Eigen::Matrix vs. boost::multi_array vs. Eigen::Ma

问题:

I'm getting puzzling results while doing fairly simple tasks to compare the performance of:

• Eigen::Matrix
• boost::multi_array
• boost::multi_array mapped to Eigen::Matrix using Eigen::Map

This is an abridged version of my test code; a fuller version can be found at: http://pastebin.com/faZ7TvJG.

boost::multi_array<double, 2, Eigen::aligned_allocator<double> > boost_multi_array;
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> eigen_matrix;
Eigen::Map<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> > boost_multi_array_mapped(boost_multi_array.data(), rows, cols);

double
    tmp_sum = 0,
    tmp_time = omp_get_wtime();

for(size_t i=0; i<iterations; i++)
{
    for(size_t j=0; j<rows; j++)
    {
        for(size_t k=0; k<cols; k++)
        {
            //if(k%2==0)
            //{ // commented out are the different options
                //tmp_sum += boost_multi_array[j][k];
                //tmp_sum += boost_multi_array_mapped(j,k);
                tmp_sum += eigen_matrix(j,k);
            //}
        }
    }
}

const double sequential_access_time = omp_get_wtime() - tmp_time;

The results are as follows:

Sequential Access:
   BOOST (MAPPED)   : 1.45763s
   EIGEN            : 1.45736s
   BOOST            : 2.58971s

If I use an if-statement to skip every second element, I then get the following results:

Alternating Access:
   BOOST (MAPPED)   : 1.67301s
   EIGEN            : 2.08834s
   BOOST            : 2.35295s

Inspecting the assembly shows that in the sequential access case, Eigen is faster because the sum becomes vectorized, while it does not when using raw boost::multi_array.

My questions then are:

1. Why is boost::multi_array not vectorized, while Eigen::Matrix is?
2. Why would a multi_array mapped to Eigen be faster than a "native" Eigen data structure?

For compilation I use the following:

g++ -I /usr/include/eigen3 test.cpp -Wall -O3 -DNDEBUG -DBOOST_DISABLE_ASSERTS -fopenmp -ffast-math -funroll-loops -march=native -mtune=native -o array_test

Thanks for your answers.