Package org.apache.commons.math.analysis.interpolation

Class LoessInterpolator

java.lang.Object
org.apache.commons.math.analysis.interpolation.LoessInterpolator
All Implemented Interfaces:
Serializable, UnivariateRealInterpolator
public class LoessInterpolator extends Object implements UnivariateRealInterpolator, 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
See Also:

  • Field Details

    • DEFAULT_BANDWIDTH

      public static final double DEFAULT_BANDWIDTH
      Default value of the bandwidth parameter.
      See Also:

    • DEFAULT_ROBUSTNESS_ITERS

      public static final int DEFAULT_ROBUSTNESS_ITERS
      Default value of the number of robustness iterations.
      See Also:

    • DEFAULT_ACCURACY

      public static final double DEFAULT_ACCURACY
      Default value for accuracy.
      Since:
      2.1
      See Also:

  • 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) throws MathException
      Constructs 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.
      Throws:
      MathException - if bandwidth does not lie in the interval [0,1] or if robustnessIters is negative.
      See Also:

    • LoessInterpolator

      public LoessInterpolator(double bandwidth, int robustnessIters, double accuracy) throws MathException
      Constructs 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:
      MathException - if bandwidth does not lie in the interval [0,1] or if robustnessIters is negative.
      Since:
      2.1
      See Also:

  • Method Details

    • 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, double[] weights) throws MathException
      Compute a weighted loess fit on the data at the original abscissae.
      Parameters:
      xval - the arguments for the interpolation points
      yval - the values for the interpolation points
      weights - point weights: coefficients by which the robustness weight of a point is multiplied
      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
      Since:
      2.1

    • 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