GF Padé continuation

Detailed Description

Padé analytic continuation from Matsubara to real frequencies.

Functions
void	triqs::gfs::pade (gf_view< mesh::refreq, scalar_valued > gr, gf_const_view< mesh::imfreq, scalar_valued > gw, int n_points, double freq_offset)
	Analytically continue a scalar Matsubara Green's function to the real-frequency axis via Pade.
template<MemoryGf< mesh::refreq > GR, MemoryGf< mesh::imfreq > GW> requires (GR::target_rank > 0 && GW::target_rank > 0)
void	triqs::gfs::pade (GR &gr, GW const &gw, int n_points, double freq_offset)
	Analytically continue a matrix-valued Matsubara Green's function to the real-frequency axis via Pade.

Function Documentation

pade() [1/2]

void triqs::gfs::pade	(	gf_view< mesh::refreq, scalar_valued >	gr,
		gf_const_view< mesh::imfreq, scalar_valued >	gw,
		int	n_points,
		double	freq_offset )

#include <triqs/gfs/transform/pade.cpp>

Analytically continue a scalar Matsubara Green's function to the real-frequency axis via Pade.

Builds a Pade approximant from the first n_points positive Matsubara frequencies of gw and evaluates it on the real-frequency mesh of gr, shifted into the upper half-plane by freq_offset, i.e. at \( \omega + i\,\eta \) with \( \eta = \) freq_offset. The result is written into gr.

Parameters

gr	The real-frequency Green's function to fill (modified in place).
gw	The input scalar Matsubara Green's function.
n_points	Number of Matsubara frequencies used to construct the Pade approximant.
freq_offset	Imaginary shift \( \eta \) added to the real-frequency axis during evaluation.

Definition at line 34 of file pade.cpp.

pade() [2/2]

template<MemoryGf< mesh::refreq > GR, MemoryGf< mesh::imfreq > GW>
requires (GR::target_rank > 0 && GW::target_rank > 0)

void triqs::gfs::pade	(	GR &	gr,
		GW const &	gw,
		int	n_points,
		double	freq_offset )

#include <triqs/gfs/transform/pade.hpp>

Analytically continue a matrix-valued Matsubara Green's function to the real-frequency axis via Pade.

Applies the scalar Pade continuation element-wise over the target indices of gw and gr, which must share the same target shape.

Template Parameters

GR	The type of the real-frequency Green's function (must have a refreq mesh).
GW	The type of the Matsubara Green's function (must have an imfreq mesh).

Parameters

gr	The real-frequency Green's function to fill (modified in place).
gw	The input Matsubara Green's function.
n_points	Number of Matsubara frequencies used to construct each Pade approximant.
freq_offset	Imaginary shift \( \eta \) added to the real-frequency axis during evaluation.

Definition at line 72 of file pade.hpp.