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

Class PolynomialSplineFunction

java.lang.Object
org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction
All Implemented Interfaces:
DifferentiableUnivariateRealFunction, UnivariateRealFunction
public class PolynomialSplineFunction extends Object implements DifferentiableUnivariateRealFunction
Represents a polynomial spline function.

A polynomial spline function consists of a set of interpolating polynomials and an ascending array of domain knot points, determining the intervals over which the spline function is defined by the constituent polynomials. The polynomials are assumed to have been computed to match the values of another function at the knot points. The value consistency constraints are not currently enforced by PolynomialSplineFunction itself, but are assumed to hold among the polynomials and knot points passed to the constructor.

N.B.: The polynomials in the polynomials property must be centered on the knot points to compute the spline function values. See below.

The domain of the polynomial spline function is [smallest knot, largest knot]. Attempts to evaluate the function at values outside of this range generate IllegalArgumentExceptions.

The value of the polynomial spline function for an argument x is computed as follows:

  1. The knot array is searched to find the segment to which x belongs. If x is less than the smallest knot point or greater than the largest one, an IllegalArgumentException is thrown.
  2. Let j be the index of the largest knot point that is less than or equal to x. The value returned is
    polynomials[j](x - knot[j])

  • Constructor Details

    • PolynomialSplineFunction

      public PolynomialSplineFunction(double[] knots, PolynomialFunction[] polynomials)
      Construct a polynomial spline function with the given segment delimiters and interpolating polynomials.

      The constructor copies both arrays and assigns the copies to the knots and polynomials properties, respectively.

      Parameters:
      knots - spline segment interval delimiters
      polynomials - polynomial functions that make up the spline
      Throws:
      NullPointerException - if either of the input arrays is null
      IllegalArgumentException - if knots has length less than 2, polynomials.length != knots.length - 1 , or the knots array is not strictly increasing.

  • Method Details

    • value

      public double value(double v) throws ArgumentOutsideDomainException
      Compute the value for the function. See PolynomialSplineFunction for details on the algorithm for computing the value of the function.

      Specified by:
      value in interface UnivariateRealFunction
      Parameters:
      v - the point for which the function value should be computed
      Returns:
      the value
      Throws:
      ArgumentOutsideDomainException - if v is outside of the domain of of the spline function (less than the smallest knot point or greater than the largest knot point)

    • derivative

      public UnivariateRealFunction derivative()
      Returns the derivative of the polynomial spline function as a UnivariateRealFunction
      Specified by:
      derivative in interface DifferentiableUnivariateRealFunction
      Returns:
      the derivative function

    • polynomialSplineDerivative

      public PolynomialSplineFunction polynomialSplineDerivative()
      Returns the derivative of the polynomial spline function as a PolynomialSplineFunction
      Returns:
      the derivative function

    • getN

      public int getN()
      Returns the number of spline segments = the number of polynomials = the number of knot points - 1.
      Returns:
      the number of spline segments

    • getPolynomials

      public PolynomialFunction[] getPolynomials()
      Returns a copy of the interpolating polynomials array.

      Returns a fresh copy of the array. Changes made to the copy will not affect the polynomials property.

      Returns:
      the interpolating polynomials

    • getKnots

      public double[] getKnots()
      Returns an array copy of the knot points.

      Returns a fresh copy of the array. Changes made to the copy will not affect the knots property.

      Returns:
      the knot points