java.lang.Object
- org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction

All Implemented Interfaces:

DifferentiableUnivariateFunction, UnivariateDifferentiableFunction, UnivariateFunction
```
public class PolynomialSplineFunction
extends java.lang.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])

Field Summary

Fields
Modifier and Type	Field	Description
`private double[]`	`knots`	Spline segment interval delimiters (knots).
`private int`	`n`	Number of spline segments.
`private PolynomialFunction[]`	`polynomials`	The polynomial functions that make up the spline.

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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	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.
`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

- Field Detail
  - knots
```
private final double[] knots
```
    Spline segment interval delimiters (knots). Size is n + 1 for n segments.
  - polynomials
```
private final PolynomialFunction[] polynomials
```
    The polynomial functions that make up the spline. The first element determines the value of the spline over the first subinterval, the second over the second, etc. Spline function values are determined by evaluating these functions at (x - knot[i]) where i is the knot segment to which x belongs.
  - n
```
private final int n
```
    Number of spline segments. It is equal to the number of polynomials and to the number of partition points - 1.
- 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.

Class PolynomialSplineFunction

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

knots

polynomials

n

Constructor Detail

PolynomialSplineFunction

Method Detail

value

derivative

polynomialSplineDerivative

value

getN

getPolynomials

getKnots

isValidPoint