Defines the class of Chebyshev polynomials. More...

#include <Basis.h>

Inheritance diagram for SSAGES::Chebyshev:

Public Member Functions
	Chebyshev (unsigned int polyOrd, double boundLow, double boundUp, unsigned int nbins)
	Constructor. More...

double	ChangeVariable (double x)
	Transforms variable from absolute value to [-1,1] between boundaries. More...

double	Evaluate (double x, int n)
	Calculates the output of the basis function. More...

double	EvalGrad (double x, int n)
	Calculates the gradient of the basis function. More...

double	Weight (double x)
	Calculates the weight of the basis function. More...

double	GetNorm (int)
	Gets the norm of the basis function. More...

Public Member Functions inherited from SSAGES::BasisFunction
	BasisFunction (unsigned int polyOrd, unsigned int nbins, bool isFinite, bool zeroOrder, double boundLow, double boundUp)
	Constructor. More...

unsigned int	GetOrder ()
	Gets the order of the current polynomial. More...

unsigned int	GetBins ()
	Gets the number of bins for the discretization. More...

bool	GetZeroOrder ()
	Gets the flag for constant-order polynomials. More...

double	GetLower ()
	Gets the lower bound on the CV. More...

double	GetUpper ()
	Gets the upper bound on the CV. More...

double	GetRange ()
	Gets the magnitude of the range of bounds. More...

virtual	~BasisFunction ()
	Destructor.

Static Public Member Functions
static Chebyshev *	Build (const Json::Value &json, const std::string &path, unsigned int nbins)
	Build BasisFunction from JSON value. More...

Static Public Member Functions inherited from SSAGES::BasisFunction
static BasisFunction *	Build (const Json::Value &json, const std::string &path, unsigned int nbins)
	Build BasisFunction from JSON value. More...

Additional Inherited Members
Protected Attributes inherited from SSAGES::BasisFunction
unsigned int	polyOrd_
	Order of the polynomial.

unsigned int	nbins_
	Number of bins.

bool	isFinite_
	Flag for finite-range polynomials.

bool	zeroOrder_
	Flag for constant-order polynomials.

double	boundLow_
	Lower bound on CV.

double	boundUp_
	Upper bound on CV.

Detailed Description

Defines the class of Chebyshev polynomials.

Definition at line 193 of file Basis.h.

Constructor & Destructor Documentation

◆ Chebyshev()

SSAGES::Chebyshev::Chebyshev	(	unsigned int	polyOrd,
		double	boundLow,
		double	boundUp,
		unsigned int	nbins
	)

inline

Constructor.

Parameters

polyOrd	Order of Chebyshev polynomial.
boundLow	Lower bounds of restraint springs.
boundUp	Upper bounds of restraint springs.
nbins	Number of bins.

Constructs an instance of the Chebyshev function class.

Definition at line 207 of file Basis.h.

                                                                                              :
         BasisFunction(polyOrd, nbins, true, false, boundLow, boundUp)
         {
         }

Referenced by Build().

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Member Function Documentation

◆ Build()

Chebyshev * SSAGES::Chebyshev::Build	(	const Json::Value &	json,
		const std::string &	path,
		unsigned int	nbins
	)

static

Build BasisFunction from JSON value.

Build the Chebyshev polynomial

Parameters

json	JSON value node.
path	Path for JSON path specification.
nbins	Number of bins.

Returns: Pointer to new BasisFunction.

Definition at line 22 of file Basis.cpp.

     {
         Json::ObjectRequirement validator;
         Json::Value schema;
         Json::CharReaderBuilder rbuilder;
         Json::CharReader* reader = rbuilder.newCharReader();
  
         reader->parse(JsonSchema::ChebyshevBasis.c_str(),
                       JsonSchema::ChebyshevBasis.c_str() + JsonSchema::ChebyshevBasis.size(),
                       &schema, nullptr);
         validator.Parse(schema, path);
  
         //Validate Inputs
         validator.Validate(json, path);
         if(validator.HasErrors())
             throw BuildException(validator.GetErrors());
  
         return new Chebyshev(
                 json["polynomial_order"].asInt(),
                 json["lower_bound"].asDouble(),
                 json["upper_bound"].asDouble(),
                 nbin
             );
     }

References Chebyshev(), Json::Requirement::GetErrors(), Json::Requirement::HasErrors(), Json::ObjectRequirement::Parse(), and Json::ObjectRequirement::Validate().

Referenced by SSAGES::BasisFunction::Build().

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◆ ChangeVariable()

double SSAGES::Chebyshev::ChangeVariable ( double x )

inline

Transforms variable from absolute value to [-1,1] between boundaries.

Parameters

x	Variable to transform.

Returns: Relative value between lower (-1) and upper (1) bounds on CV.

Definition at line 218 of file Basis.h.

         {
             return (x-boundLow_)*2.0/(boundUp_ - boundLow_)-1.0;
         }

References SSAGES::BasisFunction::boundLow_, and SSAGES::BasisFunction::boundUp_.

Referenced by EvalGrad(), Evaluate(), and Weight().

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◆ EvalGrad()

double SSAGES::Chebyshev::EvalGrad	(	double	,
		int
	)

inlinevirtual

Calculates the gradient of the basis function.

Parameters

val	Input value for function.
order	Order of the polynomial.

Returns: Gradient for function.

Reimplemented from SSAGES::BasisFunction.

Definition at line 231 of file Basis.h.

         {
             double xMod = ChangeVariable(x);
             return n == 0 ? 0.0 :
                     n == 1 ? 1.0 :
                     2.0*(Evaluate(x,n-1) + xMod * EvalGrad(x,n-1)) - EvalGrad(x,n-2);
         }

References ChangeVariable(), and Evaluate().

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◆ Evaluate()

double SSAGES::Chebyshev::Evaluate	(	double	,
		int
	)

inlinevirtual

Calculates the output of the basis function.

Parameters

val	Input value for function.
order	Order of the polynomial.

Returns: Output value for function.

Reimplemented from SSAGES::BasisFunction.

Definition at line 223 of file Basis.h.

         {
             double xMod = ChangeVariable(x);
             return n == 0 ? 1.0 : 
                     n == 1 ? xMod :
                     2.0*xMod*Evaluate(x,n-1) - Evaluate(x,n-2);
         }

References ChangeVariable().

Referenced by EvalGrad().

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◆ GetNorm()

double SSAGES::Chebyshev::GetNorm ( int )

inlinevirtual

Gets the norm of the basis function.

Parameters

order Order of the polynomial.

Returns: Norm of a specific order of polynomial.

Reimplemented from SSAGES::BasisFunction.

Definition at line 245 of file Basis.h.

         {
             return 2.0/M_PI;
         }

◆ Weight()

double SSAGES::Chebyshev::Weight ( double )

inlinevirtual

Calculates the weight of the basis function.

Parameters

val	Input value for function.

Returns: Weight of function.

Reimplemented from SSAGES::BasisFunction.

Definition at line 239 of file Basis.h.

         {
             double xMod = ChangeVariable(x);
             return 1.0/sqrt(1.0-xMod*xMod);
         }

References ChangeVariable().

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

/home/michael/development/SSAGES/src/Utility/Basis.h
/home/michael/development/SSAGES/src/Utility/Basis.cpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Chebyshev()

Member Function Documentation

◆ Build()

◆ ChangeVariable()

◆ EvalGrad()

◆ Evaluate()

◆ GetNorm()

◆ Weight()