Real time and frequency meshes

Detailed Description

Mesh types for real time and frequency domains.

Classes
class	triqs::mesh::refreq
	Real frequency mesh type. More...
class	triqs::mesh::refreq_log
	Logarithmic real frequency mesh type. More...
class	triqs::mesh::refreq_pts
	Real frequency mesh type from arbitrary sorted frequency points. More...
class	triqs::mesh::retime
	Real time mesh type. More...

Functions
auto	triqs::mesh::evaluate (refreq const &m, auto const &f, double w)
	Linear interpolation of a function \( f \) defined on a triqs::mesh::refreq mesh at a real frequency \(\omega \in [\omega_{\text{min}}, \omega_{\text{max}}] \).
auto	triqs::mesh::evaluate (refreq_log const &m, auto const &f, double w)
	Linear interpolation of a function \( f \) defined on a triqs::mesh::refreq_log mesh at a real frequency \( \omega \).
auto	triqs::mesh::evaluate (refreq_pts const &m, auto const &f, double w)
	Linear interpolation of a function \( f \) defined on a triqs::mesh::refreq_pts mesh at a real frequency \( \omega \).
auto	triqs::mesh::evaluate (retime const &m, auto const &f, double t)
	Linear interpolation of a function \( f \) defined on a triqs::mesh::retime mesh at a real time point \(t \in [t_{\mathrm{min}}, t_{\mathrm{max}}] \).
retime	triqs::mesh::make_adjoint_mesh (refreq const &m, bool shift_half_bin=false)
	Create the adjoint real-time mesh to a given real-frequency mesh.
refreq	triqs::mesh::make_adjoint_mesh (retime const &m, bool shift_half_bin=false)
	Create the adjoint real-frequency mesh to a given real-time mesh.

Function Documentation

evaluate() [1/4]

auto triqs::mesh::evaluate	(	refreq const &	m,
		auto const &	f,
		double	w )

#include <triqs/mesh/refreq.hpp>

Linear interpolation of a function \( f \) defined on a triqs::mesh::refreq mesh at a real frequency \(\omega \in [\omega_{\text{min}}, \omega_{\text{max}}] \).

It simply calls the triqs::mesh::refreq::evaluate method of the mesh.

Parameters

m	triqs::mesh::refreq mesh.
f	Callable object \( f \) containing the function values \( f_n = f(\omega(n)) \) at the mesh points.
w	Real frequency \( \omega \) at which to interpolate the function.

Returns

Linear interpolation of \( f(\omega) \).

Definition at line 150 of file refreq.hpp.

evaluate() [2/4]

auto triqs::mesh::evaluate ( refreq_log const & m, auto const & f, double w )

inline

#include <triqs/mesh/refreq_log.hpp>

Linear interpolation of a function \( f \) defined on a triqs::mesh::refreq_log mesh at a real frequency \( \omega \).

We find the bracketing mesh points using binary search and calculate

\[ f(\omega) \approx f_{i_l} \cdot w_l + f_{i_r} \cdot w_r \]

where \( i_l \) and \( i_r \) are the indices of the mesh points bracketing \( \omega \), and \( w_l \) and \( w_r \) are the interpolation weights.

Parameters

m	triqs::mesh::refreq_log mesh.
f	Callable object containing the function values at the mesh points.
w	Real frequency at which to interpolate.

Returns

Linear interpolation of \( f(\omega) \).

Definition at line 401 of file refreq_log.hpp.

evaluate() [3/4]

auto triqs::mesh::evaluate ( refreq_pts const & m, auto const & f, double w )

inline

#include <triqs/mesh/refreq_pts.hpp>

Linear interpolation of a function \( f \) defined on a triqs::mesh::refreq_pts mesh at a real frequency \( \omega \).

We find the bracketing mesh points using binary search and calculate

\[ f(\omega) \approx f_{i_l} \cdot w_l + f_{i_r} \cdot w_r \]

where \( i_l \) and \( i_r \) are the indices of the mesh points bracketing \( \omega \), and \( w_l \) and \( w_r \) are the interpolation weights.

Parameters

m	triqs::mesh::refreq_pts mesh.
f	Callable object containing the function values at the mesh points.
w	Real frequency at which to interpolate.

Returns

Linear interpolation of \( f(\omega) \).

Definition at line 370 of file refreq_pts.hpp.

evaluate() [4/4]

auto triqs::mesh::evaluate	(	retime const &	m,
		auto const &	f,
		double	t )

#include <triqs/mesh/retime.hpp>

Linear interpolation of a function \( f \) defined on a triqs::mesh::retime mesh at a real time point \(t \in [t_{\mathrm{min}}, t_{\mathrm{max}}] \).

It simply calls the triqs::mesh::retime::evaluate method of the mesh.

Parameters

m	triqs::mesh::retime mesh.
f	Callable object \( f \) containing the function values \( f_n = f(t(n)) \) at the mesh points.
t	Real time point \( t \) at which to interpolate the function.

Returns

Linear interpolation of \( f(t) \).

Definition at line 145 of file retime.hpp.

make_adjoint_mesh() [1/2]

retime triqs::mesh::make_adjoint_mesh ( refreq const & m, bool shift_half_bin = false )

inlinenodiscard

#include <triqs/mesh/adjoint.hpp>

Create the adjoint real-time mesh to a given real-frequency mesh.

The resulting time mesh is defined on the interval \( [t_{\text{min}}, t_{\text{max}}] \) with \( t_{\text{max}} = \pi (N - 1) / (N \Delta) \) and \( t_{\text{min}} = -t_{\text{max}} \), where \( N \) and \( \Delta \) are the size and step size of the given real frequency mesh, respectively.

If shift_half_bin is true, the time mesh is shifted by half a bin to the right, i.e. by \( \pi / (N \Delta) \).

Parameters

m	Input mesh.
shift_half_bin	If true, shift the time mesh by half a bin to the right.

Returns

Real time mesh on the interval \( [t_{\text{min}}, t_{\text{max}}] \) with \( N \) equally spaced mesh points.

Definition at line 133 of file adjoint.hpp.

make_adjoint_mesh() [2/2]

refreq triqs::mesh::make_adjoint_mesh ( retime const & m, bool shift_half_bin = false )

inlinenodiscard

#include <triqs/mesh/adjoint.hpp>

Create the adjoint real-frequency mesh to a given real-time mesh.

The resulting frequency mesh is defined on the interval \( [\omega_{\text{min}}, \omega_{\text{max}}] \) with \( \omega_{\text{max}} = \pi (N - 1) / (N \Delta) \) and \( \omega_{\text{min}} = -\omega_{\text{max}} \), where \( N \) and \( \Delta \) are the size and step size of the given real time mesh, respectively.

If shift_half_bin is true, the frequency mesh is shifted by half a bin to the right, i.e. by \( \pi / (N \Delta) \).

Parameters

m	Input mesh.
shift_half_bin	If true, shift the frequency mesh by half a bin to the right.

Returns

Real frequency mesh on the interval \( [\omega_{\text{min}}, \omega_{\text{max}}] \) with \( N \) equally spaced mesh points.

Definition at line 110 of file adjoint.hpp.