Matsubara frequencies

Detailed Description

Tools to represent and manipulate Matsubara frequencies.

Arithmetic operations between Matsubara frequencies and scalars are performed using the complex values of the Matsubara frequencies.

Classes
struct	triqs::mesh::matsubara_freq
	Represents a Matsubara frequency \( i\omega_n \). More...

Functions
bool	triqs::mesh::kronecker (matsubara_freq const &iw)
	Kronecker delta function for a single Matsubara frequency.
bool	triqs::mesh::kronecker (matsubara_freq const &iw1, matsubara_freq const &iw2)
	Kronecker delta function for two Matsubara frequencies.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator* (matsubara_freq const &iw, T &&y)
	Binary * operation for a triqs::mesh::matsubara_freq and some numeric type.
auto	triqs::mesh::operator* (matsubara_freq const &iw1, matsubara_freq const &iw2)
	Multiplication operator for two triqs::mesh::matsubara_freq objects.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator* (T &&x, matsubara_freq const &iw)
	Binary * operation for some numeric type and a triqs::mesh::matsubara_freq.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator+ (matsubara_freq const &iw, T &&y)
	Binary + operation for a triqs::mesh::matsubara_freq and some numeric type.
matsubara_freq	triqs::mesh::operator+ (matsubara_freq const &iw1, matsubara_freq const &iw2)
	Addition operator for two triqs::mesh::matsubara_freq objects.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator+ (T &&x, matsubara_freq const &iw)
	Binary + operation for some numeric type and a triqs::mesh::matsubara_freq.
matsubara_freq	triqs::mesh::operator- (matsubara_freq const &iw)
	Unary minus operator for a triqs::mesh::matsubara_freq object.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator- (matsubara_freq const &iw, T &&y)
	Binary - operation for a triqs::mesh::matsubara_freq and some numeric type.
matsubara_freq	triqs::mesh::operator- (matsubara_freq const &iw1, matsubara_freq const &iw2)
	Subtraction operator for two triqs::mesh::matsubara_freq objects.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator- (T &&x, matsubara_freq const &iw)
	Binary - operation for some numeric type and a triqs::mesh::matsubara_freq.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator/ (matsubara_freq const &iw, T &&y)
	Binary / operation for a triqs::mesh::matsubara_freq and some numeric type.
auto	triqs::mesh::operator/ (matsubara_freq const &iw1, matsubara_freq const &iw2)
	Divison operator for two triqs::mesh::matsubara_freq objects.
template<typename T> requires (not std::is_base_of_v<matsubara_freq, std::decay_t<T>>)
auto	triqs::mesh::operator/ (T &&x, matsubara_freq const &iw)
	Binary / operation for some numeric type and a triqs::mesh::matsubara_freq.
std::ostream &	triqs::mesh::operator<< (std::ostream &sout, matsubara_freq const &iw)
	Write a triqs::mesh::matsubara_freq to a std::ostream.

Function Documentation

kronecker() [1/2]

bool triqs::mesh::kronecker ( matsubara_freq const & iw )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Kronecker delta function for a single Matsubara frequency.

Parameters

iw	triqs::mesh::matsubara_freq object.

Returns

True, if the index of the Matsubara frequency is zero, false otherwise.

Definition at line 201 of file matsubara_freq.hpp.

kronecker() [2/2]

bool triqs::mesh::kronecker ( matsubara_freq const & iw1, matsubara_freq const & iw2 )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Kronecker delta function for two Matsubara frequencies.

Parameters

iw1	triqs::mesh::matsubara_freq object.
iw2	triqs::mesh::matsubara_freq object.

Returns

True, if the indices of the Matsubara frequencies are equal, false otherwise.

Definition at line 210 of file matsubara_freq.hpp.

operator*()

auto triqs::mesh::operator* ( matsubara_freq const & iw1, matsubara_freq const & iw2 )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Multiplication operator for two triqs::mesh::matsubara_freq objects.

The mulitiplication is performed on the complex numbers corresponding to the Matsubara frequencies.

Parameters

iw1	Left hand side frequency operand.
iw2	Right hand side frequency operand.

Returns

Resulting std::complex<double>.

Definition at line 172 of file matsubara_freq.hpp.

operator+()

matsubara_freq triqs::mesh::operator+ ( matsubara_freq const & iw1, matsubara_freq const & iw2 )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Addition operator for two triqs::mesh::matsubara_freq objects.

The addition is performed directly on the indices. The resulting Matsubara frequency has

• fermionic statistics, if one and only one of the operands has fermionic statistics and
• bosonic statistics otherwise.

Parameters

iw1	Left hand side frequency operand.
iw2	Right hand side frequency operand.

Returns

Resulting triqs::mesh::matsubara_freq object.

Definition at line 118 of file matsubara_freq.hpp.

operator-() [1/2]

matsubara_freq triqs::mesh::operator- ( matsubara_freq const & iw )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Unary minus operator for a triqs::mesh::matsubara_freq object.

For fermions, it adds \( +1 \) to the index and flips its sign. For bosons, it just flips the sign of the index.

Parameters

iw	Frequency operand.

Returns

Resulting triqs::mesh::matsubara_freq object.

Definition at line 146 of file matsubara_freq.hpp.

operator-() [2/2]

matsubara_freq triqs::mesh::operator- ( matsubara_freq const & iw1, matsubara_freq const & iw2 )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Subtraction operator for two triqs::mesh::matsubara_freq objects.

The subtraction is performed directly on the indices. The resulting Matsubara frequency has

• fermionic statistics, if one and only one of the operands has fermionic statistics and
• bosonic statistics otherwise.

Parameters

iw1	Left hand side frequency operand.
iw2	Right hand side frequency operand.

Returns

Resulting triqs::mesh::matsubara_freq object.

Definition at line 133 of file matsubara_freq.hpp.

operator/()

auto triqs::mesh::operator/ ( matsubara_freq const & iw1, matsubara_freq const & iw2 )

inlinenodiscard

#include <triqs/mesh/matsubara_freq.hpp>

Divison operator for two triqs::mesh::matsubara_freq objects.

The division is performed on the complex numbers corresponding to the Matsubara frequencies.

Parameters

iw1	Left hand side frequency operand.
iw2	Right hand side frequency operand.

Returns

Resulting std::complex<double>.

Definition at line 159 of file matsubara_freq.hpp.

operator<<()

std::ostream & triqs::mesh::operator<< ( std::ostream & sout, matsubara_freq const & iw )

inline

#include <triqs/mesh/matsubara_freq.hpp>

Write a triqs::mesh::matsubara_freq to a std::ostream.

Parameters

sout	std::ostream object.
iw	Frequency to be written.

Returns

Reference to std::ostream object.

Definition at line 105 of file matsubara_freq.hpp.