org.ptolemy.qss.util

Class PolynomialRoot

java.lang.Object

org.ptolemy.qss.util.PolynomialRoot

public final class PolynomialRoot
extends java.lang.Object

Find roots of polynomials.

Stand-alone utility functions.

TODO: Need a unit test for this class.

Since:

Ptolemy II 11.0

Version:

$id$

Author:

David M. Lorenzetti, Contributor: Thierry S. Nouidui

Pt.AcceptedRating:

red (reviewmoderator) // FIXME: Fill in.

Pt.ProposedRating:

red (dmlorenzetti)

Constructor Summary

Constructors

Constructor and Description
PolynomialRoot()

Method Summary

Modifier and Type	Method and Description
static double	findMinimumPositiveRoot2(double qea, double qeb, double qec) Find the smallest positive real root of a second-order (quadratic) equation.
static double	findMinimumPositiveRoot3(double cea, double ceb, double cec, double ced, double absTol, double relTol) Find the smallest positive real root of a third-order (cubic) equation.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PolynomialRoot

public PolynomialRoot()

Method Detail

findMinimumPositiveRoot2

public static final double findMinimumPositiveRoot2(double qea,
                                                    double qeb,
                                                    double qec)

Find the smallest positive real root of a second-order (quadratic) equation.

Equation is a*x^2 + b*x + c = 0.

Parameters:

qea - Coefficient `a`.

qeb - Coefficient `b`.

qec - Coefficient `c`.

Returns:

The smallest positive real root. Return `Double.POSITIVE_INFINITY` if no root. Return 0 if only nonpositive roots.

findMinimumPositiveRoot3

public static final double findMinimumPositiveRoot3(double cea,
                                                    double ceb,
                                                    double cec,
                                                    double ced,
                                                    double absTol,
                                                    double relTol)

Find the smallest positive real root of a third-order (cubic) equation.

Equation is a*x^3 + b*x^2 + c*x + d = 0.

TODO: Switch from bracketing solution, to one based on algebraic solution to cubic equation. Expect to have to tune up the roots it gives, using NR, just to account for numerical issues. But still may be more direct, maybe faster.

Parameters:

cea - Coefficient `a`.

ceb - Coefficient `b`.

cec - Coefficient `c`.

ced - Coefficient `d`.

absTol - The size of residual at which end search.

relTol - The fractional difference in bracket on x, at which end search.

Returns:

The smallest positive real root. Return `Double.POSITIVE_INFINITY` if no root. Return 0 if only nonpositive roots.