Eigen performance with different expressions of the same computation.

t.cpp

// Compile with:  g++ -I/usr/include/eigen3  -std=c++11 -O3    t.cpp   -o t

#include <Eigen/Dense>
#include <chrono>
#include <iostream>
#include <cmath>

using Eigen::MatrixXcf;
using Eigen::MatrixXf;

const int NUM_TIMES=1000;

using ArrayXf  = Eigen::Array <float, Eigen::Dynamic, Eigen::Dynamic>;
using ArrayXcf = Eigen::Array <std::complex<float>, Eigen::Dynamic, Eigen::Dynamic>;

float test1( const MatrixXcf & mat )
{
    ArrayXcf arr  = mat.array();
    ArrayXcf conj = arr.conjugate();
    ArrayXcf magc = arr * conj;
    ArrayXf  mag  = magc.real();
    return mag.sum();
}

float test2( const MatrixXcf & mat )
{
    return ( mat.array() * mat.array().conjugate() ).real().sum();
}

float test3( const MatrixXcf & mat )
{
    ArrayXcf magc   = ( mat.array() * mat.array().conjugate() );

    ArrayXf mag     = magc.real();
    return mag.sum();
}

int main(int argc, char *argv[])
{
    uint64_t test1_us =0, test2_us =0;
    uint64_t test3_us =0;

    MatrixXcf m(8*1024, 4);

    float res1, res2, res3;

    for (int i = 0; i < NUM_TIMES; ++i) {
        m.setRandom();

        {
            auto tick = std::chrono::steady_clock::now();

            res1 = test1(m);

            auto tock = std::chrono::steady_clock::now();
            test1_us += (std::chrono::duration_cast<std::chrono::microseconds>(tock-tick)).count();
        }

        {
            auto tick = std::chrono::steady_clock::now();

            res2 = test2(m);

            auto tock = std::chrono::steady_clock::now();
            test2_us += (std::chrono::duration_cast<std::chrono::microseconds>(tock-tick)).count();
        }

        {
            auto tick = std::chrono::steady_clock::now();

            res3 = test3(m);

            auto tock = std::chrono::steady_clock::now();
            test3_us += (std::chrono::duration_cast<std::chrono::microseconds>(tock-tick)).count();
        }

        if ( abs(res1 - res2) > 1e-10  )
            throw std::runtime_error("Tests give inconsistent results");
        if ( abs(res3 - res2) > 1e-10  )
            throw std::runtime_error("Tests give inconsistent results");
    }

    std::cout
        << "test1_us: " << test1_us << std::endl
        << "test2_us: " << test2_us << std::endl
        << "test3_us: " << test3_us << std::endl;

    return 0;
}