Base class for computing PPCKO algorithm computations. Polymorphism is known at compile-time (CRTP) More...

#include <PPC_KO.hpp>

Public Member Functions
template<typename STOR_OBJ>
	PPC_KO_base (STOR_OBJ &&X, int number_threads)
	Constructor: centers data, evaluate mean function, sample covariance, sample cross-covariance and its square.

std::size_t	m () const
	Getter for the number of evaluation of the curve/surface.

std::size_t	n () const
	Getter for the number of time instants.

KO_Traits::StoringMatrix	X () const
	Getter for fts data matrix (centered)

KO_Traits::StoringArray	means () const
	Getter for the mean function.

KO_Traits::StoringMatrix	Cov () const
	Getter for the covariance operator estimate.

double	trace_cov () const
	Getter for the covariance operator estimate's trace.

KO_Traits::StoringMatrix &	CovReg ()
	Setter for the regularized sample covariance operator.

KO_Traits::StoringMatrix	rho () const
	Getter for the autoregressive operator estimate.

KO_Traits::StoringMatrix	a () const
	Getter for the predictive loadings (PPCs directions)

KO_Traits::StoringMatrix	b () const
	Getter for the predictive factors factor (PPCs weights)

std::vector< double >	explanatory_power () const
	Getter for the cumulative explanatory power of the PPCs.

double	alpha () const
	Getter for the regularization parameter.

double &	alpha ()
	Setter for the regularization parameter.

int	k () const
	Getter for the number of retained PPCs.

int &	k ()
	Setter for the number of retained PPCs.

double	threshold_ppc () const
	Getter for the requested explanatory power of the retained PPCs.

double &	threshold_ppc ()
	Setter for the requested explanatory power of the retained PPCs.

valid_err_variant	ValidErr () const
	Getter for the validation errors.

valid_err_variant &	ValidErr ()
	Setter for the validation errors.

int	number_threads () const
	Getter for the number of threads for OMP.

std::tuple< int, KO_Traits::StoringVector, KO_Traits::StoringMatrix >	PPC_retained ()
	Retaining the the PPCs: pairs eigenvalue-eigenvector and their number.

void	KO_algo ()
	Performing PPCKO algorithm once regularization parameter is selected and k or it is fixed or to be retained through explanatory power. Computes PPCs, direction and weight, their number and their cumulative explanatory power, and the estimate of the autoregressive operator.

KO_Traits::StoringArray	prediction () const
	Performs one-step ahead prediction of the fts. The mean function is added.

std::vector< double >	scores () const
	Computes the scores of the PPCs, defined as scalar product between the direction and the fts at the last instant.

std::vector< std::array< double, 2 > >	sd_scores_dir_wei () const
	Computes the standard deviation of the scores of directions and weights.

void	solve ()
	Method to solve PPCKO according to which cross-validation is performed, if any.

Detailed Description

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>
class PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >

Base class for computing PPCKO algorithm computations. Polymorphism is known at compile-time (CRTP)

Template Parameters

D	type of the derived class (for static polymorphism thorugh CRTP): 'PPC_KO_NoCV': alpha has to be passed as paramter. k can be passed as paramter or selected through explanatory power criterion
solver	if algorithm solved inverting the regularized covariance or avoiding it through gep (not possible if retaining the number of PPCs with explanatory power criterion)
k_imp	if k is imposed or has to be found through explanatory power criterion
valid_err_ret	if validation error are stored
cv_strat	strategy for splitting training/validation sets
err_eval	how to evaluate the loss between prediction on validation set and validation set

It is the base class. Polymorphism is known at compile time thanks to Curiously Recursive Template Pattern (CRTP)

Constructor & Destructor Documentation

◆ PPC_KO_base()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

template<typename STOR_OBJ>

PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::PPC_KO_base	(	STOR_OBJ &&	X,
		int	number_threads )

inline

Constructor: centers data, evaluate mean function, sample covariance, sample cross-covariance and its square.

Parameters

X	fts
number_threads	number of threads for OMP

Universal constructor: move semantic used to optimazing handling big size objects

Note: eventual usage of 'pragma' directive for OMP

Member Function Documentation

◆ a()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringMatrix PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::a ( ) const

inline

Getter for the predictive loadings (PPCs directions)

Returns: the private m_a

◆ alpha() [1/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

double & PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::alpha ( )

inline

Setter for the regularization parameter.

Returns: the private m_alpha (non-const)

◆ alpha() [2/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

double PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::alpha ( ) const

inline

Getter for the regularization parameter.

Returns: the private m_alpha

◆ b()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringMatrix PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::b ( ) const

inline

Getter for the predictive factors factor (PPCs weights)

Returns: the private m_b

◆ Cov()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringMatrix PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::Cov ( ) const

inline

Getter for the covariance operator estimate.

Returns: the private m_Cov

◆ CovReg()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringMatrix & PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::CovReg ( )

inline

Setter for the regularized sample covariance operator.

Returns: the private m_CovReg (non-const)

◆ explanatory_power()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

std::vector< double > PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::explanatory_power ( ) const

inline

Getter for the cumulative explanatory power of the PPCs.

Returns: the private m_explanatory_power

◆ k() [1/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

int & PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::k ( )

inline

Setter for the number of retained PPCs.

Returns: the private m_k (non-const)

◆ k() [2/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

int PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::k ( ) const

inline

Getter for the number of retained PPCs.

Returns: the private m_k

◆ KO_algo()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

void PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::KO_algo ( )

Performing PPCKO algorithm once regularization parameter is selected and k or it is fixed or to be retained through explanatory power. Computes PPCs, direction and weight, their number and their cumulative explanatory power, and the estimate of the autoregressive operator.

Modifying the private members of the class corresponding to the computed quantities

Modifying the private members of the class corresponding to the computed quantities.

◆ m()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

std::size_t PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::m ( ) const

inline

Getter for the number of evaluation of the curve/surface.

Returns: the private m_m

◆ means()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringArray PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::means ( ) const

inline

Getter for the mean function.

Returns: the private m_means

◆ n()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

std::size_t PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::n ( ) const

inline

Getter for the number of time instants.

Returns: the private m_n

◆ number_threads()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

int PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::number_threads ( ) const

inline

Getter for the number of threads for OMP.

Returns: the private m_number_threads

◆ PPC_retained()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

std::tuple< int, KO_Traits::StoringVector, KO_Traits::StoringMatrix > PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::PPC_retained ( )

Retaining the the PPCs: pairs eigenvalue-eigenvector and their number.

Returns: a tuple containing: the number of retained PPCs, the eigenvalues of phi/of GEP, the eigenvectors of phi/of GEP

The PPCs are computed according to the solver strategy using 'Spectra'. Only the first k pairs eigenvalue/eigenvactor are evaluated, corresponding to the k laregest eigenvalues, if k imposed. If instead (only for 'SOLVER::ex_solver') are computed using the explanatory power criterion, the k pairs eigenvalues-eigenvectors are computed increasing the number of computed ones until the requested explanatory power is reached

◆ prediction()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringArray PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::prediction ( ) const

Performs one-step ahead prediction of the fts. The mean function is added.

Returns: the array of the prediction

◆ rho()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringMatrix PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::rho ( ) const

inline

Getter for the autoregressive operator estimate.

Returns: the private m_rho

◆ scores()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

std::vector< double > PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::scores ( ) const

Computes the scores of the PPCs, defined as scalar product between the direction and the fts at the last instant.

Returns: a vector containing the score of each PPC

◆ sd_scores_dir_wei()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

std::vector< std::array< double, 2 > > PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::sd_scores_dir_wei ( ) const

Computes the standard deviation of the scores of directions and weights.

Returns: a vector (of size equal to the number of PPCs) containing arrays with two elements (standard deviation of direction and weight score of the PPC)

Scores of directions are computed as the scalar product of the direction and the fts in the instants between 2 and n.
- Scores of weights are computed as the scalar product of the weight and the fts in the instants between 1 and n-1

◆ solve()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

void PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::solve ( )

inline

Method to solve PPCKO according to which cross-validation is performed, if any.

Entails downcasting of base class with a static cast of pointer to the derived-known-at-compile-time class, CRTP fashion

◆ threshold_ppc() [1/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

double & PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::threshold_ppc ( )

inline

Setter for the requested explanatory power of the retained PPCs.

Returns: the private m_threshold_ppc (non-const)

◆ threshold_ppc() [2/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

double PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::threshold_ppc ( ) const

inline

Getter for the requested explanatory power of the retained PPCs.

Returns: the private m_threshold_ppc

◆ trace_cov()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

double PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::trace_cov ( ) const

inline

Getter for the covariance operator estimate's trace.

Returns: the private m_trace_cov

◆ ValidErr() [1/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

valid_err_variant & PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::ValidErr ( )

inline

Setter for the validation errors.

Returns: the private m_valid_err (non-const)

◆ ValidErr() [2/2]

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

valid_err_variant PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::ValidErr ( ) const

inline

Getter for the validation errors.

Returns: the private m_valid_err

◆ X()

template<class D, SOLVER solver, K_IMP k_imp, VALID_ERR_RET valid_err_ret, CV_STRAT cv_strat, CV_ERR_EVAL cv_err_eval>

KO_Traits::StoringMatrix PPC_KO_base< D, solver, k_imp, valid_err_ret, cv_strat, cv_err_eval >::X ( ) const

inline

Getter for fts data matrix (centered)

Returns: the private m_X

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

src/PPC_KO.hpp
src/PPC_KO_imp.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ PPC_KO_base()

Member Function Documentation

◆ a()

◆ alpha() [1/2]

◆ alpha() [2/2]

◆ b()

◆ Cov()

◆ CovReg()

◆ explanatory_power()

◆ k() [1/2]

◆ k() [2/2]

◆ KO_algo()

◆ m()

◆ means()

◆ n()

◆ number_threads()

◆ PPC_retained()

◆ prediction()

◆ rho()

◆ scores()

◆ sd_scores_dir_wei()

◆ solve()

◆ threshold_ppc() [1/2]

◆ threshold_ppc() [2/2]

◆ trace_cov()

◆ ValidErr() [1/2]

◆ ValidErr() [2/2]

◆ X()