Purification_sp2acc is a class which provides an interface for SP2 recursive expansion. More...

#include <purification_sp2.h>

Inheritance diagram for Purification_sp2< MatrixType >:

Public Types
typedef PurificationGeneral< MatrixType >::real	real
typedef PurificationGeneral< MatrixType >::IntervalType	IntervalType
typedef PurificationGeneral< MatrixType >::NormType	NormType
typedef PurificationGeneral< MatrixType >::VectorTypeInt	VectorTypeInt
typedef PurificationGeneral< MatrixType >::VectorTypeReal	VectorTypeReal
typedef generalVector	VectorType
Public Types inherited from PurificationGeneral< MatrixType >
typedef ergo_real	real
typedef intervalType	IntervalType
typedef mat::normType	NormType
typedef std::vector< int >	VectorTypeInt
typedef std::vector< real >	VectorTypeReal
typedef generalVector	VectorType
typedef MatrixType	MatrixTypeWrapper

Public Member Functions
	Purification_sp2 ()
void	set_init_params ()
void	get_poly (const int it, int &poly)
void	set_poly (const int it)
void	estimate_number_of_iterations (int &numit)
void	purify_X (const int it)
void	purify_bounds (const int it)
void	save_other_iter_info (IterationInfo &iter_info, int it)
void	apply_inverse_poly_vector (const int it, VectorTypeReal &bounds_from_it)
void	return_constant_C (const int it, real &Cval)
real	apply_poly (const int it, real x)
real	compute_derivative (const int it, real x, real &DDf)
Public Member Functions inherited from PurificationGeneral< MatrixType >
	PurificationGeneral ()
virtual void	initialize (const MatrixType &F_, const IntervalType &lumo_bounds_, const IntervalType &homo_bounds_, int maxit_, real error_sub_, real error_eig_, bool use_new_stopping_criterion_, NormType norm_truncation, NormType norm_stop_crit, int nocc_)
	Set imporatant parameters for the recursive expansion.
virtual void	PurificationStart ()
	Start recursive expansion.
virtual void	clear ()
	Clear all matrices in the class.
void	set_spectrum_bounds (real eigmin, real eigmax)
	Set spectrum bounds.
void	get_spectrum_bounds (real &eigmin, real &eigmax)
	Get spectrum bounds.
int	get_exact_number_of_puri_iterations ()
int	get_est_number_of_puri_iterations ()
virtual real	total_subspace_error (int it)
void	set_eigenvectors_params (string eigenvectors_method_, string eigenvectors_iterative_method_, real eigensolver_accuracy_, int eigensolver_maxiter_, int scf_step_, bool try_eigv_on_next_iteration_if_fail_)
	Set parameters for computing eigenvectors.
void	set_eigenvectors_params (string eigenvectors_method_, string eigenvectors_iterative_method_, real eigensolver_accuracy_, int eigensolver_maxiter_, int scf_step_, bool try_eigv_on_next_iteration_if_fail_, bool use_prev_vector_as_initial_guess_, const std::vector< VectorType > &eigVecOCCRef, const std::vector< VectorType > &eigVecUNOCCRef)
	Set parameters for computing eigenvectors - long version.
void	extract_computed_eigenpairs (std::vector< VectorType > &eigVecUNOCCref, std::vector< VectorType > &eigVecOCCref, std::vector< real > &eigValUNOCCref, std::vector< real > &eigValOCCref)
void	set_compute_eigenvectors_in_each_iteration ()
void	unset_compute_eigenvectors_in_each_iteration ()
void	set_number_of_eigenvectors_to_compute (const int occ, const int unocc)
int	get_number_of_occ_eigenvectors_to_compute () const
int	get_number_of_unocc_eigenvectors_to_compute () const
void	set_jump_over_X_iter_proj_method (int val)
int	get_jump_over_X_iter_proj_method () const
void	set_go_back_X_iter_proj_method (int val)
int	get_go_back_X_iter_proj_method () const
void	compute_eigenvectors_without_diagonalization_on_F (const MatrixType &F, int eigensolver_maxiter_for_F)
void	gen_matlab_file_norm_diff (const char *filename) const
	Create MATLAB .m file which plots the idempotency error in each recursive expansion iteration.
void	gen_matlab_file_threshold (const char *filename) const
	Create MATLAB .m file which plots the actual introduced error after truncation of the matrix X_i in each recursive expansion iteration.
void	gen_matlab_file_nnz (const char *filename) const
	Create MATLAB .m file which plots the number of non-zero elements in matrices X_i and X_i^2 in each recursive expansion iteration.
void	gen_matlab_file_eigs (const char *filename) const
	Create MATLAB .m file which plots the homo and lumo bounds in each recursive expansion iteration.
void	gen_matlab_file_time (const char *filename) const
	Create MATLAB .m file which creates a bar plot presenting time spent on various parts of the iteration (such as matrix square and computation of eigenvectors) in each recursive expansion iteration.
virtual	~PurificationGeneral ()
	Create MATLAB .m file which plots a condition number of a problem of computing the density matrix in each recursive expansion iteration.

Additional Inherited Members
Static Public Member Functions inherited from PurificationGeneral< MatrixType >
static real	get_epsilon ()
	Get machine epsilon.
static real	get_max_double ()
	Get largest number.
static real	get_min_double ()
	Get smallest number.
Public Attributes inherited from PurificationGeneral< MatrixType >
PuriInfo	info
	Fill in during purification with useful information.
MatrixType	X
	Matrix X.
MatrixType	Xsq
	Matrix X^2.
Protected Member Functions inherited from PurificationGeneral< MatrixType >
virtual bool	is_initialized () const
	Check is function initialize() is already called.
virtual bool	puri_is_prepared () const
	Check is function prepare_to_purification() is already called.
virtual void	prepare_to_purification ()
	Prepare data for recursive expansion.
virtual void	prepare_to_purification_eigenvectors ()
	Prepare data related to the eigenvectors computations.
virtual void	purification_process ()
	Run recursive expansion.
virtual void	eigenvalue_bounds_estimation ()
	Estimate eigenvalues near homo-lumo gap.
void	save_matrix_now (string str)
void	save_matrix_A_now (const MatrixType &A, string str)
virtual void	compute_spectrum_bounds ()
	Compute spectrum bounds.
virtual void	compute_X ()
	Get matrix X0 by mapping spectrum of F into [0,1] in reverse order.
void	map_bounds_to_0_1 ()
	Get eigenvalue bounds for X0.
virtual void	check_standard_stopping_criterion (const real XmX2_norm, int &stop)
	Check stopping criterion (obsolete).
virtual void	check_new_stopping_criterion (const int it, const real XmX2_norm_it, const real XmX2_norm_itm2, const real XmX2_trace, int &stop, real &estim_order)
	Check stopping criterion.
virtual void	stopping_criterion (IterationInfo &iter_info, int &stop, real &estim_order)
	Choose stopping criterion and check it.
int	get_int_eig_iter_method (string eigenvectors_iterative_method)
int	get_int_eig_method (string eigenvectors_method)
void	compute_eigenvectors_without_diagonalization (int it, IterationInfo &iter_info)
	Compute HOMO and LUMO eigenvalues and eigenvectors of the matrix F.
void	compute_eigenvectors_without_diagonalization_last_iter_proj ()
void	projection_method_one_puri_iter (int current_iteration)
void	compute_eigenvector (MatrixType const &M, std::vector< VectorType > &eigVec, std::vector< real > &eigVal, int it, bool is_homo)
void	set_eigenvectors_params_basic (string eigenvectors_method_, string eigenvectors_iterative_method_, real eigensolver_accuracy_, int eigensolver_maxiter_, int scf_step_, bool try_eigv_on_next_iteration_if_fail_, bool use_prev_vector_as_initial_guess_)
	Set parameters for computing eigenvectors.
double	get_nnz_X (size_t &nnzX)
	Get nnz of X in %.
double	get_nnz_X ()
	Get nnz of X in %.
double	get_nnz_Xsq (size_t &nnzXsq)
	Get nnz of X^2 in %.
double	get_nnz_Xsq ()
	Get nnz of X^2 in %.
void	estimate_homo_lumo (const VectorTypeReal &XmX2_norm_mixed, const VectorTypeReal &XmX2_norm_frob, const VectorTypeReal &XmX2_trace)
	Get homo and lumo bounds from traces and norms of Xi-Xi^2.
void	get_eigenvalue_estimates (const VectorTypeReal &XmX2_norm_mixed, const VectorTypeReal &XmX2_norm_frob, const VectorTypeReal &XmX2_trace)
	Get homo and lumo bounds from traces and norms of Xi-Xi^2.
virtual void	determine_iteration_for_eigenvectors ()
	Determine in which iterations will be computed homo and lumo eigenvectors.
virtual void	get_iterations_for_lumo_and_homo (int &chosen_iter_lumo, int &chosen_iter_homo)
	Find the best iterations for computing eigenvectors.
virtual void	check_eigenvectors_at_the_end ()
virtual void	discard_homo_eigenvector ()
virtual void	discard_lumo_eigenvector ()
void	output_norms_and_traces (IterationInfo &iter_info) const
void	output_separate_total_times (PuriInfo &info) const
void	output_time_WriteAndReadAll () const
void	check_homo_lumo_eigenvalues (real &eigVal, VectorType &eigVec, bool &is_homo, bool &is_lumo, const int iter)
void	get_eigenvalue_of_F_from_eigv_of_Xi (real &eigVal, const VectorType &eigVec)
void	save_selected_eigenvector_to_file (const VectorType &v, int num, bool is_homo, int it=-1)
virtual void	truncate_matrix (real &thresh, int it)
virtual void	set_truncation_parameters ()
void	find_shifts_every_iter ()
	/brief Find shifts sigma which will be used for construction of the filtering polynomial for computing eigenvectors.
void	writeToTmpFile (MatrixType &A) const
void	readFromTmpFile (MatrixType &A) const
virtual void	apply_inverse_poly_vector (const int it, VectorTypeReal &bounds_from_it)=0
virtual void	return_constant_C (const int it, real &Cval)=0
virtual real	apply_poly (const int it, real x)=0
virtual real	compute_derivative (const int it, real x, real &DDf)=0
Protected Attributes inherited from PurificationGeneral< MatrixType >
MatrixType	F
	Matrix F.
std::vector< MatrixType >	vec_matrices_Xi
	Save matrices Xi in each iteration (if used projection method for computing eigenvectors).
bool	initialized_flag
bool	puri_is_prepared_flag
bool	use_new_stopping_criterion
	True for new stopping criterion.
int	additional_iterations
	Do a few more iterations after convergence.
int	maxit
	Maximum number of iterations.
int	check_stopping_criterion_iter
	Iteration when to start to check stopping criterion.
int	nocc
	Number of occupied orbitals.
NormType	normPuriTrunc
	Norm used for the truncation of matrices.
NormType	normPuriStopCrit
	Norm used in the stopping criterion Can be mat::frobNorm, mat::mixedNorm, or mat::euclNorm.
real	error_sub
	Allowed error in invariant subspaces.
real	error_eig
	Error in eigenvalues (used just in old stopping criterion).
real	error_per_it
	Error allowed in each iteration due to truncation.
real	constant_C
	Asymptotic constant C needed for the new stopping criterion.
real	gammaStopEstim
	Used on the stopping criterion for estimation of eigenvalues from purification.
VectorTypeInt	VecPoly
	Polynomials computed in the function estimated_number_of_iterations() VecPoly[i] = 1 if we use X=X^2 VecPoly[i] = 0 if we use X=2X-X^2 (or their accelerated versions)
VectorTypeReal	VecGap
	Gap computed using inner homo and lumo bounds on each iteration.
VectorTypeReal	ITER_ERROR_VEC
	(Eigenvectors) Maximum error introduced in each iteration.
VectorTypeReal	SIGMA_HOMO_VEC
VectorTypeReal	SIGMA_LUMO_VEC
	(Eigenvectors) Approximation of shifts in each iteration.
VectorTypeReal	EIG_ABS_GAP_LUMO_VEC
VectorTypeReal	EIG_ABS_GAP_HOMO_VEC
	(Eigenvectors) Absolute and relative gap in filter for lumo eigenvalue.
VectorTypeReal	EIG_REL_GAP_LUMO_VEC
VectorTypeReal	EIG_REL_GAP_HOMO_VEC
	(Eigenvectors) Absolute and relative gap in filter for homo eigenvalue.
int	number_of_occ_eigenvectors
int	number_of_unocc_eigenvectors
int	jump_over_X_iter_proj_method
int	go_back_X_iter_proj_method
IntervalType	homo_bounds
	(1-homo) bounds for Xi in iteration i
IntervalType	lumo_bounds
	Lumo bounds for Xi in iteration i.
IntervalType	homo_bounds_X0
	Initial lumo bounds for X.
IntervalType	lumo_bounds_X0
	Initial lumo bounds for X.
IntervalType	homo_bounds_F
	Initial lumo bounds for F.
IntervalType	lumo_bounds_F
	Initial homo bounds for F.
IntervalType	homo_bounds_F_new
IntervalType	lumo_bounds_F_new
IntervalType	spectrum_bounds
	Outer bounds for the whole spectrum of F/Xi.
bool	computed_spectrum_bounds
int	eigenvectors_method
	Chosen method for computing eigenvectors.
int	eigenvectors_iterative_method
	Chosen eigensolver.
real	eigensolver_accuracy
	Accuracy of the eigenvalue problem solver.
int	eigensolver_maxiter
	Maximum number of iterations for eigensolver.
string	eigenvectors_method_str
string	eigenvectors_iterative_method_str
bool	use_prev_vector_as_initial_guess
bool	compute_eigenvectors_in_this_SCF_cycle
bool	try_eigv_on_next_iteration_if_fail
VectorType	eigVecLUMORef
VectorType	eigVecHOMORef
std::vector< VectorType >	eigVecOCC
	Here we save eigenvectors corresponding to the occupied orbitals.
std::vector< VectorType >	eigVecUNOCC
	Here we save eigenvectors corresponding to the unoccupied orbitals.
std::vector< real >	eigValOCC
	Here we save eigenvalues corresponding to the occupied orbitals.
std::vector< real >	eigValUNOCC
	Here we save eigenvalues corresponding to the unoccupied orbitals.
real	eigValLUMO
real	eigValHOMO
int	iter_for_homo
int	iter_for_lumo
VectorTypeInt	good_iterations_homo
	Iterations where homo eigenvector can be computed.
VectorTypeInt	good_iterations_lumo
	Iterations where homo eigenvector can be computed.
VectorTypeInt	really_good_iterations_homo
	Iterations where homo eigenvector is actually computed.
VectorTypeInt	really_good_iterations_lumo
	Iterations where lumo eigenvector is actually computed.
int	scf_step
bool	compute_eigenvectors_in_each_iteration
	Compute homo and lumo eigenpairs in every iteration and save eigenvectors in txt files.