A collection of tools for mathmatical function root finding, maximization, etc (eventually) This class contains only static methods, and cannot be instantiated. More...

#include <FunctionTools.h>

Collaboration diagram for Isis::FunctionTools:

Static Public Member Functions
static QList< double >	realLinearRoots (double coeffLinearTerm, double coeffConstTerm)
	Find the real roots (0 or 1) of a linear equation Form: coeffLinearTerm*X + coeffConstTerm = 0.0 NOTE: in the case of infinite roots an empty set is returned. More...

static QList< double >	realQuadraticRoots (double coeffQuadTerm, double coeffLinearTerm, double coeffConstTerm)
	The correct way to find the real roots of a quadratic (0, 1, or 2) (according to numerical recipies 3rd edtion page 227). More...

static QList< double >	realCubicRoots (double coeffCubicTerm, double coeffQuadTerm, double coeffLinearTerm, double coeffConstTerm)
	Find the real roots of a cubic (1, 2, or 3) (see numerical recipies 3rd edtion page 227) Form: coeffCubicTermX^3 + coeffQuadTermX^2 + coeffLinearTerm*X + coeffConstTerm = 0.0. More...

template<typename Functor >
static bool	brentsRootFinder (Functor &func, const QList< double > pt1, const QList< double > pt2, double tol, int maxIter, double &root)
	Van Wijngaarden-Dekker-Brent Method for root finding on a discreetly defined function meaning that we can evaluate the function for discreet points, but we lack a global function and derivative definitions. More...

Detailed Description

A collection of tools for mathmatical function root finding, maximization, etc (eventually) This class contains only static methods, and cannot be instantiated.

Author: 2012-05-07 Orrin Thomas

Member Function Documentation

◆ brentsRootFinder()

template<typename Functor >

static bool Isis::FunctionTools::brentsRootFinder	(	Functor &	func,
		const QList< double >	pt1,
		const QList< double >	pt2,
		double	tol,
		int	maxIter,
		double &	root
	)

inlinestatic

Van Wijngaarden-Dekker-Brent Method for root finding on a discreetly defined function meaning that we can evaluate the function for discreet points, but we lack a global function and derivative definitions.

See Numerical Recipes 3rd eddition pages 454-456.

This method requires that the root be bounded on the interval [pt1,pt2], and is gaurenteed to convege a root (by Brent) in the interval as long the function is continous and can evaluated on that interval.
Note that if there are multiple roots on the interval the function will find one of them and there is no particular gaurentee which one. Note, also that I have changed the convergance criteria to enforce the nearness of the function to zero rather than the precision of the root.

Parameters

func	template parameter that must have a double operator()(double) defined
pt1	one of the already defined points (x, y) that bracket the root
pt2	one of the already defined points (x, y) that bracket the root
tol	how close to zero the function must come before iterations stop
maxiter	the maximum number of iterations before stoping the root search
root	the returned root (if any)

Returns: bool true if the solution converged, false otherwise

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

◆ realCubicRoots()

static QList<double> Isis::FunctionTools::realCubicRoots	(	double	coeffCubicTerm,
		double	coeffQuadTerm,
		double	coeffLinearTerm,
		double	coeffConstTerm
	)

inlinestatic

Find the real roots of a cubic (1, 2, or 3) (see numerical recipies 3rd edtion page 227) Form: coeffCubicTerm*X^3 + coeffQuadTerm*X^2 + coeffLinearTerm*X + coeffConstTerm = 0.0.

Parameters

coeffCubicTerm	coefficient of the cubic term
coeffQuadTerm	coefficient of the quadratic term
coefflinearTerm	coefficient of the linear term
coeffConstTerm	coefficient of the constant term

References realQuadraticRoots(), and Isis::TWOPI.

Referenced by Isis::KaguyaMiCameraDistortionMap::SetUndistortedFocalPlane().

◆ realLinearRoots()

static QList<double> Isis::FunctionTools::realLinearRoots	(	double	coeffLinearTerm,
		double	coeffConstTerm
	)

inlinestatic

Find the real roots (0 or 1) of a linear equation Form: coeffLinearTerm*X + coeffConstTerm = 0.0 NOTE: in the case of infinite roots an empty set is returned.

Parameters

coefflinearTerm	coefficient of the linear term
coeffConstTerm	coefficient of the constant term

Referenced by realQuadraticRoots().

◆ realQuadraticRoots()

static QList<double> Isis::FunctionTools::realQuadraticRoots	(	double	coeffQuadTerm,
		double	coeffLinearTerm,
		double	coeffConstTerm
	)

inlinestatic

The correct way to find the real roots of a quadratic (0, 1, or 2) (according to numerical recipies 3rd edtion page 227).

Form: coeffQuadTerm*X^2 + coeffLinearTerm*X + coeffConstTerm = 0.0

Parameters

coeffQuadTerm	coefficient of the quadratic term
coefflinearTerm	coefficient of the linear term
coeffConstTerm	coefficient of the constant term

References realLinearRoots().

Referenced by realCubicRoots(), and Isis::KaguyaMiCameraDistortionMap::SetUndistortedFocalPlane().

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

/usgs/pkgs/isis3.9.0_docs/ISIS3/isis/src/base/objs/FunctionTools/FunctionTools.h

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ brentsRootFinder()

◆ realCubicRoots()

◆ realLinearRoots()

◆ realQuadraticRoots()