Package org.ddogleg.solver

Class PolynomialOps

java.lang.Object

org.ddogleg.solver.PolynomialOps

public class PolynomialOps
extends Object

Constructor Summary

Constructors

Constructor	Description
PolynomialOps()

Method Summary

Modifier and Type	Method	Description
static Polynomial	add(Polynomial a, Polynomial b, @Nullable Polynomial results)	Adds two polynomials together.
static int	countRealRoots(Polynomial poly)
static PolynomialRoots	createRootFinder(int maxCoefficients, RootFinderType which)	Creates different polynomial root finders.
static double	cubicRealRoot(double c0, double c1, double c2, double c3)	Returns a real root to the cubic polynomial: 0 = c0 + c1*x + c2*x^2 + c3*c^3.
static Polynomial	derivative(Polynomial poly, @Nullable Polynomial deriv)
static void	divide(Polynomial numerator, Polynomial denominator, Polynomial quotient, Polynomial remainder)	Polynomial division.
static Polynomial	multiply(Polynomial a, Polynomial b, @Nullable Polynomial result)	Multiplies the two polynomials together.
static double	quadraticVertex(double a, double b)	Given the coefficients compute the vertex (minimum/maximum) of the quadratic.
static double	refineRoot(Polynomial poly, double root, int maxIterations)

Methods inherited from class java.lang.Object

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

Constructor Details

PolynomialOps

public PolynomialOps()

Method Details

quadraticVertex

public static double quadraticVertex(double a,
 double b)

Given the coefficients compute the vertex (minimum/maximum) of the quadratic. y = a*x² + b*x + c

Parameters:

a - quadratic coefficient.

b - quadratic coefficient.

Returns:

The quadratic's vertex.

derivative

public static Polynomial derivative(Polynomial poly,
 @Nullable
 @Nullable Polynomial deriv)

refineRoot

public static double refineRoot(Polynomial poly,
 double root,
 int maxIterations)

divide

public static void divide(Polynomial numerator,
 Polynomial denominator,
 Polynomial quotient,
 Polynomial remainder)

Polynomial division. Computes both the quotient and the remainder.

quotient = numerator/denominator
remainder = numerator % denominator

Parameters:

numerator - Numerator in the division. Not modified.

denominator - Denominator in the division. Not modified.

quotient - Output quotient, Modified.

remainder - Output remainder. Modified.

multiply

public static Polynomial multiply(Polynomial a,
 Polynomial b,
 @Nullable
 @Nullable Polynomial result)

Multiplies the two polynomials together.

Parameters:

a - Polynomial

b - Polynomial

result - Optional storage parameter for the results. Must be have enough coefficients to store the results. If null a new instance is declared.

Returns:

Results of the multiplication

add

public static Polynomial add(Polynomial a,
 Polynomial b,
 @Nullable
 @Nullable Polynomial results)

Adds two polynomials together. The lengths of the polynomials do not need to be the zero, but the 'missing' coefficients are assumed to be zero.

Parameters:

a - Polynomial

b - Polynomial

results - Optional storage for resulting polynomial. If null a new instance is declared. If not null its length must be the same as the largest polynomial 'a' or 'b'.

Returns:

Polynomial 'a' and 'b' added together.

countRealRoots

public static int countRealRoots(Polynomial poly)

createRootFinder

public static PolynomialRoots createRootFinder(int maxCoefficients,
 RootFinderType which)

Creates different polynomial root finders.

Parameters:

maxCoefficients - The maximum number of coefficients that will be processed. This is the order + 1

which - 0 = Sturm and 1 = companion matrix.

Returns:

PolynomialRoots

cubicRealRoot

public static double cubicRealRoot(double c0,
 double c1,
 double c2,
 double c3)

Returns a real root to the cubic polynomial: 0 = c0 + c1*x + c2*x^2 + c3*c^3. There can be other real roots. WARNING: This technique is much less stable than using one of the RootFinder algorithms

Parameters:

c0 - Polynomial coefficient for power 0

c1 - Polynomial coefficient for power 1

c2 - Polynomial coefficient for power 2

c3 - Polynomial coefficient for power 3

Returns:

A real root of the polynomial