为什么并行矩阵乘法需要这么长时间？

Question

我创建在并行计算一个复杂矩阵的情况下进行测试代码。

我正在计算CPU。

我观察到完成所有块大约需要3秒钟。

有人可以解释为什么需要这么长时间吗？

代码

utils.hpp

#pragma once

#include <chrono>
#include <armadillo>

namespace utils
{
    class watch : std::chrono::steady_clock {
        time_point start_ = now();
    public: auto elapsed_sec() const {return std::chrono::duration<double>(now() - start_).count();}
    };

    void op_herk(arma::cx_mat && A, arma::cx_mat & C)
    {
        using blas_int = int;
        using T = double;

        const char uplo = 'U';
        const char trans_A = 'N';
        const auto n = blas_int(C.n_cols);
        const auto k = blas_int(A.n_cols);
        const T local_alpha = T(1);
        const T local_beta  = T(0);
        const blas_int lda = n;

        arma::blas::herk<T>( &uplo, &trans_A, &n, &k, &local_alpha, A.mem, &lda, &local_beta, C.memptr(), &n);
        arma::herk_helper::inplace_conj_copy_upper_tri_to_lower_tri(C);
    }
}

threadpoll

#pragma once

#include <boost/thread.hpp>
#include <boost/asio.hpp>
#include <boost/asio/thread_pool.hpp>

class ThreadPool {
public:
    explicit ThreadPool(size_t size = boost::thread::hardware_concurrency()) : threadPool(size)
    { }

    template<typename F>
    void addTask(F &&f)
    {
        boost::asio::post(threadPool, std::forward<F>(f));
    }
    void wait()
    {
        threadPool.wait();
    }

    ~ThreadPool()
    {
        threadPool.join();
    }
private:
    boost::asio::thread_pool threadPool;
};

main.cpp

#include <armadillo>
#include "Utils.h"
#include "ThreadPool.h"

int main() {
    ThreadPool threadPool;
    arma::cx_mat test (256, 30000 , arma::fill::randu);
    arma::vec averageTime(30, arma::fill::zeros);
    std::vector<arma::cx_mat > results(30);
    for(auto &it : results)
        it.set_size(256, 256);

    {
        for(int i = 0; i < 30; ++i)
        {
            threadPool.addTask([i = i, &results, &averageTime, test = test.submat(arma::span::all, arma::span(0, 20000)), _ = utils::watch() ]() {
                utils::op_herk(test, results[i]);
                arma::vec r = arma::sort(arma::eig_sym(results[i]), "descent");
                std::cout << _.elapsed_sec() << '\n';
                averageTime[i] = _.elapsed_sec();
            });
        }
        threadPool.wait();
        std::cout << "average " << arma::sum(averageTime)/averageTime.size() <<std::endl;
    }
    return 0;
}

参数： GCC 9.4 计算机：英特尔6个内核，12个线程； Armadillo 10.7.3 OpenBlas 0.3.17

cmake参数：set（cmake_cxx_flags_release“ $ {cmake_cxx_flags} -msse2 -o3 -mtune -mtune =本机=本地-flto”）

我的结果：

1.16084
1.16434
1.16571
1.16601
1.17055
1.17118
1.17382
1.17511
1.1767
1.17981
1.18254
1.18537
2.40071
2.40225
2.4025
2.40511
2.40545
2.40565
2.40583
2.40941
2.40972
2.40974
2.41172
2.41291
3.23446
3.23592
3.23734
3.23972
3.24305
3.24484
3.24728
average 2.14871