java.lang.Object

org.apache.commons.math4.analysis.interpolation.LoessInterpolator

All Implemented Interfaces:: java.io.Serializable, UnivariateInterpolator

public class LoessInterpolator
extends java.lang.Object
implements UnivariateInterpolator, 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 one to build a spline on the obtained loess fit.

Since:: 2.0
See Also:: Serialized Form

Field Summary

Fields
Modifier and Type	Field	Description
`static double`	`DEFAULT_ACCURACY`	Default value for accuracy.
`static double`	`DEFAULT_BANDWIDTH`	Default value of the bandwidth parameter.
`static int`	`DEFAULT_ROBUSTNESS_ITERS`	Default value of the number of robustness iterations.

Constructor Summary

Constructors
Constructor	Description
`LoessInterpolator()`	Constructs a new `LoessInterpolator` with a bandwidth of `DEFAULT_BANDWIDTH`, `DEFAULT_ROBUSTNESS_ITERS` robustness iterations and an accuracy of {#link #DEFAULT_ACCURACY}.
`LoessInterpolator(double bandwidth, int robustnessIters)`	Construct a new `LoessInterpolator` with given bandwidth and number of robustness iterations.
`LoessInterpolator(double bandwidth, int robustnessIters, double accuracy)`	Construct a new `LoessInterpolator` with given bandwidth, number of robustness iterations and accuracy.

Method Summary

Modifier and Type	Method	Description
`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.
`double[]`	`smooth(double[] xval, double[] yval, double[] weights)`	Compute a weighted loess fit on the data at the original abscissae.

Methods inherited from class java.lang.Object

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

Field Details
- 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
- DEFAULT_ACCURACY
  
  public static final double DEFAULT_ACCURACY
  
  Default value for accuracy.
  
  Since:
  
  2.1
  
  See Also:
  
  Constant Field Values
Constructor Details
- LoessInterpolator
  
  public LoessInterpolator()
  
  Constructs a new LoessInterpolator with a bandwidth of DEFAULT_BANDWIDTH, DEFAULT_ROBUSTNESS_ITERS robustness iterations and an accuracy of {#link #DEFAULT_ACCURACY}. See LoessInterpolator(double, int, double) for an explanation of the parameters.
- LoessInterpolator
  
  public LoessInterpolator(double bandwidth, int robustnessIters)
  
  Construct a new LoessInterpolator with given bandwidth and number of robustness iterations.
  Calling this constructor is equivalent to calling {link LoessInterpolator(bandwidth, robustnessIters, LoessInterpolator.DEFAULT_ACCURACY)
  
  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.
  
  See Also:
  
  LoessInterpolator(double, int, double)
- LoessInterpolator
  
  public LoessInterpolator(double bandwidth, int robustnessIters, double accuracy) throws OutOfRangeException, NotPositiveException
  
  Construct a new LoessInterpolator with given bandwidth, number of robustness iterations and accuracy.
  
  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.
  
  accuracy - If the median residual at a certain robustness iteration is less than this amount, no more iterations are done.
  
  Throws:
  
  OutOfRangeException - if bandwidth does not lie in the interval [0,1].
  
  NotPositiveException - if robustnessIters is negative.
  
  Since:
  
  2.1
  
  See Also:
  
  LoessInterpolator(double, int)
Method Details
- interpolate
  
  public final PolynomialSplineFunction interpolate(double[] xval, double[] yval) throws NonMonotonicSequenceException, DimensionMismatchException, NoDataException, NotFiniteNumberException, NumberIsTooSmallException
  
  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 UnivariateInterpolator
  
  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:
  
  NonMonotonicSequenceException - if xval not sorted in strictly increasing order.
  
  DimensionMismatchException - if xval and yval have different sizes.
  
  NoDataException - if xval or yval has zero size.
  
  NotFiniteNumberException - if any of the arguments and values are not finite real numbers.
  
  NumberIsTooSmallException - if the bandwidth is too small to accomodate the size of the input data (i.e. the bandwidth must be larger than 2/n).
- smooth
  
  public final double[] smooth(double[] xval, double[] yval, double[] weights) throws NonMonotonicSequenceException, DimensionMismatchException, NoDataException, NotFiniteNumberException, NumberIsTooSmallException
  
  Compute a weighted loess fit on the data at the original abscissae.
  
  Parameters:
  
  xval - Arguments for the interpolation points.
  
  yval - Values for the interpolation points.
  
  weights - point weights: coefficients by which the robustness weight of a point is multiplied.
  
  Returns:
  
  the values of the loess fit at corresponding original abscissae.
  
  Throws:
  
  NonMonotonicSequenceException - if xval not sorted in strictly increasing order.
  
  DimensionMismatchException - if xval and yval have different sizes.
  
  NoDataException - if xval or yval has zero size.
  
  NotFiniteNumberException - if any of the arguments and values are not finite real numbers.
  
  NumberIsTooSmallException - if the bandwidth is too small to accomodate the size of the input data (i.e. the bandwidth must be larger than 2/n).
  
  Since:
  
  2.1
- smooth
  
  public final double[] smooth(double[] xval, double[] yval) throws NonMonotonicSequenceException, DimensionMismatchException, NoDataException, NotFiniteNumberException, NumberIsTooSmallException
  
  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:
  
  NonMonotonicSequenceException - if xval not sorted in strictly increasing order.
  
  DimensionMismatchException - if xval and yval have different sizes.
  
  NoDataException - if xval or yval has zero size.
  
  NotFiniteNumberException - if any of the arguments and values are not finite real numbers.
  
  NumberIsTooSmallException - if the bandwidth is too small to accomodate the size of the input data (i.e. the bandwidth must be larger than 2/n).

Class LoessInterpolator

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Details

Constructor Details

Method Details