Class LoessInterpolator

java.lang.Object
org.apache.commons.math3.analysis.interpolation.LoessInterpolator
All Implemented Interfaces:
Serializable, UnivariateInterpolator
public class LoessInterpolator extends Object implements UnivariateInterpolator, 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:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private final double
    accuracy
    If the median residual at a certain robustness iteration is less than this amount, no more iterations are done.
    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.
    static final double
    DEFAULT_ACCURACY
    Default value for accuracy.
    static final double
    DEFAULT_BANDWIDTH
    Default value of the bandwidth parameter.
    static final int
    DEFAULT_ROBUSTNESS_ITERS
    Default value of the number of robustness iterations.
    private final int
    robustnessIters
    The number of robustness iterations parameter: this many robustness iterations are done.
    private static final long
    serialVersionUID
    serializable version identifier.

  • 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
    private static void
    checkAllFiniteReal(double[] values)
    Check that all elements of an array are finite real numbers.
    final 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.
    private static int
    nextNonzero(double[] weights, int i)
    Return the smallest index j such that j > i && (j == weights.length || weights[j] != 0).
    final double[]
    smooth(double[] xval, double[] yval)
    Compute a loess fit on the data at the original abscissae.
    final double[]
    smooth(double[] xval, double[] yval, double[] weights)
    Compute a weighted 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, double[] weights, 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], ignoring zero weights.

    Methods inherited from class 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:

    • 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:

    • serialVersionUID

      private static final long serialVersionUID
      serializable version identifier.
      See Also:

    • 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.

    • accuracy

      private final double accuracy
      If the median residual at a certain robustness iteration is less than this amount, no more iterations are done.

  • Constructor Details

  • 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).

    • updateBandwidthInterval

      private static void updateBandwidthInterval(double[] xval, double[] weights, 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], ignoring zero weights.
      Parameters:
      xval - Arguments array.
      weights - Weights array.
      i - 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 (right==xval.length-1 or xval[right+1] - xval[i] > xval[i] - xval[left]). The array will be updated.

    • nextNonzero

      private static int nextNonzero(double[] weights, int i)
      Return the smallest index j such that j > i && (j == weights.length || weights[j] != 0).
      Parameters:
      weights - Weights array.
      i - Index from which to start search.
      Returns:
      the smallest compliant index.

    • tricube

      private static double tricube(double x)
      Compute the tricube weight function
      Parameters:
      x - Argument.
      Returns:
      (1 - |x|3)3 for |x| < 1, 0 otherwise.

    • checkAllFiniteReal

      private static void checkAllFiniteReal(double[] values)
      Check that all elements of an array are finite real numbers.
      Parameters:
      values - Values array.
      Throws:
      NotFiniteNumberException - if one of the values is not a finite real number.