#include <ChebyshevSolver.h>

Public Types
enum	GreensFunctionType { Advanced, Retarded, Principal, NonPrincipal }

Public Member Functions
	ChebyshevSolver ()

	~ChebyshevSolver ()

void	setModel (Model *model)

Model *	getModel ()

void	setScaleFactor (double scaleFactor)

double	getScaleFactor ()

void	calculateCoefficients (std::vector< Index > &to, Index from, std::complex< double > *coefficients, int numCoefficients, double broadening=0.0001)

void	calculateCoefficients (Index to, Index from, std::complex< double > *coefficients, int numCoefficients, double broadening=0.0001)

void	calculateCoefficientsGPU (std::vector< Index > &to, Index from, std::complex< double > *coefficients, int numCoefficients, double broadening=0.0001)

void	calculateCoefficientsGPU (Index to, Index from, std::complex< double > *coefficients, int numCoefficients, double broadening=0.0001)

void	calculateCoefficientsWithCutoff (Index to, Index from, std::complex< double > *coefficients, int numCoefficients, double componentCutoff, double broadening=0.0001)

void	generateLookupTable (int numCoefficeints, int energyResolution, double lowerBound=-1., double upperBound=1.)

void	loadLookupTableGPU ()

void	destroyLookupTableGPU ()

void	generateGreensFunction (std::complex< double > greensFunction, std::complex< double > coefficients, int numCoefficients, int energyResolution, double lowerBound=-1., double upperBound=1., GreensFunctionType type=GreensFunctionType::Retarded)

void	generateGreensFunction (std::complex< double > greensFunction, std::complex< double > coefficients, GreensFunctionType type=GreensFunctionType::Retarded)

void	generateGreensFunctionGPU (std::complex< double > greensFunction, std::complex< double > coefficients, GreensFunctionType type=GreensFunctionType::Retarded)

std::complex< double >	getMonolopoulosABCDamping (double distanceToEdge, double boundarySize, double e=1., double c=2.62)

void	setDamping (std::complex< double > *damping)

void	setTalkative (bool isTalkative)

Detailed Description

The ChebyshevSolver can be used to calculate Green's function for a given Model. The implementation is based on PhysRevLett.105.167006. The ChebyshevSolver can be run on CPU, GPU, or a mixture of both. The calculation of Chebyshev coefficients scales as $O(n)$ with each of the following: dimension of the Hilbert space and number of Chebyshev coefficients. The generation of Green's functions scales as $O(n)$ with the following: Number of coefficients, energy resolution, and the number of Green's functions.

Member Enumeration Documentation

enum TBTK::ChebyshevSolver::GreensFunctionType

strong

Enum used to indicate the type of Green's function to generate.

Constructor & Destructor Documentation

TBTK::ChebyshevSolver::ChebyshevSolver ( )

Constructor.

TBTK::ChebyshevSolver::~ChebyshevSolver ( )

Destructor.

Member Function Documentation

void TBTK::ChebyshevSolver::calculateCoefficients	(	std::vector< Index > &	to,
		Index	from,
		std::complex< double > *	coefficients,
		int	numCoefficients,
		double	broadening = `0.0001`
	)

Calculates the Chebyshev coefficients for $G_{ij}(E)$ , where $i = \textrm{to}$ is a set of indices and $j = \textrm{from}$ . Runs on CPU.

Parameters

to	vector of 'to'-indeces, or 's.
from	'From'-index, or .
coefficients	Pointer to array able to hold numCoefficients $\times$ toIndeices.size() coefficients.
numCoefficients	Number of coefficients to calculate for each to-index.
broadening	Broadening to use in convolusion of coefficients to remedy Gibb's osciallations.

void TBTK::ChebyshevSolver::calculateCoefficients	(	Index	to,
		Index	from,
		std::complex< double > *	coefficients,
		int	numCoefficients,
		double	broadening = `0.0001`
	)

Calculates the Chebyshev coefficients for $G_{ij}(E)$ , where $i = \textrm{to}$ and $j = \textrm{from}$ . Runs on CPU.

Parameters

to	'To'-index, or .
from	'From'-index, or .
coefficients	Pointer to array able to hold numCoefficients coefficients.
numCoefficients	Number of coefficients to calculate.
broadening	Broadening to use in convolusion of coefficients to remedy Gibb's osciallations.

void TBTK::ChebyshevSolver::calculateCoefficientsGPU	(	std::vector< Index > &	to,
		Index	from,
		std::complex< double > *	coefficients,
		int	numCoefficients,
		double	broadening = `0.0001`
	)

Calculates the Chebyshev coefficients for $G_{ij}(E)$ , where $i = \textrm{to}$ is a set of indices and $j = \textrm{from}$ . Runs on GPU.

Parameters

to	vector of 'to'-indeces, or 's.
from	'From'-index, or .
coefficients	Pointer to array able to hold numCoefficients $\times$ toIndeices.size() coefficients.
numCoefficients	Number of coefficients to calculate for each to-index.
broadening	Broadening to use in convolusion of coefficients to remedy Gibb's osciallations.

void TBTK::ChebyshevSolver::calculateCoefficientsGPU	(	Index	to,
		Index	from,
		std::complex< double > *	coefficients,
		int	numCoefficients,
		double	broadening = `0.0001`
	)

Calculates the Chebyshev coefficients for $G_{ij}(E)$ , where $i = \textrm{to}$ and $j = \textrm{from}$ . Runs on GPU.

Parameters

to	'To'-index, or .
from	'From'-index, or .
coefficients	Pointer to array able to hold numCoefficients coefficients.
numCoefficients	Number of coefficients to calculate.
broadening	Broadening to use in convolusion of coefficients to remedy Gibb's osciallations.

void TBTK::ChebyshevSolver::calculateCoefficientsWithCutoff	(	Index	to,
		Index	from,
		std::complex< double > *	coefficients,
		int	numCoefficients,
		double	componentCutoff,
		double	broadening = `0.0001`
	)

Experimental.

void TBTK::ChebyshevSolver::destroyLookupTableGPU ( )

Free memory allocated on GPU with ChebyshevSolver::loadLookupTableGPU

void TBTK::ChebyshevSolver::generateGreensFunction	(	std::complex< double > *	greensFunction,
		std::complex< double > *	coefficients,
		int	numCoefficients,
		int	energyResolution,
		double	lowerBound = `-1.`,
		double	upperBound = `1.`,
		GreensFunctionType	type = `GreensFunctionType::Retarded`
	)

Genererate Green's function. Does not use lookup table generated by ChebyshevSolver::generateLookupTable. Runs on CPU.

Parameters

greensFunction	Pointer to array able to hold Green's function. Has to be able to hold energyResolution elements.
coefficients	Chebyshev coefficients calculated by ChebyshevSolver::calculateCoefficients.
numCoefficeints	Number of coefficients in coefficients.
energyResolution	Number of elements in greensFunction.
lowerBound	Lower bound, has to be larger or equal to -scaleFactor set by setScaleFactor (default value 1).
upperBound	Upper bound, has to be smaller or equal to scaleFactor setBy setScaleFactor (default value 1).

void TBTK::ChebyshevSolver::generateGreensFunction	(	std::complex< double > *	greensFunction,
		std::complex< double > *	coefficients,
		GreensFunctionType	type = `GreensFunctionType::Retarded`
	)

Genererate Green's function. Uses lookup table generated by ChebyshevSolver::generateLookupTable. Runs on CPU.

Parameters

greensFunction	Pointer to array able to hold Green's function. Has to be able to hold energyResolution elements.
coefficients	Chebyshev coefficients calculated by ChebyshevSolver::calculateCoefficients.

numCoefficients and energyResolution are here the values specified in the call to ChebyshevSolver::generateLookupTable

void TBTK::ChebyshevSolver::generateGreensFunctionGPU	(	std::complex< double > *	greensFunction,
		std::complex< double > *	coefficients,
		GreensFunctionType	type = `GreensFunctionType::Retarded`
	)

Genererate Green's function. Uses lookup table generated by ChebyshevSolver::generateLookupTable. Runs on GPU.

Parameters

greensFunction	Pointer to array able to hold Green's function. Has to be able to hold energyResolution elements.
coefficients	Chebyshev coefficients calculated by ChebyshevSolver::calculateCoefficients.

numCoefficients and energyResolution are here the values specified in the call to ChebyshevSolver::generateLookupTable

void TBTK::ChebyshevSolver::generateLookupTable	(	int	numCoefficeints,
		int	energyResolution,
		double	lowerBound = `-1.`,
		double	upperBound = `1.`
	)

Generate lokup table for quicker generation of multiple Green's functions. Required if evaluation is to be performed on GPU.

Parameters

numCoefficeints	Number of coefficients used in Chebyshev
lowerBound	Lower bound, has to be larger or equal to -scaleFactor set by setScaleFactor (default value 1).
upperBound	Upper bound, has to be smaller or equal to scaleFactor setBy setScaleFactor (default value 1). expansion.

Model * TBTK::ChebyshevSolver::getModel ( )

inline

Get model.

complex< double > TBTK::ChebyshevSolver::getMonolopoulosABCDamping	(	double	distanceToEdge,
		double	boundarySize,
		double	e = `1.`,
		double	c = `2.62`
	)

Damping potential based on J. Chem. Phys. 117, 9552 (2002).

Parameters

distanceToEdge	Distance from edge to the point at which to calculate the damping factor.
boundarySize	Size of the boundary region.
b	Tuning parameter for optimizing the potential
c	Tuning parameter for optimizing the potential

Returns: exp(-gamma), where gamma = 0 in the interior, infty outside the edge, and determined by the function described in J. Chem. Phys. 117, 9552 (2002), inside the boundary region.

double TBTK::ChebyshevSolver::getScaleFactor ( )

inline

Get scale factor.

void TBTK::ChebyshevSolver::loadLookupTableGPU ( )

Load lookup table generated by ChebyshevSolver::generateLookupTable onto GPU.

void TBTK::ChebyshevSolver::setDamping ( std::complex< double > * damping )

inline

Set damping mask. The damping mask will be used as prefactor in the modified Chebyshev expansion used for implementing absorbing boundary conditions. If set to NULL (default), no damping term will be applied.

void TBTK::ChebyshevSolver::setModel ( Model * model )

Set model to work on.

void TBTK::ChebyshevSolver::setScaleFactor ( double scaleFactor )

inline

Set scale factor.

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

/home/kristofer/TBTK/TBTK/calc/TightBindingLib/include/ChebyshevSolver.h
/home/kristofer/TBTK/TBTK/calc/TightBindingLib/src/ChebyshevSolver.cpp

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation