LoessInterpolator (Commons MATH 3.5)

java.lang.Object
- org.apache.commons.math3.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 and Description
`private double`	`accuracy` If the median residual at a certain robustness iteration is less than this amount, no more iterations are done.
`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_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.
`private int`	`robustnessIters` The number of robustness iterations parameter: this many robustness iterations are done.
`private static long`	`serialVersionUID` serializable version identifier.

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 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

Methods
Modifier and Type	Method and Description
`private static void`	`checkAllFiniteReal(double[] values)` Check that all elements of an array are finite real numbers.
`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)`.
`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.
`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 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
  - serialVersionUID
```
private static final long serialVersionUID
```
    serializable version identifier.
    
    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.
  - 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 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 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 Detail
  - 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.

Class LoessInterpolator

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_BANDWIDTH

DEFAULT_ROBUSTNESS_ITERS

DEFAULT_ACCURACY

serialVersionUID

bandwidth

robustnessIters

accuracy

Constructor Detail

LoessInterpolator

LoessInterpolator

LoessInterpolator

Method Detail

interpolate

smooth

smooth

updateBandwidthInterval

nextNonzero

tricube

checkAllFiniteReal