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<div class="subTitle">org.apache.commons.math3.analysis.interpolation</div>
<h2 title="Class LoessInterpolator" class="title">Class LoessInterpolator</h2>
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<pre>public class <span class="strong">LoessInterpolator</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/UnivariateInterpolator.html" title="interface in org.apache.commons.math3.analysis.interpolation">UnivariateInterpolator</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre>
<div class="block">Implements the <a href="http://en.wikipedia.org/wiki/Local_regression">
Local Regression Algorithm</a> (also Loess, Lowess) for interpolation of
real univariate functions.
<p/>
For reference, see
<a href="http://www.math.tau.ac.il/~yekutiel/MA seminar/Cleveland 1979.pdf">
William S. Cleveland - Robust Locally Weighted Regression and Smoothing
Scatterplots</a>
<p/>
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.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.0</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: LoessInterpolator.java 1379904 2012-09-01 23:54:52Z erans $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../serialized-form.html#org.apache.commons.math3.analysis.interpolation.LoessInterpolator">Serialized Form</a></dd></dl>
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<th class="colLast" scope="col">Field and Description</th>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_ACCURACY">DEFAULT_ACCURACY</a></strong></code>
<div class="block">Default value for accuracy.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_BANDWIDTH">DEFAULT_BANDWIDTH</a></strong></code>
<div class="block">Default value of the bandwidth parameter.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_ROBUSTNESS_ITERS">DEFAULT_ROBUSTNESS_ITERS</a></strong></code>
<div class="block">Default value of the number of robustness iterations.</div>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator()">LoessInterpolator</a></strong>()</code>
<div class="block">Constructs a new <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>LoessInterpolator</code></a>
with a bandwidth of <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_BANDWIDTH"><code>DEFAULT_BANDWIDTH</code></a>,
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_ROBUSTNESS_ITERS"><code>DEFAULT_ROBUSTNESS_ITERS</code></a> robustness iterations
and an accuracy of {#link #DEFAULT_ACCURACY}.</div>
</td>
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<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator(double, int)">LoessInterpolator</a></strong>(double&nbsp;bandwidth,
int&nbsp;robustnessIters)</code>
<div class="block">Construct a new <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>LoessInterpolator</code></a>
with given bandwidth and number of robustness iterations.</div>
</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator(double, int, double)">LoessInterpolator</a></strong>(double&nbsp;bandwidth,
int&nbsp;robustnessIters,
double&nbsp;accuracy)</code>
<div class="block">Construct a new <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>LoessInterpolator</code></a>
with given bandwidth, number of robustness iterations and accuracy.</div>
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<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialSplineFunction</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#interpolate(double[], double[])">interpolate</a></strong>(double[]&nbsp;xval,
double[]&nbsp;yval)</code>
<div class="block">Compute an interpolating function by performing a loess fit
on the data at the original abscissae and then building a cubic spline
with a
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/SplineInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>SplineInterpolator</code></a>
on the resulting fit.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#smooth(double[], double[])">smooth</a></strong>(double[]&nbsp;xval,
double[]&nbsp;yval)</code>
<div class="block">Compute a loess fit on the data at the original abscissae.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#smooth(double[], double[], double[])">smooth</a></strong>(double[]&nbsp;xval,
double[]&nbsp;yval,
double[]&nbsp;weights)</code>
<div class="block">Compute a weighted loess fit on the data at the original abscissae.</div>
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<h4>DEFAULT_BANDWIDTH</h4>
<pre>public static final&nbsp;double DEFAULT_BANDWIDTH</pre>
<div class="block">Default value of the bandwidth parameter.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../constant-values.html#org.apache.commons.math3.analysis.interpolation.LoessInterpolator.DEFAULT_BANDWIDTH">Constant Field Values</a></dd></dl>
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<pre>public static final&nbsp;int DEFAULT_ROBUSTNESS_ITERS</pre>
<div class="block">Default value of the number of robustness iterations.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../constant-values.html#org.apache.commons.math3.analysis.interpolation.LoessInterpolator.DEFAULT_ROBUSTNESS_ITERS">Constant Field Values</a></dd></dl>
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<h4>DEFAULT_ACCURACY</h4>
<pre>public static final&nbsp;double DEFAULT_ACCURACY</pre>
<div class="block">Default value for accuracy.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../constant-values.html#org.apache.commons.math3.analysis.interpolation.LoessInterpolator.DEFAULT_ACCURACY">Constant Field Values</a></dd></dl>
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<h4>LoessInterpolator</h4>
<pre>public&nbsp;LoessInterpolator()</pre>
<div class="block">Constructs a new <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>LoessInterpolator</code></a>
with a bandwidth of <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_BANDWIDTH"><code>DEFAULT_BANDWIDTH</code></a>,
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_ROBUSTNESS_ITERS"><code>DEFAULT_ROBUSTNESS_ITERS</code></a> robustness iterations
and an accuracy of {#link #DEFAULT_ACCURACY}.
See <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator(double, int, double)"><code>LoessInterpolator(double, int, double)</code></a> for an explanation of
the parameters.</div>
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<h4>LoessInterpolator</h4>
<pre>public&nbsp;LoessInterpolator(double&nbsp;bandwidth,
int&nbsp;robustnessIters)</pre>
<div class="block">Construct a new <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>LoessInterpolator</code></a>
with given bandwidth and number of robustness iterations.
<p>
Calling this constructor is equivalent to calling {link <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator(double, int, double)"><code>LoessInterpolator(bandwidth,
robustnessIters, LoessInterpolator.DEFAULT_ACCURACY)</code></a>
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>bandwidth</code> - 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.</br>
A sensible value is usually 0.25 to 0.5, the default value is
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_BANDWIDTH"><code>DEFAULT_BANDWIDTH</code></a>.</dd><dd><code>robustnessIters</code> - This many robustness iterations are done.</br>
A sensible value is usually 0 (just the initial fit without any
robustness iterations) to 4, the default value is
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_ROBUSTNESS_ITERS"><code>DEFAULT_ROBUSTNESS_ITERS</code></a>.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator(double, int, double)"><code>LoessInterpolator(double, int, double)</code></a></dd></dl>
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<pre>public&nbsp;LoessInterpolator(double&nbsp;bandwidth,
int&nbsp;robustnessIters,
double&nbsp;accuracy)
throws <a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></pre>
<div class="block">Construct a new <a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>LoessInterpolator</code></a>
with given bandwidth, number of robustness iterations and accuracy.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>bandwidth</code> - 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.</br>
A sensible value is usually 0.25 to 0.5, the default value is
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_BANDWIDTH"><code>DEFAULT_BANDWIDTH</code></a>.</dd><dd><code>robustnessIters</code> - This many robustness iterations are done.</br>
A sensible value is usually 0 (just the initial fit without any
robustness iterations) to 4, the default value is
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#DEFAULT_ROBUSTNESS_ITERS"><code>DEFAULT_ROBUSTNESS_ITERS</code></a>.</dd><dd><code>accuracy</code> - If the median residual at a certain robustness iteration
is less than this amount, no more iterations are done.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if bandwidth does not lie in the interval [0,1].</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>robustnessIters</code> is negative.</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html#LoessInterpolator(double, int)"><code>LoessInterpolator(double, int)</code></a></dd></dl>
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<h4>interpolate</h4>
<pre>public final&nbsp;<a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialSplineFunction</a>&nbsp;interpolate(double[]&nbsp;xval,
double[]&nbsp;yval)
throws <a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></pre>
<div class="block">Compute an interpolating function by performing a loess fit
on the data at the original abscissae and then building a cubic spline
with a
<a href="../../../../../../org/apache/commons/math3/analysis/interpolation/SplineInterpolator.html" title="class in org.apache.commons.math3.analysis.interpolation"><code>SplineInterpolator</code></a>
on the resulting fit.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/UnivariateInterpolator.html#interpolate(double[], double[])">interpolate</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/UnivariateInterpolator.html" title="interface in org.apache.commons.math3.analysis.interpolation">UnivariateInterpolator</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>xval</code> - the arguments for the interpolation points</dd><dd><code>yval</code> - the values for the interpolation points</dd>
<dt><span class="strong">Returns:</span></dt><dd>A cubic spline built upon a loess fit to the data at the original abscissae</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if <code>xval</code> not sorted in
strictly increasing order.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>xval</code> and <code>yval</code> have
different sizes.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>xval</code> or <code>yval</code> has zero size.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></code> - if any of the arguments and values are
not finite real numbers.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the bandwidth is too small to
accomodate the size of the input data (i.e. the bandwidth must be
larger than 2/n).</dd></dl>
</li>
</ul>
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<h4>smooth</h4>
<pre>public final&nbsp;double[]&nbsp;smooth(double[]&nbsp;xval,
double[]&nbsp;yval,
double[]&nbsp;weights)
throws <a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></pre>
<div class="block">Compute a weighted loess fit on the data at the original abscissae.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>xval</code> - Arguments for the interpolation points.</dd><dd><code>yval</code> - Values for the interpolation points.</dd><dd><code>weights</code> - point weights: coefficients by which the robustness weight
of a point is multiplied.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the values of the loess fit at corresponding original abscissae.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if <code>xval</code> not sorted in
strictly increasing order.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>xval</code> and <code>yval</code> have
different sizes.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>xval</code> or <code>yval</code> has zero size.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></code> - if any of the arguments and values are
not finite real numbers.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the bandwidth is too small to
accomodate the size of the input data (i.e. the bandwidth must be
larger than 2/n).</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd></dl>
</li>
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<h4>smooth</h4>
<pre>public final&nbsp;double[]&nbsp;smooth(double[]&nbsp;xval,
double[]&nbsp;yval)
throws <a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></pre>
<div class="block">Compute a loess fit on the data at the original abscissae.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>xval</code> - the arguments for the interpolation points</dd><dd><code>yval</code> - the values for the interpolation points</dd>
<dt><span class="strong">Returns:</span></dt><dd>values of the loess fit at corresponding original abscissae</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if <code>xval</code> not sorted in
strictly increasing order.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>xval</code> and <code>yval</code> have
different sizes.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>xval</code> or <code>yval</code> has zero size.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></code> - if any of the arguments and values are
not finite real numbers.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the bandwidth is too small to
accomodate the size of the input data (i.e. the bandwidth must be
larger than 2/n).</dd></dl>
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