fr.cnes.sirius.patrius.math.analysis.interpolation

Class LoessInterpolator

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.interpolation.LoessInterpolator

All Implemented Interfaces:

UnivariateInterpolator, Serializable

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

Version:

$Id: LoessInterpolator.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and 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 and 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 bandwidthIn, int robustnessItersIn) Construct a new LoessInterpolator with given bandwidth and number of robustness iterations.
LoessInterpolator(double bandwidthIn, int robustnessItersIn, double accuracyIn) Construct a new LoessInterpolator with given bandwidth, number of robustness iterations and accuracy.

Method Summary

Modifier and Type	Method and 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 Detail

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 Detail

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 bandwidthIn,
                         int robustnessItersIn)

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:

bandwidthIn - 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.

robustnessItersIn - 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 bandwidthIn,
                         int robustnessItersIn,
                         double accuracyIn)

Construct a new LoessInterpolator with given bandwidth, number of robustness iterations and accuracy.

Parameters:

bandwidthIn - 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.

robustnessItersIn - 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.

accuracyIn - 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 Detail

interpolate

public 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.

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)

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)

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).