org.ddogleg.solver

Class PolynomialSolver

java.lang.Object

org.ddogleg.solver.PolynomialSolver

public class PolynomialSolver
extends java.lang.Object

Provides functions for finding the roots of polynomials

Constructor Summary

Constructors

Constructor and Description
PolynomialSolver()

Method Summary

Modifier and Type	Method and Description
static PolynomialRoots	createRootFinder(RootFinderType type, int maxDegree) Creates a generic polynomial root finding class which will return all real or all real and complex roots depending on the algorithm selected.
static double	cubicDiscriminant(double a, double b, double c, double d) The cubic discriminant is used to determine the type of roots.
static double	cubicRootReal(double a, double b, double c, double d) A cubic polynomial of the form "f(x) = a + b*x + c*x2 + d*x3" has three roots.
static org.ejml.data.Complex64F[]	polynomialRootsEVD(double... coefficients) Finds real and imaginary roots in a polynomial using the companion matrix and Eigenvalue decomposition.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolynomialSolver

public PolynomialSolver()

Method Detail

createRootFinder

public static PolynomialRoots createRootFinder(RootFinderType type,
                                               int maxDegree)

Creates a generic polynomial root finding class which will return all real or all real and complex roots depending on the algorithm selected.

Parameters:

type - Which algorithm is to be returned.

maxDegree - Maximum degree of the polynomial being considered.

Returns:

Root finding algorithm.

polynomialRootsEVD

public static org.ejml.data.Complex64F[] polynomialRootsEVD(double... coefficients)

Finds real and imaginary roots in a polynomial using the companion matrix and Eigenvalue decomposition. The coefficients order is specified from smallest to largest. Example, 5 + 6*x + 7*x^2 + 8*x^3 = [5,6,7,8]

Parameters:

coefficients - Polynomial coefficients from smallest to largest.

Returns:

The found roots.

cubicRootReal

public static double cubicRootReal(double a,
                                   double b,
                                   double c,
                                   double d)

A cubic polynomial of the form "f(x) = a + b*x + c*x² + d*x³" has three roots. These roots will either be all real or one real and two imaginary. This function will return a root which is always real.

WARNING: Not as numerically stable as polynomialRootsEVD(double...), but still fairly stable.

Parameters:

a - polynomial coefficient.

b - polynomial coefficient.

c - polynomial coefficient.

d - polynomial coefficient.

Returns:

A real root of the cubic polynomial

cubicDiscriminant

public static double cubicDiscriminant(double a,
                                       double b,
                                       double c,
                                       double d)

The cubic discriminant is used to determine the type of roots.

• if d > 0, then three distinct real roots
• if d = 0, then it has a multiple root and all will be real
• if d < 0, then one real and two non-real complex conjugate roots

From http://en.wikipedia.org/wiki/Cubic_function November 17, 2011

Parameters:

a - polynomial coefficient.

b - polynomial coefficient.

c - polynomial coefficient.

d - polynomial coefficient.

Returns:

Cubic discriminant