void inverse(gf_view<imtime,scalar_valued> gt, gf_view<imfreq,scalar_valued> const gw){
using namespace impl_local_matsubara;
static bool Green_Function_Are_Complex_in_time = false;
// If the Green function are NOT complex, then one use the symmetry property
// fold the sum and get a factor 2
auto ta = gw(freq_infty());
//TO BE MODIFIED AFTER SCALAR IMPLEMENTATION TODO
dcomplex d= ta(1)(0,0), A= ta.get_or_zero(2)(0,0), B = ta.get_or_zero(3)(0,0);
double b1, b2, b3;
dcomplex a1, a2, a3;
double beta=gw.domain().beta;
size_t L= gt.mesh().size() - ( gt.mesh().kind() == full_bins ? 1 : 0); //L can be different from gt.mesh().size() (depending on the mesh kind) and is given to the FFT algorithm
dcomplex iomega = dcomplex(0.0,1.0) * std::acos(-1) / beta;
dcomplex iomega2 = -iomega * 2 * gt.mesh().delta() * (gt.mesh().kind() == half_bins ? 0.5 : 0.0) ;
double fact = (Green_Function_Are_Complex_in_time ? 1 : 2)/beta;
g_in.resize( gw.mesh().size());
g_out.resize(gt.mesh().size());
if (gw.domain().statistic == Fermion){
b1 = 0; b2 =1; b3 =-1;
a1 = d-B; a2 = (A+B)/2; a3 = (B-A)/2;
}
else {
b1 = -0.5; b2 =-1; b3 =1;
a1=4*(d-B)/3; a2=B-(d+A)/2; a3=d/6+A/2+B/3;
}
g_in() = 0;
for (auto & w: gw.mesh()) {
g_in[ w.index() ] = fact * exp(w.index()*iomega2) * ( gw[w] - (a1/(w-b1) + a2/(w-b2) + a3/(w-b3)) );
}
// for bosons GF(w=0) is divided by 2 to avoid counting it twice
if (gw.domain().statistic == Boson && !Green_Function_Are_Complex_in_time ) g_in(0) *= 0.5;
details::fourier_base(g_in, g_out, L, false);
// CORRECT FOR COMPLEX G(tau) !!!
typedef double gt_result_type;
//typedef typename gf<imtime>::mesh_type::gf_result_type gt_result_type;
if (gw.domain().statistic == Fermion){
for (auto & t : gt.mesh()){
gt[t] = convert_green<gt_result_type> ( g_out( t.index() == L ? 0 : t.index() ) * exp(-iomega*t)
+ oneFermion(a1,b1,t,beta) + oneFermion(a2,b2,t,beta)+ oneFermion(a3,b3,t,beta) );
}
}
else {
for (auto & t : gt.mesh())
gt[t] = convert_green<gt_result_type> ( g_out( t.index() == L ? 0 : t.index() )
+ oneBoson(a1,b1,t,beta) + oneBoson(a2,b2,t,beta) + oneBoson(a3,b3,t,beta) );
}
if (gt.mesh().kind() == full_bins)
gt.on_mesh(L) = -gt.on_mesh(0)-convert_green<gt_result_type>(ta(1)(0,0));
// set tail
gt.singularity() = gw.singularity();
}
void pade (gf_view<refreq> &gr, gf_view<imfreq> const &gw, int n_points, double freq_offset) {
// make sure the GFs have the same structure
//assert(gw.shape() == gr.shape());
// copy the tail. it doesn't need to conform to the pade approximant
gr.singularity() = gw.singularity();
auto sh = gw.data().shape().front_pop();
int N1 = sh[0], N2 = sh[1];
for (int n1=0; n1<N1; n1++) {
for (int n2=0; n2<N2; n2++) {
arrays::vector<dcomplex> z_in(n_points); // complex points
arrays::vector<dcomplex> u_in(n_points); // values at these points
arrays::vector<dcomplex> a(n_points); // corresponding Pade coefficients
for (int i=0; i < n_points; ++i) z_in(i) = gw.mesh()[i];
for (int i=0; i < n_points; ++i) u_in(i) = gw.on_mesh(i)(n1,n2);
triqs::utility::pade_approximant PA(z_in,u_in);
gr() = 0.0;
for (auto om : gr.mesh()) {
dcomplex e = om + dcomplex(0.0,1.0)*freq_offset;
gr[om](n1,n2) = PA(e);
}
}
}
}
