Use Davidson algorithm to solve A*V=E*V. More...

#include <davidsonsolver.h>

Collaboration diagram for votca::xtp::DavidsonSolver:

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Classes
struct	ProjectedSpace

struct	RitzEigenPair

Public Member Functions
	DavidsonSolver (Logger &log)

void	set_iter_max (Index N)

void	set_max_search_space (Index N)

void	set_tolerance (std::string tol)

void	set_correction (std::string method)

void	set_size_update (std::string update_size)

void	set_matrix_type (std::string mt)

Eigen::ComputationInfo	info () const

Eigen::VectorXd	eigenvalues () const

Eigen::MatrixXd	eigenvectors () const

Index	num_iterations () const

template<typename MatrixReplacement >
void	solve (const MatrixReplacement &A, Index neigen, Index size_initial_guess=0)

Private Types
enum	CORR { DPR , OLSEN }

enum	UPDATE { MIN , SAFE , MAX }

enum	MATRIX_TYPE { SYMM , HAM }

using	ArrayXb = Eigen::Array<bool, Eigen::Dynamic, 1>

Private Member Functions
template<typename MatrixReplacement >
void	updateProjection (const MatrixReplacement &A, ProjectedSpace &proj) const

RitzEigenPair	getRitzEigenPairs (const ProjectedSpace &proj) const

Eigen::MatrixXd	qr (const Eigen::MatrixXd &A) const

RitzEigenPair	getHarmonicRitz (const ProjectedSpace &proj) const

RitzEigenPair	getRitz (const ProjectedSpace &proj) const

Index	getSizeUpdate (Index neigen) const

void	checkOptions (Index operator_size)

void	printOptions (Index operator_size) const

void	printTiming (const std::chrono::time_point< std::chrono::system_clock > &start) const

void	printIterationData (const RitzEigenPair &rep, const ProjectedSpace &proj, Index neigen) const

ArrayXl	argsort (const Eigen::VectorXd &V) const

Eigen::MatrixXd	setupInitialEigenvectors (Index size_initial_guess) const

Eigen::MatrixXd	extract_vectors (const Eigen::MatrixXd &V, const ArrayXl &idx) const

void	orthogonalize (Eigen::MatrixXd &V, Index nupdate) const

void	gramschmidt (Eigen::MatrixXd &A, Index nstart) const

Eigen::VectorXd	computeCorrectionVector (const Eigen::VectorXd &qj, double lambdaj, const Eigen::VectorXd &Aqj) const

Eigen::VectorXd	dpr (const Eigen::VectorXd &r, double lambda) const

Eigen::VectorXd	olsen (const Eigen::VectorXd &r, const Eigen::VectorXd &x, double lambda) const

ProjectedSpace	initProjectedSpace (Index neigen, Index size_initial_guess) const

Index	extendProjection (const RitzEigenPair &rep, ProjectedSpace &proj) const

bool	checkConvergence (const RitzEigenPair &rep, ProjectedSpace &proj, Index neigen) const

void	restart (const RitzEigenPair &rep, ProjectedSpace &proj, Index newtestvectors) const

void	storeConvergedData (const RitzEigenPair &rep, Index neigen)

void	storeNotConvergedData (const RitzEigenPair &rep, const ArrayXb &root_converged, Index neigen)

void	storeEigenPairs (const RitzEigenPair &rep, Index neigen)

Private Attributes
Logger &	log_

Index	iter_max_ = 50

Index	i_iter_ = 0

double	tol_ = 1E-4

Index	max_search_space_ = 0

Eigen::VectorXd	Adiag_

Index	restart_size_ = 0

CORR	davidson_correction_ = CORR::DPR

UPDATE	davidson_update_ = UPDATE::SAFE

MATRIX_TYPE	matrix_type_ = MATRIX_TYPE::SYMM

Eigen::VectorXd	eigenvalues_

Eigen::MatrixXd	eigenvectors_

Eigen::ComputationInfo	info_ = Eigen::ComputationInfo::NoConvergence

Detailed Description

Use Davidson algorithm to solve A*V=E*V.

For a rough overview https://joshuagoings.com/2013/08/23/davidsons-method/ For the symmetric case we simply extract the smallest eigenvalues For the non-symmetric case we need the smallest non-negative eigenvalues These are harder to extract, because iterative methods tend to converge towards extreme eigenvalues, thus we use harmonic ritz values.

Definition at line 47 of file davidsonsolver.h.

Member Typedef Documentation

◆ ArrayXb

using votca::xtp::DavidsonSolver::ArrayXb = Eigen::Array<bool, Eigen::Dynamic, 1>

private

Definition at line 125 of file davidsonsolver.h.

Member Enumeration Documentation

◆ CORR

enum votca::xtp::DavidsonSolver::CORR

private

Enumerator
DPR
OLSEN

Definition at line 133 of file davidsonsolver.h.

◆ MATRIX_TYPE

enum votca::xtp::DavidsonSolver::MATRIX_TYPE

private

Enumerator
SYMM
HAM

Definition at line 139 of file davidsonsolver.h.

◆ UPDATE

enum votca::xtp::DavidsonSolver::UPDATE

private

Enumerator
MIN
SAFE
MAX

Definition at line 136 of file davidsonsolver.h.

Constructor & Destructor Documentation

◆ DavidsonSolver()

votca::xtp::DavidsonSolver::DavidsonSolver ( Logger & log )

Definition at line 32 of file davidsonsolver.cc.

Member Function Documentation

◆ argsort()

ArrayXl votca::xtp::DavidsonSolver::argsort ( const Eigen::VectorXd & V ) const

private

Definition at line 175 of file davidsonsolver.cc.

◆ checkConvergence()

bool votca::xtp::DavidsonSolver::checkConvergence	(	const RitzEigenPair &	rep,
		DavidsonSolver::ProjectedSpace &	proj,
		Index	neigen ) const

private

Definition at line 350 of file davidsonsolver.cc.

◆ checkOptions()

void votca::xtp::DavidsonSolver::checkOptions ( Index operator_size )

private

Definition at line 47 of file davidsonsolver.cc.

◆ computeCorrectionVector()

Eigen::VectorXd votca::xtp::DavidsonSolver::computeCorrectionVector	(	const Eigen::VectorXd &	qj,
		double	lambdaj,
		const Eigen::VectorXd &	Aqj ) const

private

Definition at line 392 of file davidsonsolver.cc.

◆ dpr()

Eigen::VectorXd votca::xtp::DavidsonSolver::dpr	(	const Eigen::VectorXd &	r,
		double	lambda ) const

private

Definition at line 419 of file davidsonsolver.cc.

◆ eigenvalues()

Eigen::VectorXd votca::xtp::DavidsonSolver::eigenvalues ( ) const

inline

Definition at line 60 of file davidsonsolver.h.

◆ eigenvectors()

Eigen::MatrixXd votca::xtp::DavidsonSolver::eigenvectors ( ) const

inline

Definition at line 61 of file davidsonsolver.h.

◆ extendProjection()

Index votca::xtp::DavidsonSolver::extendProjection	(	const RitzEigenPair &	rep,
		DavidsonSolver::ProjectedSpace &	proj ) const

private

Definition at line 357 of file davidsonsolver.cc.

◆ extract_vectors()

Eigen::MatrixXd votca::xtp::DavidsonSolver::extract_vectors	(	const Eigen::MatrixXd &	V,
		const ArrayXl &	idx ) const

private

Definition at line 383 of file davidsonsolver.cc.

◆ getHarmonicRitz()

DavidsonSolver::RitzEigenPair votca::xtp::DavidsonSolver::getHarmonicRitz ( const ProjectedSpace & proj ) const

private

Definition at line 244 of file davidsonsolver.cc.

◆ getRitz()

DavidsonSolver::RitzEigenPair votca::xtp::DavidsonSolver::getRitz ( const ProjectedSpace & proj ) const

private

Definition at line 224 of file davidsonsolver.cc.

◆ getRitzEigenPairs()

DavidsonSolver::RitzEigenPair votca::xtp::DavidsonSolver::getRitzEigenPairs ( const ProjectedSpace & proj ) const

private

Definition at line 210 of file davidsonsolver.cc.

◆ getSizeUpdate()

Index votca::xtp::DavidsonSolver::getSizeUpdate ( Index neigen ) const

private

Definition at line 152 of file davidsonsolver.cc.

◆ gramschmidt()

void votca::xtp::DavidsonSolver::gramschmidt	(	Eigen::MatrixXd &	A,
		Index	nstart ) const

private

Definition at line 445 of file davidsonsolver.cc.

◆ info()

Eigen::ComputationInfo votca::xtp::DavidsonSolver::info ( ) const

inline

Definition at line 59 of file davidsonsolver.h.

◆ initProjectedSpace()

DavidsonSolver::ProjectedSpace votca::xtp::DavidsonSolver::initProjectedSpace	(	Index	neigen,
		Index	size_initial_guess ) const

private

Definition at line 337 of file davidsonsolver.cc.

◆ num_iterations()

Index votca::xtp::DavidsonSolver::num_iterations ( ) const

inline

Definition at line 62 of file davidsonsolver.h.

◆ olsen()

Eigen::VectorXd votca::xtp::DavidsonSolver::olsen	(	const Eigen::VectorXd &	r,
		const Eigen::VectorXd &	x,
		double	lambda ) const

private

Definition at line 427 of file davidsonsolver.cc.

◆ orthogonalize()

void votca::xtp::DavidsonSolver::orthogonalize	(	Eigen::MatrixXd &	V,
		Index	nupdate ) const

private

Definition at line 441 of file davidsonsolver.cc.

◆ printIterationData()

void votca::xtp::DavidsonSolver::printIterationData	(	const RitzEigenPair &	rep,
		const ProjectedSpace &	proj,
		Index	neigen ) const

private

Definition at line 90 of file davidsonsolver.cc.

◆ printOptions()

void votca::xtp::DavidsonSolver::printOptions ( Index operator_size ) const

private

Definition at line 67 of file davidsonsolver.cc.

◆ printTiming()

void votca::xtp::DavidsonSolver::printTiming ( const std::chrono::time_point< std::chrono::system_clock > & start ) const

private

Definition at line 34 of file davidsonsolver.cc.

◆ qr()

Eigen::MatrixXd votca::xtp::DavidsonSolver::qr ( const Eigen::MatrixXd & A ) const

private

Definition at line 483 of file davidsonsolver.cc.

◆ restart()

void votca::xtp::DavidsonSolver::restart	(	const RitzEigenPair &	rep,
		DavidsonSolver::ProjectedSpace &	proj,
		Index	newtestvectors ) const

private

Definition at line 493 of file davidsonsolver.cc.

◆ set_correction()

void votca::xtp::DavidsonSolver::set_correction ( std::string method )

Definition at line 114 of file davidsonsolver.cc.

◆ set_iter_max()

void votca::xtp::DavidsonSolver::set_iter_max ( Index N )

inline

Definition at line 52 of file davidsonsolver.h.

◆ set_matrix_type()

void votca::xtp::DavidsonSolver::set_matrix_type ( std::string mt )

Definition at line 104 of file davidsonsolver.cc.

◆ set_max_search_space()

void votca::xtp::DavidsonSolver::set_max_search_space ( Index N )

inline

Definition at line 53 of file davidsonsolver.h.

◆ set_size_update()

void votca::xtp::DavidsonSolver::set_size_update ( std::string update_size )

Definition at line 139 of file davidsonsolver.cc.

◆ set_tolerance()

void votca::xtp::DavidsonSolver::set_tolerance ( std::string tol )

Definition at line 125 of file davidsonsolver.cc.

◆ setupInitialEigenvectors()

Eigen::MatrixXd votca::xtp::DavidsonSolver::setupInitialEigenvectors ( Index size_initial_guess ) const

private

Definition at line 183 of file davidsonsolver.cc.

◆ solve()

template<typename MatrixReplacement >

void votca::xtp::DavidsonSolver::solve	(	const MatrixReplacement &	A,
		Index	neigen,
		Index	size_initial_guess = 0 )

inline

Definition at line 65 of file davidsonsolver.h.

◆ storeConvergedData()

void votca::xtp::DavidsonSolver::storeConvergedData	(	const RitzEigenPair &	rep,
		Index	neigen )

private

Definition at line 518 of file davidsonsolver.cc.

◆ storeEigenPairs()

void votca::xtp::DavidsonSolver::storeEigenPairs	(	const RitzEigenPair &	rep,
		Index	neigen )

private

Definition at line 552 of file davidsonsolver.cc.

◆ storeNotConvergedData()

void votca::xtp::DavidsonSolver::storeNotConvergedData	(	const RitzEigenPair &	rep,
		const ArrayXb &	root_converged,
		Index	neigen )

private

Definition at line 527 of file davidsonsolver.cc.

◆ updateProjection()

template<typename MatrixReplacement >

void votca::xtp::DavidsonSolver::updateProjection	(	const MatrixReplacement &	A,
		ProjectedSpace &	proj ) const

inlineprivate

Definition at line 172 of file davidsonsolver.h.

Member Data Documentation

◆ Adiag_

Eigen::VectorXd votca::xtp::DavidsonSolver::Adiag_

private

Definition at line 131 of file davidsonsolver.h.

◆ davidson_correction_

CORR votca::xtp::DavidsonSolver::davidson_correction_ = CORR::DPR

private

Definition at line 134 of file davidsonsolver.h.

◆ davidson_update_

UPDATE votca::xtp::DavidsonSolver::davidson_update_ = UPDATE::SAFE

private

Definition at line 137 of file davidsonsolver.h.

◆ eigenvalues_

Eigen::VectorXd votca::xtp::DavidsonSolver::eigenvalues_

private

Definition at line 142 of file davidsonsolver.h.

◆ eigenvectors_

Eigen::MatrixXd votca::xtp::DavidsonSolver::eigenvectors_

private

Definition at line 143 of file davidsonsolver.h.

◆ i_iter_

Index votca::xtp::DavidsonSolver::i_iter_ = 0

private

Definition at line 128 of file davidsonsolver.h.

◆ info_

Eigen::ComputationInfo votca::xtp::DavidsonSolver::info_ = Eigen::ComputationInfo::NoConvergence

private

Definition at line 144 of file davidsonsolver.h.

◆ iter_max_

Index votca::xtp::DavidsonSolver::iter_max_ = 50

private

Definition at line 127 of file davidsonsolver.h.

◆ log_

Logger& votca::xtp::DavidsonSolver::log_

private

Definition at line 126 of file davidsonsolver.h.

◆ matrix_type_

MATRIX_TYPE votca::xtp::DavidsonSolver::matrix_type_ = MATRIX_TYPE::SYMM

private

Definition at line 140 of file davidsonsolver.h.

◆ max_search_space_

Index votca::xtp::DavidsonSolver::max_search_space_ = 0

private

Definition at line 130 of file davidsonsolver.h.

◆ restart_size_

Index votca::xtp::DavidsonSolver::restart_size_ = 0

private

Definition at line 132 of file davidsonsolver.h.

◆ tol_

double votca::xtp::DavidsonSolver::tol_ = 1E-4

private

Definition at line 129 of file davidsonsolver.h.

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

xtp/include/votca/xtp/davidsonsolver.h
xtp/src/libxtp/davidsonsolver.cc

Classes

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ ArrayXb

Member Enumeration Documentation

◆ CORR

◆ MATRIX_TYPE

◆ UPDATE

Constructor & Destructor Documentation

◆ DavidsonSolver()

Member Function Documentation

◆ argsort()

◆ checkConvergence()

◆ checkOptions()

◆ computeCorrectionVector()

◆ dpr()

◆ eigenvalues()

◆ eigenvectors()

◆ extendProjection()

◆ extract_vectors()

◆ getHarmonicRitz()

◆ getRitz()

◆ getRitzEigenPairs()

◆ getSizeUpdate()

◆ gramschmidt()

◆ info()

◆ initProjectedSpace()

◆ num_iterations()

◆ olsen()

◆ orthogonalize()

◆ printIterationData()

◆ printOptions()

◆ printTiming()

◆ qr()

◆ restart()

◆ set_correction()

◆ set_iter_max()

◆ set_matrix_type()

◆ set_max_search_space()

◆ set_size_update()

◆ set_tolerance()

◆ setupInitialEigenvectors()

◆ solve()

◆ storeConvergedData()

◆ storeEigenPairs()

◆ storeNotConvergedData()

◆ updateProjection()

Member Data Documentation

◆ Adiag_

◆ davidson_correction_

◆ davidson_update_

◆ eigenvalues_

◆ eigenvectors_

◆ i_iter_

◆ info_

◆ iter_max_

◆ log_

◆ matrix_type_

◆ max_search_space_

◆ restart_size_

◆ tol_