org.apache.commons.math.analysis.interpolation
Class LoessInterpolator

java.lang.Object
  org.apache.commons.math.analysis.interpolation.LoessInterpolator

All Implemented Interfaces:

java.io.Serializable, UnivariateRealInterpolator

public class LoessInterpolator
extends java.lang.Object
implements UnivariateRealInterpolator, java.io.Serializable

Implements the Local Regression Algorithm (also Loess, Lowess) for interpolation of real univariate functions.

For reference, see William S. Cleveland - Robust Locally Weighted Regression and Smoothing Scatterplots

This class implements both the loess method and serves as an interpolation adapter to it, allowing to build a spline on the obtained loess fit.

Since:

2.0

Version:

$Revision: 794709 $ $Date: 2009-07-16 11:09:02 -0400 (Thu, 16 Jul 2009) $

See Also:

Serialized Form

Field Summary

private double	bandwidth The bandwidth parameter: when computing the loess fit at a particular point, this fraction of source points closest to the current point is taken into account for computing a least-squares regression.
static double	DEFAULT_BANDWIDTH Default value of the bandwidth parameter.
static int	DEFAULT_ROBUSTNESS_ITERS Default value of the number of robustness iterations.
private int	robustnessIters The number of robustness iterations parameter: this many robustness iterations are done.
private static long	serialVersionUID serializable version identifier.

Constructor Summary

LoessInterpolator()
Constructs a new LoessInterpolator with a bandwidth of DEFAULT_BANDWIDTH and DEFAULT_ROBUSTNESS_ITERS robustness iterations.

LoessInterpolator(double bandwidth, int robustnessIters)
Constructs a new LoessInterpolator with given bandwidth and number of robustness iterations.

Method Summary

private static void	checkAllFiniteReal(double[] values, boolean isAbscissae) Check that all elements of an array are finite real numbers.
private static void	checkStrictlyIncreasing(double[] xval) Check that elements of the abscissae array are in a strictly increasing order.
PolynomialSplineFunction	interpolate(double[] xval, double[] yval) Compute an interpolating function by performing a loess fit on the data at the original abscissae and then building a cubic spline with a SplineInterpolator on the resulting fit.
double[]	smooth(double[] xval, double[] yval) Compute a loess fit on the data at the original abscissae.
private static double	tricube(double x) Compute the tricube weight function
private static void	updateBandwidthInterval(double[] xval, int i, int[] bandwidthInterval) Given an index interval into xval that embraces a certain number of points closest to xval[i-1], update the interval so that it embraces the same number of points closest to xval[i]

Methods inherited from class java.lang.Object

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

Field Detail

serialVersionUID

private static final long serialVersionUID

serializable version identifier.

See Also:

Constant Field Values

DEFAULT_BANDWIDTH

public static final double DEFAULT_BANDWIDTH

Default value of the bandwidth parameter.

See Also:

Constant Field Values

DEFAULT_ROBUSTNESS_ITERS

public static final int DEFAULT_ROBUSTNESS_ITERS

Default value of the number of robustness iterations.

See Also:

Constant Field Values

bandwidth

private final double bandwidth

The bandwidth parameter: when computing the loess fit at a particular point, this fraction of source points closest to the current point is taken into account for computing a least-squares regression.

A sensible value is usually 0.25 to 0.5.

robustnessIters

private final int robustnessIters

The number of robustness iterations parameter: this many robustness iterations are done.

A sensible value is usually 0 (just the initial fit without any robustness iterations) to 4.

Constructor Detail

LoessInterpolator

public LoessInterpolator()

Constructs a new LoessInterpolator with a bandwidth of DEFAULT_BANDWIDTH and DEFAULT_ROBUSTNESS_ITERS robustness iterations. See LoessInterpolator(double, int) for an explanation of the parameters.

LoessInterpolator

public LoessInterpolator(double bandwidth,
                         int robustnessIters)
                  throws MathException

Constructs a new LoessInterpolator with given bandwidth and number of robustness iterations.

Parameters:

bandwidth - when computing the loess fit at a particular point, this fraction of source points closest to the current point is taken into account for computing a least-squares regression.
A sensible value is usually 0.25 to 0.5, the default value is DEFAULT_BANDWIDTH.

robustnessIters - This many robustness iterations are done.
A sensible value is usually 0 (just the initial fit without any robustness iterations) to 4, the default value is DEFAULT_ROBUSTNESS_ITERS.

Throws:

MathException - if bandwidth does not lie in the interval [0,1] or if robustnessIters is negative.

Method Detail

interpolate

public final PolynomialSplineFunction interpolate(double[] xval,
                                                  double[] yval)
                                           throws MathException

Compute an interpolating function by performing a loess fit on the data at the original abscissae and then building a cubic spline with a SplineInterpolator on the resulting fit.

Specified by:

interpolate in interface UnivariateRealInterpolator

Parameters:

xval - the arguments for the interpolation points

yval - the values for the interpolation points

Returns:

A cubic spline built upon a loess fit to the data at the original abscissae

Throws:

MathException - if some of the following conditions are false:

• Arguments and values are of the same size that is greater than zero
• The arguments are in a strictly increasing order
• All arguments and values are finite real numbers

smooth

public final double[] smooth(double[] xval,
                             double[] yval)
                      throws MathException

Compute a loess fit on the data at the original abscissae.

Parameters:

xval - the arguments for the interpolation points

yval - the values for the interpolation points

Returns:

values of the loess fit at corresponding original abscissae

Throws:

MathException - if some of the following conditions are false:

• Arguments and values are of the same size that is greater than zero
• The arguments are in a strictly increasing order
• All arguments and values are finite real numbers

updateBandwidthInterval

private static void updateBandwidthInterval(double[] xval,
                                            int i,
                                            int[] bandwidthInterval)

Given an index interval into xval that embraces a certain number of points closest to xval[i-1], update the interval so that it embraces the same number of points closest to xval[i]

Parameters:

xval - arguments array

i - the index around which the new interval should be computed

bandwidthInterval - a two-element array {left, right} such that:

(left==0 or xval[i] - xval[left-1] > xval[right] - xval[i])

and also

(right==xval.length-1 or xval[right+1] - xval[i] > xval[i] - xval[left]). The array will be updated.

tricube

private static double tricube(double x)

Compute the tricube weight function

Parameters:

x - the argument

Returns:

(1-|x|^3)^3

checkAllFiniteReal

private static void checkAllFiniteReal(double[] values,
                                       boolean isAbscissae)
                                throws MathException

Check that all elements of an array are finite real numbers.

Parameters:

values - the values array

isAbscissae - if true, elements are abscissae otherwise they are ordinatae

Throws:

MathException - if one of the values is not a finite real number

checkStrictlyIncreasing

private static void checkStrictlyIncreasing(double[] xval)
                                     throws MathException

Check that elements of the abscissae array are in a strictly increasing order.

Parameters:

xval - the abscissae array

Throws:

MathException - if the abscissae array is not in a strictly increasing order