mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 03:33:50 +01:00
40f8cb5c18
- necessary otherwise the class gf and the namespace have the same name, leading to some confusion, and need to qualify some functions (specially on gcc). Same naming conventions as arrays.
101 lines
3.3 KiB
C++
101 lines
3.3 KiB
C++
#define TRIQS_ARRAYS_ENFORCE_BOUNDCHECK
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#include <triqs/gf/refreq.hpp>
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#include <triqs/gf/retime.hpp>
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#include <triqs/gf/local/fourier_real.hpp>
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#include <triqs/arrays.hpp>
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using triqs::arrays::make_shape;
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using triqs::gfs::refreq;
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using triqs::gfs::retime;
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using triqs::gfs::make_gf;
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double lorentzian(double w, double a){
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return 2*a / (w*w + a*a) ;
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};
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std::complex<double> lorentzian_inverse(double t, double a){
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return std::exp(-a*std::abs(t)) ;
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};
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double theta(double x){
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return x>0 ? 1.0 : ( x<0 ? 0.0 : 0.5 ) ;
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};
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int main() {
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double precision=10e-10;
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H5::H5File file("fourier_real_time.h5",H5F_ACC_TRUNC);
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std::complex<double> I(0,1);
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//Test on the tail: GF in frequency that is a lorentzian, with its singularity, TF and TF^-1.
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double wmax=10;
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int Nw=1001;
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auto Gw1 = make_gf<refreq> (-wmax, wmax, Nw, make_shape(1,1),triqs::gfs::full_bins);
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double a = Gw1.mesh().delta() * sqrt( Gw1.mesh().size() );
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for(auto const & w:Gw1.mesh()) Gw1(w)=lorentzian(w,a);
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Gw1.singularity()(2)=triqs::arrays::matrix<double>{{2.0*a}};
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h5_write(file,"Gw1",Gw1); // the original lorentzian
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auto Gt1 = inverse_fourier(Gw1);
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h5_write(file,"Gt1",Gt1); // the lorentzian TF : lorentzian_inverse
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// verification that TF(TF^-1)=Id
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auto Gw1b = fourier(Gt1);
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for(auto const & w:Gw1b.mesh()){
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Gw1b(w)-=Gw1(w);
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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";
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}
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h5_write(file,"Gw1b",Gw1b); // must be 0
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// verification that TF is the lorentzian_inverse function
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for(auto const & t:Gt1.mesh()){
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Gt1(t)-=lorentzian_inverse(t,a);
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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";
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}
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h5_write(file,"Gt1b",Gt1); // must be 0
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//Test on the tail: GF in time that is a decreasing exponential
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double tmax=10.;
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int Nt=501;
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auto Gt2 = make_gf<retime> (-tmax, tmax, Nt, make_shape(1,1));
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a = 2*acos(-1.) / ( Gt2.mesh().delta() *sqrt( Gt2.mesh().size() ) );
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for(auto const & t:Gt2.mesh()) Gt2(t) = 0.5 *I * ( lorentzian_inverse(-t,a)*theta(-t)-lorentzian_inverse(t,a)*theta(t) );
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//for(auto const & t:Gt2.mesh()) Gt2(t) = 0.5_j * ( lorentzian_inverse(-t,a)*theta(-t)-lorentzian_inverse(t,a)*theta(t) );
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Gt2.singularity()(1)=triqs::arrays::matrix<double>{{1.0}};
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h5_write(file,"Gt2",Gt2);
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auto Gw2 = fourier(Gt2);
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h5_write(file,"Gw2",Gw2);
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for(auto const & w:Gw2.mesh()){
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Gw2(w)-= 0.5/(w+a*I)+0.5/(w-a*I);
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//Gw2(w)-= 0.5/(w+a*1_j)+0.5/(w-a*1_j);
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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";
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}
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h5_write(file,"Gw2b",Gw2);
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//Test : GF in time is a simple trigonometric function, the result is a sum of Dirac functions
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tmax=4*acos(-1.);
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auto Gt3 = make_gf<retime> (-tmax, tmax, Nt, make_shape(1,1));
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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.)) ;
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//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.)) ;
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h5_write(file,"Gt3",Gt3);
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auto Gw3 = fourier(Gt3);
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h5_write(file,"Gw3",Gw3);
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}
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