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

Class PolynomialFunctionNewtonForm

  • All Implemented Interfaces:
    UnivariateRealFunction
    public class PolynomialFunctionNewtonForm
extends java.lang.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
    Version:
    $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $

    • Constructor Summary

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

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      protected void computeCoefficients()
      Calculate the normal polynomial coefficients given the Newton form.
      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.
      protected static void verifyInputArray​(double[] a, double[] c)
      Verifies that the input arrays are valid.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • PolynomialFunctionNewtonForm

        public PolynomialFunctionNewtonForm​(double[] a,
                                    double[] c)
                             throws java.lang.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:
        java.lang.IllegalArgumentException - if input arrays are not valid

    • Method Detail

      • 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,
                              java.lang.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
        java.lang.IllegalArgumentException - if inputs are not valid

      • computeCoefficients

        protected void computeCoefficients()
        Calculate the normal polynomial coefficients given the Newton form. It also uses nested multiplication but takes O(N^2) time.

      • verifyInputArray

        protected static void verifyInputArray​(double[] a,
                                       double[] c)
                                throws java.lang.IllegalArgumentException
        Verifies that the input arrays are valid.

        The centers must be distinct for interpolation purposes, but not for general use. Thus it is not verified here.

        Parameters:
        a - the coefficients in Newton form formula
        c - the centers
        Throws:
        java.lang.IllegalArgumentException - if not valid
        See Also:
        DividedDifferenceInterpolator.computeDividedDifference(double[], double[])