PecosApproximation Class Reference

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

Inheritance diagram for PecosApproximation:

Public Member Functions
	PecosApproximation ()
	default constructor
	PecosApproximation (ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
	standard ProblemDescDB-driven constructor
	PecosApproximation (const SharedApproxData &shared_data)
	alternate constructor
	~PecosApproximation ()
	destructor
void	expansion_coefficient_flag (bool coeff_flag)
	set pecosBasisApprox.configOptions.expansionCoeffFlag
bool	expansion_coefficient_flag () const
	get pecosBasisApprox.configOptions.expansionCoeffFlag
void	expansion_gradient_flag (bool grad_flag)
	set pecosBasisApprox.configOptions.expansionGradFlag
bool	expansion_gradient_flag () const
	get pecosBasisApprox.configOptions.expansionGradFlag
void	clear_component_effects ()
	clear unused Sobol' indices
void	compute_component_effects ()
	Performs global sensitivity analysis using Sobol' indices by computing component (main and interaction) effects.
void	compute_total_effects ()
	Performs global sensitivity analysis using Sobol' indices by computing total effects.
const Pecos::RealVector &	sobol_indices () const
	return polyApproxRep->sobolIndices
const Pecos::RealVector &	total_sobol_indices () const
	return polyApproxRep->totalSobolIndices
size_t	sparsity () const
	return the number of non-zero coefficients for this QoI
Pecos::ULongULongMap	sparse_sobol_index_map () const
	return RegressOrthogPolyApproximation::sparseSobolIndexMap
const Pecos::RealVector &	dimension_decay_rates () const
	return OrthogPolyApproximation::decayRates
void	allocate_arrays ()
	invoke Pecos::PolynomialApproximation::allocate_arrays()
void	initialize_covariance (Approximation &approx_2)
	initialize covariance accumulators with pointers to other QoI
void	clear_covariance_pointers ()
	clear covariance pointers to other QoI
void	initialize_products ()
	initialize covariance accumulators (also reinitialize after change in stats type)
bool	product_interpolants ()
	query whether product interpolants are defined (non-empty)
Real	mean ()
	return the mean of the expansion, where all active variables are random
Real	mean (const Pecos::RealVector &x)
	return the mean of the expansion for a given parameter vector, where a subset of the active variables are random
Real	combined_mean ()
	return the mean of the combined expansion, treating all variables as random
Real	combined_mean (const Pecos::RealVector &x)
	return the mean of the combined expansion for a given parameter vector, where a subset of the active variables are treated as random
const Pecos::RealVector &	mean_gradient ()
	return the gradient of the expansion mean for a given parameter vector, where all active variables are random
const Pecos::RealVector &	mean_gradient (const Pecos::RealVector &x, const Pecos::SizetArray &dvv)
	return the gradient of the expansion mean for a given parameter vector and given DVV, where a subset of the active variables are random
Real	variance ()
	return the variance of the expansion, where all active vars are random
Real	variance (const Pecos::RealVector &x)
	return the variance of the expansion for a given parameter vector, where a subset of the active variables are random
const Pecos::RealVector &	variance_gradient ()
	return the gradient of the expansion variance for a given parameter vector, where all active variables are random
const Pecos::RealVector &	variance_gradient (const Pecos::RealVector &x, const Pecos::SizetArray &dvv)
	return the gradient of the expansion variance for a given parameter vector and given DVV, where a subset of the active variables are random
Real	covariance (Approximation &approx_2)
	return the covariance between two response expansions, treating all variables as random
Real	covariance (const Pecos::RealVector &x, Approximation &approx_2)
	return the covariance between two response expansions, treating a subset of the variables as random
Real	combined_covariance (Approximation &approx_2)
	return the covariance between two combined response expansions, where all active variables are random
Real	combined_covariance (const Pecos::RealVector &x, Approximation &approx_2)
	return the covariance between two combined response expansions, where a subset of the active variables are random
Real	beta (bool cdf_flag, Real z_bar)
	return the reliability index (mapped from z_bar), where all active variables are random
Real	beta (const RealVector &x, bool cdf_flag, Real z_bar)
	return the reliability index (mapped from z_bar), treating a subset of variables as random
Real	combined_beta (bool cdf_flag, Real z_bar)
	return the reliability index (mapped from z_bar), where all active variables are random
Real	combined_beta (const RealVector &x, bool cdf_flag, Real z_bar)
	return the reliability index (mapped from z_bar), treating a subset of variables as random
Real	delta_mean ()
	return the change in mean resulting from expansion refinement, where all active variables are random
Real	delta_mean (const RealVector &x)
	return the change in mean resulting from expansion refinement, treating a subset of variables as random
Real	delta_combined_mean ()
	return the change in mean resulting from combined expansion refinement, where all active variables are random
Real	delta_combined_mean (const RealVector &x)
	return the change in mean resulting from combined expansion refinement, treating a subset of variables as random
Real	delta_std_deviation ()
	return the change in standard deviation resulting from expansion refinement, where all active variables are random
Real	delta_std_deviation (const RealVector &x)
	return the change in standard deviation resulting from expansion refinement, treating a subset of variables as random
Real	delta_combined_std_deviation ()
	return the change in standard deviation resulting from combined expansion refinement, where all active variables are random
Real	delta_combined_std_deviation (const RealVector &x)
	return the change in standard deviation resulting from combined expansion refinement, treating a subset of variables as random
Real	delta_variance ()
	return the change in variance resulting from expansion refinement, where all active variables are random
Real	delta_variance (const RealVector &x)
	return the change in variance resulting from expansion refinement, treating a subset of variables as random
Real	delta_combined_variance ()
	return the change in variance resulting from combined expansion refinement, where all active variables are random
Real	delta_combined_variance (const RealVector &x)
	return the change in variance resulting from combined expansion refinement, treating a subset of variables as random
Real	delta_covariance (Approximation &approx_2)
	return the change in covariance resulting from expansion refinement, where all active variables are random
Real	delta_covariance (const Pecos::RealVector &x, Approximation &approx_2)
	return the change in covariance resulting from expansion refinement, where a subset of the active variables are random
Real	delta_combined_covariance (Approximation &approx_2)
	return the change in covariance resulting from expansion refinement, where all active variables are random
Real	delta_combined_covariance (const Pecos::RealVector &x, Approximation &approx_2)
	return the change in covariance resulting from expansion refinement, where a subset of the active variables are random
Real	delta_beta (bool cdf_flag, Real z_bar)
	return the change in reliability index (mapped from z_bar) resulting from expansion refinement, where all active variables are random
Real	delta_beta (const RealVector &x, bool cdf_flag, Real z_bar)
	return the change in reliability index (mapped from z_bar) resulting from expansion refinement, treating a subset of variables as random
Real	delta_combined_beta (bool cdf_flag, Real z_bar)
	return the change in reliability index (mapped from z_bar) resulting from expansion refinement, where all active variables are random
Real	delta_combined_beta (const RealVector &x, bool cdf_flag, Real z_bar)
	return the change in reliability index (mapped from z_bar) resulting from expansion refinement, treating a subset of variables as random
Real	delta_z (bool cdf_flag, Real beta_bar)
	return the change in response level (mapped from beta_bar) resulting from expansion refinement, where all active variables are random
Real	delta_z (const RealVector &x, bool cdf_flag, Real beta_bar)
	return the change in response level (mapped from beta_bar) resulting from expansion refinement, where a subset of the active variables are random
Real	delta_combined_z (bool cdf_flag, Real beta_bar)
	return the change in response level (mapped from beta_bar) resulting from expansion refinement, where all active variables are random
Real	delta_combined_z (const RealVector &x, bool cdf_flag, Real beta_bar)
	return the change in response level (mapped from beta_bar) resulting from expansion refinement, where a subset of the active variables are random
void	compute_moments (bool full_stats=true, bool combined_stats=false)
	compute moments up to the order supported by the Pecos polynomial approximation
void	compute_moments (const Pecos::RealVector &x, bool full_stats=true, bool combined_stats=false)
	compute moments in all-variables mode up to the order supported by the Pecos polynomial approximation
const RealVector &	moments () const
	return primary moments using Pecos::PolynomialApproximation::moments()
const RealVector &	expansion_moments () const
	return expansion moments from Pecos::PolynomialApproximation
const RealVector &	numerical_integration_moments () const
	return numerical moments from Pecos::PolynomialApproximation
const RealVector &	combined_moments () const
	return combined moments from multilevel-muktifidelity expansion roll-up
Real	moment (size_t i) const
	return primary moment using Pecos::PolynomialApproximation::moment(i)
void	moment (Real mom, size_t i)
	set primary moment using Pecos::PolynomialApproximation::moment(i)
Real	combined_moment (size_t i) const
	return Pecos::PolynomialApproximation::combinedMoments[i]
void	combined_moment (Real mom, size_t i)
	set Pecos::PolynomialApproximation::combinedMoments[i]
void	clear_computed_bits ()
	clear tracking of computed moments, due to a change that invalidates previous results
void	build_linear_system (RealMatrix &A, const UShort2DArray &multi_index)
	construct the Vandermonde matrix "A" for PCE regression for Ax = b
void	augment_linear_system (const RealVectorArray &samples, RealMatrix &A, const UShort2DArray &multi_index)
Pecos::BasisApproximation &	pecos_basis_approximation ()
	return pecosBasisApprox
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	clear_model_keys ()
	reset initial state by removing all model keys for an approximation
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	clear_current_active_data ()
	clear current build data in preparation for next build More...
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 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 Real	mean (const RealVector &x)
	return the mean of the expansion for a given parameter vector, where a subset of the active variables are random
virtual Real	combined_mean (const RealVector &x)
	return the mean of the combined expansion for a given parameter vector, where a subset of the active variables are random
virtual const RealVector &	mean_gradient (const RealVector &x, const SizetArray &dvv)
	return the gradient of the expansion mean
virtual Real	variance (const RealVector &x)
	return the variance of the expansion for a given parameter vector, where a subset of the active variables are random
virtual const RealVector &	variance_gradient (const RealVector &x, const SizetArray &dvv)
virtual Real	covariance (const RealVector &x, Approximation &approx_2)
	return the covariance between two response expansions, treating a subset of the variables as random
virtual 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
virtual void	compute_moments (const RealVector &x, bool full_stats=true, bool combined_stats=false)
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 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 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)
	assign active key in approxData and update_active_iterators()
Real	value (const Variables &vars)
	retrieve the approximate function value for a given parameter vector
const Pecos::RealVector &	gradient (const Variables &vars)
	retrieve the approximate function gradient for a given parameter vector
const Pecos::RealSymMatrix &	hessian (const Variables &vars)
	retrieve the approximate function Hessian for a given parameter vector
int	min_coefficients () const
	return the minimum number of samples (unknowns) required to build the derived class approximation type in numVars dimensions
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	finalize_coefficients ()
	finalize approximation by applying all remaining trial sets
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
bool	advancement_available ()
	check if resolution advancement (e.g., order, rank) is available for this approximation instance
void	print_coefficients (std::ostream &s, bool normalized)
	print the coefficient array computed in build()/rebuild()
RealVector	approximation_coefficients (bool normalized) const
	return expansion coefficients in a form consistent with the shared multi-index
void	approximation_coefficients (const RealVector &approx_coeffs, bool normalized)
	set expansion coefficients in a form consistent with the shared multi-index
void	coefficient_labels (std::vector< std::string > &coeff_labels) const
	print the coefficient array computed in build()/rebuild()
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...
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
void	approx_type_to_basis_type (const String &approx_type, short &basis_type)
	utility to convert Dakota type string to Pecos type enumeration

Private Attributes
Pecos::BasisApproximation	pecosBasisApprox
	the Pecos basis approximation, encompassing orthogonal and interpolation polynomial approximations
std::shared_ptr< Pecos::PolynomialApproximation >	polyApproxRep
	convenience pointer to representation of Pecos polynomial approximation

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

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

build()

void build ( )

inlineprotectedvirtual

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::build(), and PecosApproximation::pecosBasisApprox.

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

• PecosApproximation.hpp
• PecosApproximation.cpp