Cpp+Eigen3计算能带程序

这是C++加Eigen3实现的计算能带程序，在不优化的情况下，速度没有matlab快，甚至没有python+numpy快，但是后面会有比较多的for循环，以及通过优化后，速度会大大提升。另外需要搭配一个Python的画图程序。

测试需要加上编译器-O3优化：

g++ -std=c++11 -O3 .\Hatree-Fork.cpp -o main

#include <iostream>
#include <cmath>
#include <complex>
#include <vector>
#include <fstream>
#include <iomanip>
#include "../Eigen3/Eigen/Dense"

#define EIGEN_USE_MKL_ALL
#define EIGEN_VECTORIZE_SSE4_2

const double PI = acos(-1);
const double t = -1;                                      // 最近邻hopping 
const int N = 64;                                         // y方向宽度


// linspace函数
std::vector<double> linspace(const double min, const double max, const int n){
    std::vector<double> result;
    int iterator = 0;
    for (int i = 0; i <= n-2; i++){
        double temp = min + i*(max-min)/(floor((double)n) - 1);
        result.insert(result.begin() + iterator, temp);
        iterator += 1;
    }
    result.insert(result.begin() + iterator, max);
    return result;
}


Eigen::MatrixXcd Hamiltonian0(const double k){
    Eigen::Matrix2cd T = Eigen::Matrix2cd::Zero(2,2);
    Eigen::Matrix2cd Dup = Eigen::Matrix2cd::Zero(2,2);
    T(0,1) = t*(1.0+exp(std::complex<double>(0,-k)));
    T(1,0) = t*(1.0+exp(std::complex<double>(0,k)));
    Dup(1,0) = std::complex<double>(t,0);
    Eigen::Matrix2cd Ddown = Dup.transpose();
    Eigen::MatrixXcd H = Eigen::MatrixXcd::Zero(2*N,2*N);
    H.block<2,2>(0,0) = T;
    for(int i=2;i<2*N;i+=2){
        H.block<2,2>(i,i) = T;
        H.block<2,2>(i-2,i) = Dup;
        H.block<2,2>(i,i-2) = Ddown;
    }
    return H;
}

void test_band(std::vector<double>& ks){
    /*
    输出文件格式如下: 每一行第一列为k值，后面为对应的能量
    */
    std::ofstream out("Ek.txt");
    int kn = ks.size();
    out<<kn<<std::endl;
    for(auto k:ks){
        auto Hk = Hamiltonian0(k);
        Eigen::SelfAdjointEigenSolver<Eigen::MatrixXcd> eigensolver(Hk);
        //if (eigensolver.info() != Eigen::Success) abort();
        out << k << " ";
        for(int i = 0;i<2*N;i++){
            out <<eigensolver.eigenvalues()(i)<<" ";
        }
        out << std::endl;
    }
}



int main()
{
    double t = -1;
    int nk = 1024;
    int N = 64;
    auto ks = linspace(0,2*PI, nk);
    clock_t startTime,endTime;
    startTime = clock();              //计时开始
    std::cout<<"------start run-------"<<std::endl;
    test_band(ks);
    endTime = clock();
    std::cout << "The run time is: " <<(double)(endTime - startTime) / CLOCKS_PER_SEC << "s" << std::endl;
}

画图程序

import matplotlib.pyplot as plt
import numpy as np

f = open("Ek.txt","r")
data = []
n = int(f.readline())
for i in range(n):
    line = f.readline()
    data.append(list(map(float,line.strip().split(" "))))
data = np.matrix(data)
k = data[:,0]
Ek = data[:,1:]
n, m = Ek.shape
for i in range(m):
    plt.plot(k,Ek[:,i])
plt.show()
f.close()

 

来源：oschina

链接：https://my.oschina.net/u/4328465/blog/4873731