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

Class PolynomialFunctionLagrangeForm

  • All Implemented Interfaces:
    UnivariateRealFunction
    public class PolynomialFunctionLagrangeForm
extends java.lang.Object
implements UnivariateRealFunction
    Implements the representation of a real polynomial function in Lagrange Form. For reference, see Introduction to Numerical Analysis, ISBN 038795452X, chapter 2.

    The approximated function should be smooth enough for Lagrange polynomial to work well. Otherwise, consider using splines instead.

    Since:
    1.2
    Version:
    $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $

    • Constructor Summary

      Constructors 
      Constructor Description
      PolynomialFunctionLagrangeForm​(double[] x, double[] y)
      Construct a Lagrange polynomial with the given abscissas and function values.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      protected void computeCoefficients()
      Calculate the coefficients of Lagrange polynomial from the interpolation data.
      int degree()
      Returns the degree of the polynomial.
      static double evaluate​(double[] x, double[] y, double z)
      Evaluate the Lagrange polynomial using Neville's Algorithm.
      double[] getCoefficients()
      Returns a copy of the coefficients array.
      double[] getInterpolatingPoints()
      Returns a copy of the interpolating points array.
      double[] getInterpolatingValues()
      Returns a copy of the interpolating values array.
      double value​(double z)
      Compute the value for the function.
      static void verifyInterpolationArray​(double[] x, double[] y)
      Verifies that the interpolation arrays are valid.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • PolynomialFunctionLagrangeForm

        public PolynomialFunctionLagrangeForm​(double[] x,
                                      double[] y)
                               throws java.lang.IllegalArgumentException
        Construct a Lagrange polynomial with the given abscissas and function values. The order of interpolating points are not important.

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

        Parameters:
        x - interpolating points
        y - function values at interpolating points
        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

      • getInterpolatingPoints

        public double[] getInterpolatingPoints()
        Returns a copy of the interpolating points array.

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

        Returns:
        a fresh copy of the interpolating points array

      • getInterpolatingValues

        public double[] getInterpolatingValues()
        Returns a copy of the interpolating values array.

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

        Returns:
        a fresh copy of the interpolating values array

      • getCoefficients

        public double[] getCoefficients()
        Returns a copy of the coefficients array.

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

        Note that coefficients computation can be ill-conditioned. Use with caution and only when it is necessary.

        Returns:
        a fresh copy of the coefficients array

      • evaluate

        public static double evaluate​(double[] x,
                              double[] y,
                              double z)
                       throws DuplicateSampleAbscissaException,
                              java.lang.IllegalArgumentException
        Evaluate the Lagrange polynomial using Neville's Algorithm. It takes O(N^2) time.

        This function is made public static so that users can call it directly without instantiating PolynomialFunctionLagrangeForm object.

        Parameters:
        x - the interpolating points array
        y - the interpolating values array
        z - the point at which the function value is to be computed
        Returns:
        the function value
        Throws:
        DuplicateSampleAbscissaException - if the sample has duplicate abscissas
        java.lang.IllegalArgumentException - if inputs are not valid

      • computeCoefficients

        protected void computeCoefficients()
                            throws java.lang.ArithmeticException
        Calculate the coefficients of Lagrange polynomial from the interpolation data. It takes O(N^2) time.

        Note this computation can be ill-conditioned. Use with caution and only when it is necessary.

        Throws:
        java.lang.ArithmeticException - if any abscissas coincide

      • verifyInterpolationArray

        public static void verifyInterpolationArray​(double[] x,
                                            double[] y)
                                     throws java.lang.IllegalArgumentException
        Verifies that the interpolation arrays are valid.

        The arrays features checked by this method are that both arrays have the same length and this length is at least 2.

        The interpolating points must be distinct. However it is not verified here, it is checked in evaluate() and computeCoefficients().

        Parameters:
        x - the interpolating points array
        y - the interpolating values array
        Throws:
        java.lang.IllegalArgumentException - if not valid
        See Also:
        evaluate(double[], double[], double), computeCoefficients()