A class for representing and using expansions of orthogonal multivariate polynomials. More...

#include <PolynomialChaosExpansion.h>

Inheritance diagram for muq::Approximation::PolynomialChaosExpansion:

Detailed Description

A class for representing and using expansions of orthogonal multivariate polynomials.

A particular polynomial chaos expansion for a function from R^n->R^m. This class uses some the MultiIndexSet class to define PCE terms that are in the expansion. For each PCE term and output, there is a coefficient. The PCE is built from 1D polynomials specified so each dimension may have independent polynomial choices.

See also: BasisExpansion, PCEFactory

Definition at line 28 of file PolynomialChaosExpansion.h.

Public Member Functions
	PolynomialChaosExpansion (std::shared_ptr< OrthogonalPolynomial > const &basisCompsIn, std::shared_ptr< muq::Utilities::MultiIndexSet > const &multisIn, Eigen::MatrixXd const &coeffsIn)

	PolynomialChaosExpansion (std::shared_ptr< OrthogonalPolynomial > const &basisCompsIn, std::shared_ptr< muq::Utilities::MultiIndexSet > const &multisIn, unsigned int outputDim)

	PolynomialChaosExpansion (std::vector< std::shared_ptr< IndexedScalarBasis >> const &basisCompsIn, std::shared_ptr< muq::Utilities::MultiIndexSet > const &multisIn, Eigen::MatrixXd const &coeffsIn)

	PolynomialChaosExpansion (std::vector< std::shared_ptr< IndexedScalarBasis >> const &basisCompsIn, std::shared_ptr< muq::Utilities::MultiIndexSet > const &multisIn, unsigned int outputDim)

virtual	~PolynomialChaosExpansion ()=default

Eigen::VectorXd	Variance () const
	compute the variance of the current expansion More...

Eigen::MatrixXd	Covariance () const

Eigen::VectorXd	Mean () const

Eigen::VectorXd	Magnitude () const
	Compute the L2 norm of each output. More...

Eigen::VectorXd	TotalSensitivity (unsigned int targetDim) const
	Compute the Sobol total sensitivity index for the input dimension, for each output dimension. More...

Eigen::MatrixXd	TotalSensitivity () const
	Compute all Sobol total sensitivities. Rows are outputs, each column is an input. More...

Eigen::VectorXd	SobolSensitivity (unsigned int targetDim) const
	Compute the main sensitivity index for the input dimension, for each output dimension. More...

Eigen::VectorXd	SobolSensitivity (std::vector< unsigned int > const &targetDims) const

Eigen::MatrixXd	MainSensitivity () const

virtual void	ToHDF5 (muq::Utilities::H5Object &group) const override
	Write PCE to HDF5 file. More...

Public Member Functions inherited from muq::Approximation::BasisExpansion
	BasisExpansion (std::vector< std::shared_ptr< IndexedScalarBasis >> const &basisCompsIn, bool coeffInput=false)

	BasisExpansion (std::vector< std::shared_ptr< IndexedScalarBasis >> const &basisCompsIn, std::shared_ptr< muq::Utilities::MultiIndexSet > multisIn, bool coeffInput=false)

	BasisExpansion (std::vector< std::shared_ptr< IndexedScalarBasis >> const &basisCompsIn, std::shared_ptr< muq::Utilities::MultiIndexSet > multisIn, Eigen::MatrixXd const &coeffsIn, bool coeffInput=false)

virtual	~BasisExpansion ()=default

virtual unsigned	NumTerms () const

Eigen::MatrixXd	BuildVandermonde (Eigen::MatrixXd const &evalPts) const

Eigen::MatrixXd	BuildDerivMatrix (Eigen::MatrixXd const &evalPts, int wrtDim) const

Eigen::MatrixXd	SecondDerivative (unsigned outputDim, unsigned wrtDim1, unsigned wrtDim2, Eigen::VectorXd const &evalPt, Eigen::MatrixXd const &coeffs)

Eigen::MatrixXd	SecondDerivative (unsigned outputDim, unsigned wrtDim1, unsigned wrtDim2, Eigen::VectorXd const &evalPt)

Eigen::MatrixXd	GetCoeffs () const

void	SetCoeffs (Eigen::MatrixXd const &allCoeffs)

const std::shared_ptr< muq::Utilities::MultiIndexSet >	Multis () const

virtual void	ToHDF5 (std::string filename, std::string groupName="/") const
	Saves the expansion to group in an HDF5 file. More...

Public Member Functions inherited from muq::Modeling::ModPiece
	ModPiece (std::vector< int > const &inputSizes, std::vector< int > const &outputSizes)

	ModPiece (Eigen::VectorXi const &inputSizes, Eigen::VectorXi const &outputSizes)

virtual	~ModPiece ()=default

virtual double	GetRunTime (const std::string &method="Evaluate") const override
	Get the average run time for one of the implemented methods. More...

virtual void	ResetCallTime () override
	Resets the number of call and times. More...

virtual unsigned long int	GetNumCalls (const std::string &method="Evaluate") const override
	get the number of times one of the implemented methods has been called. More...

virtual std::vector< Eigen::VectorXd > const &	Evaluate (std::vector< Eigen::VectorXd > const &input)
	Evaluate the ModPiece. More...

virtual std::vector< Eigen::VectorXd > const &	Evaluate (ref_vector< Eigen::VectorXd > const &input)

	VARIADIC_TO_REFVECTOR (Evaluate, Eigen::VectorXd, std::vector< Eigen::VectorXd > const &)

virtual Eigen::VectorXd const &	Gradient (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)
	Compute the Gradient \(J^Tv\). More...

virtual Eigen::VectorXd const &	Gradient (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)

Eigen::VectorXd const &	Gradient (unsigned int outWrt, unsigned int inWrt, Eigen::VectorXd const &last, Eigen::VectorXd const &sens)

template<typename... Args>
Eigen::VectorXd const &	Gradient (unsigned int wrtOut, unsigned int wrtIn, Args const &... args)

Eigen::VectorXd const &	ApplyHessian (unsigned int outWrt, unsigned int inWrt1, unsigned int inWrt2, Eigen::VectorXd const &last, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

template<typename... Args>
Eigen::VectorXd const &	ApplyHessian (unsigned int wrtOut, unsigned int wrtIn1, unsigned int wrtIn2, Args const &... args)

virtual Eigen::MatrixXd const &	Jacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input)
	Compute the Jacobian of this ModPiece. More...

virtual Eigen::MatrixXd const &	Jacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input)

template<typename... Args>
Eigen::MatrixXd const &	Jacobian (unsigned int outWrt, unsigned int inWrt, Args const &... args)

template<typename... Args>
Eigen::MatrixXd	JacobianByFD (unsigned int outWrt, unsigned int inWrt, Args const &... args)

template<typename... Args>
Eigen::MatrixXd	ApplyJacobianByFD (unsigned int outWrt, unsigned int inWrt, Args const &... args)

virtual Eigen::VectorXd const &	ApplyJacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)
	Apply the Jacobian of this ModPiece to a vector. More...

virtual Eigen::VectorXd const &	ApplyJacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)

Eigen::VectorXd const &	ApplyJacobian (unsigned int outWrt, unsigned int inWrt, Eigen::VectorXd const &last, Eigen::VectorXd const &sens)

template<typename... Args>
Eigen::VectorXd const &	ApplyJacobian (unsigned int wrtOut, unsigned int wrtIn, Args const &... args)

virtual Eigen::VectorXd	GradientByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)

virtual Eigen::VectorXd	GradientByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)

virtual Eigen::MatrixXd	JacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input)

virtual Eigen::MatrixXd	JacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input)

virtual Eigen::VectorXd	ApplyJacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd	ApplyJacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd const &	ApplyHessian (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd const &	ApplyHessian (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd	ApplyHessianByFD (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd	ApplyHessianByFD (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

void	EnableCache ()

void	DisableCache ()

bool	CacheStatus () const

virtual void	SetWarnLevel (unsigned int newLevel)

Public Member Functions inherited from muq::Modeling::WorkPiece
	WorkPiece ()
	Create a muq::Modeling::WorkPiece with no fixed number of inputs and outputs and variable input/output types. More...

	WorkPiece (int const num, WorkPiece::Fix const fix=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece with either a fixed number of inputs or outputs and variable input/output types. More...

	WorkPiece (int const numIns, int const numOuts)
	Create a muq::Modeling::WorkPiece with a fixed number of inputs and outputs but variable input/output types. More...

	WorkPiece (std::vector< std::string > const &types, WorkPiece::Fix const fix=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece with either a fixed number of inputs with specified types or a fixed number of outputs with specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &types, WorkPiece::Fix const fix=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece where either some of the inputs have specified types or some of the outputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &types, int const num, WorkPiece::Fix const fixTypes=WorkPiece::Fix::Inputs, WorkPiece::Fix const fixNum=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece where either some of the inputs have specified types or some of the outputs have specified types and either the number of inputs or the number of outputs is fixed. More...

	WorkPiece (std::vector< std::string > const &types, int const num)
	Create a muq::Modeling::WorkPiece with a fixed number of inputs with specified types and a fixed number of outputs (of uknown type) More...

	WorkPiece (int const num, std::vector< std::string > const &types)
	Create a muq::Modeling::WorkPiece with a fixed number of outputs with specified types and a fixed number of inputs (of uknown type) More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const numIns, int const numOuts)
	Create a muq::Modeling::WorkPiece where some of the inputs are known and we know the input and output numbers. More...

	WorkPiece (int const numIns, std::map< unsigned int, std::string > const &outTypes, int const numOuts)
	Create a muq::Modeling::WorkPiece where some of the outputs are known and we know the input and output numbers. More...

	WorkPiece (std::vector< std::string > const &inTypes, std::vector< std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece with a fixed number of inputs and outputs with specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, std::vector< std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece where some of the inputs are known and all of the outputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const num, std::vector< std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece where some of the inputs are known with a known number of inputs and all of the outputs have specified types. More...

	WorkPiece (std::vector< std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece where some of the outputs and all of the inputs have specified types. More...

	WorkPiece (std::vector< std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes, int const num)
	Create a muq::Modeling::WorkPiece where some of the outputs with a known number of outputs and all of the inputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const numIn, std::map< unsigned int, std::string > const &outTypes)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types with a fixed number of inputs. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes, int const numOut)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types with a fixed number of outputs. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const numIn, std::map< unsigned int, std::string > const &outTypes, int const numOut)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types with a fixed number of inputs and outputs. More...

virtual	~WorkPiece ()
	Default destructor. More...

std::vector< boost::any > const &	Evaluate (std::vector< boost::any > const &ins)
	Evaluate this muq::Modeling::WorkPiece. More...

std::vector< boost::any > const &	Evaluate (ref_vector< boost::any > const &ins)
	Evaluate this muq::Modeling::WorkPiece using references to the inputs. More...

std::vector< boost::any > const &	Evaluate ()
	Evaluate this muq::Modeling::WorkPiece in the case that there are no inputs. More...

template<typename... Args>
std::vector< boost::any > const &	Evaluate (Args... args)
	Evalaute this muq::Modeling::WorkPiece using multiple arguments. More...

std::string const &	Name ()
	Get the (unique) name of this work piece. More...

void	SetName (std::string const &newName)
	Set the name of this work piece. More...

std::string	InputType (unsigned int inputNum, bool const demangle=true) const
	Get the input type (if we know it) for a specific input. More...

int	InputSize (unsigned int inputNum) const
	Get the length of a vector valued input with fixed size. More...

void	SetInputSize (unsigned int inputNum, int newSize)

std::string	OutputType (unsigned int outputNum, bool const demangle=true) const
	Get the output type (if we know it) for a specific output. More...

std::map< unsigned int, std::string >	OutputTypes () const
	Get the output types. More...

std::map< unsigned int, std::string >	InputTypes () const
	Get the input types. More...

unsigned int	ID () const
	Get the unique ID number. More...

Static Public Member Functions
static std::shared_ptr< PolynomialChaosExpansion >	ComputeWeightedSum (std::vector< std::shared_ptr< PolynomialChaosExpansion >> expansions, Eigen::VectorXd const &weights)

static std::shared_ptr< PolynomialChaosExpansion >	FromHDF5 (std::string filename, std::string groupName="/")
	Loads an expansion from an HDF5 file. More...

static std::shared_ptr< PolynomialChaosExpansion >	FromHDF5 (muq::Utilities::H5Object &group)
	Loads the expansion from an existing HDF5 group. More...

Static Public Member Functions inherited from muq::Approximation::BasisExpansion
static std::shared_ptr< BasisExpansion >	FromHDF5 (std::string filename, std::string groupName="/")
	Loads an expansion from an HDF5 file. More...

static std::shared_ptr< BasisExpansion >	FromHDF5 (muq::Utilities::H5Object &group)
	Loads the expansion from an existing HDF5 group. More...

Static Public Member Functions inherited from muq::Modeling::WorkPiece
static ref_vector< const boost::any >	ToRefVector (std::vector< boost::any > const &anyVec)
	Create vector of references from a vector of boost::any's. More...

static ref_vector< const Eigen::VectorXd >	ToRefVector (std::vector< Eigen::VectorXd > const &anyVec)

Friends
class	PCEFactory

Additional Inherited Members
Public Attributes inherited from muq::Modeling::ModPiece
const Eigen::VectorXi	inputSizes

const Eigen::VectorXi	outputSizes

Public Attributes inherited from muq::Modeling::WorkPiece
int	numInputs
	The number of inputs. More...

int	numOutputs
	The number of outputs. More...

Constructor & Destructor Documentation

◆ PolynomialChaosExpansion() [1/4]

PolynomialChaosExpansion::PolynomialChaosExpansion	(	std::shared_ptr< OrthogonalPolynomial > const &	basisCompsIn,
		std::shared_ptr< muq::Utilities::MultiIndexSet > const &	multisIn,
		Eigen::MatrixXd const &	coeffsIn
	)

Definition at line 13 of file PolynomialChaosExpansion.cpp.

◆ PolynomialChaosExpansion() [2/4]

PolynomialChaosExpansion::PolynomialChaosExpansion	(	std::shared_ptr< OrthogonalPolynomial > const &	basisCompsIn,
		std::shared_ptr< muq::Utilities::MultiIndexSet > const &	multisIn,
		unsigned int	outputDim
	)

Definition at line 20 of file PolynomialChaosExpansion.cpp.

◆ PolynomialChaosExpansion() [3/4]

PolynomialChaosExpansion::PolynomialChaosExpansion	(	std::vector< std::shared_ptr< IndexedScalarBasis >> const &	basisCompsIn,
		std::shared_ptr< muq::Utilities::MultiIndexSet > const &	multisIn,
		Eigen::MatrixXd const &	coeffsIn
	)

Definition at line 27 of file PolynomialChaosExpansion.cpp.

◆ PolynomialChaosExpansion() [4/4]

PolynomialChaosExpansion::PolynomialChaosExpansion	(	std::vector< std::shared_ptr< IndexedScalarBasis >> const &	basisCompsIn,
		std::shared_ptr< muq::Utilities::MultiIndexSet > const &	multisIn,
		unsigned int	outputDim
	)

Definition at line 33 of file PolynomialChaosExpansion.cpp.

◆ ~PolynomialChaosExpansion()

virtual muq::Approximation::PolynomialChaosExpansion::~PolynomialChaosExpansion ( )

virtualdefault

Member Function Documentation

◆ ComputeWeightedSum() [1/2]

std::shared_ptr< PolynomialChaosExpansion > PolynomialChaosExpansion::ComputeWeightedSum	(	std::vector< std::shared_ptr< PolynomialChaosExpansion >>	expansions,
		Eigen::VectorXd const &	weights
	)

static

Compute the weighted sum of polynomial expansions. Slow, because it assumes you haven't been tracking which polynomials to keep, so it does that, then calls the private method. If you know already, your class should be a friend and use the private method directly, as that will be faster.

Definition at line 162 of file PolynomialChaosExpansion.cpp.

Referenced by muq::Approximation::AdaptiveSmolyakPCE::AddEstimates().

◆ ComputeWeightedSum() [2/2]

std::shared_ptr< PolynomialChaosExpansion > PolynomialChaosExpansion::ComputeWeightedSum	(	std::vector< std::shared_ptr< PolynomialChaosExpansion >>	expansions,
		Eigen::VectorXd const &	weights,
		std::shared_ptr< muq::Utilities::MultiIndexSet > const &	polynomials,
		std::vector< std::vector< unsigned int >> const &	locToGlob
	)

staticprivate

An internal function to compute the weighted sum of polynomial expansions if you already know which polynomials are included, where polynomials is a clean copy not used by other expansions. Actually does the addition.

Definition at line 134 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::coeffs, and nlohmann::detail::dtoa_impl::k.

◆ Covariance()

Eigen::MatrixXd PolynomialChaosExpansion::Covariance ( ) const

Definition at line 84 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::basisComps, muq::Approximation::BasisExpansion::coeffs, GetNormalizationVec(), muq::Modeling::ModPiece::inputSizes, and muq::Modeling::ModPiece::outputSizes.

◆ FromHDF5() [1/2]

std::shared_ptr< PolynomialChaosExpansion > PolynomialChaosExpansion::FromHDF5 ( muq::Utilities::H5Object & group )

static

Loads the expansion from an existing HDF5 group.

This function will read the multiindices in an an HDF5 dataset and construct an instance of the MultiIndexSet class.

Parameters

[in] group An HDF5 group containing the "multiindices", "coefficients", and "basis_types" datasets.

See also: BasisExpansion::ToHDF5

Definition at line 298 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::FromHDF5(), and muq::Utilities::H5Object::Path().

◆ FromHDF5() [2/2]

std::shared_ptr< PolynomialChaosExpansion > PolynomialChaosExpansion::FromHDF5	(	std::string	filename,
		std::string	groupName = `"/"`
	)

static

Loads an expansion from an HDF5 file.

This function works in tandem with the BasisExpansion::ToHDF5 function. It will read the multiindices, coefficients, and scalar basis type from the HDF5 file and construct a BasisExpansion. See the BasisExpansion::ToHDF5 function for the details of these datasets.

Parameters

[in]	filename	A string to an HDF5 file. If the file doesn't exist or the correct datasets don't exist, an exception will be thrown.
[in]	dsetName	The path to the HDF5 group containing expansion datasets.

Returns: std::shared_ptr<BasisExpansion>

See also: BasisExpansion::ToHDF5

Definition at line 290 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::FromHDF5().

◆ GetNormalizationVec()

Eigen::VectorXd PolynomialChaosExpansion::GetNormalizationVec ( ) const

private

This function returns the sqrt of the normalization, sqrt(<p*p>), for each PCE basis function p. NB: This function does not change depending on the coefficients.

Definition at line 40 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::basisComps, nlohmann::detail::dtoa_impl::k, and muq::Approximation::BasisExpansion::multis.

Referenced by Covariance(), Magnitude(), SobolSensitivity(), TotalSensitivity(), and Variance().

◆ Magnitude()

Eigen::VectorXd PolynomialChaosExpansion::Magnitude ( ) const

Compute the L2 norm of each output.

Definition at line 124 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::coeffs, and GetNormalizationVec().

◆ MainSensitivity()

Eigen::MatrixXd PolynomialChaosExpansion::MainSensitivity ( ) const

Compute all the main sensitivities (e.g., one term Sobol sensitivity indices). Rows are outputs, each column is an input.

Definition at line 273 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::coeffs, muq::Modeling::ModPiece::inputSizes, and SobolSensitivity().

◆ Mean()

Eigen::VectorXd PolynomialChaosExpansion::Mean ( ) const

Definition at line 118 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::coeffs.

◆ SobolSensitivity() [1/2]

Eigen::VectorXd PolynomialChaosExpansion::SobolSensitivity ( std::vector< unsigned int > const & targetDims ) const

Computes the Sobol sensitivity for a group of input parameters.

Definition at line 240 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::basisComps, muq::Approximation::BasisExpansion::coeffs, GetNormalizationVec(), muq::Modeling::ModPiece::inputSizes, nlohmann::detail::dtoa_impl::k, muq::Approximation::BasisExpansion::multis, muq::Approximation::BasisExpansion::NumTerms(), and Variance().

◆ SobolSensitivity() [2/2]

Eigen::VectorXd PolynomialChaosExpansion::SobolSensitivity ( unsigned int targetDim ) const

Compute the main sensitivity index for the input dimension, for each output dimension.

Definition at line 235 of file PolynomialChaosExpansion.cpp.

Referenced by MainSensitivity().

◆ ToHDF5()

void PolynomialChaosExpansion::ToHDF5 ( muq::Utilities::H5Object & group ) const

overridevirtual

Write PCE to HDF5 file.

This is the same as BasisExpansion::ToHDF5, but adds additional attribute specifiying that this is a PCE.

Reimplemented from muq::Approximation::BasisExpansion.

Definition at line 284 of file PolynomialChaosExpansion.cpp.

References muq::Utilities::H5Object::attrs, and muq::Approximation::BasisExpansion::ToHDF5().

◆ TotalSensitivity() [1/2]

Eigen::MatrixXd PolynomialChaosExpansion::TotalSensitivity ( ) const

Compute all Sobol total sensitivities. Rows are outputs, each column is an input.

Definition at line 225 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::coeffs, and muq::Modeling::ModPiece::inputSizes.

◆ TotalSensitivity() [2/2]

Eigen::VectorXd PolynomialChaosExpansion::TotalSensitivity ( unsigned int targetDim ) const

Compute the Sobol total sensitivity index for the input dimension, for each output dimension.

Definition at line 204 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::basisComps, muq::Approximation::BasisExpansion::coeffs, GetNormalizationVec(), muq::Modeling::ModPiece::inputSizes, muq::Approximation::BasisExpansion::multis, and Variance().

◆ Variance()

Eigen::VectorXd PolynomialChaosExpansion::Variance ( ) const

compute the variance of the current expansion

Definition at line 60 of file PolynomialChaosExpansion.cpp.

References muq::Approximation::BasisExpansion::basisComps, muq::Approximation::BasisExpansion::coeffs, GetNormalizationVec(), and muq::Modeling::ModPiece::inputSizes.

Referenced by SobolSensitivity(), and TotalSensitivity().

Friends And Related Function Documentation

◆ PCEFactory

friend class PCEFactory

friend

Definition at line 29 of file PolynomialChaosExpansion.h.

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

doxygen_prep/MUQ/Approximation/PolynomialChaos/PolynomialChaosExpansion.h
doxygen_prep/modules/Approximation/src/PolynomialChaos/PolynomialChaosExpansion.cpp

Detailed Description

Public Member Functions

Static Public Member Functions

Friends

Additional Inherited Members

Constructor & Destructor Documentation

◆ PolynomialChaosExpansion() [1/4]

◆ PolynomialChaosExpansion() [2/4]

◆ PolynomialChaosExpansion() [3/4]

◆ PolynomialChaosExpansion() [4/4]

◆ ~PolynomialChaosExpansion()

Member Function Documentation

◆ ComputeWeightedSum() [1/2]

◆ ComputeWeightedSum() [2/2]

◆ Covariance()

◆ FromHDF5() [1/2]

◆ FromHDF5() [2/2]

◆ GetNormalizationVec()

◆ Magnitude()

◆ MainSensitivity()

◆ Mean()

◆ SobolSensitivity() [1/2]

◆ SobolSensitivity() [2/2]

◆ ToHDF5()

◆ TotalSensitivity() [1/2]

◆ TotalSensitivity() [2/2]

◆ Variance()

Friends And Related Function Documentation

◆ PCEFactory