Contains all basis type specific definitions and operations needed to generate a PCSet. More...

#include <PCBasis.h>

Public Member Functions
	PCBasis (const string type="LU", const double alpha=0.0, const double betta=1.0, const int maxord=10)
	Constructor: initializes the univariate basis type and order.

	~PCBasis ()
	Destructor.

void	Init1dQuadPoints (int qdpts)
	Initialize the quadrature points and weights and store the information in arrays quadPoints_, quadWeights_,quadIndices_.

void	Eval1dBasisAtQuadPoints ()
	Evaluate polynomial 1d basis functions at quadrature points and store in the private variable psi1d_.

void	Eval1dBasisAtCustPoints (Array2D< double > &psi, int kord, const Array1D< double > &custPoints)
	Evaluate polynomial 1d basis functions up to the order kord at custom points given by an array custPoints Returns the evaluations in the first argument psi, where the number of rows are the number of points, and columns correspond to successive orders.

double	EvalBasis (const double &xi, Array1D< double > &basisEvals) const
	Evaluate 1d basis functions for the given value of random variable xi. Return the value of the basis functions for all orders in the passed Array1D array (indexed by their order), also returns the highest-order value.

double	EvalBasis (const double &xi, const int kord, double *basisEvals) const
	Evaluate 1d basis functions for the given value of random variable xi. Return the value of the basis functions for all orders in the passed double * array (indexed by their order), also returns the highest-order value.

void	Eval1dNormSq_Exact (int kord)
	Evaluate the norms (squared) of the basis functions exactly and stores in the private array psi1dSqExact_.

void	EvalDerivBasis (const double &xi, Array1D< double > &basisDEvals)
	Evaluate derivative of 1d non-normalized Legendre basis.

void	Eval1dDerivBasisAtCustPoints (Array2D< double > &dpsi, int kord, const Array1D< double > &custPoints)

void	Eval2ndDerivBasis (const double &xi, Array1D< double > &ddP)

void	Eval2ndDerivCustPoints (Array2D< double > &psi, int kord, Array1D< double > &custPoints)

void	Get1dNormsSq (Array1D< double > &psi1dSq) const
	Get the norms-squared of the basis functions. Returns the values for each basis function in the passed Array1D array.

void	Get1dNormsSqExact (Array1D< double > &psi1dSqExact) const
	Get the analytic norms-squared of the basis functions. Returns the values for each basis function in the passed Array1D array.

void	GetRandSample (Array1D< double > &randSamples)
	Get samples of the random variables associated with the current PC basis functions and return them in the 1D array randSamples. Take as many samples as the length of the array randSamples.

void	GetRandSample (double *randSamples, const int &nSamp)
	Get nSamp samples of the random variables associated with the current PC basis functions and return them in the double* randSamples.

int	GetSeed () const
	Get the random number generator seed.

void	SeedRandNumGen (const int &seed)
	Function to (re)seed the random number generator used to sample the Basis functions.

void	GetQuadRule (Array2D< double > &qPoints, Array1D< double > &qWeights, Array2D< int > &qIndices)
	Get the quadrature integration information.

void	GetQuadPoints (Array2D< double > &quadPoints) const
	Get the quadrature points in the passed Array2D array.

void	GetQuadWeights (Array1D< double > &quadWeights) const
	Get the quadrature weights in the passed Array1D array.

void	GetQuadIndices (Array2D< int > &quadIndices) const
	Get the quadrature points' indices in the passed Array1D array.

void	GetBasisAtQuadPoints (Array2D< double > &psi1d) const
	Get the basis values at quadrature points in the passed Array2D array.

string	GetPCType () const
	Get the PC type.

double	GetAlpha () const
	Get the value of the parameter alpha.

double	GetBeta () const
	Get the value of the parameter beta.

Private Member Functions
	PCBasis (const PCBasis &obj)
	Dummy default constructor, which should not be used as it is not well defined Therefore we make it private so it is not accessible.

void	Eval1dNormSq (int kord)
	Evaluate the norms (squared) of the basis functions and stores in the private array psi1dSq_.

double	NormSq_Exact (int kord)
	Evaluate 1d norm of order kord exactly.

Private Attributes
string	type_
	String indicator of type of basis functions used.

Array2D< double >	quadPoints_
	Array to store quadrature points.

Array1D< double >	quadWeights_
	Array to store quadrature weights.

Array2D< int >	quadIndices_
	Array to store quadrature point indexing; useful only for nested rules.

Array2D< double >	psi1d_
	Array to store basis functions evaluated at quadrature points for each order: psi1d_(iqp,iord) contains the value of the polynomial chaos basis of order iord at the location of quadrature point iqp.

Array1D< double >	psi1dSq_
	Array with the norms squared of the 1D basis functions for each order.

Array1D< double >	psi1dSqExact_
	Array with the exact norms squared of the 1D basis functions for each order.

int	maxord_
	Maximal order of any dimension.

int	narg_
	Number of parameters to specify the basis.

double	alpha_
	Parameter alpha for PCs that require a parameter (LG,SW,JB)

double	beta_
	Parameter beta for PCs that require two parameters (SW,JB)

dsfmt_t	rnstate_
	Random sequence state for dsfmt.

int	rSeed_
	The seed used for the random number generators that sample the xi's in the basis functions.

Detailed Description

Contains all basis type specific definitions and operations needed to generate a PCSet.

Constructor & Destructor Documentation

◆ PCBasis() [1/2]

PCBasis::PCBasis	(	const string	type = "LU",
		const double	alpha = 0.0,
		const double	betta = 1.0,
		const int	maxord = 10 )

Constructor: initializes the univariate basis type and order.

Currently, the only valid types are Hermite-Gaussian, denoted with "HG", Legendre-Uniform, denoted with "LU", or Laguerre-Gamma, denoted with "LG". (Where the shape parameter for the Gamma distribution is alpha + 1 = 2)

Todo: At some point, the basis selection should probably be implemented in a more elegant way using base and inherited classes. For the time being, Hermite-Gaussian or Legendre-Uniform will probably be the most commonly used cases. The parameters alpha and betta are relevant only for LG, SW and JB chaoses

Note: Maxord specifies the maximal order up to which the computations are performed

◆ ~PCBasis()

PCBasis::~PCBasis ( )

inline

Destructor.

◆ PCBasis() [2/2]

PCBasis::PCBasis ( const PCBasis & obj )

inlineprivate

Dummy default constructor, which should not be used as it is not well defined Therefore we make it private so it is not accessible.

Note: All parameters are intialized to dummy values.

Dummy copy constructor, which should not be used as it is currently not well defined. Therefore we make it private so it is not accessible.

Note: I am not sure actually whether the initialization performed below is legal as it requires access to private data members of the class that is passed in.

Member Function Documentation

◆ Eval1dBasisAtCustPoints()

void PCBasis::Eval1dBasisAtCustPoints	(	Array2D< double > &	psi,
		int	kord,
		const Array1D< double > &	custPoints )

Evaluate polynomial 1d basis functions up to the order kord at custom points given by an array custPoints Returns the evaluations in the first argument psi, where the number of rows are the number of points, and columns correspond to successive orders.

◆ Eval1dBasisAtQuadPoints()

void PCBasis::Eval1dBasisAtQuadPoints ( )

Evaluate polynomial 1d basis functions at quadrature points and store in the private variable psi1d_.

◆ Eval1dDerivBasisAtCustPoints()

void PCBasis::Eval1dDerivBasisAtCustPoints	(	Array2D< double > &	dpsi,
		int	kord,
		const Array1D< double > &	custPoints )

◆ Eval1dNormSq()

void PCBasis::Eval1dNormSq ( int kord )

private

Evaluate the norms (squared) of the basis functions and stores in the private array psi1dSq_.

◆ Eval1dNormSq_Exact()

void PCBasis::Eval1dNormSq_Exact ( int kord )

Evaluate the norms (squared) of the basis functions exactly and stores in the private array psi1dSqExact_.

◆ Eval2ndDerivBasis()

void PCBasis::Eval2ndDerivBasis	(	const double &	xi,
		Array1D< double > &	ddP )

◆ Eval2ndDerivCustPoints()

void PCBasis::Eval2ndDerivCustPoints	(	Array2D< double > &	psi,
		int	kord,
		Array1D< double > &	custPoints )

◆ EvalBasis() [1/2]

double PCBasis::EvalBasis	(	const double &	xi,
		Array1D< double > &	basisEvals ) const

Evaluate 1d basis functions for the given value of random variable xi. Return the value of the basis functions for all orders in the passed Array1D array (indexed by their order), also returns the highest-order value.

Note: For custom 'pdf' option, a file containing the polynomial recursion coefficients, called 'ab.dat', is required.

Todo: Import the recursion coefficients in a more friendly fashion.

◆ EvalBasis() [2/2]

double PCBasis::EvalBasis	(	const double &	xi,
		const int	kord,
		double *	basisEvals ) const

Evaluate 1d basis functions for the given value of random variable xi. Return the value of the basis functions for all orders in the passed double * array (indexed by their order), also returns the highest-order value.

◆ EvalDerivBasis()

void PCBasis::EvalDerivBasis	(	const double &	xi,
		Array1D< double > &	basisDEvals )

Evaluate derivative of 1d non-normalized Legendre basis.

◆ Get1dNormsSq()

void PCBasis::Get1dNormsSq ( Array1D< double > & psi1dSq ) const

inline

Get the norms-squared of the basis functions. Returns the values for each basis function in the passed Array1D array.

◆ Get1dNormsSqExact()

void PCBasis::Get1dNormsSqExact ( Array1D< double > & psi1dSqExact ) const

inline

Get the analytic norms-squared of the basis functions. Returns the values for each basis function in the passed Array1D array.

◆ GetAlpha()

double PCBasis::GetAlpha ( ) const

inline

Get the value of the parameter alpha.

◆ GetBasisAtQuadPoints()

void PCBasis::GetBasisAtQuadPoints ( Array2D< double > & psi1d ) const

inline

Get the basis values at quadrature points in the passed Array2D array.

◆ GetBeta()

double PCBasis::GetBeta ( ) const

inline

Get the value of the parameter beta.

◆ GetPCType()

string PCBasis::GetPCType ( ) const

inline

Get the PC type.

◆ GetQuadIndices()

void PCBasis::GetQuadIndices ( Array2D< int > & quadIndices ) const

inline

Get the quadrature points' indices in the passed Array1D array.

◆ GetQuadPoints()

void PCBasis::GetQuadPoints ( Array2D< double > & quadPoints ) const

inline

Get the quadrature points in the passed Array2D array.

Note: Although quadPoints is a 2D array, its second dimension is equal to 1

◆ GetQuadRule()

void PCBasis::GetQuadRule	(	Array2D< double > &	qPoints,
		Array1D< double > &	qWeights,
		Array2D< int > &	qIndices )

Get the quadrature integration information.

◆ GetQuadWeights()

void PCBasis::GetQuadWeights ( Array1D< double > & quadWeights ) const

inline

Get the quadrature weights in the passed Array1D array.

◆ GetRandSample() [1/2]

void PCBasis::GetRandSample ( Array1D< double > & randSamples )

Get samples of the random variables associated with the current PC basis functions and return them in the 1D array randSamples. Take as many samples as the length of the array randSamples.

Note: This function does NOT reset the random number seed before sampling

◆ GetRandSample() [2/2]

void PCBasis::GetRandSample	(	double *	randSamples,
		const int &	nSamp )

Get nSamp samples of the random variables associated with the current PC basis functions and return them in the double* randSamples.

Note: This function does NOT reset the random number seed before sampling

◆ GetSeed()

int PCBasis::GetSeed ( ) const

inline

Get the random number generator seed.

◆ Init1dQuadPoints()

void PCBasis::Init1dQuadPoints ( int qdpts )

Initialize the quadrature points and weights and store the information in arrays quadPoints_, quadWeights_,quadIndices_.

Note: Uses an arbitrary number of quad. points.; The default implementation relies on N_q=2*p+1 quadrature points, where p is the maximal order and N_q is the number of quadrature points

Todo: Come up with a smarter way to pick the number of quadrature points

Note: Quadrature points are set according to the basis function type; quadPoints is a 2D array but its second dimension is equal to 1.

◆ NormSq_Exact()

double PCBasis::NormSq_Exact ( int kord )

private

Evaluate 1d norm of order kord exactly.

◆ SeedRandNumGen()

void PCBasis::SeedRandNumGen ( const int & seed )

Function to (re)seed the random number generator used to sample the Basis functions.

Member Data Documentation

◆ alpha_

double PCBasis::alpha_

private

Parameter alpha for PCs that require a parameter (LG,SW,JB)

◆ beta_

double PCBasis::beta_

private

Parameter beta for PCs that require two parameters (SW,JB)

◆ maxord_

int PCBasis::maxord_

private

Maximal order of any dimension.

◆ narg_

int PCBasis::narg_

private

Number of parameters to specify the basis.

◆ psi1d_

Array2D<double> PCBasis::psi1d_

private

Array to store basis functions evaluated at quadrature points for each order: psi1d_(iqp,iord) contains the value of the polynomial chaos basis of order iord at the location of quadrature point iqp.

◆ psi1dSq_

Array1D<double> PCBasis::psi1dSq_

private

Array with the norms squared of the 1D basis functions for each order.

◆ psi1dSqExact_

Array1D<double> PCBasis::psi1dSqExact_

private

Array with the exact norms squared of the 1D basis functions for each order.

◆ quadIndices_

Array2D<int> PCBasis::quadIndices_

private

Array to store quadrature point indexing; useful only for nested rules.

◆ quadPoints_

Array2D<double> PCBasis::quadPoints_

private

Array to store quadrature points.

◆ quadWeights_

Array1D<double> PCBasis::quadWeights_

private

Array to store quadrature weights.

◆ rnstate_

dsfmt_t PCBasis::rnstate_

private

Random sequence state for dsfmt.

Todo: need more functionalities to get/set this variable from user

◆ rSeed_

int PCBasis::rSeed_

private

The seed used for the random number generators that sample the xi's in the basis functions.

This seed is set to 1 during the class construction and can be reset with the SeedRandNumGen function

See also: SeedRandNumGen

◆ type_

string PCBasis::type_

private

String indicator of type of basis functions used.

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

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PCBasis() [1/2]

◆ ~PCBasis()

◆ PCBasis() [2/2]

Member Function Documentation

◆ Eval1dBasisAtCustPoints()

◆ Eval1dBasisAtQuadPoints()

◆ Eval1dDerivBasisAtCustPoints()

◆ Eval1dNormSq()

◆ Eval1dNormSq_Exact()

◆ Eval2ndDerivBasis()

◆ Eval2ndDerivCustPoints()

◆ EvalBasis() [1/2]

◆ EvalBasis() [2/2]

◆ EvalDerivBasis()

◆ Get1dNormsSq()

◆ Get1dNormsSqExact()

◆ GetAlpha()

◆ GetBasisAtQuadPoints()

◆ GetBeta()

◆ GetPCType()

◆ GetQuadIndices()

◆ GetQuadPoints()

◆ GetQuadRule()

◆ GetQuadWeights()

◆ GetRandSample() [1/2]

◆ GetRandSample() [2/2]

◆ GetSeed()

◆ Init1dQuadPoints()

◆ NormSq_Exact()

◆ SeedRandNumGen()

Member Data Documentation

◆ alpha_

◆ beta_

◆ maxord_

◆ narg_

◆ psi1d_

◆ psi1dSq_

◆ psi1dSqExact_

◆ quadIndices_

◆ quadPoints_

◆ quadWeights_

◆ rnstate_

◆ rSeed_

◆ type_