// }}}
void CheckElementsGUE() { // {{{
int dim=40, ElementsEnsemble=1000;
#ifdef ASK
std::clog << "Inserte dim ";
cin >> dim;
std::cout <<std::endl ;
std::clog << "Inserte ElementsEnsemble ";
cin >> ElementsEnsemble;
std::cout <<std::endl ;
#endif
std::clog << "dim="<<dim<<" ElementsEnsemble="<<ElementsEnsemble<<std::endl ;
itpp::cmat H;
double DiagonalAverage=0, DiagonalSigma=0,OffDiagonalSigma=0;
std::complex<double> OffDiagonalAverage=0;
for (int iEnsemble=0; iEnsemble<ElementsEnsemble; iEnsemble++) {
H=RandomGUE(dim);
for(int i=0; i<dim; i++) {
DiagonalAverage+=real(H(i,i));
DiagonalSigma+=pow(abs(H(i,i)),2);
for(int j=i+1; j<dim; j++) {
// OffDiagonalAverage+=H(i,j);
OffDiagonalAverage+= H(i,j) ;
// OffDiagonalSigma+=pow(abs(real(H(i,j))),2)
// +complex(0,1)*pow(abs(imag(H(i,j))),2);
OffDiagonalSigma+=pow(abs(H(i,j)),2);
}
}
}
DiagonalAverage/=(dim*ElementsEnsemble);
DiagonalSigma/=(dim*ElementsEnsemble);
OffDiagonalAverage/=(0.5*dim*(dim-1)*ElementsEnsemble);
OffDiagonalSigma/=(0.5*dim*(dim-1)*ElementsEnsemble);
std::clog << "Aca se muestra que la matriz cumple con las relaciones de"<<std::endl ;
std::clog << "\\bar{V_ij} = 0 " <<std::endl ;
std::clog << "\\bar{V_ij V_kl} = \\delta_il \\delta_jk " <<std::endl ;
std::clog << "\\bar{|V_ij|^2} = 1 " <<std::endl ;
std::clog << "tando para elementos diagonales como no diagonales. " <<std::endl ;
std::clog << "Como sigue, en orden ,deben ser 0, 1, 0 , 0, 1 " <<std::endl ;
std::cout << DiagonalAverage <<std::endl ;
std::cout << DiagonalSigma <<std::endl ;
std::cout << OffDiagonalAverage.real() <<std::endl ;
std::cout << OffDiagonalAverage.imag() <<std::endl ;
std::cout << OffDiagonalSigma<<std::endl ;
}
// }}}
// }}}
// Checking things {{{
void PrintElementsGUE(){ // {{{
int dim=4;
#ifdef ASK
std::clog << "Inserte dim "; cin >> dim;
#endif
std::clog << "dim="<<dim;
itpp::cmat H;
for (int n_ensemble=0;n_ensemble<100;n_ensemble++){
H=RandomGUE(dim);
for(int i=0;i<dim;i++){
std::cout << real(H(i,i)) << std::endl ;
for(int j=i+1;j<dim;j++){
std::cout <<H(j,i)<<std::endl ;
}
}
}
}
