Eigen c++ 线性代数比 numpy 慢得多——这是怎么回事？

问：

我编译了以下 C++ 程序，并使用优化 O3 使用 GCC 对其进行编译。得到的矩阵逆比等效的简单 numpy 代码 b=np.linalg.inv（a） 慢约 3-4 倍。我的印象是 Eigen 速度超快，所以我一定做错了什么，但我不知道是什么。

有人可以告诉我我可以做些什么来改进代码吗？

c++ 代码是

#include <iostream>
#include <iomanip>
#include <chrono>
#include <Eigen/LU>
#include <Eigen/Dense>

using Eigen::MatrixXd;

int main()
{
  const int max_rep = 5;
  const int N=1000;
  MatrixXd inv_m(N,N);

  std::cout << "**** Eigen Library -- matrix inversion speed test ****" << std::endl;
  std::cout << "Matrix size = " << N << std::endl;
  
  for(int i=1;i<=max_rep;i++) {
    MatrixXd m = MatrixXd::Random(N,N);
    auto start = std::chrono::system_clock::now();
    inv_m = m.inverse();
    auto stop = std::chrono::system_clock::now();
    std::cout << "Test no." << std::setw(3) << i;
    std::cout << ", CPU time = " 
          << std::chrono::duration<double>{stop - start}.count()
              << " seconds." << std::endl;
  }  
  return 0;
}

Python 代码是

import numpy as np
import time

for n in range(500, 5001, 500):
a=np.random.rand(n,n)
    t=time.time();
    b=np.linalg.inv(a)
    t=time.time()-t;
    print(f'Size {n=:5d}, {t=:.2f}')

我对 numpy 和 Eigen 代码进行了基准测试，并期望 Eigen 更快，但结果恰恰相反。（这也适用于计算特征值，而不仅仅是逆的特殊情况）。

numpy 配置是

In [26]: np.show_config()
blas_mkl_info:
  NOT AVAILABLE
blis_info:
  NOT AVAILABLE
openblas_info:
  NOT AVAILABLE
accelerate_info:
  NOT AVAILABLE
atlas_3_10_blas_threads_info:
  NOT AVAILABLE
atlas_3_10_blas_info:
  NOT AVAILABLE
atlas_blas_threads_info:
  NOT AVAILABLE
atlas_blas_info:
  NOT AVAILABLE
blas_info:
    libraries = ['blas', 'blas']
    library_dirs = ['/usr/lib/x86_64-linux-gnu']
    include_dirs = ['/usr/local/include', '/usr/include']
    language = c
    define_macros = [('HAVE_CBLAS', None)]
blas_opt_info:
    define_macros = [('NO_ATLAS_INFO', 1), ('HAVE_CBLAS', None)]
    libraries = ['blas', 'blas']
    library_dirs = ['/usr/lib/x86_64-linux-gnu']
    include_dirs = ['/usr/local/include', '/usr/include']
    language = c
lapack_mkl_info:
  NOT AVAILABLE
openblas_lapack_info:
  NOT AVAILABLE
openblas_clapack_info:
  NOT AVAILABLE
flame_info:
  NOT AVAILABLE
atlas_3_10_threads_info:
  NOT AVAILABLE
atlas_3_10_info:
  NOT AVAILABLE
atlas_threads_info:
  NOT AVAILABLE
atlas_info:
  NOT AVAILABLE
lapack_info:
    libraries = ['lapack', 'lapack']
    library_dirs = ['/usr/lib/x86_64-linux-gnu']
    language = f77
lapack_opt_info:
    libraries = ['lapack', 'lapack', 'blas', 'blas']
    library_dirs = ['/usr/lib/x86_64-linux-gnu']
    language = c
    define_macros = [('NO_ATLAS_INFO', 1), ('HAVE_CBLAS', None)]
    include_dirs = ['/usr/local/include', '/usr/include']
Supported SIMD extensions in this NumPy install:
    baseline = SSE,SSE2,SSE3
    found = SSSE3,SSE41,POPCNT,SSE42,AVX,F16C,FMA3,AVX2
    not found = AVX512F,AVX512CD,AVX512_KNL,AVX512_KNM,AVX512_SKX,AVX512_CLX,AVX512_CNL,AVX512_ICL