Python在简单数组查找上的小循环的性能问题
Performance issues in Python for small loops over simple array look-ups
为什么简单的循环和/或简单的数组查找在Python中如此缓慢?
具体来说，在下面的例子中，Python(使用pypy)比c++(使用-O2)慢大约9倍。性能损失的技术原因是什么?是机器代码中Python循环的实现吗?编译器使用的优化的差异?内存管理?还是别的什么?
# File: timing.py
import sys
T = [
[ 0, 6, 7, 7, 7, 8, 6, 7, 8,19,20, 7, 7, 7, 7, 7, 7,21,22,19,20,21,22,29, 7, 7, 7, 7, 7,29,35,36, 7, 7, 7,35,36, 7, 7,],
[ 9, 7,10, 7, 7, 7, 1, 7,23, 7, 7, 1,23, 7, 7, 7, 7, 7, 7, 9,10,30,31, 7, 9,10,30,31, 7,23, 7, 7,23, 7, 7,30,31,30,31,],
[ 7, 7, 2,11,12, 7, 7, 7, 7, 7, 7,11,12,24,25,26,27, 7, 7, 7, 7, 7, 7, 7,24,25,26,27,32, 7, 7, 7,32,37,38, 7, 7,37,38,],
[13, 7,14, 7, 7, 7, 3, 7,28, 7, 7, 3,28, 7, 7, 7, 7, 7, 7,13,14,33,34, 7,13,14,33,34, 7,28, 7, 7,28, 7, 7,33,34,33,34,],
[15, 7,16, 7, 7, 7, 7, 7, 4, 7, 7, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7,15,16, 7, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[17, 7,18, 7, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7,17,18, 7, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[19, 7,20, 7, 7, 7, 6, 7,29, 7, 7, 6,29, 7, 7, 7, 7, 7, 7,19,20,35,36, 7,19,20,35,36, 7,29, 7, 7,29, 7, 7,35,36,35,36,],
[ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[21, 7,22, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7,21,22, 7, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 9, 1, 7, 7, 7,23, 1, 7,23, 9,10, 7, 7, 7, 7, 7, 7,30,31, 9,10,30,31,23, 7, 7, 7, 7, 7,23,30,31, 7, 7, 7,30,31, 7, 7,],
[ 7, 7,10, 1,23, 7, 7, 7, 7, 7, 7, 1,23, 9,10,30,31, 7, 7, 7, 7, 7, 7, 7, 9,10,30,31,23, 7, 7, 7,23,30,31, 7, 7,30,31,],
[24, 7,25, 7, 7, 7,11, 7,32, 7, 7,11,32, 7, 7, 7, 7, 7, 7,24,25,37,38, 7,24,25,37,38, 7,32, 7, 7,32, 7, 7,37,38,37,38,],
[26, 7,27, 7, 7, 7, 7, 7,12, 7, 7, 7,12, 7, 7, 7, 7, 7, 7, 7, 7,26,27, 7, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[13, 3, 7, 7, 7,28, 3, 7,28,13,14, 7, 7, 7, 7, 7, 7,33,34,13,14,33,34,28, 7, 7, 7, 7, 7,28,33,34, 7, 7, 7,33,34, 7, 7,],
[ 7, 7,14, 3,28, 7, 7, 7, 7, 7, 7, 3,28,13,14,33,34, 7, 7, 7, 7, 7, 7, 7,13,14,33,34,28, 7, 7, 7,28,33,34, 7, 7,33,34,],
[15, 7, 7, 7, 7, 4, 7, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7,15,16, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,16, 7, 4, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[17, 7, 7, 7, 7, 5, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7,17,18, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,18, 7, 5, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[19, 6, 7, 7, 7,29, 6, 7,29,19,20, 7, 7, 7, 7, 7, 7,35,36,19,20,35,36,29, 7, 7, 7, 7, 7,29,35,36, 7, 7, 7,35,36, 7, 7,],
[ 7, 7,20, 6,29, 7, 7, 7, 7, 7, 7, 6,29,19,20,35,36, 7, 7, 7, 7, 7, 7, 7,19,20,35,36,29, 7, 7, 7,29,35,36, 7, 7,35,36,],
[21, 7, 7, 7, 7, 8, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7,21,22, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,22, 7, 8, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[30, 7,31, 7, 7, 7, 7, 7,23, 7, 7, 7,23, 7, 7, 7, 7, 7, 7, 7, 7,30,31, 7, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[24,11, 7, 7, 7,32,11, 7,32,24,25, 7, 7, 7, 7, 7, 7,37,38,24,25,37,38,32, 7, 7, 7, 7, 7,32,37,38, 7, 7, 7,37,38, 7, 7,],
[ 7, 7,25,11,32, 7, 7, 7, 7, 7, 7,11,32,24,25,37,38, 7, 7, 7, 7, 7, 7, 7,24,25,37,38,32, 7, 7, 7,32,37,38, 7, 7,37,38,],
[26, 7, 7, 7, 7,12, 7, 7,12, 7, 7, 7, 7, 7, 7, 7, 7,26,27, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,27, 7,12, 7, 7, 7, 7, 7, 7, 7,12, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[33, 7,34, 7, 7, 7, 7, 7,28, 7, 7, 7,28, 7, 7, 7, 7, 7, 7, 7, 7,33,34, 7, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[35, 7,36, 7, 7, 7, 7, 7,29, 7, 7, 7,29, 7, 7, 7, 7, 7, 7, 7, 7,35,36, 7, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[30, 7, 7, 7, 7,23, 7, 7,23, 7, 7, 7, 7, 7, 7, 7, 7,30,31, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,31, 7,23, 7, 7, 7, 7, 7, 7, 7,23, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[37, 7,38, 7, 7, 7, 7, 7,32, 7, 7, 7,32, 7, 7, 7, 7, 7, 7, 7, 7,37,38, 7, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[33, 7, 7, 7, 7,28, 7, 7,28, 7, 7, 7, 7, 7, 7, 7, 7,33,34, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,34, 7,28, 7, 7, 7, 7, 7, 7, 7,28, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[35, 7, 7, 7, 7,29, 7, 7,29, 7, 7, 7, 7, 7, 7, 7, 7,35,36, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,36, 7,29, 7, 7, 7, 7, 7, 7, 7,29, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[37, 7, 7, 7, 7,32, 7, 7,32, 7, 7, 7, 7, 7, 7, 7, 7,37,38, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
[ 7, 7,38, 7,32, 7, 7, 7, 7, 7, 7, 7,32, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,],
]
M = range(39)
idempotents = [0,2,6,7,8,9,11,12,14,16,17,19,21,25,27]
omega = [0,7,2,7,7,7,6,7,8,9,7,11,12,7,14,7,16,17,7,19,7,21,7,7,7,25,7,27,7,7,7,7,7,7,7,7,7,7,7]
def check():
for e in idempotents:
for x in M:
ex = T[e][x]
for s in M:
es = T[e][s]
for f in idempotents:
exf = T[ex][f]
esf = T[es][f]
for y in M:
exfy = omega[T[exf][y]]
for t in M:
tesf = omega[T[t][esf]]
if T[T[exfy][exf]][tesf] != T[T[exfy][esf]][tesf]:
return 0
return 1
sys.exit(check())
c++代码(需要c++ 11，因为新的数组初始化和迭代语法):
// File: timing.cc
// Compile via 'g++ -std=c++11 -O2 timing.cc'
// Run via 'time ./a.out'
#include <vector>
#include <cstddef>
int main(int, char **) {
const size_t N = 39;
typedef unsigned element_t;
const std::vector<std::vector<element_t>> T{{
{{ 0, 6, 7, 7, 7, 8, 6, 7, 8,19,20, 7, 7, 7, 7, 7, 7,21,22,19,20,21,22,29, 7, 7, 7, 7, 7,29,35,36, 7, 7, 7,35,36, 7, 7,}},
{{ 9, 7,10, 7, 7, 7, 1, 7,23, 7, 7, 1,23, 7, 7, 7, 7, 7, 7, 9,10,30,31, 7, 9,10,30,31, 7,23, 7, 7,23, 7, 7,30,31,30,31,}},
{{ 7, 7, 2,11,12, 7, 7, 7, 7, 7, 7,11,12,24,25,26,27, 7, 7, 7, 7, 7, 7, 7,24,25,26,27,32, 7, 7, 7,32,37,38, 7, 7,37,38,}},
{{13, 7,14, 7, 7, 7, 3, 7,28, 7, 7, 3,28, 7, 7, 7, 7, 7, 7,13,14,33,34, 7,13,14,33,34, 7,28, 7, 7,28, 7, 7,33,34,33,34,}},
{{15, 7,16, 7, 7, 7, 7, 7, 4, 7, 7, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7,15,16, 7, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{17, 7,18, 7, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7,17,18, 7, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{19, 7,20, 7, 7, 7, 6, 7,29, 7, 7, 6,29, 7, 7, 7, 7, 7, 7,19,20,35,36, 7,19,20,35,36, 7,29, 7, 7,29, 7, 7,35,36,35,36,}},
{{ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{21, 7,22, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7,21,22, 7, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 9, 1, 7, 7, 7,23, 1, 7,23, 9,10, 7, 7, 7, 7, 7, 7,30,31, 9,10,30,31,23, 7, 7, 7, 7, 7,23,30,31, 7, 7, 7,30,31, 7, 7,}},
{{ 7, 7,10, 1,23, 7, 7, 7, 7, 7, 7, 1,23, 9,10,30,31, 7, 7, 7, 7, 7, 7, 7, 9,10,30,31,23, 7, 7, 7,23,30,31, 7, 7,30,31,}},
{{24, 7,25, 7, 7, 7,11, 7,32, 7, 7,11,32, 7, 7, 7, 7, 7, 7,24,25,37,38, 7,24,25,37,38, 7,32, 7, 7,32, 7, 7,37,38,37,38,}},
{{26, 7,27, 7, 7, 7, 7, 7,12, 7, 7, 7,12, 7, 7, 7, 7, 7, 7, 7, 7,26,27, 7, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{13, 3, 7, 7, 7,28, 3, 7,28,13,14, 7, 7, 7, 7, 7, 7,33,34,13,14,33,34,28, 7, 7, 7, 7, 7,28,33,34, 7, 7, 7,33,34, 7, 7,}},
{{ 7, 7,14, 3,28, 7, 7, 7, 7, 7, 7, 3,28,13,14,33,34, 7, 7, 7, 7, 7, 7, 7,13,14,33,34,28, 7, 7, 7,28,33,34, 7, 7,33,34,}},
{{15, 7, 7, 7, 7, 4, 7, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7,15,16, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,16, 7, 4, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7,15,16, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{17, 7, 7, 7, 7, 5, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7,17,18, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,18, 7, 5, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7,17,18, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{19, 6, 7, 7, 7,29, 6, 7,29,19,20, 7, 7, 7, 7, 7, 7,35,36,19,20,35,36,29, 7, 7, 7, 7, 7,29,35,36, 7, 7, 7,35,36, 7, 7,}},
{{ 7, 7,20, 6,29, 7, 7, 7, 7, 7, 7, 6,29,19,20,35,36, 7, 7, 7, 7, 7, 7, 7,19,20,35,36,29, 7, 7, 7,29,35,36, 7, 7,35,36,}},
{{21, 7, 7, 7, 7, 8, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7,21,22, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,22, 7, 8, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7,21,22, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{30, 7,31, 7, 7, 7, 7, 7,23, 7, 7, 7,23, 7, 7, 7, 7, 7, 7, 7, 7,30,31, 7, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{24,11, 7, 7, 7,32,11, 7,32,24,25, 7, 7, 7, 7, 7, 7,37,38,24,25,37,38,32, 7, 7, 7, 7, 7,32,37,38, 7, 7, 7,37,38, 7, 7,}},
{{ 7, 7,25,11,32, 7, 7, 7, 7, 7, 7,11,32,24,25,37,38, 7, 7, 7, 7, 7, 7, 7,24,25,37,38,32, 7, 7, 7,32,37,38, 7, 7,37,38,}},
{{26, 7, 7, 7, 7,12, 7, 7,12, 7, 7, 7, 7, 7, 7, 7, 7,26,27, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,27, 7,12, 7, 7, 7, 7, 7, 7, 7,12, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7,26,27, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{33, 7,34, 7, 7, 7, 7, 7,28, 7, 7, 7,28, 7, 7, 7, 7, 7, 7, 7, 7,33,34, 7, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{35, 7,36, 7, 7, 7, 7, 7,29, 7, 7, 7,29, 7, 7, 7, 7, 7, 7, 7, 7,35,36, 7, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{30, 7, 7, 7, 7,23, 7, 7,23, 7, 7, 7, 7, 7, 7, 7, 7,30,31, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,31, 7,23, 7, 7, 7, 7, 7, 7, 7,23, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7,30,31, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{37, 7,38, 7, 7, 7, 7, 7,32, 7, 7, 7,32, 7, 7, 7, 7, 7, 7, 7, 7,37,38, 7, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{33, 7, 7, 7, 7,28, 7, 7,28, 7, 7, 7, 7, 7, 7, 7, 7,33,34, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,34, 7,28, 7, 7, 7, 7, 7, 7, 7,28, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7,33,34, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{35, 7, 7, 7, 7,29, 7, 7,29, 7, 7, 7, 7, 7, 7, 7, 7,35,36, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,36, 7,29, 7, 7, 7, 7, 7, 7, 7,29, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7,35,36, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{37, 7, 7, 7, 7,32, 7, 7,32, 7, 7, 7, 7, 7, 7, 7, 7,37,38, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
{{ 7, 7,38, 7,32, 7, 7, 7, 7, 7, 7, 7,32, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7,37,38, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,}},
}};
const std::vector<element_t> idempotents{{0,2,6,7,8,9,11,12,14,16,17,19,21,25,27}};
const std::vector<element_t> omega{{0,7,2,7,7,7,6,7,8,9,7,11,12,7,14,7,16,17,7,19,7,21,7,7,7,25,7,27,7,7,7,7,7,7,7,7,7,7,7}};
element_t ex, es, exf, esf, exfy, tesf;
for(auto e: idempotents) {
for(size_t x = 0; x < N; ++x) {
ex = T[e][x];
for(size_t s = 0; s < N; ++s) {
es = T[e][s];
for(auto f: idempotents) {
exf = T[ex][f];
esf = T[es][f];
for(size_t y = 0; y < N; ++y) {
exfy = omega[T[exf][y]];
for(size_t t = 0; t < N; ++t) {
tesf = omega[T[t][esf]];
if(T[T[exfy][exf]][tesf] != T[T[exfy][esf]][tesf])
return 0;
}}}}}}
return 1;
}
(不要询问代码的详细功能。粗略地说，实现了一个代数形式语言理论背景下的决策过程;该代码验证了由乘法表T给出的单oid的身份。特别是，代码不是一个人为的示例，而是一个真实的应用程序。当然，人们可以在形式语言理论的背景下讨论"应用"。
-
time python timing.py输出2m18.389s -
g++ -std=c++11 -O2 timing.cc && time ./a.out输出0m1.064s
0m9.329s time pypy timing.py输出编辑
- 为了更公平的比较，我做了一些
g++似乎自动合并的优化。我重新排序了循环，并将变量赋值尽可能地向外移动(正如评论所建议的那样)。这使得pypy的加速因子约为2.5,python的加速因子约为2。 同样为了公平起见，我使用了动态大小的 - 我删除了关于为什么numpy较慢(注释表明我没有正确使用它)以及为什么在脚本的主要部分执行循环较慢的旁白(众所周知，Python使用局部变量比使用全局变量更快;
- 我知道c++和Python有不同的作用域。我也知道c++是编译的，而Python通常是解释的(这就是为什么我使用
pypy)。我想知道为什么pypy在这段特定代码上如此慢的最终技术原因。(使用numpy和numba可能能够获得接近本机的性能，但这不是我的问题的精神，因为它实际上将所有的计算转移回C代码。)我相应地澄清了我的问题。
std::vector而不是恒定大小的std::array。numpy和python循环的简短回答
如果您正确使用numpy，则将所有内容再次推回到c级。
长回答
怎么能这样呢?
我将在这里展示一点我的评论的意思，以及如何使用numpy避免不必要的循环。让我们看一下原始代码，假设您已经将所有列表放入np中。np.asarray(list).
for e in idempotents:
for x in M:
ex = T[e][x]
直接翻译为:
T[idempotents]
为什么?
Numpy数组可以使用索引数组进行索引。如。T[0]返回矩阵t的所有列(实际上是所有以下维度)，因此T[0]==T[0,:]用于2d数组。由于循环遍历所有幂等幂函数作为下标，然后遍历T[e][x]列中的所有元素，因此T[idempotents]与这两个循环相同。
详细信息见这里。
, es
下一个是
for e in idempotents:
for x in M:
ex = T[e][x]
for s in M:
es = T[e][s]
由于没有必要重新执行整个循环，因此转换为
es=ex
因为我们使用的是python，所以矩阵es甚至没有被复制，只是被引用。
exf,养
我现在跳过代码片段中的一些for循环。
for f in idempotents:
exf = T[ex][f]
esf = T[es][f]
现在你再次用幂等向量访问最外层的索引。所以我们可以用同样的方法对numpy做同样的事情:
T[T[idempotents]]
print T[T[idempotents]].shape
>> (15, 39, 39)
现在，我们有一个维度为(15,39,39)的数组，因为对于二维数组T[幂等幂]的每个元素，你返回T的元素，这基本上是第三个循环。
exf = T[T[idempotents]]
esf = exf
从这里开始变得更复杂，我将跳过其余部分。它将是如下行:
Ti = T[idempotents] # T[e][x] == T[e][s] by loop definition
TTi = T[Ti] # T[T[e][x]]
TTi.shape = -1 , 39 # bring first index back into shape
exf = TTi[:, idempotents] # T[T[e][x]][f]
esf = exf # T[T[e][s]][f] == T[T[e][x]][f] by loop definition
Texf = T[exf].ravel()
exfy = omega[Texf]
TTexf = T.T[exf].ravel() # tesf = omega[T[t][esf]] # since I cannot index fast along t I use the transpose of T
tesf = omega[TTexf]
因为Python在运行时解释它的输入，而c++编译器能够执行主要的优化，特别是对于固定大小数组的for循环。
有些编译器甚至会计算嵌套for循环的整个输出。
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