C3Approximation Class Reference

Derived approximation class for global basis polynomials. More...

Inheritance diagram for C3Approximation:

Public Member Functions
	C3Approximation ()
	default constructor
	C3Approximation (ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
	standard ProblemDescDB-driven constructor
	C3Approximation (const SharedApproxData &shared_data)
	alternate constructor
C3FnTrainData &	active_ftd ()
	return the active C3FnTrainData instance in levelApprox
C3FnTrainData &	combined_ftd ()
	return combinedC3FTData
size_t	regression_size ()
size_t	regression_size (const SizetVector &ranks, size_t max_rank, const UShortArray &orders, unsigned short max_order)
void	recover_function_train_ranks (struct FunctionTrain *ft)
void	recover_function_train_orders (const std::vector< OneApproxOpts * > &a_opts)
void	expansion_coefficient_flag (bool coeff_flag)
bool	expansion_coefficient_flag () const
void	expansion_gradient_flag (bool grad_flag)
bool	expansion_gradient_flag () const
void	compute_moments (bool full_stats=true, bool combined_stats=false)
void	compute_moments (const Pecos::RealVector &x, bool full_stats=true, bool combined_stats=false)
const RealVector &	moments () const
const RealVector &	expansion_moments () const
const RealVector &	numerical_integration_moments () const
const RealVector &	combined_moments () const
Real	moment (size_t i) const
void	moment (Real mom, size_t i)
Real	combined_moment (size_t i) const
void	combined_moment (Real mom, size_t i)
void	compute_component_effects ()
void	compute_total_effects ()
void	compute_all_sobol_indices (size_t)
Real	total_sobol_index (size_t)
Real	main_sobol_index (size_t)
void	sobol_iterate_apply (void(*)(double, size_t, size_t *, void *), void *)
Real	mean ()
	return the mean of the expansion, where all active vars are random
Real	mean (const RealVector &)
	return the mean of the expansion for a given parameter vector, where a subset of the active variables are random
const RealVector &	mean_gradient ()
	return the gradient of the expansion mean
const RealVector &	mean_gradient (const RealVector &, const SizetArray &)
	return the gradient of the expansion mean
Real	variance ()
	return the variance of the expansion, where all active vars are random
Real	variance (const RealVector &)
	return the variance of the expansion for a given parameter vector, where a subset of the active variables are random
const RealVector &	variance_gradient ()
const RealVector &	variance_gradient (const RealVector &, const SizetArray &)
Real	covariance (Approximation &approx_2)
	return the covariance between two response expansions, treating all variables as random
Real	covariance (const RealVector &x, Approximation &approx_2)
	return the covariance between two response expansions, treating a subset of the variables as random
Real	skewness ()
Real	kurtosis ()
Real	third_central ()
Real	fourth_central ()
Real	combined_mean ()
	return the mean of the combined expansion, where all active vars are random
Real	combined_mean (const RealVector &)
	return the mean of the combined expansion for a given parameter vector, where a subset of the active variables are random
Real	combined_variance ()
Real	combined_variance (const RealVector &)
Real	combined_covariance (Approximation &approx_2)
	return the covariance between two combined response expansions, where all active variables are random
Real	combined_covariance (const RealVector &x, Approximation &approx_2)
	return the covariance between two combined response expansions, where a subset of the active variables are random
Real	combined_third_central ()
Real	combined_fourth_central ()
void	synchronize_surrogate_data ()
	update surrData to define aggregated data from raw data, when indicated by an active aggregated key
void	generate_synthetic_data (Pecos::SurrogateData &surr_data, const Pecos::ActiveKey &active_key, short combine_type)
	generate synthetic data for the surrogate QoI prediction corresponding to the level key preceding active key; for use in surplus estimation for new level data relative to a previous level's surrogate prediction
Public Member Functions inherited from Approximation
	Approximation ()
	default constructor More...
	Approximation (ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
	standard constructor for envelope More...
	Approximation (const SharedApproxData &shared_data)
	alternate constructor More...
	Approximation (const Approximation &approx)
	copy constructor More...
virtual	~Approximation ()
	destructor
Approximation	operator= (const Approximation &approx)
	assignment operator
virtual void	build (int num_resp)
	overloaded build to support field-based approximations; builds from scratch More...
virtual void	export_model (const StringArray &var_labels=StringArray(), const String &fn_label="", const String &export_prefix="", const unsigned short export_format=NO_MODEL_FORMAT)
	exports the approximation; if export_format > NO_MODEL_FORMAT, uses all 3 parameters, otherwise extracts these from the Approximation's sharedDataRep to build a filename
virtual void	export_model (const Variables &vars, const String &fn_label="", const String &export_prefix="", const unsigned short export_format=NO_MODEL_FORMAT)
	approximation export that generates labels from the passed Variables, since only the derived classes know how the variables are ordered w.r.t. the surrogate build; if export_format > NO_MODEL_FORMAT, uses all 3 parameters, otherwise extracts these from the Approximation's sharedDataRep to build a filename
virtual void	replace (const IntResponsePair &response_pr, size_t fn_index)
	replace the response data
virtual void	finalize_coefficients ()
	finalize approximation by applying all remaining trial sets
virtual void	clear_current_active_data ()
	clear current build data in preparation for next build More...
virtual RealVector	values (const Variables &vars)
	retrieve the approximate function values for a given parameter vector
virtual Real	prediction_variance (const Variables &vars)
	retrieve the variance of the predicted value for a given parameter vector
virtual Real	value (const RealVector &c_vars)
	retrieve the approximate function value for a given parameter vector
virtual RealVector	values (const RealVector &c_vars)
	retrieve the approximate function value for a given parameter vector
virtual const RealVector &	gradient (const RealVector &c_vars)
	retrieve the approximate function gradient for a given parameter vector
virtual const RealSymMatrix &	hessian (const RealVector &c_vars)
	retrieve the approximate function Hessian for a given parameter vector
virtual Real	prediction_variance (const RealVector &c_vars)
	retrieve the variance of the predicted value for a given parameter vector
virtual void	compute_moments (const RealVector &x, bool full_stats=true, bool combined_stats=false)
virtual void	clear_component_effects ()
virtual const RealVector &	sobol_indices () const
virtual const RealVector &	total_sobol_indices () const
virtual ULongULongMap	sparse_sobol_index_map () const
virtual bool	diagnostics_available ()
	check if diagnostics are available for this approximation type
virtual Real	diagnostic (const String &metric_type)
	retrieve a single diagnostic metric for the diagnostic type specified
virtual RealArray	cv_diagnostic (const StringArray &metric_types, unsigned num_folds)
	retrieve diagnostic metrics for the diagnostic types specified, applying
virtual void	primary_diagnostics (size_t fn_index)
	compute and print all requested diagnostics and cross-validation
virtual RealArray	challenge_diagnostic (const StringArray &metric_types, const RealMatrix &challenge_points, const RealVector &challenge_responses)
	compute requested diagnostics for user provided challenge pts
virtual void	challenge_diagnostics (size_t fn_index, const RealMatrix &challenge_points, const RealVector &challenge_responses)
	compute and print all requested diagnostics for user provided challenge pts
virtual RealVector	approximation_coefficients (bool normalized) const
	return the coefficient array computed by build()/rebuild()
virtual void	approximation_coefficients (const RealVector &approx_coeffs, bool normalized)
	set the coefficient array from external sources, rather than computing with build()/rebuild()
virtual void	coefficient_labels (std::vector< std::string > &coeff_labels) const
	print the coefficient array computed in build()/rebuild()
virtual void	print_coefficients (std::ostream &s, bool normalized)
	print the coefficient array computed in build()/rebuild()
virtual int	recommended_coefficients () const
	return the recommended number of samples (unknowns) required to build the derived class approximation type in numVars dimensions
virtual int	num_constraints () const
	return the number of constraints to be enforced via an anchor point
virtual size_t	num_components () const
	return the number of approximation components (1 for scalars)
virtual void	clear_computed_bits ()
	clear tracking of computed moments, due to (expansion) change that invalidates previous results
virtual void	map_variable_labels (const Variables &dfsm_vars)
	if needed, map passed all variable labels to approximation's labels
int	min_points (bool constraint_flag) const
	return the minimum number of points required to build the approximation type in numVars dimensions. Uses *_coefficients() and num_constraints().
int	recommended_points (bool constraint_flag) const
	return the recommended number of samples to build the approximation type in numVars dimensions (default same as min_points)
void	pop_data (bool save_data)
	removes entries from end of SurrogateData::{vars,resp}Data (last points appended, or as specified in args)
void	push_data ()
	restores SurrogateData state prior to previous pop()
void	finalize_data ()
	finalize SurrogateData by applying all remaining trial sets
const Pecos::SurrogateData &	surrogate_data () const
	return approxData
Pecos::SurrogateData &	surrogate_data ()
	return approxData
void	add (const Variables &vars, bool v_copy, const Response &response, size_t fn_index, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
	create SurrogateData{Vars,Resp} and append to SurrogateData:: {varsData,respData,dataIdentifiers}
void	add (const Real *c_vars, bool v_copy, const Response &response, size_t fn_index, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
	create SurrogateData{Vars,Resp} and append to SurrogateData:: {varsData,respData,dataIdentifiers}
void	add (const Pecos::SurrogateDataVars &sdv, bool v_copy, const Response &response, size_t fn_index, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
	create a SurrogateDataResp and append to SurrogateData:: {varsData,respData,dataIdentifiers}
void	add (const Pecos::SurrogateDataVars &sdv, bool v_copy, const Pecos::SurrogateDataResp &sdr, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
	append to SurrogateData::{varsData,respData,dataIdentifiers}
void	add_array (const RealMatrix &sample_vars, bool v_copy, const RealVector &sample_resp, bool r_copy, size_t key_index=_NPOS)
	add surrogate data from the provided sample and response data, assuming continuous variables and function values only More...
void	pop_count (size_t count, size_t key_index)
	appends to SurrogateData::popCountStack (number of entries to pop from end of SurrogateData::{vars,resp}Data, based on size of last data append)
void	clear_data ()
	clear SurrogateData::{vars,resp}Data for activeKey + embedded keys More...
void	clear_active_data ()
	clear active approximation data
void	clear_inactive_data ()
	clear inactive approximation data
void	clear_active_popped ()
	clear SurrogateData::popped{Vars,Resp}Trials,popCountStack for activeKey
void	clear_popped ()
	clear SurrogateData::popped{Vars,Resp}Trials,popCountStack for all keys
void	set_bounds (const RealVector &c_l_bnds, const RealVector &c_u_bnds, const IntVector &di_l_bnds, const IntVector &di_u_bnds, const RealVector &dr_l_bnds, const RealVector &dr_u_bnds)
	set approximation lower and upper bounds (currently only used by graphics)
std::shared_ptr< Approximation >	approx_rep () const
	returns approxRep for access to derived class member functions that are not mapped to the top Approximation level

Protected Member Functions
void	active_model_key (const Pecos::ActiveKey &key)
	activate an approximation state based on its multi-index key
void	clear_model_keys ()
	reset initial state by removing all model keys for an approximation
Real	value (const Variables &vars)
	retrieve the approximate function value for a given parameter vector
const RealVector &	gradient (const Variables &vars)
	retrieve the approximate function gradient for a given parameter vector
const RealSymMatrix &	hessian (const Variables &vars)
	retrieve the approximate function Hessian for a given parameter vector
bool	advancement_available ()
	check if resolution advancement (e.g., order, rank) is available for this approximation instance
void	build ()
	builds the approximation from scratch More...
void	rebuild ()
	rebuilds the approximation incrementally
void	pop_coefficients (bool save_data)
	removes entries from end of SurrogateData::{vars,resp}Data (last points appended, or as specified in args)
void	push_coefficients ()
	restores state prior to previous pop()
void	combine_coefficients ()
	combine all level approximations into a single aggregate approximation
void	combined_to_active_coefficients (bool clear_combined=true)
	promote combined approximation into active approximation
void	clear_inactive_coefficients ()
	prune inactive coefficients following combination and promotion to active
int	min_coefficients () const
	return the minimum number of samples (unknowns) required to build the derived class approximation type in numVars dimensions
Protected Member Functions inherited from Approximation
	Approximation (BaseConstructor, const ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
	constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
	Approximation (NoDBBaseConstructor, const SharedApproxData &shared_data)
	constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
std::shared_ptr< Approximation >	get_approx (ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
	Used only by the standard envelope constructor to initialize approxRep to the appropriate derived type. More...
std::shared_ptr< Approximation >	get_approx (const SharedApproxData &shared_data)
	Used only by the alternate envelope constructor to initialize approxRep to the appropriate derived type. More...
Pecos::SurrogateDataVars	variables_to_sdv (const Real *sample_c_vars)
	create a SurrogateDataVars instance from a Real*
Pecos::SurrogateDataVars	variables_to_sdv (const Variables &vars)
	create a SurrogateDataVars instance by extracting data from a Variables object
Pecos::SurrogateDataResp	response_to_sdr (const Response &response, size_t fn_index)
	create a SurrogateDataResp instance by extracting data for a particular QoI from a Response object
void	add (const Pecos::SurrogateDataVars &sdv, bool v_copy, const Pecos::SurrogateDataResp &sdr, bool r_copy, bool anchor_flag)
	tracks a new data point by appending to SurrogateData::{vars,Resp}Data
void	add (int eval_id)
	tracks a new data point by appending to SurrogateData::dataIdentifiers
void	check_points (size_t num_build_pts)
	Check number of build points against minimum required.
void	assign_key_index (size_t key_index)
	extract and assign i-th embedded active key

Private Member Functions
bool	max_rank_advancement_available ()
bool	max_order_advancement_available ()
Real	stored_value (const RealVector &c_vars, const Pecos::ActiveKey &key)
void	compute_derived_statistics (C3FnTrainData &ftd, size_t num_mom, bool overwrite=false)
void	compute_derived_statistics_av (C3FnTrainData &ftd, size_t num_mom, bool overwrite=false)
void	check_function_gradient ()
	differentiate the ft to form its gradient, if not previously performed
void	check_function_hessian ()
	differentiate the ftg to form the ft Hessian, if not previously performed
Real	mean (C3FnTrainData &ftd)
	compute mean corresponding to the passed FT expansion
Real	mean (const RealVector &x, C3FnTrainData &ftd)
	compute mean corresponding to the passed FT expansion
Real	variance (C3FnTrainData &ftd)
	compute variance corresponding to the passed FT expansion
Real	variance (const RealVector &x, C3FnTrainData &ftd)
	compute variance corresponding to the passed FT expansion
Real	covariance (C3FnTrainData &ftd1, C3FnTrainData &ftd2)
	compute variance corresponding to the passed FT expansion
Real	covariance (const RealVector &x, C3FnTrainData &ftd1, C3FnTrainData &ftd2)
	compute variance corresponding to the passed FT expansion
Real	third_central (C3FnTrainData &ftd)
	compute 3rd central moment corresponding to the passed FT expansion
Real	fourth_central (C3FnTrainData &ftd)
	compute 4th central moment corresponding to the passed FT expansion
Real	skewness (C3FnTrainData &ftd)
	compute skewness corresponding to the passed FT expansion
Real	kurtosis (C3FnTrainData &ftd)
	compute excess kurtosis corresponding to the passed FT expansion

Private Attributes
std::map< Pecos::ActiveKey, C3FnTrainData >	levelApprox
	set of pointers to QoI approximation data for each model key
std::map< Pecos::ActiveKey, C3FnTrainData >::iterator	levApproxIter
	iterator to active levelApprox
C3FnTrainData	prevC3FTData
	the previous approximation, cached for restoration
std::map< Pecos::ActiveKey, std::deque< C3FnTrainData > >	poppedLevelApprox
	bookkeeping for previously evaluated FT approximations that may be restored
C3FnTrainData	combinedC3FTData
	the combined approximation, summed across model keys
RealVector	secondaryMoments
	secondary (numerical) moments: inactive
RealVector	combinedMoments
	combined moments from multilevel-multifidelity FT rollup
bool	expansionCoeffFlag
	flag indicating need to build a fn train approximation for this QoI
bool	expansionCoeffGradFlag
	flag indicating need to build a fn train gradient approx for this QoI

Additional Inherited Members
Protected Attributes inherited from Approximation
Pecos::SurrogateData	approxData
	contains the variables/response data for constructing a single approximation model (one response function). There is only one SurrogateData instance per Approximation, although it may contain keys for different model forms/resolutions and aggregations (e.g., discrepancies) among forms/resolutions.
RealVector	approxGradient
	gradient of the approximation returned by gradient()
RealSymMatrix	approxHessian
	Hessian of the approximation returned by hessian()
String	approxLabel
	label for approximation, if applicable
std::shared_ptr< SharedApproxData >	sharedDataRep
	contains the approximation data that is shared among the response set
std::shared_ptr< Approximation >	approxRep
	pointer to the letter (initialized only for the envelope)

Detailed Description

Derived approximation class for global basis polynomials.

The PecosApproximation class provides a global approximation based on basis polynomials. This includes orthogonal polynomials used for polynomial chaos expansions and interpolation polynomials used for stochastic collocation.

Member Function Documentation

regression_size()

size_t regression_size	(	const SizetVector &	ranks,
		size_t	max_rank,
		const UShortArray &	orders,
		unsigned short	max_order
	)

compute the regression size (number of unknowns) for ranks per dimension and (polynomial) basis orders per dimension

References Dakota::abort_handler(), Approximation::sharedDataRep, and Dakota::sum().

recover_function_train_orders()

void recover_function_train_orders

(

const std::vector< OneApproxOpts * > &

a_opts

)

returns the recovered orders, reflecting the latest CV if adapt_order

References C3Approximation::levApproxIter, and Approximation::sharedDataRep.

Referenced by C3Approximation::build().

build()

void build ( )

protectedvirtual

builds the approximation from scratch

This is the common base class portion of the virtual fn and is insufficient on its own; derived implementations should explicitly invoke (or reimplement) this base class contribution.

Reimplemented from Approximation.

References Approximation::approxData, Approximation::build(), C3FnTrainData::free_all(), C3FnTrainData::function_train(), C3Approximation::levApproxIter, C3Approximation::recover_function_train_orders(), Approximation::sharedDataRep, C3Approximation::synchronize_surrogate_data(), Dakota::SZ_MAX, and Dakota::write_precision.

Referenced by C3Approximation::rebuild().

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

• C3Approximation.hpp
• C3Approximation.cpp