org.apache.commons.math3.analysis.polynomials
Class PolynomialFunction

java.lang.Object
  org.apache.commons.math3.analysis.polynomials.PolynomialFunction

All Implemented Interfaces:

Serializable, DifferentiableUnivariateFunction, UnivariateDifferentiableFunction, UnivariateFunction

public class PolynomialFunction
extends Object
implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction, Serializable

Immutable representation of a real polynomial function with real coefficients.

Horner's Method is used to evaluate the function.

Version:

$Id: PolynomialFunction.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Serialized Form

Nested Class Summary

static class

PolynomialFunction.Parametric Dedicated parametric polynomial class.

Constructor Summary

PolynomialFunction(double[] c)
Construct a polynomial with the given coefficients.

Method Summary

PolynomialFunction	add(PolynomialFunction p) Add a polynomial to the instance.
int	degree() Returns the degree of the polynomial.
UnivariateFunction	derivative() Returns the derivative as a UnivariateFunction.
protected static double[]	differentiate(double[] coefficients) Returns the coefficients of the derivative of the polynomial with the given coefficients.
boolean	equals(Object obj)
protected static double	evaluate(double[] coefficients, double argument) Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
double[]	getCoefficients() Returns a copy of the coefficients array.
int	hashCode()
PolynomialFunction	multiply(PolynomialFunction p) Multiply the instance by a polynomial.
PolynomialFunction	negate() Negate the instance.
PolynomialFunction	polynomialDerivative() Returns the derivative as a PolynomialFunction.
PolynomialFunction	subtract(PolynomialFunction p) Subtract a polynomial from the instance.
String	toString() Returns a string representation of the polynomial.
DerivativeStructure	value(DerivativeStructure t) Simple mathematical function.
double	value(double x) Compute the value of the function for the given argument.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

PolynomialFunction

public PolynomialFunction(double[] c)
                   throws NullArgumentException,
                          NoDataException

Construct a polynomial with the given coefficients. The first element of the coefficients array is the constant term. Higher degree coefficients follow in sequence. The degree of the resulting polynomial is the index of the last non-null element of the array, or 0 if all elements are null.

The constructor makes a copy of the input array and assigns the copy to the coefficients property.

Parameters:

c - Polynomial coefficients.

Throws:

NullArgumentException - if c is null.

NoDataException - if c is empty.

Method Detail

value

public double value(double x)

Compute the value of the function for the given argument.

The value returned is
coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]

Specified by:

value in interface UnivariateFunction

Parameters:

x - Argument for which the function value should be computed.

Returns:

the value of the polynomial at the given point.

See Also:

UnivariateFunction.value(double)

degree

public int degree()

Returns the degree of the polynomial.

Returns:

the degree of the polynomial.

getCoefficients

public double[] getCoefficients()

Returns a copy of the coefficients array.

Changes made to the returned copy will not affect the coefficients of the polynomial.

Returns:

a fresh copy of the coefficients array.

evaluate

protected static double evaluate(double[] coefficients,
                                 double argument)
                          throws NullArgumentException,
                                 NoDataException

Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.

Parameters:

coefficients - Coefficients of the polynomial to evaluate.

argument - Input value.

Returns:

the value of the polynomial.

Throws:

NoDataException - if coefficients is empty.

NullArgumentException - if coefficients is null.

value

public DerivativeStructure value(DerivativeStructure t)
                          throws NullArgumentException,
                                 NoDataException

Simple mathematical function.

UnivariateDifferentiableFunction classes compute both the value and the first derivative of the function.

Specified by:

value in interface UnivariateDifferentiableFunction

Parameters:

t - function input value

Returns:

function result

Throws:

NoDataException - if coefficients is empty.

NullArgumentException - if coefficients is null.

Since:

3.1

add

public PolynomialFunction add(PolynomialFunction p)

Add a polynomial to the instance.

Parameters:

p - Polynomial to add.

Returns:

a new polynomial which is the sum of the instance and p.

subtract

public PolynomialFunction subtract(PolynomialFunction p)

Subtract a polynomial from the instance.

Parameters:

p - Polynomial to subtract.

Returns:

a new polynomial which is the difference the instance minus p.

negate

public PolynomialFunction negate()

Negate the instance.

Returns:

a new polynomial.

multiply

public PolynomialFunction multiply(PolynomialFunction p)

Multiply the instance by a polynomial.

Parameters:

p - Polynomial to multiply by.

Returns:

a new polynomial.

differentiate

protected static double[] differentiate(double[] coefficients)
                                 throws NullArgumentException,
                                        NoDataException

Returns the coefficients of the derivative of the polynomial with the given coefficients.

Parameters:

coefficients - Coefficients of the polynomial to differentiate.

Returns:

the coefficients of the derivative or null if coefficients has length 1.

Throws:

NoDataException - if coefficients is empty.

NullArgumentException - if coefficients is null.

polynomialDerivative

public PolynomialFunction polynomialDerivative()

Returns the derivative as a PolynomialFunction.

Returns:

the derivative polynomial.

derivative

public UnivariateFunction derivative()

Returns the derivative as a UnivariateFunction.

Specified by:

derivative in interface DifferentiableUnivariateFunction

Returns:

the derivative function.

toString

public String toString()

Returns a string representation of the polynomial.

The representation is user oriented. Terms are displayed lowest degrees first. The multiplications signs, coefficients equals to one and null terms are not displayed (except if the polynomial is 0, in which case the 0 constant term is displayed). Addition of terms with negative coefficients are replaced by subtraction of terms with positive coefficients except for the first displayed term (i.e. we display -3 for a constant negative polynomial, but 1 - 3 x + x^2 if the negative coefficient is not the first one displayed).

Overrides:

toString in class Object

Returns:

a string representation of the polynomial.

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object