DiFfRG::MatsubaraQuadrature< NT > Class Template Reference

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=powr< 10 >(2), 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=powr< 10 >(2), const int vacuum_quad_size=48, const int precision_factor=1)
	Update the quadrature rule with new parameters.
const std::vector< NT > &	nodes () const
	Get the nodes of the quadrature rule.
const std::vector< NT > &	weights () const
	Get the weights of the quadrature rule.
int	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.
const NT *	device_nodes ()
	Return the device-side nodes of the quadrature rule.
const NT *	device_weights ()
	Return the device-side weights of the quadrature rule.

Private Member Functions
void	move_device_data ()
	Move the nodes and weights to the device, if they are not already there.
void	reinit_0 ()
	Construct a quadrature rule for T=0.

Private Attributes
NT	T
NT	typical_E
std::vector< NT >	x
	Nodes of the quadrature rule.
std::vector< NT >	w
	Weights of the quadrature rule.
int	m_size
	The number of nodes in the quadrature rule.
thrust::device_vector< NT >	device_x
	Device-side nodes of the quadrature rule.
thrust::device_vector< NT >	device_w
	Device-side weights of 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 = powr< 10 >(2),
		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

device_nodes()

template<typename NT >

const NT * DiFfRG::MatsubaraQuadrature< NT >::device_nodes

(

)

Return the device-side nodes of the quadrature rule.

Returns

const NT*

device_weights()

template<typename NT >

const NT * DiFfRG::MatsubaraQuadrature< NT >::device_weights

(

)

Return the device-side weights of the quadrature rule.

Returns

const NT*

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.

move_device_data()

template<typename NT >

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

private

Move the nodes and weights to the device, if they are not already there.

nodes()

template<typename NT >

const std::vector< NT > & DiFfRG::MatsubaraQuadrature< NT >::nodes

(

)

const

Get the nodes of the quadrature rule.

Returns

The nodes of the quadrature rule.

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 = powr< 10 >(2),
		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 >

int 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 >

const std::vector< NT > & DiFfRG::MatsubaraQuadrature< NT >::weights

(

)

const

Get the weights of the quadrature rule.

Returns

The weights of the quadrature rule.

Member Data Documentation

device_w

template<typename NT >

thrust::device_vector<NT> DiFfRG::MatsubaraQuadrature< NT >::device_w

private

Device-side weights of the quadrature rule.

device_x

template<typename NT >

thrust::device_vector<NT> DiFfRG::MatsubaraQuadrature< NT >::device_x

private

Device-side nodes of the quadrature rule.

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

w

template<typename NT >

std::vector<NT> DiFfRG::MatsubaraQuadrature< NT >::w

private

Weights of the quadrature rule.

x

template<typename NT >

std::vector<NT> DiFfRG::MatsubaraQuadrature< NT >::x

private

Nodes of the quadrature rule.

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

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