org.apache.commons.math3.analysis.interpolation
Class SplineInterpolator

java.lang.Object
  extended by org.apache.commons.math3.analysis.interpolation.SplineInterpolator
All Implemented Interfaces:
UnivariateInterpolator

public class SplineInterpolator
extends Object
implements UnivariateInterpolator

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.

Version:
$Id: SplineInterpolator.java 1379905 2012-09-01 23:56:50Z erans $

Constructor Summary
SplineInterpolator()
           
 
Method Summary
 PolynomialSplineFunction interpolate(double[] x, double[] 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 DimensionMismatchException,
                                            NumberIsTooSmallException,
                                            NonMonotonicSequenceException
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:
DimensionMismatchException - if x and y have different sizes.
NonMonotonicSequenceException - if x is not sorted in strict increasing order.
NumberIsTooSmallException - if the size of x is smaller than 3.


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