A Class For Solving Chemistry Systems Based On Sparse Matrices. More...

#include <DensityMatrixSolvers.h>

Inheritance diagram for NTPoly::DensityMatrixSolvers:

Static Public Member Functions
static void	PM (const Matrix_ps &Hamiltonian, const Matrix_ps &InverseSquareRoot, double trace, Matrix_ps &Density, double &energy_value_out, double &chemical_potential_out, const SolverParameters &solver_parameters)

static void	TRS2 (const Matrix_ps &Hamiltonian, const Matrix_ps &InverseSquareRoot, double trace, Matrix_ps &Density, double &energy_value_out, double &chemical_potential_out, const SolverParameters &solver_parameters)

static void	TRS4 (const Matrix_ps &Hamiltonian, const Matrix_ps &InverseSquareRoot, double trace, Matrix_ps &Density, double &energy_value_out, double &chemical_potential_out, const SolverParameters &solver_parameters)

static void	HPCP (const Matrix_ps &Hamiltonian, const Matrix_ps &InverseSquareRoot, double trace, Matrix_ps &Density, double &energy_value_out, double &chemical_potential_out, const SolverParameters &solver_parameters)

static void	ScaleAndFold (const Matrix_ps &Hamiltonian, const Matrix_ps &InverseSquareRoot, double trace, Matrix_ps &Density, double homo, double lumo, double &energy_value_out, const SolverParameters &solver_parameters)

static void	DenseDensity (const Matrix_ps &Hamiltonian, const Matrix_ps &InverseSquareRoot, double trace, Matrix_ps &Density, double &energy_value_out, double &chemical_potential_out, const SolverParameters &solver_parameters)

static void	EnergyDensityMatrix (const Matrix_ps &Hamiltonian, const Matrix_ps &Density, Matrix_ps &EnergyDensity, double threshold=0.0)

static void	McWeenyStep (const Matrix_ps &D, Matrix_ps &DOut, double threshold=0.0)

static void	McWeenyStep (const Matrix_ps &D, const Matrix_ps &S, Matrix_ps &DOut, double threshold=0.0)

Additional Inherited Members
Static Protected Member Functions inherited from NTPoly::SolverBase
static const int *	GetIH (const Matrix_ps &dsm)

static int *	GetIH (Matrix_ps &dsm)

static const int *	GetIH (const SolverParameters &csp)

static int *	GetIH (SolverParameters &csp)

Detailed Description

A Class For Solving Chemistry Systems Based On Sparse Matrices.

Member Function Documentation

◆ DenseDensity()

void NTPoly::DensityMatrixSolvers::DenseDensity	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	InverseSquareRoot,
		double	trace,
		Matrix_ps &	Density,
		double &	energy_value_out,
		double &	chemical_potential_out,
		const SolverParameters &	solver_parameters
	)

static

Compute the density matrix using a dense solver.

Parameters

Hamiltonian	the matrix to compute the corresponding density from.
InverseSquareRoot	of the overlap matrix.
trace	of the density matrix (usually the number of electrons).
Density	the density matrix computed by this routine.
energy_value_out	the energy of the system (optional).
chemical_potential_out	the chemical potential calculated.
solver_parameters	parameters for the solver

◆ EnergyDensityMatrix()

void NTPoly::DensityMatrixSolvers::EnergyDensityMatrix	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	Density,
		Matrix_ps &	EnergyDensity,
		double	threshold = `0.0`
	)

static

Compute the energy-weighted density matrix.

Parameters

Hamiltonian	the matrix to compute from.
Density	the density matrix.
EnergyDensity	the energy-weighted density matrix to compute.
threshold	for flushing small values to zero.

◆ HPCP()

void NTPoly::DensityMatrixSolvers::HPCP	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	InverseSquareRoot,
		double	trace,
		Matrix_ps &	Density,
		double &	energy_value_out,
		double &	chemical_potential_out,
		const SolverParameters &	solver_parameters
	)

static

Compute the density matrix from a Hamiltonian using the HPCP method. Based on the algorithm presented in: [6]

Parameters

Hamiltonian	the matrix to compute the corresponding density from.
InverseSquareRoot	of the overlap matrix.
trace	of the density matrix (usually the number of electrons).
Density	the density matrix computed by this routine.
energy_value_out	the energy of the system (optional).
chemical_potential_out	the chemical potential calculated.
solver_parameters	parameters for the solver

◆ McWeenyStep() [1/2]

void NTPoly::DensityMatrixSolvers::McWeenyStep	(	const Matrix_ps &	D,
		const Matrix_ps &	S,
		Matrix_ps &	DOut,
		double	threshold = `0.0`
	)

static

Take one McWeeny Step DOut = 3*DSD - 2*DSDSD

Parameters

D	the density matrix.
S	the overlap matrix.
DOut	a more purified matrix.
threshold	for flushing small values to zero.

◆ McWeenyStep() [2/2]

void NTPoly::DensityMatrixSolvers::McWeenyStep	(	const Matrix_ps &	D,
		Matrix_ps &	DOut,
		double	threshold = `0.0`
	)

static

Take one McWeeny Step DOut = 3*DD - 2*DDD

Parameters

D	the density matrix.
DOut	a more purified matrix.
threshold	for flushing small values to zero.

◆ PM()

void NTPoly::DensityMatrixSolvers::PM	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	InverseSquareRoot,
		double	trace,
		Matrix_ps &	Density,
		double &	energy_value_out,
		double &	chemical_potential_out,
		const SolverParameters &	solver_parameters
	)

static

Compute the density matrix from a Hamiltonian using the PM method. Based on the PM algorithm presented in [4]

Parameters

Hamiltonian	the matrix to compute the corresponding density from.
InverseSquareRoot	of the overlap matrix.
trace	of the density matrix (usually the number of electrons).
Density	the density matrix computed by this routine.
energy_value_out	the energy of the system (optional).
chemical_potential_out	the chemical potential calculated.
solver_parameters	parameters for the solver

◆ ScaleAndFold()

void NTPoly::DensityMatrixSolvers::ScaleAndFold	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	InverseSquareRoot,
		double	trace,
		Matrix_ps &	Density,
		double	homo,
		double	lumo,
		double &	energy_value_out,
		const SolverParameters &	solver_parameters
	)

static

Compute the density matrix from a Hamiltonian using the Scale and Fold method. Based on the method of [5] . Note that for this method, you must provide the value of the homo and lumo gap. It is not necessary for these to be accurate, but give a conservative value.

Parameters

Hamiltonian	the matrix to compute the corresponding density from.
InverseSquareRoot	of the overlap matrix.
trace	of the density matrix (usually the number of electrons).
Density	the density matrix computed by this routine.
homo	A conservative estimate of the highest occupied eigenvalue.
lumo	A conservative estimate of the lowest unoccupied eigenvalue.
energy_value_out	the energy of the system (optional).
solver_parameters	parameters for the solver

◆ TRS2()

void NTPoly::DensityMatrixSolvers::TRS2	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	InverseSquareRoot,
		double	trace,
		Matrix_ps &	Density,
		double &	energy_value_out,
		double &	chemical_potential_out,
		const SolverParameters &	solver_parameters
	)

static

Compute the density matrix from a Hamiltonian using the TRS2 method. Based on the TRS2 algorithm presented in: [3].

Parameters

Hamiltonian	the matrix to compute the corresponding density from.
InverseSquareRoot	of the overlap matrix.
trace	of the density matrix (usually the number of electrons).
Density	the density matrix computed by this routine.
energy_value_out	the energy of the system (optional).
chemical_potential_out	the chemical potential calculated.
solver_parameters	parameters for the solver

◆ TRS4()

void NTPoly::DensityMatrixSolvers::TRS4	(	const Matrix_ps &	Hamiltonian,
		const Matrix_ps &	InverseSquareRoot,
		double	trace,
		Matrix_ps &	Density,
		double &	energy_value_out,
		double &	chemical_potential_out,
		const SolverParameters &	solver_parameters
	)

static

Compute the density matrix from a Hamiltonian using the TRS4 method. Based on the TRS4 algorithm presented in: [3] .

Parameters

Hamiltonian	the matrix to compute the corresponding density from.
InverseSquareRoot	of the overlap matrix.
trace	of the density matrix (usually the number of electrons).
Density	the density matrix computed by this routine.
energy_value_out	the energy of the system (optional).
chemical_potential_out	the chemical potential calculated.
solver_parameters	parameters for the solver

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

/Users/wddawson/Desktop/NTPoly/Source/CPlusPlus/DensityMatrixSolvers.h
/Users/wddawson/Desktop/NTPoly/Source/CPlusPlus/DensityMatrixSolvers.cc

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ DenseDensity()

◆ EnergyDensityMatrix()

◆ HPCP()

◆ McWeenyStep() [1/2]

◆ McWeenyStep() [2/2]

◆ PM()

◆ ScaleAndFold()

◆ TRS2()

◆ TRS4()