triqs::gfs::fit_hermitian_tail

#include <triqs/gfs.hpp>

Synopsis

1. template<int N, typename G, typename A = typenameG::>

   std::pair<typename A::regular_type, double> fit_hermitian_tail (G const & g,

   A const & known_moments = {})
2. template<int N, typename BG, typename A = std::vector<typenameBG::g_t::data_t::regular_type>

   std::pair<std::vector<typename BG::g_t::data_t::regular_type>, double> fit_hermitian_tail (BG const & bg,

   A const & known_moments = {})

Documentation

1) Fit the tail of a Green function using a least-squares fitting procedure

imposing the symmetry \(G[i\omega](i,j) = G[-i\omega](j,i)^*\)

2) Fit the tail of a Block Green function using a least-squares fitting procedure

imposing the symmetry \(G[i\omega](i,j) = G[-i\omega](j,i)^*\) for each block

Template parameters

• N The position of the frequency mesh in case of a product mesh [default: 0]
• G The type of the Green function object
• A The type of the high-frequency moments
• BG The type of the Block Green function (block_gf, block_gf_view, block_gf_const_view)
• AG The type of the high-frequecy moments for Block Green functions (e.g. std::vector<array>)

Parameters

• g The Green function object to fit the tail for
• known_moments The object containing the known high-frequency moments
• bg The Block Green function object to fit the tail for

Returns

A pair of the tail object and the fitting error

Example

#include <triqs/gfs.hpp>
#include <triqs/mesh.hpp>
#include <iomanip>

using namespace triqs::gfs;
using namespace triqs::mesh;
nda::clef::placeholder<0> iw_;

int main() {
  double beta = 1.0;
  int n_iw    = 100;
  auto g      = gf<imfreq>{{beta, Fermion, n_iw}, {1, 1}};
  g[iw_] << 1.0 / iw_;
  auto [tail, err] = fit_hermitian_tail(g);
  std::cout << std::setprecision(2) << "Error: " << err << "\nTail:  " << tail;
}

Output

Error: 7.6e-19
Tail:  [(1.9e-16,0),(1,0),(1.8e-10,0),(1.6e-09,0),(5.6e-05,0),(-0.00035,0),(5.8,0)]