Package org.apache.commons.math.analysis.polynomials

Class PolynomialFunctionNewtonForm

java.lang.Object

org.apache.commons.math.analysis.polynomials.PolynomialFunctionNewtonForm

All Implemented Interfaces:

UnivariateRealFunction

public class PolynomialFunctionNewtonForm
extends Object
implements UnivariateRealFunction

Implements the representation of a real polynomial function in Newton Form. For reference, see Elementary Numerical Analysis, ISBN 0070124477, chapter 2.

The formula of polynomial in Newton form is p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... + a[n](x-c[0])(x-c[1])...(x-c[n-1]) Note that the length of a[] is one more than the length of c[]

Since:

1.2

Constructor Summary

Constructors

Constructor	Description
PolynomialFunctionNewtonForm(double[] a, double[] c)	Construct a Newton polynomial with the given a[] and c[].

Method Summary

Modifier and Type	Method	Description
int	degree()	Returns the degree of the polynomial.
static double	evaluate(double[] a, double[] c, double z)	Evaluate the Newton polynomial using nested multiplication.
double[]	getCenters()	Returns a copy of the centers array.
double[]	getCoefficients()	Returns a copy of the coefficients array.
double[]	getNewtonCoefficients()	Returns a copy of coefficients in Newton form formula.
double	value(double z)	Calculate the function value at the given point.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolynomialFunctionNewtonForm

public PolynomialFunctionNewtonForm(double[] a,
                                    double[] c)
                             throws IllegalArgumentException

Construct a Newton polynomial with the given a[] and c[]. The order of centers are important in that if c[] shuffle, then values of a[] would completely change, not just a permutation of old a[].

The constructor makes copy of the input arrays and assigns them.

Parameters:

a - the coefficients in Newton form formula

c - the centers

Throws:

IllegalArgumentException - if input arrays are not valid

Method Detail

value

public double value(double z)
             throws FunctionEvaluationException

Calculate the function value at the given point.

Specified by:

value in interface UnivariateRealFunction

Parameters:

z - the point at which the function value is to be computed

Returns:

the function value

Throws:

FunctionEvaluationException - if a runtime error occurs

See Also:

UnivariateRealFunction.value(double)

degree

public int degree()

Returns the degree of the polynomial.

Returns:

the degree of the polynomial

getNewtonCoefficients

public double[] getNewtonCoefficients()

Returns a copy of coefficients in Newton form formula.

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

Returns:

a fresh copy of coefficients in Newton form formula

getCenters

public double[] getCenters()

Returns a copy of the centers array.

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

Returns:

a fresh copy of the centers array

getCoefficients

public double[] getCoefficients()

Returns a copy of the coefficients array.

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

Returns:

a fresh copy of the coefficients array

evaluate

public static double evaluate(double[] a,
                              double[] c,
                              double z)
                       throws FunctionEvaluationException,
                              IllegalArgumentException

Evaluate the Newton polynomial using nested multiplication. It is also called Horner's Rule and takes O(N) time.

Parameters:

a - the coefficients in Newton form formula

c - the centers

z - the point at which the function value is to be computed

Returns:

the function value

Throws:

FunctionEvaluationException - if a runtime error occurs

IllegalArgumentException - if inputs are not valid