org.apache.commons.math3.analysis.polynomials

## Class PolynomialSplineFunction

• java.lang.Object
• org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction
• All Implemented Interfaces:
DifferentiableUnivariateFunction, UnivariateDifferentiableFunction, UnivariateFunction

public class PolynomialSplineFunction
extends Object
implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction
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 and Description
PolynomialSplineFunction(double[] knots, PolynomialFunction[] polynomials)
Construct a polynomial spline function with the given segment delimiters and interpolating polynomials.
• ### Method Summary

Methods
Modifier and Type Method and Description
UnivariateFunction derivative()
Get the derivative of the polynomial spline function.
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.
DerivativeStructure value(DerivativeStructure t)
Simple mathematical function.
double value(double v)
Compute the value for the function.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### PolynomialSplineFunction

public PolynomialSplineFunction(double[] knots,
PolynomialFunction[] polynomials)
throws NullArgumentException,
NumberIsTooSmallException,
DimensionMismatchException,
NonMonotonicSequenceException
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:
NullArgumentException - if either of the input arrays is null.
NumberIsTooSmallException - if knots has length less than 2.
DimensionMismatchException - if polynomials.length != knots.length - 1.
NonMonotonicSequenceException - if the knots array is not strictly increasing.
• ### Method Detail

• #### 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).
• #### derivative

public UnivariateFunction derivative()
Get the derivative of the polynomial spline function.
Specified by:
derivative in interface DifferentiableUnivariateFunction
Returns:
the derivative function.
• #### 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.