Twitterの1D-Newton法の速度比較のコード（C++版時間計測付き）

newton_time.cpp

#include <chrono>   // for std::chrono
#include <fstream>  // for std::ofstream
#include <iomanip>  // for std::setprecision
#include <ios>      // for std::ios::fixed, std::ios::floatfield, std::scientific
#include <iostream> // for std::cout
#include <utility>  // for std::make_pair, std::pair
#include <vector>   // for std::vector

namespace {
std::pair<double, double> Runge_Kutta_4th(double x, double v, double dt, double mass, double k);
double force(double x, double mass, double k);
}

int main()
{
    using namespace std::chrono;
    using clock = std::chrono::high_resolution_clock;

    auto const mass = 1.0;
    auto const k = 1.0;
    auto const dt = 1e-2;
    auto const nt = 100000000;

    clock::time_point cp[5];

    cp[0] = clock::now();
    std::vector<double> xt(nt + 1);
    std::vector<double> vt(nt + 1);
    cp[1] = clock::now();

    auto x = 0.0;
    auto v = 1.0;

    for (auto it = 0; it <= nt; it++) {
        xt[it] = x;
        vt[it] = v;
        auto const ret = Runge_Kutta_4th(x, v, dt, mass, k);
        x = ret.first;
        v = ret.second;
    }
    cp[2] = clock::now();

    std::ofstream ofs("result_cpp.out");
    ofs.setf(std::ios::scientific);
    for (auto it = nt - 1000; it <= nt; it++) {
        ofs << std::setprecision(7) << static_cast<double>(it) * dt << ' ' << xt[it] << ' ' << vt[it] << '\n';
    }
    cp[3] = clock::now();

    xt.resize(0);
    xt.shrink_to_fit();
    vt.resize(0);
    vt.shrink_to_fit();
    cp[4] = clock::now();

    std::cout.setf(std::ios::fixed, std::ios::floatfield);
    for (auto i = 0; i < 4; i++) {
        std::cout << std::setprecision(4)
        << "Elapsed time cp[" << i << "] = "
        << duration_cast<duration<double>>(cp[i + 1] - cp[i]).count()
        << " (sec)\n";
    }

    return 0;
}

namespace {
std::pair<double, double> Runge_Kutta_4th(double x, double v, double dt, double mass, double k)
{
    auto const x1 = v;
    auto const v1 = force(x, mass, k);

    auto const x2 = v + 0.5 * dt * v1;
    auto const v2 = force(x + 0.5 * x1 * dt, mass, k);

    auto const x3 = v + 0.5 * dt * v2;
    auto const v3 = force(x + 0.5 * x2 * dt, mass, k);

    auto const x4 = v + dt * v3;
    auto const v4 = force(x + x3 * dt, mass, k);

    x += (x1 + 2 * x2 + 2 * x3 + x4) * dt / 6.0;
    v += (v1 + 2 * v2 + 2 * v3 + v4) * dt / 6.0;

    return std::make_pair(x, v);
}

double force(double x, double mass, double k)
{
    return -x * k / mass;
}
}