GF Legendre-Matsubara transform

Detailed Description

Transform between the Legendre and Matsubara representations.

Functions
template<typename G>
gf_keeper< tags::legendre, mesh::imfreq, typename G::target_t >	triqs::gfs::imfreq_to_legendre (G const &gw)
	Tag a Matsubara Green's function for assignment to a Legendre Green's function.
template<typename G>
gf_keeper< tags::legendre, mesh::imtime, typename G::target_t >	triqs::gfs::imtime_to_legendre (G const &gt)
	Tag an imaginary-time Green's function for assignment to a Legendre Green's function.
template<typename G1, typename G2> requires (is_gf_v<G1, mesh::imfreq>)
void	triqs::gfs::legendre_matsubara_direct (G1 &&gw, G2 const &gl)
	Fill a Matsubara Green's function from a Legendre Green's function.
template<typename G1, typename G2> requires (is_gf_v<G2, mesh::imfreq>)
void	triqs::gfs::legendre_matsubara_inverse (G1 &&gl, G2 const &gw)
	Fill a Legendre Green's function from a Matsubara Green's function.
template<typename G>
gf_keeper< tags::legendre, mesh::legendre, typename G::target_t >	triqs::gfs::legendre_to_imfreq (G const &gl)
	Tag a Legendre Green's function for assignment to a Matsubara Green's function.
template<typename G>
gf_keeper< tags::legendre, mesh::legendre, typename G::target_t >	triqs::gfs::legendre_to_imtime (G const &gl)
	Tag a Legendre Green's function for assignment to an imaginary-time Green's function.

Function Documentation

imfreq_to_legendre()

template<typename G>

gf_keeper< tags::legendre, mesh::imfreq, typename G::target_t > triqs::gfs::imfreq_to_legendre ( G const & gw )

inline

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

Tag a Matsubara Green's function for assignment to a Legendre Green's function.

Returns a lightweight handle that, when assigned to a Legendre Green's function, triggers the inverse Matsubara-to-Legendre transform, e.g. gl() = imfreq_to_legendre(gw).

Template Parameters

G	The type of the input Matsubara Green's function.

Parameters

gw	The input imaginary-frequency Green's function.

Returns

A handle holding a const view of gw tagged for the imfreq-to-Legendre transform.

Definition at line 215 of file legendre_matsubara.hpp.

imtime_to_legendre()

template<typename G>

gf_keeper< tags::legendre, mesh::imtime, typename G::target_t > triqs::gfs::imtime_to_legendre ( G const & gt )

inline

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

Tag an imaginary-time Green's function for assignment to a Legendre Green's function.

Returns a lightweight handle that, when assigned to a Legendre Green's function, triggers the inverse imaginary-time-to-Legendre transform, e.g. gl() = imtime_to_legendre(gt).

Template Parameters

G	The type of the input imaginary-time Green's function.

Parameters

gt	The input imaginary-time Green's function.

Returns

A handle holding a const view of gt tagged for the imtime-to-Legendre transform.

Definition at line 230 of file legendre_matsubara.hpp.

legendre_matsubara_direct()

template<typename G1, typename G2>
requires (is_gf_v<G1, mesh::imfreq>)

void triqs::gfs::legendre_matsubara_direct	(	G1 &&	gw,
		G2 const &	gl )

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

Fill a Matsubara Green's function from a Legendre Green's function.

Performs the direct Legendre-to-Matsubara transform in imaginary frequency, \( G(i\omega_n) = \sum_l T_{nl}\, G_l \), where \( T_{nl} \) is the Legendre-to-Matsubara transformation matrix and \( G_l \) are the Legendre coefficients. The result is written into gw.

Template Parameters

G1	The type of the output Matsubara Green's function (must have an imfreq mesh).
G2	The type of the input Legendre Green's function (must have a legendre mesh).

Parameters

gw	The imaginary-frequency Green's function to fill (modified in place).
gl	The input Legendre Green's function.

Definition at line 68 of file legendre_matsubara.hpp.

legendre_matsubara_inverse()

template<typename G1, typename G2>
requires (is_gf_v<G2, mesh::imfreq>)

void triqs::gfs::legendre_matsubara_inverse	(	G1 &&	gl,
		G2 const &	gw )

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

Fill a Legendre Green's function from a Matsubara Green's function.

Performs the inverse Matsubara-to-Legendre transform. Starting from an imaginary-frequency Green's function, the data is first transformed to imaginary time via a Fourier transform (which uses the high-frequency tail) and the imaginary-time overload is then applied to obtain the Legendre coefficients \( G_l \). The result is written into gl.

Template Parameters

G1	The type of the output Legendre Green's function (must have a legendre mesh).
G2	The type of the input Matsubara Green's function (must have an imfreq mesh).

Parameters

gl	The Legendre Green's function to fill (modified in place).
gw	The input imaginary-frequency Green's function.

Definition at line 119 of file legendre_matsubara.hpp.

legendre_to_imfreq()

template<typename G>

gf_keeper< tags::legendre, mesh::legendre, typename G::target_t > triqs::gfs::legendre_to_imfreq ( G const & gl )

inline

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

Tag a Legendre Green's function for assignment to a Matsubara Green's function.

Returns a lightweight handle that, when assigned to an imaginary-frequency Green's function, triggers the direct Legendre-to-Matsubara transform, e.g. gw() = legendre_to_imfreq(gl).

Template Parameters

G	The type of the input Legendre Green's function.

Parameters

gl	The input Legendre Green's function.

Returns

A handle holding a const view of gl tagged for the Legendre-to-imfreq transform.

Definition at line 185 of file legendre_matsubara.hpp.

legendre_to_imtime()

template<typename G>

gf_keeper< tags::legendre, mesh::legendre, typename G::target_t > triqs::gfs::legendre_to_imtime ( G const & gl )

inline

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

Tag a Legendre Green's function for assignment to an imaginary-time Green's function.

Returns a lightweight handle that, when assigned to an imaginary-time Green's function, triggers the direct Legendre-to-imaginary-time transform, e.g. gt() = legendre_to_imtime(gl).

Template Parameters

G	The type of the input Legendre Green's function.

Parameters

gl	The input Legendre Green's function.

Returns

A handle holding a const view of gl tagged for the Legendre-to-imtime transform.

Definition at line 200 of file legendre_matsubara.hpp.