Package org.apache.commons.math4.analysis.polynomials

Class PolynomialSplineFunction

java.lang.Object
org.apache.commons.math4.analysis.polynomials.PolynomialSplineFunction
All Implemented Interfaces:
UnivariateDifferentiableFunction, UnivariateFunction
public class PolynomialSplineFunction
extends java.lang.Object
implements UnivariateDifferentiableFunction
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 Summary

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

  • Method Summary

    Modifier and Type Method Description
    double[] getKnots()
    Get an array copy of the knot points.
    int getN()
    Get the number of spline segments.
    PolynomialFunction[] getPolynomials()
    Get a copy of the interpolating polynomials array.
    boolean isValidPoint​(double x)
    Indicates whether a point is within the interpolation range.
    PolynomialSplineFunction polynomialSplineDerivative()
    Get the derivative of the polynomial spline function.
    double value​(double v)
    Compute the value for the function.
    DerivativeStructure value​(DerivativeStructure t)
    Simple mathematical function.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

  • Method Details

    • value

      public double value​(double v)
      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 UnivariateFunction
      Parameters:
      v - Point for which the function value should be computed.
      Returns:
      the value.
      Throws:
      OutOfRangeException - if v is outside of the domain of the spline function (smaller than the smallest knot point or larger than the largest knot point).

    • polynomialSplineDerivative

      public PolynomialSplineFunction polynomialSplineDerivative()
      Get the derivative of the polynomial spline function.
      Returns:
      the derivative function.

    • value

      public DerivativeStructure value​(DerivativeStructure t)
      Simple mathematical function.

      UnivariateDifferentiableFunction classes compute both the value and the first derivative of the function.

      Specified by:
      value in interface UnivariateDifferentiableFunction
      Parameters:
      t - function input value
      Returns:
      function result
      Since:
      3.1

    • getN

      public int getN()
      Get the number of spline segments. It is also the number of polynomials and the number of knot points - 1.
      Returns:
      the number of spline segments.

    • getPolynomials

      public PolynomialFunction[] getPolynomials()
      Get a copy of the interpolating polynomials array. It 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()
      Get an array copy of the knot points. It returns a fresh copy of the array. Changes made to the copy will not affect the knots property.
      Returns:
      the knot points.

    • isValidPoint

      public boolean isValidPoint​(double x)
      Indicates whether a point is within the interpolation range.
      Parameters:
      x - Point.
      Returns:
      true if x is a valid point.