Class PolynomialFunctionLagrangeForm

java.lang.Object
org.apache.commons.math.analysis.polynomials.PolynomialFunctionLagrangeForm
All Implemented Interfaces:
UnivariateRealFunction

public class PolynomialFunctionLagrangeForm extends 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 Details

    • PolynomialFunctionLagrangeForm

      public PolynomialFunctionLagrangeForm(double[] x, double[] y) throws 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:
      IllegalArgumentException - if input arrays are not valid
  • Method Details

    • value

      public double value(double z) throws FunctionEvaluationException
      Compute the value for the function.
      Specified by:
      value in interface UnivariateRealFunction
      Parameters:
      z - the point for which the function value should be computed
      Returns:
      the value
      Throws:
      FunctionEvaluationException - if the function evaluation fails
    • 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, 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
      IllegalArgumentException - if inputs are not valid
    • computeCoefficients

      protected void computeCoefficients() throws 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:
      ArithmeticException - if any abscissas coincide
    • verifyInterpolationArray

      public static void verifyInterpolationArray(double[] x, double[] y) throws 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:
      IllegalArgumentException - if not valid
      See Also: