Class LoessInterpolator
- java.lang.Object
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- org.apache.commons.math3.analysis.interpolation.LoessInterpolator
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- 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
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Field Summary
Fields Modifier and Type Field 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.
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Constructor Summary
Constructors Constructor Description LoessInterpolator()
Constructs a newLoessInterpolator
with a bandwidth ofDEFAULT_BANDWIDTH
,DEFAULT_ROBUSTNESS_ITERS
robustness iterations and an accuracy of {#link #DEFAULT_ACCURACY}.LoessInterpolator(double bandwidth, int robustnessIters)
Construct a newLoessInterpolator
with given bandwidth and number of robustness iterations.LoessInterpolator(double bandwidth, int robustnessIters, double accuracy)
Construct a newLoessInterpolator
with given bandwidth, number of robustness iterations and accuracy.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method 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 aSplineInterpolator
on the resulting fit.private static int
nextNonzero(double[] weights, int i)
Return the smallest indexj
such thatj > 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 functionprivate 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 toxval[i-1]
, update the interval so that it embraces the same number of points closest toxval[i]
, ignoring zero weights.
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Field Detail
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DEFAULT_BANDWIDTH
public static final double DEFAULT_BANDWIDTH
Default value of the bandwidth parameter.- See Also:
- Constant Field Values
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DEFAULT_ROBUSTNESS_ITERS
public static final int DEFAULT_ROBUSTNESS_ITERS
Default value of the number of robustness iterations.- See Also:
- Constant Field Values
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DEFAULT_ACCURACY
public static final double DEFAULT_ACCURACY
Default value for accuracy.- Since:
- 2.1
- See Also:
- Constant Field Values
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serialVersionUID
private static final long serialVersionUID
serializable version identifier.- See Also:
- Constant Field Values
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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.
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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.
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accuracy
private final double accuracy
If the median residual at a certain robustness iteration is less than this amount, no more iterations are done.
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Constructor Detail
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LoessInterpolator
public LoessInterpolator()
Constructs a newLoessInterpolator
with a bandwidth ofDEFAULT_BANDWIDTH
,DEFAULT_ROBUSTNESS_ITERS
robustness iterations and an accuracy of {#link #DEFAULT_ACCURACY}. SeeLoessInterpolator(double, int, double)
for an explanation of the parameters.
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LoessInterpolator
public LoessInterpolator(double bandwidth, int robustnessIters)
Construct a newLoessInterpolator
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 isDEFAULT_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 isDEFAULT_ROBUSTNESS_ITERS
.- See Also:
LoessInterpolator(double, int, double)
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LoessInterpolator
public LoessInterpolator(double bandwidth, int robustnessIters, double accuracy) throws OutOfRangeException, NotPositiveException
Construct a newLoessInterpolator
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 isDEFAULT_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 isDEFAULT_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
- ifrobustnessIters
is negative.- Since:
- 2.1
- See Also:
LoessInterpolator(double, int)
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Method Detail
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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 aSplineInterpolator
on the resulting fit.- Specified by:
interpolate
in interfaceUnivariateInterpolator
- Parameters:
xval
- the arguments for the interpolation pointsyval
- the values for the interpolation points- Returns:
- A cubic spline built upon a loess fit to the data at the original abscissae
- Throws:
NonMonotonicSequenceException
- ifxval
not sorted in strictly increasing order.DimensionMismatchException
- ifxval
andyval
have different sizes.NoDataException
- ifxval
oryval
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).
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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
- ifxval
not sorted in strictly increasing order.DimensionMismatchException
- ifxval
andyval
have different sizes.NoDataException
- ifxval
oryval
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
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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 pointsyval
- the values for the interpolation points- Returns:
- values of the loess fit at corresponding original abscissae
- Throws:
NonMonotonicSequenceException
- ifxval
not sorted in strictly increasing order.DimensionMismatchException
- ifxval
andyval
have different sizes.NoDataException
- ifxval
oryval
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).
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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 toxval[i-1]
, update the interval so that it embraces the same number of points closest toxval[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.
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nextNonzero
private static int nextNonzero(double[] weights, int i)
Return the smallest indexj
such thatj > i && (j == weights.length || weights[j] != 0)
.- Parameters:
weights
- Weights array.i
- Index from which to start search.- Returns:
- the smallest compliant index.
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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.
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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.
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