nmrPolynomialBase Class Reference

#include <nmrPolynomialBase.h>

Inheritance diagram for nmrPolynomialBase:

Public Types
enum	InsertStatus { INSERT_FAIL = -1 , INSERT_NEW = 0 , INSERT_REPLACE = 1 }
typedef double	ValueType
typedef double	VariableType
typedef double	CoefficientType
typedef nmrPolynomialTermPowerIndex::VariableIndexType	VariableIndexType
typedef nmrPolynomialTermPowerIndex::PowerType	PowerType
typedef nmrPolynomialTermPowerIndex::MultinomialCoefficientType	TermCounterType

Public Member Functions
	nmrPolynomialBase (VariableIndexType numVariables, PowerType minDegree, PowerType maxDegree)
virtual	~nmrPolynomialBase ()
VariableIndexType	GetNumVariables () const
PowerType	GetMinDegree () const
PowerType	GetMaxDegree () const
virtual TermCounterType	GetNumberOfTerms () const =0
TermCounterType	GetMaxNumberOfTerms () const
virtual bool	IsEmpty () const =0
virtual void virtual SetMinDegree(PowerType newMin) CISST_THROW(std void virtual SetMaxDegree(PowerType newMax) CISST_THROW(std void	FillAllTerms ()=0
bool	CanIncludeIndex (const nmrPolynomialTermPowerIndex &term) const
virtual bool	IncludesIndex (const nmrPolynomialTermPowerIndex &target) const =0
virtual TermCounterType	GetIndexPosition (const nmrPolynomialTermPowerIndex &term) const =0
virtual void	RemoveTerm (const nmrPolynomialTermPowerIndex &where)=0
virtual void	Clear ()=0
virtual InsertStatus	SetCoefficient (const nmrPolynomialTermPowerIndex &where, CoefficientType coefficient)=0
virtual CoefficientType	GetCoefficient (const nmrPolynomialTermPowerIndex &CMN_UNUSED(where)) const
virtual void	CollectCoefficients (CoefficientType source[]) const =0
virtual void	RestoreCoefficients (const CoefficientType source[])=0
virtual ValueType	EvaluateBasis (const nmrPolynomialTermPowerIndex &where, const nmrMultiVariablePowerBasis &variables) const =0
virtual void	EvaluateBasisVector (const nmrMultiVariablePowerBasis &variables, ValueType termBaseValues[]) const =0
virtual ValueType	EvaluateForCoefficients (const nmrMultiVariablePowerBasis &variables, const CoefficientType coefficients[]) const =0
virtual ValueType	Evaluate (const nmrMultiVariablePowerBasis &variables) const =0
virtual void	Scale (CoefficientType scaleFactor)=0
void CISST_DEPRECATED	ScaleCoefficients (CoefficientType coefficients[], CoefficientType scaleFactor) const
virtual void	AddConstant (CoefficientType shiftAmount)=0
virtual void	AddConstantToCoefficients (CoefficientType coefficients[], CoefficientType shiftAmount) const =0
virtual void	SerializeRaw (std::ostream &output) const
virtual void	DeserializeRaw (std::istream &input)

Protected Attributes
VariableIndexType	NumVariables
PowerType	MinDegree
PowerType	MaxDegree

Member Typedef Documentation

CoefficientType

typedef double nmrPolynomialBase::CoefficientType

PowerType

typedef nmrPolynomialTermPowerIndex::PowerType nmrPolynomialBase::PowerType

TermCounterType

typedef nmrPolynomialTermPowerIndex::MultinomialCoefficientType nmrPolynomialBase::TermCounterType

ValueType

typedef double nmrPolynomialBase::ValueType

VariableIndexType

typedef nmrPolynomialTermPowerIndex::VariableIndexType nmrPolynomialBase::VariableIndexType

VariableType

typedef double nmrPolynomialBase::VariableType

Member Enumeration Documentation

InsertStatus

enum nmrPolynomialBase::InsertStatus

Enumerator
INSERT_FAIL
INSERT_NEW
INSERT_REPLACE

Constructor & Destructor Documentation

nmrPolynomialBase()

nmrPolynomialBase::nmrPolynomialBase	(	VariableIndexType	numVariables,
		PowerType	minDegree,
		PowerType	maxDegree )

~nmrPolynomialBase()

virtual nmrPolynomialBase::~nmrPolynomialBase ( )

inlinevirtual

Member Function Documentation

AddConstant()

virtual void nmrPolynomialBase::AddConstant ( CoefficientType shiftAmount )

pure virtual

Add a constant value to this polynomial. That is, if p is a polynomial and s is a constant then the following returns true: ValueType v0 = p.Evaluate(); p.AddConstant(s); ValueType v1 = p.Evaluate(); v1 - v0 == s // up to floating point precision error

Note

the implementation varies between different representations of the polynomial. Specifically, terms may be added to this polynomial to support the addition of the constant.

Implemented in nmrPolynomialContainer< _TermInfo >, nmrPolynomialContainer< void * >, and nmrStandardPolynomial.

AddConstantToCoefficients()

virtual void nmrPolynomialBase::AddConstantToCoefficients ( CoefficientType coefficients[], CoefficientType shiftAmount ) const

pure virtual

Modify external coefficients so that they evaluate a new polynomial shifted by a constant amount. That is, if p is a polynomial, c is an array of external coefficients, and s is a constant, the following returns true: ValueType v0 = p.EvaluateForCoefficients(c); p.AddConstantToCoefficients(c, s); ValueType v1 = p.EvaluateForCoefficients(c); v1 - v0 == s; // up to floating point precision error

Note

The implementation of this function may vary based on the representation of the polynomial. In particular, for a Bernstein polynomial it requires that all possible terms be present in the polynomial and in the coefficients correspondingly. For a standard polynomial, it requires that this polynomial actually contains a term of power zero.

The current implementations assert that this polynomial and the external coefficients meet the preconditions for the operation. That is, we do not throw an exception but rather issue an assertion error.

Implemented in nmrPolynomialContainer< _TermInfo >, nmrPolynomialContainer< void * >, and nmrStandardPolynomial.

CanIncludeIndex()

bool nmrPolynomialBase::CanIncludeIndex

(

const nmrPolynomialTermPowerIndex &

term

)

const

Clear()

virtual void nmrPolynomialBase::Clear ( )

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, nmrPolynomialContainer< void * >, and nmrStandardPolynomial.

CollectCoefficients()

virtual void nmrPolynomialBase::CollectCoefficients ( CoefficientType source[] ) const

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

DeserializeRaw()

virtual void nmrPolynomialBase::DeserializeRaw ( std::istream & input )

virtual

Deserialize NumVariables, MinDegree, MaxDegree

Reimplemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

Evaluate()

virtual ValueType nmrPolynomialBase::Evaluate ( const nmrMultiVariablePowerBasis & variables ) const

pure virtual

Evaluate the polynomial for externally given variables

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

EvaluateBasis()

virtual ValueType nmrPolynomialBase::EvaluateBasis ( const nmrPolynomialTermPowerIndex & where, const nmrMultiVariablePowerBasis & variables ) const

pure virtual

Evaluate the basis function for a term. The term is regarded as a list of powers, without any user defined coefficient. However, for different families of polynomial the set of basis functions are different. For example, Bezier polynomials have the multinomial coefficient in addition to each user defined coefficient. Implemented for each concrete polynomial class.

Implemented in nmrStandardPolynomial.

EvaluateBasisVector()

virtual void nmrPolynomialBase::EvaluateBasisVector ( const nmrMultiVariablePowerBasis & variables, ValueType termBaseValues[] ) const

pure virtual

Evaluate a single term at the point specified by the `variables' argument, including the basis function and the term's coefficient. This function uses the internally stored coefficient. */ ValueType EvaluateTerm(const nmrPolynomialTermPowerIndex & where, const nmrMultiVariablePowerBasis & variables) const { CoefficientType coefficient = GetCoefficient(where); return EvaluateTerm(where, variables, coefficient); }

/*! Evaluate a single term at the point specified by the `variables' argument, including the basis function and the term's coefficient. This function takes the coefficient as a parameter. */ ValueType EvaluateTerm(const nmrPolynomialTermPowerIndex & where, const nmrMultiVariablePowerBasis & variables, CoefficientType coefficient) const { if (coefficient == 0) return 0; return coefficient * EvaluateBasis(where, variables); }

/*! Evaluate the basis vector for extrnally given variables. Evaluate the basis function for each terms in the polynomial, and store the results into an array of termBaseValues.

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

EvaluateForCoefficients()

virtual ValueType nmrPolynomialBase::EvaluateForCoefficients ( const nmrMultiVariablePowerBasis & variables, const CoefficientType coefficients[] ) const

pure virtual

Evaluate the polynomial at the currently specified point, using externally defined coefficients. This lets the user create many polynomials over the same set of basis functions without having to duplicate the terms. The input coefficients must be ordered the same way as the terms in this object. It is best to order them using CollectCoefficients()

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

FillAllTerms()

virtual void virtual SetMinDegree(PowerType newMin) CISST_THROW(std void virtual SetMaxDegree(PowerType newMax) CISST_THROW(std void nmrPolynomialBase::FillAllTerms ( )

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

GetCoefficient()

virtual CoefficientType nmrPolynomialBase::GetCoefficient ( const nmrPolynomialTermPowerIndex & CMN_UNUSEDwhere ) const

inlinevirtual

GetIndexPosition()

virtual TermCounterType nmrPolynomialBase::GetIndexPosition ( const nmrPolynomialTermPowerIndex & term ) const

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

GetMaxDegree()

PowerType nmrPolynomialBase::GetMaxDegree ( ) const

inline

GetMaxNumberOfTerms()

TermCounterType nmrPolynomialBase::GetMaxNumberOfTerms ( ) const

inline

GetMinDegree()

PowerType nmrPolynomialBase::GetMinDegree ( ) const

inline

GetNumberOfTerms()

virtual TermCounterType nmrPolynomialBase::GetNumberOfTerms ( ) const

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

GetNumVariables()

VariableIndexType nmrPolynomialBase::GetNumVariables ( ) const

inline

IncludesIndex()

virtual bool nmrPolynomialBase::IncludesIndex ( const nmrPolynomialTermPowerIndex & target ) const

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

IsEmpty()

virtual bool nmrPolynomialBase::IsEmpty ( ) const

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

RemoveTerm()

virtual void nmrPolynomialBase::RemoveTerm ( const nmrPolynomialTermPowerIndex & where )

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

RestoreCoefficients()

virtual void nmrPolynomialBase::RestoreCoefficients ( const CoefficientType source[] )

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

Scale()

virtual void nmrPolynomialBase::Scale ( CoefficientType scaleFactor )

pure virtual

Scale the polynomial by a given scalar value. Basically, it means multiplying all the term coefficient by the scale factor.

Implemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

ScaleCoefficients()

void CISST_DEPRECATED nmrPolynomialBase::ScaleCoefficients	(	CoefficientType	coefficients[],
		CoefficientType	scaleFactor ) const

Scale a given set of external coefficients which correspond to the terms of this polynomial. Basically, it means multiplying them all by the scale factor.

Parameters

coefficients	[i/o] the external coefficients to be scales (in place).
scaleFactor	the scaling factor.

Note

this function is not declared virtual, as it seems to behave uniformly for all types of polynomial representations we use. But it may have to be declared virtual eventually. Technically, it could be declared static, but I find it too far fetched.

The same rules that apply to evaluating the polynomial for external coefficients apply here as well.

the function is declared as deprecated. Generally, using the Multiply operation on cisstVector containers of coefficients should be prefered.

SerializeRaw()

virtual void nmrPolynomialBase::SerializeRaw ( std::ostream & output ) const

virtual

Serialize NumVariables, MinDegree, MaxDegree

Reimplemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

SetCoefficient()

virtual InsertStatus nmrPolynomialBase::SetCoefficient ( const nmrPolynomialTermPowerIndex & where, CoefficientType coefficient )

pure virtual

Implemented in nmrPolynomialContainer< _TermInfo >, nmrPolynomialContainer< void * >, and nmrStandardPolynomial.

Member Data Documentation

MaxDegree

PowerType nmrPolynomialBase::MaxDegree

protected

MinDegree

PowerType nmrPolynomialBase::MinDegree

protected

NumVariables

VariableIndexType nmrPolynomialBase::NumVariables

protected

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

• tmp/cisst-saw/cisst/cisstNumerical/nmrPolynomialBase.h