One specific implementation of LinearEigensystem using Davidson's algorithm with modifications to manage near linear dependencies, and consequent numerical noise, in candidate expansion vectors. More...

#include <LinearEigensystemRSPT.h>

Inheritance diagram for molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >:

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Collaboration diagram for molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >:

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Detailed Description

template<class R, class Q = R, class P = std::map<size_t, typename R::value_type>>
class molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >

One specific implementation of LinearEigensystem using Davidson's algorithm with modifications to manage near linear dependencies, and consequent numerical noise, in candidate expansion vectors.

TODO add more documentation and examples

Template Parameters

R
Q
P

Public Types
using	SolverTemplate = IterativeSolverTemplate< LinearEigensystem, R, Q, P >

Public Types inherited from molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >
using	value_type = typename R::value_type
	The underlying type of elements of vectors. More...

using	scalar_type = typename array::ArrayHandler< R, R >::value_type

using	value_type_abs = typename array::ArrayHandler< R, R >::value_type_abs

using	VectorP = std::vector< value_type >

using	fapply_on_p_type = std::function< void(const std::vector< VectorP > &, const CVecRef< std::map< size_t, typename R::value_type > > &, const VecRef< R > &)>

Public Member Functions
	LinearEigensystemRSPT (const std::shared_ptr< ArrayHandlers< R, Q, P > > &handlers, const std::shared_ptr< Logger > &logger_=std::make_shared< Logger >())

bool	nonlinear () const override
	Report whether the class is a non-linear solver. More...

bool	linearEigensystem () const override

size_t	end_iteration (const VecRef< R > &parameters, const VecRef< R > &action) override
	constructs next perturbed wavefunction More...

size_t	end_iteration (std::vector< R > &parameters, std::vector< R > &action) override

size_t	end_iteration (R &parameters, R &actions) override

void	precondition (std::vector< R > &parameters, std::vector< R > &action) const
	Applies the Davidson preconditioner. More...

std::vector< scalar_type >	eigenvalues () const override
	The calculated eigenvalues of the subspace matrix. More...

virtual std::vector< scalar_type >	working_set_eigenvalues () const override

void	report (std::ostream &cout, bool endl=true) const override
	Writes a report to cout output stream. More...

void	set_hermiticity (bool hermitian) override
	Sets hermiticity of kernel. More...

bool	get_hermiticity () const override
	Gets hermiticity of kernel, if true than it is hermitian, otherwise it is not. More...

void	set_options (const Options &options) override

std::shared_ptr< Options >	get_options () const override

Public Member Functions inherited from molpro::linalg::itsolv::IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > >
	IterativeSolverTemplate ()=delete

	IterativeSolverTemplate (const IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > > &)=delete

	IterativeSolverTemplate (IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > > &&) noexcept=default

IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > > &	operator= (const IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > > &)=delete

IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > > &	operator= (IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > > &&) noexcept=default

int	add_vector (const VecRef< R > &parameters, const VecRef< R > &actions) override

int	add_vector (std::vector< R > &parameters, std::vector< R > &actions) override

int	add_vector (R &parameters, R &actions, value_type value=0) override

size_t	add_p (const CVecRef< std::map< size_t, typename R::value_type > > &pparams, const array::Span< value_type > &pp_action_matrix, const VecRef< R > &parameters, const VecRef< R > &actions, fapply_on_p_type apply_p) override

void	clearP () override

void	solution (const std::vector< int > &roots, const VecRef< R > &parameters, const VecRef< R > &residual) override

void	solution (const std::vector< int > &roots, std::vector< R > &parameters, std::vector< R > &residual) override

void	solution (R &parameters, R &residual) override

void	solution_params (const std::vector< int > &roots, std::vector< R > &parameters) override

void	solution_params (const std::vector< int > &roots, const VecRef< R > &parameters) override

void	solution_params (R &parameters) override

std::vector< size_t >	suggest_p (const CVecRef< R > &solution, const CVecRef< R > &residual, size_t max_number, double threshold) override

const std::vector< int > &	working_set () const override

size_t	n_roots () const override

void	set_n_roots (size_t roots) override

void	set_options (const Options &options) override

std::shared_ptr< Options >	get_options () const override

const std::vector< scalar_type > &	errors () const override

const Statistics &	statistics () const override

void	report (std::ostream &cout, bool endl=true) const override

void	report () const override

void	set_convergence_threshold (double thresh) override

double	convergence_threshold () const override

void	set_convergence_threshold_value (double thresh) override

double	convergence_threshold_value () const override

void	set_verbosity (Verbosity v) override

void	set_verbosity (int v) override

Verbosity	get_verbosity () const override

void	set_max_iter (int n) override

int	get_max_iter () const override

void	set_max_p (int n) override

int	get_max_p () const override

void	set_p_threshold (double threshold) override

double	get_p_threshold () const override

const subspace::Dimensions &	dimensions () const override
	Access dimensions of the subspace. More...

scalar_type	value () const override

void	set_profiler (molpro::profiler::Profiler &profiler) override

const std::shared_ptr< molpro::profiler::Profiler > &	profiler () const override

bool	solve (const VecRef< R > &parameters, const VecRef< R > &actions, const Problem< R > &problem, bool generate_initial_guess=false) override

bool	solve (R &parameters, R &actions, const Problem< R > &problem, bool generate_initial_guess=false) override

bool	solve (std::vector< R > &parameters, std::vector< R > &actions, const Problem< R > &problem, bool generate_initial_guess=false) override

bool	test_problem (const Problem< R > &problem, R &v0, R &v1, int verbosity, double threshold) const override

virtual std::vector< scalar_type >	eigenvalues () const=0
	The calculated eigenvalues of the subspace matrix. More...

virtual void	set_hermiticity (bool hermitian)=0
	Sets hermiticity of kernel. More...

virtual bool	get_hermiticity () const=0
	Gets hermiticity of kernel, if true than it is hermitian, otherwise it is not. More...

Public Member Functions inherited from molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >
virtual	~IterativeSolver ()=default

	IterativeSolver ()=default

	IterativeSolver (const IterativeSolver< R, R, std::map< size_t, typename R::value_type > > &)=delete

	IterativeSolver (IterativeSolver< R, R, std::map< size_t, typename R::value_type > > &&) noexcept=default

IterativeSolver< R, R, std::map< size_t, typename R::value_type > > &	operator= (const IterativeSolver< R, R, std::map< size_t, typename R::value_type > > &)=delete

IterativeSolver< R, R, std::map< size_t, typename R::value_type > > &	operator= (IterativeSolver< R, R, std::map< size_t, typename R::value_type > > &&) noexcept=default

virtual bool	solve (const VecRef< R > &parameters, const VecRef< R > &actions, const Problem< R > &problem, bool generate_initial_guess=false)=0
	Simplified one-call solver. More...

virtual bool	solve (R &parameters, R &actions, const Problem< R > &problem, bool generate_initial_guess=false)=0

virtual bool	solve (std::vector< R > &parameters, std::vector< R > &actions, const Problem< R > &problem, bool generate_initial_guess=false)=0

virtual int	add_vector (const VecRef< R > &parameters, const VecRef< R > &actions)=0
	Take, typically, a current solution and residual, and add it to the solution space. More...

virtual int	add_vector (std::vector< R > &parameters, std::vector< R > &action)=0

virtual int	add_vector (R &parameters, R &action, value_type value=0)=0

virtual size_t	add_p (const CVecRef< std::map< size_t, typename R::value_type > > &pparams, const array::Span< value_type > &pp_action_matrix, const VecRef< R > &parameters, const VecRef< R > &action, fapply_on_p_type apply_p)=0
	Add P-space vectors to the expansion set for linear methods. More...

virtual void	clearP ()=0

virtual void	solution (const std::vector< int > &roots, const VecRef< R > &parameters, const VecRef< R > &residual)=0
	Construct solution and residual for a given set of roots. More...

virtual void	solution (const std::vector< int > &roots, std::vector< R > &parameters, std::vector< R > &residual)=0

virtual void	solution (R &parameters, R &residual)=0

virtual void	solution_params (const std::vector< int > &roots, const VecRef< R > &parameters)=0
	Constructs parameters of selected roots. More...

virtual void	solution_params (const std::vector< int > &roots, std::vector< R > &parameters)=0

virtual void	solution_params (R &parameters)=0

virtual size_t	end_iteration (const VecRef< R > &parameters, const VecRef< R > &residual)=0
	Behaviour depends on the solver. More...

virtual size_t	end_iteration (std::vector< R > &parameters, std::vector< R > &action)=0

virtual size_t	end_iteration (R &parameters, R &action)=0

virtual bool	end_iteration_needed ()=0
	signal whether end_iteration should be called More...

virtual std::vector< size_t >	suggest_p (const CVecRef< R > &solution, const CVecRef< R > &residual, size_t max_number, double threshold)=0
	Get the solver's suggestion of which degrees of freedom would be best to add to the P-space. More...

virtual const std::vector< int > &	working_set () const=0
	Working set of roots that are not yet converged. More...

virtual std::vector< scalar_type >	working_set_eigenvalues () const

virtual size_t	n_roots () const=0

virtual void	set_n_roots (size_t nroots)=0

virtual const std::vector< scalar_type > &	errors () const=0

virtual const Statistics &	statistics () const=0

virtual void	report (std::ostream &cout, bool endl=true) const=0
	Writes a report to cout output stream. More...

virtual void	report () const=0
	Writes a report to std::cout. More...

virtual void	set_convergence_threshold (double thresh)=0
	Sets the convergence threshold. More...

virtual double	convergence_threshold () const=0
	Reports the convergence threshold. More...

virtual void	set_convergence_threshold_value (double thresh)=0
	Sets the value convergence threshold. More...

virtual double	convergence_threshold_value () const=0
	Reports the value convergence threshold. More...

virtual void	set_verbosity (Verbosity v)=0

virtual void	set_verbosity (int v)=0

virtual Verbosity	get_verbosity () const=0

virtual void	set_max_iter (int n)=0

virtual int	get_max_iter () const=0

virtual void	set_max_p (int n)=0

virtual int	get_max_p () const=0

virtual void	set_p_threshold (double thresh)=0

virtual double	get_p_threshold () const=0

virtual const subspace::Dimensions &	dimensions () const=0

virtual void	set_options (const Options &options)=0

virtual std::shared_ptr< Options >	get_options () const=0

virtual scalar_type	value () const=0
	Report the function value for the current optimum solution. More...

virtual bool	nonlinear () const=0
	Report whether the class is a non-linear solver. More...

virtual void	set_profiler (molpro::profiler::Profiler &profiler)=0
	Attach a profiler in order to collect performance data. More...

virtual const std::shared_ptr< molpro::profiler::Profiler > &	profiler () const=0

virtual bool	test_problem (const Problem< R > &problem, R &v0, R &v1, int verbosity=0, double threshold=1e-5) const=0
	Test a supplied problem class. More...

Public Attributes
std::shared_ptr< Logger >	logger

double	propose_rspace_norm_thresh = 1e-10
	vectors with norm less than threshold can be considered null. More...

double	propose_rspace_svd_thresh = 1e-12

Protected Member Functions
void	construct_residual (const std::vector< int > &roots, const CVecRef< R > &params, const VecRef< R > &actions) override
	Constructs residual for given roots provided their parameters and actions. More...

Protected Member Functions inherited from molpro::linalg::itsolv::IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > >
	IterativeSolverTemplate (std::shared_ptr< subspace::IXSpace< R, R, std::map< size_t, typename R::value_type > > > xspace, std::shared_ptr< subspace::ISubspaceSolver< R, R, std::map< size_t, typename R::value_type > > > solver, std::shared_ptr< ArrayHandlers< R, R, std::map< size_t, typename R::value_type > > > handlers, std::shared_ptr< Statistics > stats, std::shared_ptr< Logger > logger)

virtual	~IterativeSolverTemplate ()

virtual void	set_value_errors ()
	Implementation class should overload this to set errors in the current values (e.g. change in eigenvalues) More...

virtual void	construct_residual (const std::vector< int > &roots, const CVecRef< R > &params, const VecRef< R > &actions)=0
	Constructs residual for given roots provided their parameters and actions. More...

virtual bool	linearEigensystem () const

size_t	solve_and_generate_working_set (const VecRef< R > &parameters, const VecRef< R > &action)
	Solves the subspace problems and selects the working set of roots, returning their parameters and residual in parameters and action. More...

void	check_consistent_number_of_roots_and_solutions (const std::vector< TTT > &roots, const size_t nparams)

bool	end_iteration_needed () override

Static Protected Member Functions
static std::string	str (const std::vector< double > &a)

Protected Attributes
std::vector< double >	m_rspt_values
	perturbation series for the eigenvalue More...

Protected Attributes inherited from molpro::linalg::itsolv::IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > >
std::shared_ptr< ArrayHandlers< R, R, std::map< size_t, typename R::value_type > > >	m_handlers
	Array handlers. More...

std::shared_ptr< subspace::IXSpace< R, R, std::map< size_t, typename R::value_type > > >	m_xspace
	manages the subspace and associated data More...

std::shared_ptr< subspace::ISubspaceSolver< R, R, std::map< size_t, typename R::value_type > > >	m_subspace_solver
	solves the subspace problem More...

std::vector< double >	m_errors
	errors from the most recent solution More...

std::vector< double >	m_value_errors
	value errors from the most recent solution More...

std::vector< int >	m_working_set
	indices of roots in the working set More...

size_t	m_nroots
	number of roots the solver is searching for More...

double	m_convergence_threshold
	residual norms less than this mark a converged solution More...

double	m_convergence_threshold_value
	value changes less than this mark a converged solution More...

std::shared_ptr< Statistics >	m_stats
	accumulates statistics of operations performed by the solver More...

std::shared_ptr< Logger >	m_logger
	logger More...

bool	m_normalise_solution
	whether to normalise the solutions More...

fapply_on_p_type	m_apply_p
	function that evaluates effect of action on the P space projection More...

Verbosity	m_verbosity
	how much output to print in solve() More...

int	m_max_iter
	maximum number of iterations in solve() More...

size_t	m_max_p
	maximum size of P space More...

double	m_p_threshold
	threshold for selecting P space More...

bool	m_end_iteration_needed
	whether end_iteration should be called after any preconditioner More...

Member Typedef Documentation

◆ SolverTemplate

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

using molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::SolverTemplate = IterativeSolverTemplate<LinearEigensystem, R, Q, P>

Constructor & Destructor Documentation

◆ LinearEigensystemRSPT()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::LinearEigensystemRSPT	(	const std::shared_ptr< ArrayHandlers< R, Q, P > > &	handlers,
		const std::shared_ptr< Logger > &	logger_ = `std::make_shared<Logger>()`
	)

inlineexplicit

Member Function Documentation

◆ construct_residual()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

void molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::construct_residual	(	const std::vector< int > &	roots,
		const CVecRef< R > &	params,
		const VecRef< R > &	actions
	)

inlineoverrideprotectedvirtual

Constructs residual for given roots provided their parameters and actions.

Implements molpro::linalg::itsolv::IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > >.

◆ eigenvalues()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

std::vector< scalar_type > molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::eigenvalues ( ) const

inlineoverridevirtual

The calculated eigenvalues of the subspace matrix.

Implements molpro::linalg::itsolv::LinearEigensystem< R, R, std::map< size_t, typename R::value_type > >.

◆ end_iteration() [1/3]

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

size_t molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::end_iteration	(	const VecRef< R > &	parameters,
		const VecRef< R > &	action
	)

inlineoverridevirtual

constructs next perturbed wavefunction

Parameters

parameters	output new parameters for the subspace.
residual	preconditioned residuals.

Returns: number of significant parameters to calculate the action for

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ end_iteration() [2/3]

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

size_t molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::end_iteration	(	R &	parameters,
		R &	actions
	)

inlineoverridevirtual

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ end_iteration() [3/3]

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

size_t molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::end_iteration	(	std::vector< R > &	parameters,
		std::vector< R > &	action
	)

inlineoverridevirtual

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ get_hermiticity()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

bool molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::get_hermiticity ( ) const

inlineoverridevirtual

Gets hermiticity of kernel, if true than it is hermitian, otherwise it is not.

Implements molpro::linalg::itsolv::LinearEigensystem< R, R, std::map< size_t, typename R::value_type > >.

◆ get_options()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

std::shared_ptr< Options > molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::get_options ( ) const

inlineoverridevirtual

Return all options. This is no different than using getters, but can be used with forward declaration.

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ linearEigensystem()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

bool molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::linearEigensystem ( ) const

inlineoverridevirtual

Reimplemented from molpro::linalg::itsolv::IterativeSolverTemplate< LinearEigensystem, R, R, std::map< size_t, typename R::value_type > >.

◆ nonlinear()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

bool molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::nonlinear ( ) const

inlineoverridevirtual

Report whether the class is a non-linear solver.

Returns

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ precondition()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

void molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::precondition	(	std::vector< R > &	parameters,
		std::vector< R > &	action
	)		const

inline

Applies the Davidson preconditioner.

◆ report()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

void molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::report	(	std::ostream &	cout,
		bool	endl = `true`
	)		const

inlineoverridevirtual

Writes a report to cout output stream.

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ set_hermiticity()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

void molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::set_hermiticity ( bool hermitian )

inlineoverridevirtual

Sets hermiticity of kernel.

Implements molpro::linalg::itsolv::LinearEigensystem< R, R, std::map< size_t, typename R::value_type > >.

◆ set_options()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

void molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::set_options ( const Options & options )

inlineoverridevirtual

Set all spcecified options. This is no different than using setters, but can be used with forward declaration.

Implements molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

◆ str()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

static std::string molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::str ( const std::vector< double > & a )

inlinestaticprotected

◆ working_set_eigenvalues()

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

virtual std::vector< scalar_type > molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::working_set_eigenvalues ( ) const

inlineoverridevirtual

The calculated eigenvalues for roots in the working set (eigenvalue problems) or zero (otherwise)

Reimplemented from molpro::linalg::itsolv::IterativeSolver< R, R, std::map< size_t, typename R::value_type > >.

Member Data Documentation

◆ logger

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

std::shared_ptr<Logger> molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::logger

◆ m_rspt_values

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

std::vector<double> molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::m_rspt_values

protected

perturbation series for the eigenvalue

◆ propose_rspace_norm_thresh

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

double molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::propose_rspace_norm_thresh = 1e-10

vectors with norm less than threshold can be considered null.

◆ propose_rspace_svd_thresh

template<class R , class Q = R, class P = std::map<size_t, typename R::value_type>>

double molpro::linalg::itsolv::LinearEigensystemRSPT< R, Q, P >::propose_rspace_svd_thresh = 1e-12

the smallest singular value in the subspace that can be allowed when constructing the working set. Smaller singular values will lead to deletion of parameters from the Q space

Detailed Description

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ SolverTemplate

Constructor & Destructor Documentation

◆ LinearEigensystemRSPT()

Member Function Documentation

◆ construct_residual()

◆ eigenvalues()

◆ end_iteration() [1/3]

◆ end_iteration() [2/3]

◆ end_iteration() [3/3]

◆ get_hermiticity()

◆ get_options()

◆ linearEigensystem()

◆ nonlinear()

◆ precondition()

◆ report()

◆ set_hermiticity()

◆ set_options()

◆ str()

◆ working_set_eigenvalues()

Member Data Documentation

◆ logger

◆ m_rspt_values

◆ propose_rspace_norm_thresh

◆ propose_rspace_svd_thresh