org.apache.commons.math3.analysis.interpolation

Class AkimaSplineInterpolator

java.lang.Object

org.apache.commons.math3.analysis.interpolation.AkimaSplineInterpolator

All Implemented Interfaces:

UnivariateInterpolator

public class AkimaSplineInterpolator
extends java.lang.Object
implements UnivariateInterpolator

Computes a cubic spline interpolation for the data set using the Akima algorithm, as originally formulated by Hiroshi Akima in his 1970 paper "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures." J. ACM 17, 4 (October 1970), 589-602. DOI=10.1145/321607.321609 http://doi.acm.org/10.1145/321607.321609

This implementation is based on the Akima implementation in the CubicSpline class in the Math.NET Numerics library. The method referenced is CubicSpline.InterpolateAkimaSorted

The interpolate 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 Akima algorithm requires that n >= 5.

Field Summary

Fields

Modifier and Type	Field and Description
private static int	MINIMUM_NUMBER_POINTS The minimum number of points that are needed to compute the function.

Constructor Summary

Constructors

Constructor and Description
AkimaSplineInterpolator()

Method Summary

Methods

Modifier and Type	Method and Description
private double	differentiateThreePoint(double[] xvals, double[] yvals, int indexOfDifferentiation, int indexOfFirstSample, int indexOfSecondsample, int indexOfThirdSample) Three point differentiation helper, modeled off of the same method in the Math.NET CubicSpline class.
PolynomialSplineFunction	interpolate(double[] xvals, double[] yvals) Computes an interpolating function for the data set.
private PolynomialSplineFunction	interpolateHermiteSorted(double[] xvals, double[] yvals, double[] firstDerivatives) Creates a Hermite cubic spline interpolation from the set of (x,y) value pairs and their derivatives.

Methods inherited from class java.lang.Object

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

Field Detail

MINIMUM_NUMBER_POINTS

private static final int MINIMUM_NUMBER_POINTS

The minimum number of points that are needed to compute the function.

See Also:

Constant Field Values

Constructor Detail

AkimaSplineInterpolator

public AkimaSplineInterpolator()

Method Detail

interpolate

public PolynomialSplineFunction interpolate(double[] xvals,
                                   double[] yvals)
                                     throws DimensionMismatchException,
                                            NumberIsTooSmallException,
                                            NonMonotonicSequenceException

Computes an interpolating function for the data set.

Specified by:

interpolate in interface UnivariateInterpolator

Parameters:

xvals - the arguments for the interpolation points

yvals - the values for the interpolation points

Returns:

a function which interpolates the data set

Throws:

DimensionMismatchException - if xvals and yvals have different sizes.

NonMonotonicSequenceException - if xvals is not sorted in strict increasing order.

NumberIsTooSmallException - if the size of xvals is smaller than 5.

differentiateThreePoint

private double differentiateThreePoint(double[] xvals,
                             double[] yvals,
                             int indexOfDifferentiation,
                             int indexOfFirstSample,
                             int indexOfSecondsample,
                             int indexOfThirdSample)

Three point differentiation helper, modeled off of the same method in the Math.NET CubicSpline class. This is used by both the Apache Math and the Math.NET Akima Cubic Spline algorithms

Parameters:

xvals - x values to calculate the numerical derivative with

yvals - y values to calculate the numerical derivative with

indexOfDifferentiation - index of the elemnt we are calculating the derivative around

indexOfFirstSample - index of the first element to sample for the three point method

indexOfSecondsample - index of the second element to sample for the three point method

indexOfThirdSample - index of the third element to sample for the three point method

Returns:

the derivative

interpolateHermiteSorted

private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals,
                                                double[] yvals,
                                                double[] firstDerivatives)

Creates a Hermite cubic spline interpolation from the set of (x,y) value pairs and their derivatives. This is modeled off of the InterpolateHermiteSorted method in the Math.NET CubicSpline class.

Parameters:

xvals - x values for interpolation

yvals - y values for interpolation

firstDerivatives - first derivative values of the function

Returns:

polynomial that fits the function