Dakota
Version 6.19
Explore and Predict with Confidence
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Derived approximation class for global basis polynomials. More...
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 | 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 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 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 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... | |
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 | |
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.
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(), and Approximation::sharedDataRep.
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().
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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().