MatsubaraQuadrature< NT > Class Template Reference#

DiFfRG: DiFfRG::MatsubaraQuadrature< NT > Class Template Reference

DiFfRG

A quadrature rule for (bosonic) Matsubara frequencies, based on the method of Monien [1]. This class provides nodes and weights for the summation. More...

#include <matsubara.hh>

Public Member Functions
int	predict_size (const NT T, const NT typical_E=1., const int step=2)
	Calculate the number of nodes needed for a given temperature and typical energy scale.

	MatsubaraQuadrature (const NT T, const NT typical_E=1., const int step=2, const int min_size=0, const int max_size=256, const int vacuum_quad_size=48, const int precision_factor=1)
	Create a new quadrature rule for Matsubara frequencies.

	MatsubaraQuadrature ()

void	reinit (const NT T, const NT typical_E=1., const int step=2, const int min_size=0, const int max_size=256, const int vacuum_quad_size=48, const int precision_factor=1)
	Update the quadrature rule with new parameters.

size_t	size () const
	Get the size of the quadrature rule.

NT	get_T () const
	Get the temperature of the quadrature rule.

NT	get_typical_E () const
	Get the typical energy scale of the quadrature rule.

template<typename F >
auto	sum (const F &f) const
	Compute a matsubara sum of a given function.

template<typename MemorySpace >
Kokkos::View< const NT *, MemorySpace >	nodes () const

template<typename MemorySpace >
Kokkos::View< const NT *, MemorySpace >	weights () const

Private Member Functions
void	write_data (const std::vector< NT > &x, const std::vector< NT > &w)

void	reinit_0 ()
	Construct a quadrature rule for T=0.

Private Attributes
NT	T

NT	typical_E

Kokkos::View< NT *, GPU_memory >	device_nodes

Kokkos::View< NT *, GPU_memory >	device_weights

Kokkos::View< NT *, CPU_memory >	host_nodes

Kokkos::View< NT *, CPU_memory >	host_weights

int	m_size
	The number of nodes in the quadrature rule.

int	vacuum_quad_size

int	precision_factor

Detailed Description

template<typename NT>
class DiFfRG::MatsubaraQuadrature< NT >

A quadrature rule for (bosonic) Matsubara frequencies, based on the method of Monien [1]. This class provides nodes and weights for the summation.

\[ T \sum_{n=\in \mathbb{Z}} f(2\pi n T) \approx \sum_{n=1}^{N} w_i (f(x_i) + f(-x_i)) + T f(0) \]

[1] H. Monien, "Gaussian quadrature for sums: a rapidly convergent summation scheme", Math. Comp. 79, 857 (2010). doi:10.1090/S0025-5718-09-02289-3

Template Parameters

NT	numeric type to be used for all calculations

Constructor & Destructor Documentation

◆ MatsubaraQuadrature() [1/2]

template<typename NT >

DiFfRG::MatsubaraQuadrature< NT >::MatsubaraQuadrature	(	const NT	T,
		const NT	typical_E = 1.,
		const int	step = 2,
		const int	min_size = 0,
		const int	max_size = 256,
		const int	vacuum_quad_size = 48,
		const int	precision_factor = 1 )

Create a new quadrature rule for Matsubara frequencies.

Parameters

T	The temperature.
typical_E	A typical energy scale, which determines the number of nodes in the quadrature rule.
step	The step size of considered node sizes (e.g. step=2 implies only even numbers of nodes).
min_size	Minimum number of nodes.
max_size	Maximum number of nodes.

◆ MatsubaraQuadrature() [2/2]

template<typename NT >

DiFfRG::MatsubaraQuadrature< NT >::MatsubaraQuadrature ( )

Member Function Documentation

◆ get_T()

template<typename NT >

NT DiFfRG::MatsubaraQuadrature< NT >::get_T ( ) const

Get the temperature of the quadrature rule.

◆ get_typical_E()

template<typename NT >

NT DiFfRG::MatsubaraQuadrature< NT >::get_typical_E ( ) const

Get the typical energy scale of the quadrature rule.

◆ nodes()

template<typename NT >

template<typename MemorySpace >

Kokkos::View< const NT *, MemorySpace > DiFfRG::MatsubaraQuadrature< NT >::nodes ( ) const

inline

◆ predict_size()

template<typename NT >

int DiFfRG::MatsubaraQuadrature< NT >::predict_size	(	const NT	T,
		const NT	typical_E = 1.,
		const int	step = 2 )

Calculate the number of nodes needed for a given temperature and typical energy scale.

Parameters

T	The temperature.
typical_E	A typical energy scale.
step	The step size of considered node sizes (e.g. step=2 implies only even numbers of nodes).

Returns: int The number of nodes needed. If the number is negative, the T=0-limit has been reached (usually if typical_E / T > 4.4e+2, which is 64 nodes).

◆ reinit()

template<typename NT >

void DiFfRG::MatsubaraQuadrature< NT >::reinit	(	const NT	T,
		const NT	typical_E = 1.,
		const int	step = 2,
		const int	min_size = 0,
		const int	max_size = 256,
		const int	vacuum_quad_size = 48,
		const int	precision_factor = 1 )

Update the quadrature rule with new parameters.

Parameters

T	The temperature.
typical_E	A typical energy scale, which determines the number of nodes in the quadrature rule.
step	The step size of considered node sizes (e.g. step=2 implies only even numbers of nodes).
min_size	Minimum number of nodes.
max_size	Maximum number of nodes.

◆ reinit_0()

template<typename NT >

void DiFfRG::MatsubaraQuadrature< NT >::reinit_0 ( )

private

Construct a quadrature rule for T=0.

◆ size()

template<typename NT >

size_t DiFfRG::MatsubaraQuadrature< NT >::size ( ) const

Get the size of the quadrature rule.

◆ sum()

template<typename NT >

template<typename F >

auto DiFfRG::MatsubaraQuadrature< NT >::sum ( const F & f ) const

inline

Compute a matsubara sum of a given function.

Template Parameters

F	The function type.

Parameters

f	The function to be summed. Must have signature NT f(NT x).

Returns: NT The Matsubara sum of the function.

◆ weights()

template<typename NT >

template<typename MemorySpace >

Kokkos::View< const NT *, MemorySpace > DiFfRG::MatsubaraQuadrature< NT >::weights ( ) const

inline

◆ write_data()

template<typename NT >

void DiFfRG::MatsubaraQuadrature< NT >::write_data	(	const std::vector< NT > &	x,
		const std::vector< NT > &	w )

private

Member Data Documentation

◆ device_nodes

template<typename NT >

Kokkos::View<NT *, GPU_memory> DiFfRG::MatsubaraQuadrature< NT >::device_nodes

private

◆ device_weights

template<typename NT >

Kokkos::View<NT *, GPU_memory> DiFfRG::MatsubaraQuadrature< NT >::device_weights

private

◆ host_nodes

template<typename NT >

Kokkos::View<NT *, CPU_memory> DiFfRG::MatsubaraQuadrature< NT >::host_nodes

private

◆ host_weights

template<typename NT >

Kokkos::View<NT *, CPU_memory> DiFfRG::MatsubaraQuadrature< NT >::host_weights

private

◆ m_size

template<typename NT >

int DiFfRG::MatsubaraQuadrature< NT >::m_size

private

The number of nodes in the quadrature rule.

◆ precision_factor

template<typename NT >

int DiFfRG::MatsubaraQuadrature< NT >::precision_factor

private

◆ T

template<typename NT >

NT DiFfRG::MatsubaraQuadrature< NT >::T

private

◆ typical_E

template<typename NT >

NT DiFfRG::MatsubaraQuadrature< NT >::typical_E

private

◆ vacuum_quad_size

template<typename NT >

int DiFfRG::MatsubaraQuadrature< NT >::vacuum_quad_size

private

The documentation for this class was generated from the following file:

/home/runner/work/DiFfRG_current/DiFfRG_current/DiFfRG/include/DiFfRG/common/quadrature/matsubara.hh

MatsubaraQuadrature&lt; NT &gt; Class Template Reference#

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MatsubaraQuadrature() [1/2]

◆ MatsubaraQuadrature() [2/2]

Member Function Documentation

◆ get_T()

◆ get_typical_E()

◆ nodes()

◆ predict_size()

◆ reinit()

◆ reinit_0()

◆ size()

◆ sum()

◆ weights()

◆ write_data()

Member Data Documentation

◆ device_nodes

◆ device_weights

◆ host_nodes

◆ host_weights

◆ m_size

◆ precision_factor

◆ T

◆ typical_E

◆ vacuum_quad_size

MatsubaraQuadrature< NT > Class Template Reference#