triqs::gfs::fit_tail

#include <triqs/gfs.hpp>

Synopsis

  1. template<int N, typename G, typename A = typenameG::const_view_type::>
    std::pair<typename A::regular_type, double> fit_tail (G const & g, A const & known_moments = {})
  2. template<int N, typename BG, typename BA = std::vector<typenameBG::g_t::data_t::regular_type>
    std::pair<std::vector<typename BG::g_t::data_t::regular_type>, double> fit_tail (BG const & bg,
    BA const & known_moments = {})

Documentation

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

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

Template parameters

  • N The position of the frequency mesh in case of a product mesh [default: 0]

  • G The type of the Green function (gf, gf_view, gf_const_view)

  • A The type of the high-frequency moment array (array, array_view, array_const_view)

  • 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;
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_tail(g);
  std::cout << std::setprecision(2) << "Error: " << err << "\nTail:  " << tail;
}

Output

Error: 4.6e-19
Tail:  [(7.6e-17,-8e-17),(1,-9e-16),(7.3e-11,-1e-11),(-1.9e-09,-7.9e-10),(2.3e-05,-1.2e-05),(0.00059,-0.00015),(2.3,0.89)]