 2.*m

    return sqrt(res)

@cython.boundscheck(False)
@cython.wraparound(False)
def pairwise(double[: ,::1] c not None, np.intp_t x, p = True):
    cdef metric dist_func
    if p:
        dist_func = &dihedral_distances_p
    else:
        dist_func = &dihedral_distances

    cdef np.intp_t i, n_structures
    n_samples = c.shape[0]

    cdef double[::1] res = np.empty(n_samples)

    for i in range(n_samples):
        res[i] = dist_func(c, x, i)

    return res

%timeit pairwise(c, x, False)
100 loops, best of 3: 17 ms per loop    

# Parallel version
%timeit pairwise(c, x, True)
10 loops, best of 3: 37.1 ms per loop

所以我关注你的link创建二面角距离函数的 cython 版本。我们获得了一些速度，不是很多，但它仍然比 numexpr 版本慢(17 毫秒对 9.44 毫秒)。所以我尝试使用 prange 并行化函数，结果更糟(37.1ms vs 17ms vs 9.4ms)!

我错过了什么吗？

Answer 1

如果您愿意使用 http://pythran.readthedocs.io/ ，在这种情况下，您可以利用 numpy 实现并获得比 cython 更好的性能:

#pythran export np_cos_norm(float[], float[])
import numpy as np
def np_cos_norm(a, b):
    val = np.sum(1. - np.cos(a-b))
    return np.sqrt(val / 2. / a.shape[0])

并编译它:

pythran fast.py

比 cython 版本平均 x2。

如果使用:

pythran fast.py -march=native -DUSE_BOOST_SIMD -fopenmp

您将获得运行速度稍快的矢量化并行版本:

100000 loops, best of 3: 2.54 µs per loop
1000000 loops, best of 3: 674 ns per loop

100000 loops, best of 3: 16.9 µs per loop
100000 loops, best of 3: 4.31 µs per loop

10000 loops, best of 3: 176 µs per loop
10000 loops, best of 3: 42.9 µs per loop

(使用与 ev-br 相同的测试台)