org.hipparchus.analysis.interpolation

Class SplineInterpolator

java.lang.Object

org.hipparchus.analysis.interpolation.SplineInterpolator

All Implemented Interfaces:

FieldUnivariateInterpolator, UnivariateInterpolator

public class SplineInterpolator
extends Object
implements UnivariateInterpolator, FieldUnivariateInterpolator

Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set.

The interpolate(double[], double[]) method returns a PolynomialSplineFunction consisting of n cubic polynomials, defined over the subintervals determined by the x values, x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."

The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest knot point and strictly less than the largest knot point is computed by finding the subinterval to which x belongs and computing the value of the corresponding polynomial at x - x[i] where i is the index of the subinterval. See PolynomialSplineFunction for more details.

The interpolating polynomials satisfy:

1. The value of the PolynomialSplineFunction at each of the input x values equals the corresponding y value.
2. Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials "match up" at the knot points, as do their first and second derivatives).

The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires, Numerical Analysis, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.

Constructor Summary

Constructors

Constructor and Description
SplineInterpolator()

Method Summary

Modifier and Type	Method and Description
PolynomialSplineFunction	interpolate(double[] x, double[] y) Computes an interpolating function for the data set.
<T extends CalculusFieldElement<T>> FieldPolynomialSplineFunction<T>	interpolate(T[] x, T[] y) Computes an interpolating function for the data set.

Methods inherited from class java.lang.Object

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

Constructor Detail

SplineInterpolator

public SplineInterpolator()

Method Detail

interpolate

public PolynomialSplineFunction interpolate(double[] x,
                                            double[] y)
                                     throws MathIllegalArgumentException

Computes an interpolating function for the data set.

Specified by:

interpolate in interface UnivariateInterpolator

Parameters:

x - the arguments for the interpolation points

y - the values for the interpolation points

Returns:

a function which interpolates the data set

Throws:

MathIllegalArgumentException - if x and y have different sizes.

MathIllegalArgumentException - if x is not sorted in strict increasing order.

MathIllegalArgumentException - if the size of x is smaller than 3.

interpolate

public <T extends CalculusFieldElement<T>> FieldPolynomialSplineFunction<T> interpolate(T[] x,
                                                                                        T[] y)
                                                                                 throws MathIllegalArgumentException

Computes an interpolating function for the data set.

Specified by:

interpolate in interface FieldUnivariateInterpolator

Type Parameters:

T - the type of the field elements

Parameters:

x - the arguments for the interpolation points

y - the values for the interpolation points

Returns:

a function which interpolates the data set

Throws:

MathIllegalArgumentException - if x and y have different sizes.

MathIllegalArgumentException - if x is not sorted in strict increasing order.

MathIllegalArgumentException - if the size of x is smaller than 3.

Since:

1.5