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 Details

    • 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 Details

    • 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:

    • 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