Holds a polynominal as a primary type. More...

#include <PolyBase.h>

Public Member Functions
std::vector< std::complex< double > >	calcRoots (double const =-1.0)
	Calculate all the roots of the polynominal. More...

void	compress (double const)
	Two part process remove coefficients of zero or near zero: Reduce degree by eliminating all (nearly) zero leading coefficients and by making the leading coefficient one. More...

PolyBase &	derivative ()
	Take derivative of this polynomial. More...

void	divide (const PolyBase &, PolyBase &, PolyBase &, double const =-1.0) const
	Carry out polynomial division of this / pD (Euclidean algorithm) If 'this' is P(t) and the divisor is D(t) with degree(P) >= degree(D), then P(t) = Q(t)*D(t)+R(t) where Q(t) is the quotient with degree(Q) = degree(P) - degree(D) and R(t) is the remainder with degree(R) < degree(D). More...

int	getDegree () const
	Accessor to degree size. More...

PolyBase	getDerivative () const
	Take derivative. More...

PolyBase	GetInversion () const
	Inversion of the coefficients. More...

	operator const std::vector< double > & () const
	Accessor to a vector component. More...

	operator std::vector< double > & ()
	Accessor to a vector component. More...

double	operator() (double const) const
	Calculate polynomial at x. More...

PolyBase	operator* (const PolyBase &) const
	PolyBase multiplication. More...

PolyBase	operator* (double const) const
	PolyBase multiplication. More...

PolyBase &	operator*= (const PolyBase &)
	Self multiplication value. More...

PolyBase &	operator*= (double const)
	PolyBase multiplication. More...

PolyBase	operator+ (const PolyBase &) const
	PolyBase addition. More...

PolyBase	operator+ (double const) const
	PolyBase addition. More...

PolyBase &	operator+= (const PolyBase &)
	Self addition value. More...

PolyBase &	operator+= (double const)
	PolyBase addition. More...

PolyBase	operator- () const
	PolyBase negation operator. More...

PolyBase	operator- (const PolyBase &) const
	PolyBase subtraction. More...

PolyBase	operator- (double const) const
	PolyBase substractr. More...

PolyBase &	operator-= (const PolyBase &)
	Self addition value. More...

PolyBase &	operator-= (double const)
	PolyBase subtraction. More...

PolyBase	operator/ (double const) const
	PolyBase division. More...

PolyBase &	operator/= (double const)
	PolyBase division scalar. More...

double &	operator[] (int const)
	Accessor to component. More...

double	operator[] (int const) const
	Accessor to component. More...

	PolyBase (int const)
	Constructor. More...

	PolyBase (int const, double const)
	Constructor. More...

std::vector< double >	realRoots (double const =-1.0)
	Get just the real roots. More...

void	setDegree (int const)
	Set the degree value. More...

void	write (std::ostream &) const
	Basic write command. More...

Private Member Functions
int	solveCubic (std::complex< double > &, std::complex< double > &, std::complex< double > &) const
	Solves Cubic equation Compress MUST have been called. More...

int	solveQuadratic (std::complex< double > &, std::complex< double > &) const
	Solves Complex Quadratic component. More...

Private Attributes
std::vector< double >	afCoeff
	Coefficients. More...

double	Eaccuracy
	Polynomic accuracy. More...

int	iDegree
	Degree of polynomial [0 == constant]. More...

Detailed Description

Holds a polynominal as a primary type.

Version: 1.0

Author: S. Ansell and D. Eberly

Date: December 2007

This holds a single variable poynomial of primary positive type. Assumes Euclidean division, hence a remainders. Internal solution of the polynomial is possible. Conversion to other forms is not internally handled.

Todo:

Add conversion to a continued fraction.

ADD solveQuartic

Definition at line 31 of file PolyBase.h.

Constructor & Destructor Documentation

◆ PolyBase() [1/2]

Mantid::mathLevel::PolyBase::PolyBase ( int const iD )

explicit

Constructor.

Parameters

iD :: degree

Definition at line 32 of file PolyBase.cpp.

◆ PolyBase() [2/2]

Mantid::mathLevel::PolyBase::PolyBase	(	int const	iD,
		double const	E
	)

Constructor.

Parameters

iD	:: degree
E	:: Accuracy

Definition at line 40 of file PolyBase.cpp.

Member Function Documentation

◆ calcRoots()

std::vector< std::complex< double > > Mantid::mathLevel::PolyBase::calcRoots ( double const epsilon = -1.0 )

Calculate all the roots of the polynominal.

Uses the GSL which uses a Hessian reduction of the characteristic compainion matrix.

\[ A= \left( -a_{m-1}/a_m -a_{m-2}/a_m ... -a_0/a_m \right) \]

where the matrix component below A is the Indenty. However, GSL requires that the input coefficient is a_m == 1, hence the call to this->compress().

Parameters

epsilon :: tolerance factor (-ve to use default)

Returns: roots (not sorted/uniqued)

Definition at line 430 of file PolyBase.cpp.

References afCoeff, compress(), iDegree, solveCubic(), and solveQuadratic().

Referenced by realRoots().

◆ compress()

void Mantid::mathLevel::PolyBase::compress ( double const epsilon )

Two part process remove coefficients of zero or near zero: Reduce degree by eliminating all (nearly) zero leading coefficients and by making the leading coefficient one.

Parameters

epsilon :: coeficient to use to decide if a values is zero

Definition at line 347 of file PolyBase.cpp.

References afCoeff, Eaccuracy, fabs, and iDegree.

Referenced by calcRoots().

◆ derivative()

PolyBase & Mantid::mathLevel::PolyBase::derivative ( )

Take derivative of this polynomial.

Returns: dP / dx

Definition at line 317 of file PolyBase.cpp.

References afCoeff, and iDegree.

Referenced by getDerivative().

◆ divide()

void Mantid::mathLevel::PolyBase::divide	(	const PolyBase &	pD,
		PolyBase &	pQ,
		PolyBase &	pR,
		double const	epsilon = `-1.0`
	)		const

Carry out polynomial division of this / pD (Euclidean algorithm) If 'this' is P(t) and the divisor is D(t) with degree(P) >= degree(D), then P(t) = Q(t)*D(t)+R(t) where Q(t) is the quotient with degree(Q) = degree(P) - degree(D) and R(t) is the remainder with degree(R) < degree(D).

If this routine is called with degree(P) < degree(D), then Q = 0 and R = P are returned. The value of epsilon is used as a threshold on the coefficients of the remainder polynomial. If smaller, the coefficient is assumed to be zero.

Parameters

pD	:: Polynominal to divide
pQ	:: Quotant
pR	:: Remainder
epsilon	:: Tolerance [-ve to use master tolerance]

Definition at line 370 of file PolyBase.cpp.

◆ getDegree()

int Mantid::mathLevel::PolyBase::getDegree ( ) const

Accessor to degree size.

Returns: size

Definition at line 59 of file PolyBase.cpp.

References iDegree.

◆ getDerivative()

PolyBase Mantid::mathLevel::PolyBase::getDerivative ( ) const

Take derivative.

Returns: dP / dx

Definition at line 307 of file PolyBase.cpp.

References derivative().

◆ GetInversion()

PolyBase Mantid::mathLevel::PolyBase::GetInversion ( ) const

Inversion of the coefficients.

Returns: (Poly)^-1

Definition at line 335 of file PolyBase.cpp.

References afCoeff, and iDegree.

◆ operator const std::vector< double > &()

Mantid::mathLevel::PolyBase::operator const std::vector< double > & ( ) const

Accessor to a vector component.

Returns: vector

Definition at line 68 of file PolyBase.cpp.

◆ operator std::vector< double > &()

Mantid::mathLevel::PolyBase::operator std::vector< double > & ( )

Accessor to a vector component.

Returns: vector

Definition at line 77 of file PolyBase.cpp.

◆ operator()()

double Mantid::mathLevel::PolyBase::operator() ( double const X ) const

Calculate polynomial at x.

Parameters

X	:: Value to calculate poly

Returns: polyvalue(x)

Definition at line 110 of file PolyBase.cpp.

References Mantid::Geometry::X.

◆ operator*() [1/2]

PolyBase Mantid::mathLevel::PolyBase::operator* ( const PolyBase & A ) const

PolyBase multiplication.

Parameters

A	:: PolyBase multiplication

Returns: (*this*A);

Definition at line 193 of file PolyBase.cpp.

◆ operator*() [2/2]

PolyBase Mantid::mathLevel::PolyBase::operator* ( double const V ) const

PolyBase multiplication.

Parameters

V	:: Value multiplication

Returns: (*this*V);

Definition at line 226 of file PolyBase.cpp.

◆ operator*=() [1/2]

PolyBase & Mantid::mathLevel::PolyBase::operator*= ( const PolyBase & A )

Self multiplication value.

Parameters

A	:: PolyBase to add

Returns: this=A;

Definition at line 153 of file PolyBase.cpp.

References afCoeff, and iDegree.

◆ operator*=() [2/2]

PolyBase & Mantid::mathLevel::PolyBase::operator*= ( double const V )

PolyBase multiplication.

Parameters

V	:: Value to multipication

Returns: (*this*V);

Definition at line 272 of file PolyBase.cpp.

References afCoeff.

◆ operator+() [1/2]

PolyBase Mantid::mathLevel::PolyBase::operator+ ( const PolyBase & A ) const

PolyBase addition.

Parameters

A	:: PolyBase addition

Returns: (*this+A);

Definition at line 171 of file PolyBase.cpp.

◆ operator+() [2/2]

PolyBase Mantid::mathLevel::PolyBase::operator+ ( double const V ) const

PolyBase addition.

Parameters

V	:: Value Addtion

Returns: (*this+V);

Definition at line 204 of file PolyBase.cpp.

◆ operator+=() [1/2]

PolyBase & Mantid::mathLevel::PolyBase::operator+= ( const PolyBase & A )

Self addition value.

Parameters

A	:: PolyBase to add

Returns: *this+=A;

Definition at line 125 of file PolyBase.cpp.

References afCoeff, and iDegree.

◆ operator+=() [2/2]

PolyBase & Mantid::mathLevel::PolyBase::operator+= ( double const V )

PolyBase addition.

Parameters

V	:: Value to add

Returns: (*this+V);

Definition at line 250 of file PolyBase.cpp.

References afCoeff.

◆ operator-() [1/3]

PolyBase Mantid::mathLevel::PolyBase::operator- ( ) const

PolyBase negation operator.

Returns: -(*this);

Definition at line 296 of file PolyBase.cpp.

◆ operator-() [2/3]

PolyBase Mantid::mathLevel::PolyBase::operator- ( const PolyBase & A ) const

PolyBase subtraction.

Parameters

A	:: PolyBase addition

Returns: (*this-A);

Definition at line 182 of file PolyBase.cpp.

◆ operator-() [3/3]

PolyBase Mantid::mathLevel::PolyBase::operator- ( double const V ) const

PolyBase substractr.

Parameters

V	:: Value substract

Returns: (*this-V);

Definition at line 215 of file PolyBase.cpp.

◆ operator-=() [1/2]

PolyBase & Mantid::mathLevel::PolyBase::operator-= ( const PolyBase & A )

Self addition value.

Parameters

A	:: PolyBase to add

Returns: *this+=A;

Definition at line 139 of file PolyBase.cpp.

References afCoeff, and iDegree.

◆ operator-=() [2/2]

PolyBase & Mantid::mathLevel::PolyBase::operator-= ( double const V )

PolyBase subtraction.

Parameters

V	:: Value to subtract

Returns: (*this+V);

Definition at line 261 of file PolyBase.cpp.

References afCoeff.

◆ operator/()

PolyBase Mantid::mathLevel::PolyBase::operator/ ( double const V ) const

PolyBase division.

Parameters

V	:: Value division

Returns: (*this/V);

Definition at line 237 of file PolyBase.cpp.

◆ operator/=()

PolyBase & Mantid::mathLevel::PolyBase::operator/= ( double const V )

PolyBase division scalar.

Parameters

V	:: Value to divide

Returns: (*this/V);

Definition at line 284 of file PolyBase.cpp.

References afCoeff.

◆ operator[]() [1/2]

double & Mantid::mathLevel::PolyBase::operator[] ( int const i )

Accessor to component.

Parameters

i :: index

Returns: Coeficient c_i

Definition at line 98 of file PolyBase.cpp.

References afCoeff, and iDegree.

◆ operator[]() [2/2]

double Mantid::mathLevel::PolyBase::operator[] ( int const i ) const

Accessor to component.

Parameters

i :: index

Returns: Coeficient c_i

Definition at line 86 of file PolyBase.cpp.

◆ realRoots()

std::vector< double > Mantid::mathLevel::PolyBase::realRoots ( double const epsilon = -1.0 )

Get just the real roots.

Parameters

epsilon :: tolerance factor (-ve to use default)

Returns: vector of the real roots (if any)

Definition at line 412 of file PolyBase.cpp.

References calcRoots(), Eaccuracy, and fabs.

Referenced by Mantid::Geometry::Quadratic::distance().

◆ setDegree()

void Mantid::mathLevel::PolyBase::setDegree ( int const iD )

Set the degree value.

Parameters

iD :: degree

Definition at line 49 of file PolyBase.cpp.

References afCoeff, and iDegree.

◆ solveCubic()

int Mantid::mathLevel::PolyBase::solveCubic	(	std::complex< double > &	AnsA,
		std::complex< double > &	AnsB,
		std::complex< double > &	AnsC
	)		const

private

Solves Cubic equation Compress MUST have been called.

Parameters

AnsA	:: complex roots of the equation
AnsB	:: complex roots of the equation
AnsC	:: complex roots of the equation

Returns: Number of unique solutions

Definition at line 505 of file PolyBase.cpp.

References Mantid::Geometry::d.

Referenced by calcRoots().

◆ solveQuadratic()

int Mantid::mathLevel::PolyBase::solveQuadratic	(	std::complex< double > &	AnsA,
		std::complex< double > &	AnsB
	)		const

private

Solves Complex Quadratic component.

compress MUST have been called.

Parameters

AnsA	:: complex roots of the equation
AnsB	:: complex roots of the equation

Returns: Number of unique solutions

Definition at line 478 of file PolyBase.cpp.

Referenced by calcRoots().

◆ write()

void Mantid::mathLevel::PolyBase::write ( std::ostream & OX ) const

Basic write command.

Parameters

OX	:: output stream

Definition at line 574 of file PolyBase.cpp.

Referenced by Mantid::mathLevel::operator<<().

Member Data Documentation

◆ afCoeff

std::vector<double> Mantid::mathLevel::PolyBase::afCoeff

private

Coefficients.

Definition at line 34 of file PolyBase.h.

Referenced by calcRoots(), compress(), derivative(), GetInversion(), operator*=(), operator+=(), operator-=(), operator/=(), operator[](), and setDegree().

◆ Eaccuracy

double Mantid::mathLevel::PolyBase::Eaccuracy

private

Polynomic accuracy.

Definition at line 35 of file PolyBase.h.

Referenced by compress(), and realRoots().

◆ iDegree

int Mantid::mathLevel::PolyBase::iDegree

private

Degree of polynomial [0 == constant].

Definition at line 33 of file PolyBase.h.

Referenced by calcRoots(), compress(), derivative(), getDegree(), GetInversion(), operator*=(), operator+=(), operator-=(), operator[](), and setDegree().

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

Framework/Geometry/inc/MantidGeometry/Math/PolyBase.h
Framework/Geometry/src/Math/PolyBase.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PolyBase() [1/2]

◆ PolyBase() [2/2]

Member Function Documentation

◆ calcRoots()

◆ compress()

◆ derivative()

◆ divide()

◆ getDegree()

◆ getDerivative()

◆ GetInversion()

◆ operator const std::vector< double > &()

◆ operator std::vector< double > &()

◆ operator()()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/()

◆ operator/=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ realRoots()

◆ setDegree()

◆ solveCubic()

◆ solveQuadratic()

◆ write()

Member Data Documentation

◆ afCoeff

◆ Eaccuracy

◆ iDegree