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dft_tools/test/triqs/gfs/test_fourier_real_time.cpp
Olivier Parcollet 579368f24b gf. Clean Fourier
- lazy_fourier and co --> fourier
- ex fourier --> make_gf_from_fourier to make a new gf
- = fourier (g) works only iif lhs is a view, like scalar.
- updated python (commented fourier method).
2013-10-23 18:46:55 +02:00

95 lines
3.2 KiB
C++

#define TRIQS_ARRAYS_ENFORCE_BOUNDCHECK
#include <triqs/gfs.hpp>
using namespace triqs::gfs;
using namespace triqs::arrays;
#define TEST(X) std::cout << BOOST_PP_STRINGIZE((X)) << " ---> "<< (X) <<std::endl<<std::endl;
#include <triqs/gfs/local/fourier_real.hpp>
double lorentzian(double w, double a){
return 2*a / (w*w + a*a) ;
};
std::complex<double> lorentzian_inverse(double t, double a){
return std::exp(-a*std::abs(t)) ;
};
double theta(double x){
return x>0 ? 1.0 : ( x<0 ? 0.0 : 0.5 ) ;
};
int main() {
double precision=10e-10;
H5::H5File file("fourier_real_time.h5",H5F_ACC_TRUNC);
std::complex<double> I(0,1);
//Test on the tail: GF in frequency that is a lorentzian, with its singularity, TF and TF^-1.
double wmax=10;
int Nw=1001;
auto Gw1 = gf<refreq> {{-wmax, wmax, Nw,full_bins}, {1,1}};
double a = Gw1.mesh().delta() * sqrt( Gw1.mesh().size() );
for(auto const & w:Gw1.mesh()) Gw1[w]=lorentzian(w,a);
Gw1.singularity()(2)=triqs::arrays::matrix<double>{{2.0*a}};
h5_write(file,"Gw1",Gw1); // the original lorentzian
auto Gt1 = make_gf_from_inverse_fourier(Gw1);
h5_write(file,"Gt1",Gt1); // the lorentzian TF : lorentzian_inverse
// verification that TF(TF^-1)=Id
auto Gw1b = make_gf_from_fourier(Gt1);
for(auto const & w:Gw1b.mesh()){
Gw1b[w]-=Gw1[w];
if ( std::abs(Gw1b[w](0,0)) > precision) TRIQS_RUNTIME_ERROR<<" fourier_real_time error : w="<<w<<" ,G1="<<std::abs(Gw1b[w](0,0))<<"\n";
}
h5_write(file,"Gw1b",Gw1b); // must be 0
// verification that TF is the lorentzian_inverse function
for(auto const & t:Gt1.mesh()){
Gt1[t]-=lorentzian_inverse(t,a);
if ( std::abs(Gt1[t](0,0)) > precision) TRIQS_RUNTIME_ERROR<<" fourier_real_time error : t="<<t<<" ,G1="<<std::abs(Gt1[t](0,0))<<"\n";
}
h5_write(file,"Gt1b",Gt1); // must be 0
//Test on the tail: GF in time that is a decreasing exponential
double tmax=10.;
int Nt=501;
auto Gt2 = gf<retime> {{-tmax, tmax, Nt}, {1,1}};
a = 2*acos(-1.) / ( Gt2.mesh().delta() *sqrt( Gt2.mesh().size() ) );
for(auto const & t:Gt2.mesh()) Gt2[t] = 0.5 *I * ( lorentzian_inverse(-t,a)*theta(-t)-lorentzian_inverse(t,a)*theta(t) );
//for(auto const & t:Gt2.mesh()) Gt2[t] = 0.5_j * ( lorentzian_inverse(-t,a)*theta(-t)-lorentzian_inverse(t,a)*theta(t) );
Gt2.singularity()(1)=triqs::arrays::matrix<double>{{1.0}};
h5_write(file,"Gt2",Gt2);
auto Gw2 = make_gf_from_fourier(Gt2);
h5_write(file,"Gw2",Gw2);
for(auto const & w:Gw2.mesh()){
Gw2[w]-= 0.5/(w+a*I)+0.5/(w-a*I);
//Gw2[w]-= 0.5/(w+a*1_j)+0.5/(w-a*1_j);
if ( std::abs(Gw2[w](0,0)) > precision) TRIQS_RUNTIME_ERROR<<" fourier_real_time error : w="<<w<<" ,G2="<<std::abs(Gw2[w](0,0))<<"\n";
}
h5_write(file,"Gw2b",Gw2);
//Test : GF in time is a simple trigonometric function, the result is a sum of Dirac functions
tmax=4*acos(-1.);
auto Gt3 = gf<retime> {{-tmax, tmax, Nt}, {1,1}};
for(auto const & t:Gt3.mesh()) Gt3[t] = 1.0 * std::cos(10*t) + 0.25*std::sin(4*t) + 0.5 * I*std::sin(8*t+0.3*acos(-1.)) ;
//for(auto const & t:Gt3.mesh()) Gt3[t] = 1.0 * std::cos(10*t) + 0.25*std::sin(4*t) + 0.5_j*std::sin(8*t+0.3*acos(-1.)) ;
h5_write(file,"Gt3",Gt3);
auto Gw3 = make_gf_from_fourier(Gt3);
h5_write(file,"Gw3",Gw3);
}