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pade_frequencies.cpp
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pade_frequencies.cpp
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#include <Eigen/Dense>
#include <Eigen/Eigenvalues>
#include <tuple>
#include <complex>
#include <iostream>
#include <algorithm>
#include <fstream>
#include <iomanip>
#include"pade_frequencies.h"
using namespace std;
using namespace Eigen;
#include <filesystem>
namespace fs = std::filesystem;
#define MAXBUFSIZE ((int) 1e6)
// Function for sorting frequencies and residues
bool compare(int i, int j, VectorXd freqs)
{
return freqs(i) < freqs(j);
}
// Calculate Pade (N-1)/N frequencies of Fermi-Dirac distribution
// Note that Pade frequenies are purely imaginary but here considered real
// Input:
// int n number of frequency. n=1,2,3,...
// int n_approx, how many frequencies in total considered
// Output:
// double, frequency n
// double, residue n
// Note that frequencies are symmetrically on +- imaginary axes
tuple<double,double> pade_frequency(int n, int n_approx)
{
using namespace std::placeholders;
static int n_approx_old = 0;
int nm = 2*n_approx;
static VectorXd freqs = VectorXd::Zero(1);
static VectorXd residues = VectorXd::Zero(1);
VectorXd freq_temp;
VectorXd resi_temp;
// Calculate and save if not already calculated
if(n_approx != n_approx_old){
// Try to load data from file
bool success = false;
cout << "Trying to load data..." << endl;
tie(success,freq_temp,resi_temp) = load_data("PadeCoefficients",n_approx);
if(success){
n_approx_old = n_approx;
freqs = freq_temp;
residues = resi_temp;
return make_tuple(freqs(n-1),residues(n-1));
}
freqs.conservativeResize(n_approx);
residues.conservativeResize(n_approx);
MatrixXd A = MatrixXd::Zero(nm,nm);
MatrixXd B = MatrixXd::Zero(nm,nm);
for(int i = 0; i < nm; i++)
A(i,i) = -1.0 - i*2.0;
for(int i = 0; i < nm-1; i++){
B(i,i+1) = 0.5;
B(i+1,i) = 0.5;
}
MatrixXd Binv = B.inverse();
GeneralizedEigenSolver<MatrixXd> ges(nm);
ges.compute(A,B);
VectorXd eigs = ges.eigenvalues().real();
MatrixXcd V = ges.eigenvectors();
MatrixXcd Vinv = V.inverse();
VectorXd resi = VectorXd::Zero(nm);
for(int i = 0; i <nm;i++)
resi(i) = real((eigs(i)*V(0,i)*Vinv.row(i)*Binv.col(0)/4.0)(0,0));
// sort
VectorXi idx = VectorXi::LinSpaced(nm,0,nm-1);
sort(idx.data(),idx.data()+idx.size(),bind(compare,_1,_2,eigs));
VectorXd tmp1 = VectorXd::Zero(nm);
VectorXd tmp2 = VectorXd::Zero(nm);
for(int i = 0; i < nm; i++){
tmp1(i) = eigs(idx(i));
tmp2(i) = resi(idx(i));
}
freqs = tmp1.segment(n_approx,n_approx);
residues = tmp2.segment(n_approx,n_approx);
save_data("PadeCoefficients",freqs,residues);
}
n_approx_old = n_approx;
return make_tuple(freqs(n-1),residues(n-1));
}
void save_data(string base_path, const VectorXd& freqs, const VectorXd& residues)
{
IOFormat full(FullPrecision, 0, ", ", "\n", "", "","","");
string folder_name = to_string(freqs.size());
if(!fs::exists(base_path))
fs::create_directory(base_path);
string path = base_path + "/" + folder_name;
if(!fs::exists(path))
fs::create_directory(path);
ofstream freqs_file, residues_file;
freqs_file.open(path+"/freqs.csv");
residues_file.open(path+"/residues.csv");
if(freqs_file.is_open())
freqs_file << freqs.format(full);
if(residues_file.is_open())
residues_file << residues.format(full);
freqs_file.close();
residues_file.close();
}
tuple<bool,VectorXd,VectorXd> load_data(string base_path, int n_approx)
{
cout << "Loading data" << endl;
VectorXd freqs = VectorXd::Zero(1);
VectorXd residues = VectorXd::Zero(1);
string path = base_path + "/" + to_string(n_approx);
if(!fs::exists(path+"/freqs.csv")||!fs::exists(path+"/residues.csv")){
cout << "Files do not exist" << endl;
return make_tuple(false,freqs,residues);
}
cout << "File found!" << endl;
ifstream freqs_file, residues_file;
freqs_file.open(path + "/freqs.csv");
residues_file.open(path + "/residues.csv");
int freqs_cols = 0, freqs_rows = 0;
double buff[MAXBUFSIZE];
while (freqs_file.good())
{
string line;
getline(freqs_file, line);
if(line.empty())
break;
int temp_cols = 0;
stringstream stream(line);
string elem;
while(stream.good()){
getline(stream,elem,',');
buff[freqs_cols*freqs_rows+temp_cols++] = stod(elem);
}
if (temp_cols == 0)
continue;
if (freqs_cols == 0)
freqs_cols = temp_cols;
freqs_rows++;
}
freqs_file.close();
freqs.resize(freqs_rows);
for(int i = 0; i < freqs_rows; i++){
freqs(i) = buff[i];
}
int residues_cols = 0, residues_rows = 0;
while (residues_file.good())
{
string line;
getline(residues_file, line);
if(line.empty())
break;
int temp_cols = 0;
stringstream stream(line);
string elem;
while(stream.good()){
getline(stream,elem,',');
buff[residues_cols*residues_rows+temp_cols++] = stod(elem);
}
if (temp_cols == 0)
continue;
if (residues_cols == 0)
residues_cols = temp_cols;
residues_rows++;
}
residues_file.close();
residues.resize(residues_rows);
for(int i = 0; i < residues_rows; i++){
residues(i) = buff[i];
}
return make_tuple(true,freqs,residues);
}