ergo
Purification_sp2< MatrixType > Class Template Reference

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

#include <purification_sp2.h>

Inheritance diagram for Purification_sp2< MatrixType >:
PurificationGeneral< 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< realVectorTypeReal
 
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 truncate_matrix (real &threshold, 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)
 
void apply_poly_to_eigs (const int it, real &homo, real &lumo)
 
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_, int use_new_stopping_criterion_, NormType norm_truncation, NormType norm_stop_crit, int nocc_)
 Set imporatant parameters for the recursive expansion. More...
 
virtual bool is_initialized () const
 Check is function initialize() is already called. More...
 
virtual bool puri_is_prepared () const
 Check is function prepare_to_purification() is already called. More...
 
virtual void PurificationStart ()
 Start recursive expansion. More...
 
virtual void prepare_to_purification ()
 Prepare data for recursive expansion. More...
 
virtual void purification_process ()
 Run recursive expansion. More...
 
virtual void eigenvalue_bounds_estimation ()
 Estimate eigenvalues near homo-lumo gap. More...
 
virtual ~PurificationGeneral ()
 
virtual void clear ()
 Clear all matrices in the class. More...
 
void set_spectrum_bounds (real eigmin, real eigmax)
 Set spectrum bounds. More...
 
void get_spectrum_bounds (real &eigmin, real &eigmax)
 Get spectrum bounds. More...
 
int get_exact_number_of_puri_iterations ()
 
int get_est_number_of_puri_iterations ()
 
virtual real total_subspace_error (int it)
 
void gen_matlab_file_norm_diff (const char *filename) const
 Create MATLAB .m file which plots the idempotency error in each recursive expansion iteration. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
void gen_matlab_file_cond_num (const char *filename) const
 Create MATLAB .m file which plots a condition number of a problem of computing the density matrix in each recursive expansion iteration. More...
 
void gen_python_file_nnz (const char *filename) const
 Create PYTHON .py file which plots number of non-zero elements in matrices X_i and X_i^2 in each recursive expansion iteration. More...
 
void set_eigenvectors_params (string eigenvectors_method_, string eigenvectors_iterative_method_, real eigensolver_accuracy_, int eigensolver_maxiter_, int scf_step_, int use_prev_vector_as_initial_guess_, int try_eigv_on_next_iteration_if_fail_, VectorType *eigVecLUMO_, VectorType *eigVecHOMO_)
 Set parameters for computing eigenvectors. More...
 
void set_compute_eigenvectors_in_each_iteration ()
 
void unset_compute_eigenvectors_in_each_iteration ()
 
void compute_eigenvectors_without_diagonalization_on_F (const MatrixType &F, int eigensolver_maxiter_for_F)
 

Additional Inherited Members

- Static Public Member Functions inherited from PurificationGeneral< MatrixType >
static real get_epsilon ()
 Get machine epsilon. More...
 
static real get_max_double ()
 Get largest number. More...
 
static real get_min_double ()
 Get smallest number. More...
 
- Public Attributes inherited from PurificationGeneral< MatrixType >
PuriInfo info
 Fill in during purification with useful information. More...
 
MatrixType X
 Matrix X. More...
 
MatrixType Xsq
 Matrix X^2. More...
 
- Protected Member Functions inherited from PurificationGeneral< MatrixType >
void save_matrix_now (string str)
 
void compute_spectrum_bounds ()
 Compute spectrum bounds. More...
 
void compute_X ()
 Get matrix X0 by mapping spectrum of F into [0,1] in reverse order. More...
 
void map_bounds_to_0_1 ()
 Get eigenvalue bounds for X0. More...
 
virtual void check_standard_stopping_criterion (const real XmX2_norm, int &stop)
 Check stopping criterion (obsolete). More...
 
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. More...
 
virtual void stopping_criterion (IterationInfo &iter_info, int &stop, real &estim_order)
 Choose stopping criterion and check it. More...
 
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. More...
 
void compute_eigenvectors_without_diagonalization_last_iter_proj ()
 
void compute_eigenvector (MatrixType const &M, VectorType *eigVecHOMOorLUMO, int it, bool is_homo)
 
double get_nnz_X (size_t &nnzX)
 Get nnz of X in %. More...
 
double get_nnz_X ()
 Get nnz of X in %. More...
 
double get_nnz_Xsq (size_t &nnzXsq)
 Get nnz of X^2 in %. More...
 
double get_nnz_Xsq ()
 Get nnz of X^2 in %. More...
 
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. More...
 
void get_frob_norm_est (const VectorTypeReal &XmX2_norm_frob, const std::vector< real > &h_in, const std::vector< real > &l_in, VectorTypeReal &YmY2_norm_frob_est)
 
void get_eigenvalue_estimates (const VectorTypeReal &XmX2_norm_mixed, const VectorTypeReal &XmX2_norm_frob, const VectorTypeReal &XmX2_trace)
 
void propagate_values_in_each_iter (real value_unocc, real value_occ, VectorTypeReal &out_unocc, VectorTypeReal &out_occ, int nmax)
 
void determine_iteration_for_eigenvectors ()
 
void get_iterations_for_lumo_and_homo (int &chosen_iter_lumo, int &chosen_iter_homo)
 Find the best iterations for computing eigenvectors. More...
 
void check_eigenvectors_at_the_end ()
 
void discard_homo_eigenvector ()
 
void discard_lumo_eigenvector ()
 
void output_norms_and_traces (IterationInfo &iter_info) const
 
void get_interval_with_lambda (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_eigenvectors_to_file (bool is_homo, bool is_lumo, int it)
 
void set_truncation_parameters ()
 
void find_truncation_thresh_every_iter ()
 
void find_shifts_every_iter ()
 /brief Find shifts sigma which will be used for construction of the filtering polynomial for computing eigenvectors. More...
 
void find_eig_gaps_every_iter ()
 
void writeToTmpFile (MatrixType &A) const
 
void readFromTmpFile (MatrixType &A) const
 
- Protected Attributes inherited from PurificationGeneral< MatrixType >
MatrixType F
 Matrix F. More...
 
MatrixType X_homo
 
MatrixType X_lumo
 Save matrix Xi in certain iterations for computing eigenvectors (projection method). More...
 
bool initialized_flag
 
bool puri_is_prepared_flag
 
int use_new_stopping_criterion
 True for new stopping criterion. More...
 
int additional_iterations
 Do a few more iterations after convergence. More...
 
int maxit
 Maximum number of iterations. More...
 
int check_stopping_criterion_iter
 Iteration when to start to check stopping criterion. More...
 
int nocc
 Number of occupied orbitals. More...
 
NormType normPuriTrunc
 Norm used for the truncation of matrices. More...
 
NormType normPuriStopCrit
 Norm used in the stopping criterion Can be mat::frobNorm, mat::mixedNorm, or mat::euclNorm. More...
 
real error_sub
 Allowed error in invariant subspaces. More...
 
real error_eig
 Error in eigenvalues (used just in old stopping criterion). More...
 
real error_per_it
 Error allowed in each iteration due to truncation. More...
 
real constant_C
 Asymptotic constant C needed for the new stopping criterion. More...
 
real gammaStopEstim
 Used on the stopping criterion for estimation of eigenvalues from purification. More...
 
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) More...
 
VectorTypeReal VecGap
 Gap computed using inner homo and lumo bounds on each iteration. More...
 
VectorTypeReal ITER_ERROR_VEC
 (Eigenvectors) Maximum error introduced in each iteration. More...
 
VectorTypeReal SIGMA_HOMO_VEC
 
VectorTypeReal SIGMA_LUMO_VEC
 (Eigenvectors) Approximation of shifts in each iteration. More...
 
VectorTypeReal EIG_ABS_GAP_LUMO_VEC
 
VectorTypeReal EIG_ABS_GAP_HOMO_VEC
 (Eigenvectors) Absolute and relative gap in filter for lumo eigenvalue. More...
 
VectorTypeReal EIG_REL_GAP_LUMO_VEC
 
VectorTypeReal EIG_REL_GAP_HOMO_VEC
 (Eigenvectors) Absolute and relative gap in filter for homo eigenvalue. More...
 
int number_of_eigenvalues
 
IntervalType homo_bounds
 (1-homo) bounds for Xi in iteration i More...
 
IntervalType lumo_bounds
 Lumo bounds for Xi in iteration i. More...
 
IntervalType homo_bounds_X0
 Initial lumo bounds for X. More...
 
IntervalType lumo_bounds_X0
 Initial lumo bounds for X. More...
 
IntervalType homo_bounds_F
 Initial lumo bounds for F. More...
 
IntervalType lumo_bounds_F
 Initial homo bounds for F. More...
 
IntervalType homo_bounds_F_new
 
IntervalType lumo_bounds_F_new
 
IntervalType spectrum_bounds
 Outer bounds for the whole spectrum of F/Xi. More...
 
bool computed_spectrum_bounds
 
int eigenvectors_method
 Chosen method for computing eigenvectors. More...
 
int eigenvectors_iterative_method
 Chosen eigensolver. More...
 
real eigensolver_accuracy
 
int eigensolver_maxiter
 
string eigenvectors_method_str
 
string eigenvectors_iterative_method_str
 
int use_prev_vector_as_initial_guess
 
bool compute_eigenvectors_in_this_SCF_cycle
 
bool try_eigv_on_next_iteration_if_fail
 
VectorTypeeigVecLUMO
 
VectorTypeeigVecHOMO
 
VectorType eigVecLUMORef
 
VectorType eigVecHOMORef
 
real eigValLUMO
 
real eigValHOMO
 
int iter_for_homo
 
int iter_for_lumo
 
VectorTypeInt good_iterations_homo
 Iterations where homo eigenvector can be computed. More...
 
VectorTypeInt good_iterations_lumo
 Iterations where homo eigenvector can be computed. More...
 
VectorTypeInt really_good_iterations_homo
 Iterations where homo eigenvector is actually computed. More...
 
VectorTypeInt really_good_iterations_lumo
 Iterations where lumo eigenvector is actually computed. More...
 
int scf_step
 
bool compute_eigenvectors_in_each_iteration
 Compute homo and lumo eigenpairs in every iteration and save eigenvectors in txt files. More...
 

Detailed Description

template<typename MatrixType>
class Purification_sp2< MatrixType >

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

Template Parameters
MatrixTypeType of a matrix (ex. symmMatrix).

Member Typedef Documentation

◆ IntervalType

◆ NormType

template<typename MatrixType>
typedef PurificationGeneral<MatrixType>::NormType Purification_sp2< MatrixType >::NormType

◆ real

template<typename MatrixType>
typedef PurificationGeneral<MatrixType>::real Purification_sp2< MatrixType >::real

◆ VectorType

template<typename MatrixType>
typedef generalVector Purification_sp2< MatrixType >::VectorType

◆ VectorTypeInt

◆ VectorTypeReal

Constructor & Destructor Documentation

◆ Purification_sp2()

template<typename MatrixType>
Purification_sp2< MatrixType >::Purification_sp2 ( )
inline

Member Function Documentation

◆ apply_inverse_poly_vector()

template<typename MatrixType >
void Purification_sp2< MatrixType >::apply_inverse_poly_vector ( const int  it,
VectorTypeReal bounds_from_it 
)
virtual

◆ apply_poly()

template<typename MatrixType >
Purification_sp2< MatrixType >::real Purification_sp2< MatrixType >::apply_poly ( const int  it,
real  x 
)
virtual

◆ apply_poly_to_eigs()

template<typename MatrixType >
void Purification_sp2< MatrixType >::apply_poly_to_eigs ( const int  it,
real homo,
real lumo 
)
virtual

◆ compute_derivative()

template<typename MatrixType >
Purification_sp2< MatrixType >::real Purification_sp2< MatrixType >::compute_derivative ( const int  it,
real  x,
real DDf 
)
virtual

◆ estimate_number_of_iterations()

template<typename MatrixType >
void Purification_sp2< MatrixType >::estimate_number_of_iterations ( int &  numit)
virtual

◆ get_poly()

template<typename MatrixType >
void Purification_sp2< MatrixType >::get_poly ( const int  it,
int &  poly 
)

◆ purify_bounds()

template<typename MatrixType >
void Purification_sp2< MatrixType >::purify_bounds ( const int  it)
virtual

◆ purify_X()

template<typename MatrixType >
void Purification_sp2< MatrixType >::purify_X ( const int  it)
virtual

◆ return_constant_C()

template<typename MatrixType >
void Purification_sp2< MatrixType >::return_constant_C ( const int  it,
real Cval 
)
virtual

Implements PurificationGeneral< MatrixType >.

References C_SP2.

◆ save_other_iter_info()

template<typename MatrixType >
void Purification_sp2< MatrixType >::save_other_iter_info ( IterationInfo iter_info,
int  it 
)
virtual

◆ set_init_params()

◆ set_poly()

template<typename MatrixType >
void Purification_sp2< MatrixType >::set_poly ( const int  it)

References template_blas_fabs().

◆ truncate_matrix()

template<typename MatrixType >
void Purification_sp2< MatrixType >::truncate_matrix ( real threshold,
int  it 
)
virtual

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