Dakota
Version 6.20
Explore and Predict with Confidence
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Derived approximation class for Gaussian Process implementation. More...
Public Member Functions | |
GaussProcApproximation () | |
default constructor More... | |
GaussProcApproximation (const SharedApproxData &shared_data) | |
alternate constructor | |
GaussProcApproximation (const ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label) | |
standard constructor | |
~GaussProcApproximation () | |
destructor | |
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 | active_model_key (const Pecos::ActiveKey &sd_key) |
activate an approximation state based on its multi-index key | |
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 | rebuild () |
rebuilds the approximation incrementally | |
virtual void | replace (const IntResponsePair &response_pr, size_t fn_index) |
replace the response data | |
virtual void | pop_coefficients (bool save_data) |
removes entries from end of SurrogateData::{vars,resp}Data (last points appended, or as specified in args) | |
virtual void | push_coefficients () |
restores state prior to previous pop() | |
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 void | combine_coefficients () |
combine all level approximations into a single aggregate approximation | |
virtual void | combined_to_active_coefficients (bool clear_combined=true) |
promote combined approximation into active approximation | |
virtual void | clear_inactive_coefficients () |
prune inactive coefficients following combination and promotion to active | |
virtual const RealSymMatrix & | hessian (const Variables &vars) |
retrieve the approximate function Hessian 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 () |
return the mean of the expansion, where all active vars are random | |
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 () |
return the mean of the combined expansion, where all active vars 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 () |
return the gradient of the expansion mean | |
virtual const RealVector & | mean_gradient (const RealVector &x, const SizetArray &dvv) |
return the gradient of the expansion mean | |
virtual Real | variance () |
return the variance of the expansion, where all active vars are random | |
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 () |
virtual const RealVector & | variance_gradient (const RealVector &x, const SizetArray &dvv) |
virtual Real | covariance (Approximation &approx_2) |
return the covariance between two response expansions, treating all variables as random | |
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 (Approximation &approx_2) |
return the covariance between two combined response expansions, where all active variables are 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 (bool full_stats=true, bool combined_stats=false) |
virtual void | compute_moments (const RealVector &x, bool full_stats=true, bool combined_stats=false) |
virtual const RealVector & | moments () const |
virtual const RealVector & | expansion_moments () const |
virtual const RealVector & | numerical_integration_moments () const |
virtual const RealVector & | combined_moments () const |
virtual Real | moment (size_t i) const |
virtual void | moment (Real mom, size_t i) |
virtual Real | combined_moment (size_t i) const |
virtual void | combined_moment (Real mom, size_t i) |
virtual void | clear_component_effects () |
virtual void | compute_component_effects () |
virtual void | compute_total_effects () |
virtual const RealVector & | sobol_indices () const |
virtual const RealVector & | total_sobol_indices () const |
virtual ULongULongMap | sparse_sobol_index_map () const |
virtual bool | advancement_available () |
check if resolution advancement (e.g., order, rank) is available for this approximation instance | |
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 | expansion_coefficient_flag (bool) |
virtual bool | expansion_coefficient_flag () const |
virtual void | expansion_gradient_flag (bool) |
virtual bool | expansion_gradient_flag () const |
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 | |
int | min_coefficients () const |
return the minimum number of samples (unknowns) required to build the derived class approximation type in numVars dimensions | |
void | build () |
find the covariance parameters governing the Gaussian process response | |
Real | value (const Variables &vars) |
retrieve the function value for a given parameter set | |
const RealVector & | gradient (const Variables &vars) |
retrieve the function gradient at the predicted value for a given parameter set | |
Real | prediction_variance (const Variables &vars) |
retrieve the variance of the predicted value for a given parameter set | |
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 | GPmodel_build () |
Function to compute hyperparameters governing the GP. | |
void | GPmodel_apply (const RealVector &new_x, bool variance_flag, bool gradients_flag) |
Function returns a response value using the GP surface. More... | |
void | normalize_training_data () |
Normalizes the initial inputs upon which the GP surface is based. | |
void | get_trend () |
Gets the trend (basis) functions for the calculation of the mean of the GP If the order = 0, the trend is a constant, if the order = 1, trend is linear, if order = 2, trend is quadratic. | |
void | get_beta_coefficients () |
Gets the beta coefficients for the calculation of the mean of the GP. | |
int | get_cholesky_factor () |
Gets the Cholesky factorization of the covariance matrix, with error checking. | |
void | get_process_variance () |
Gets the estimate of the process variance given the values of beta and the correlation lengthscales | |
void | get_cov_matrix () |
calculates the covariance matrix for a given set of input points | |
void | get_cov_vector () |
calculates the covariance vector between a new point x and the set of inputs upon which the GP is based | |
void | optimize_theta_global () |
sets up and performs the optimization of the negative log likelihood to determine the optimal values of the covariance parameters using NCSUDirect | |
void | optimize_theta_multipoint () |
sets up and performs the optimization of the negative log likelihood to determine the optimal values of the covariance parameters using a gradient-based solver and multiple starting points | |
void | predict (bool variance_flag, bool gradients_flag) |
Calculates the predicted new response value for x in normalized space. | |
Real | calc_nll () |
calculates the negative log likelihood function (based on covariance matrix) | |
void | calc_grad_nll () |
Gets the gradient of the negative log likelihood function with respect to the correlation lengthscales, theta | |
void | get_grad_cov_vector () |
Calculate the derivatives of the covariance vector, with respect to each componeent of x. | |
void | run_point_selection () |
Runs the point selection algorithm, which will choose a subset of the training set with which to construct the GP model, and estimate the necessary parameters. | |
void | initialize_point_selection () |
Initializes the point selection routine by choosing a small initial subset of the training points. | |
void | pointsel_get_errors (RealArray &delta) |
Uses the current GP model to compute predictions at all of the training points and find the errors. | |
int | addpoint (int, IntArray &added_index) |
Adds a point to the effective training set. Returns 1 on success. | |
int | pointsel_add_sel (const RealArray &delta) |
Accepts a vector of unsorted prediction errors, determines which points should be added to the effective training set, and adds them. | |
Real | maxval (const RealArray &) const |
Return the maximum value of the elements in a vector. | |
void | pointsel_write_points () |
Writes out the training set before and after point selection. | |
void | lhood_2d_grid_eval () |
For problems with 2D input, evaluates the negative log likelihood on a grid. | |
void | writex (const char[]) |
Writes out the current training set (in original units) to a specified file. | |
void | writeCovMat (char[]) |
Writes out the covariance matrix to a specified file. | |
Static Private Member Functions | |
static void | negloglik (int mode, int n, const Teuchos::SerialDenseVector< int, double > &X, Real &fx, Teuchos::SerialDenseVector< int, double > &grad_x, int &result_mode) |
static function used by OPT++ as the objective function to optimize the hyperparameters in the covariance of the GP by minimizing the negative log likelihood | |
static void | constraint_eval (int mode, int n, const Teuchos::SerialDenseVector< int, double > &X, Teuchos::SerialDenseVector< int, double > &g, Teuchos::SerialDenseMatrix< int, double > &gradC, int &result_mode) |
static function used by OPT++ as the constraint function in the optimization of the negative log likelihood. Currently this function is empty: it is an unconstrained optimization. | |
static double | negloglikNCSU (const RealVector &x) |
function used by NCSUOptimizer to optimize negloglik objective | |
Private Attributes | |
Real | approxValue |
value of the approximation returned by value() | |
Real | approxVariance |
value of the approximation returned by prediction_variance() | |
RealMatrix | trainPoints |
A 2-D array (num sample sites = rows, num vars = columns) used to create the Gaussian process. | |
RealMatrix | trainValues |
An array of response values; one response value per sample site. | |
RealVector | trainMeans |
The mean of the input columns of trainPoints. | |
RealVector | trainStdvs |
The standard deviation of the input columns of trainPoints. | |
RealMatrix | normTrainPoints |
Current working set of normalized points upon which the GP is based. | |
RealMatrix | trendFunction |
matrix to hold the trend function | |
RealMatrix | betaCoeffs |
matrix to hold the beta coefficients for the trend function | |
RealSymMatrix | covMatrix |
The covariance matrix where each element (i,j) is the covariance between points Xi and Xj in the initial set of samples. | |
RealMatrix | covVector |
The covariance vector where each element (j,0) is the covariance between a new point X and point Xj from the initial set of samples. | |
RealMatrix | approxPoint |
Point at which a prediction is requested. This is currently a single point, but it could be generalized to be a vector of points. | |
RealMatrix | gradNegLogLikTheta |
matrix to hold the gradient of the negative log likelihood with respect to the theta correlation terms | |
Teuchos::SerialSpdDenseSolver< int, Real > | covSlvr |
The global solver for all computations involving the inverse of the covariance matrix. | |
RealMatrix | gradCovVector |
A matrix, where each column is the derivative of the covVector with respect to a particular componenet of X. | |
RealMatrix | normTrainPointsAll |
Set of all original samples available. | |
RealMatrix | trainValuesAll |
All original samples available. | |
RealMatrix | trendFunctionAll |
Trend function values corresponding to all original samples. | |
RealMatrix | Rinv_YFb |
Matrix for storing inverse of correlation matrix Rinv*(Y-FB) | |
size_t | numObs |
The number of observations on which the GP surface is built. | |
size_t | numObsAll |
The original number of observations. | |
short | trendOrder |
The number of variables in each X variable (number of dimensions of the problem). More... | |
RealVector | thetaParams |
Theta is the vector of covariance parameters for the GP. We determine the values of theta by optimization Currently, the covariance function is theta[0]*exp(-0.5*sume)+delta*pow(sige,2). sume is the sum squared of weighted distances; it involves a sum of theta[1](Xi(1)-Xj(1))^2 + theta[2](Xi(2)-Xj(2))^2 + ... where Xi(1) is the first dimension value of multi-dimensional variable Xi. delta*pow(sige,2) is a jitter term used to improve matrix computations. delta is zero for the covariance between different points and 1 for the covariance between the same point. sige is the underlying process error. | |
Real | procVar |
The process variance, the multiplier of the correlation matrix. | |
IntArray | pointsAddedIndex |
Used by the point selection algorithm, this vector keeps track all points which have been added. | |
int | cholFlag |
A global indicator for success of the Cholesky factorization. | |
bool | usePointSelection |
a flag to indicate the use of point selection | |
Static Private Attributes | |
static GaussProcApproximation * | GPinstance |
pointer to the active object instance used within the static evaluator | |
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 Gaussian Process implementation.
The GaussProcApproximation class provides a global approximation (surrogate) based on a Gaussian process. The Gaussian process is built after normalizing the function values, with zero mean. Opt++ is used to determine the optimal values of the covariance parameters, those which minimize the negative log likelihood function.
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inline |
default constructor
alternate constructor used by EffGlobalOptimization and NonDGlobalReliability that does not use a problem database defaults here are no point selectinn and quadratic trend function.
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private |
Function returns a response value using the GP surface.
The response value is computed at the design point specified by the RealVector function argument.
References Dakota::abort_handler(), GaussProcApproximation::approxPoint, GaussProcApproximation::get_cov_vector(), GaussProcApproximation::predict(), Approximation::sharedDataRep, GaussProcApproximation::trainMeans, and GaussProcApproximation::trainStdvs.
Referenced by GaussProcApproximation::gradient(), GaussProcApproximation::pointsel_get_errors(), GaussProcApproximation::prediction_variance(), and GaussProcApproximation::value().
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private |
The number of variables in each X variable (number of dimensions of the problem).
The order of the basis function for the mean of the GP If the order = 0, the trend is a constant, if the order = 1, trend is linear, if order = 2, trend is quadratic.
Referenced by GaussProcApproximation::GaussProcApproximation(), GaussProcApproximation::get_beta_coefficients(), GaussProcApproximation::get_trend(), GaussProcApproximation::GPmodel_build(), and GaussProcApproximation::predict().