RSCG_cpp

This is made for c++11.

This package can calculate the elements of the Green's function:

$$G_ij(σk) = ([σj I - A]^-1)_{ij},$$

with the use of the reduced-shifted conjugate gradient method (See, Y. Nagai, Y. Shinohara, Y. Futamura, and T. Sakurai,[arXiv:1607.03992v2 or DOI:10.7566/JPSJ.86.014708]). One can obtain G_{ij}(\sigma_k) with different frequencies \sigma_k, simultaneously.

The matrix should be symmetric or hermitian.

This is to understand the method. I do not guarantee result with the use of this code.

#include <iostream>
#include <functional>
#include <vector>
#include <array>

#include "rscg.cpp"

using namespace std;

template <int N>
vector <double> matmul(const std::array<std::array <double, N>,N> &H, vector <double> &x){
    vector <double> Ax(N);
    for(int i = 0; i < N; i++){
        for(int j = 0; j < N; j++){
        Ax[i] += H[i][j]*x[j];
        };
    };
    return Ax;
};

int main() {
    std::array<std::array<double, 3>, 3> H{ {
        { 1, 0, 3 },
        { 0, 2, 0 },
        { 3, 0, 5 }
    } };
    vector <double> x(3,1.0);
    auto f = std::bind(matmul<3>,H,std::placeholders::_1);

    RSCG* rscg;
    rscg = new RSCG(3,f);
    vector<complex <double> > vec_z(2,0.2);
    vec_z[0] = 0.2*1i;
    vec_z[1] = 4.0 + 0.5*1i;
    cout << vec_z[0] << std::endl;
    vector<complex <double> > Gij = rscg->calc_greenfunction_realH(0,0,vec_z);
    cout << "RSCG" << Gij[0] << " exact: 1.12377 - 0.383299 I" << std::endl;
    cout << "RSCG" << Gij[1] << " exact: 0.0844022 - 0.0339264 I" <<std::endl;
};