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<div class="subTitle">edu.rit.numeric</div>
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<h2 title="Class RobustFit" class="title">Class RobustFit</h2>
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<div class="contentContainer">
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<ul class="inheritance">
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<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
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<li>edu.rit.numeric.RobustFit</li>
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<br>
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<pre>public class <span class="strong">RobustFit</span>
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extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
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<div class="block">Class RobustFit uses a robust estimation procedure to fit a series of
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(<I>x,y</I>) data points to a model. The data series is an instance of class
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<a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a>. The model is represented by a <a href="../../../edu/rit/numeric/ParameterizedFunction.html" title="interface in edu.rit.numeric">ParameterizedFunction</a> that computes the <I>y</I> value, given an <I>x</I>
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value. The model also has <I>parameters</I>.
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<P>
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Given a data series, a model function, and an initial guess for the parameter
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values, class RobustFit's <TT>fit()</TT> method finds parameter values that
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minimize the following <I>metric:</I>
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<P>
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<B>Σ</B><SUB><I>i</I></SUB>
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<I>ρ</I> (<I>y</I><SUB><I>i</I></SUB> −
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<I>f</I> (<I>x</I><SUB><I>i</I></SUB>, parameters))
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<P>
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where <I>f</I> is the model function and <I>ρ</I> is one of these metric
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functions:
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<UL>
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<P><LI>
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Normal: <I>ρ</I> (<I>z</I>) = <I>z</I><SUP>2</SUP>/2
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<P><LI>
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Exponential: <I>ρ</I> (<I>z</I>) = |<I>z</I>|
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<P><LI>
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Cauchy (default): <I>ρ</I> (<I>z</I>) = log (1 + <I>z</I><SUP>2</SUP>/2)
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</UL>
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<P>
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In other words, the <TT>fit()</TT> method <I>fits</I> the model to the data
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by adjusting the parameters to minimize the metric.
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<P>
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The metric function is the negative logarithm of the probability distribution
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of the errors in the <I>y</I> values. The above metric functions correspond
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to normal, two-sided exponential, and Cauchy error distributions.
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<P>
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The metric functions differ in how they treat <I>outliers,</I> i.e., data
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points that deviate from the model. The normal metric function gives
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increasing weights to points with increasing deviations. However, because of
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the increasing weights, outlier points may skew the fit (hence, this is not
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really a "robust" metric function). The exponential metric function gives
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equal weights to all points, regardless of deviation. This reduces the
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influence of outliers on the fit, yielding a more robust fit. With the
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Cauchy metric function, the weights first increase, then decrease as the
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deviations increase. This reduces the influence of outliers even further.
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<P>
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The <TT>fit()</TT> method uses class <a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html" title="class in edu.rit.numeric">MDMinimizationDownhillSimplex</a> to find the parameter values that minimize the
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metric. The inputs to and outputs from the <TT>fit()</TT> method are stored
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in fields of an instance of class RobustFit.
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<P>
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The <TT>fitWithDistribution()</TT> method uses the <I>bootstrapping</I>
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technique to determine the distribution of the model parameters, which
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depends on the error distribution of the data points. Bootstrapping performs
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multiple iterations of the model fitting procedure. On each iteration, a
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trial data set the same size as the original data set is created by sampling
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the original data points with replacement, and model parameters for the trial
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data set are computed. The <TT>fitWithDistribution()</TT> method outputs a
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series of the parameter values found at each iteration; the confidence region
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for the parameters; and the goodness-of-fit <I>p</I>-value.</div>
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</li>
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</ul>
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<h3>Field Summary</h3>
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<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Field Summary table, listing fields, and an explanation">
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<caption><span>Fields</span><span class="tabEnd"> </span></caption>
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<tr>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<th class="colLast" scope="col">Field and Description</th>
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<tr class="altColor">
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<td class="colFirst"><code>static <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#CAUCHY">CAUCHY</a></strong></code>
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<div class="block">The Cauchy metric function.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>double[]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#confidenceRegionLowerBound">confidenceRegionLowerBound</a></strong></code>
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<div class="block">The lower bound of the confidence region for the model parameters.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>double[]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#confidenceRegionUpperBound">confidenceRegionUpperBound</a></strong></code>
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<div class="block">The upper bound of the confidence region for the model parameters.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code><a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#data">data</a></strong></code>
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<div class="block">The data series.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#EXPONENTIAL">EXPONENTIAL</a></strong></code>
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<div class="block">The exponential metric function.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>int</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#M">M</a></strong></code>
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<div class="block">The number of parameters in the model, <I>M</I>.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code><a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#metric">metric</a></strong></code>
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<div class="block">The metric function.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>double[]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#metricSeries">metricSeries</a></strong></code>
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<div class="block">The metric values for the model parameter distribution.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#metricValue">metricValue</a></strong></code>
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<div class="block">The metric value.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code><a href="../../../edu/rit/numeric/ParameterizedFunction.html" title="interface in edu.rit.numeric">ParameterizedFunction</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#model">model</a></strong></code>
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<div class="block">The model function.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#NORMAL">NORMAL</a></strong></code>
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<div class="block">The normal metric function.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>double[]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#param">param</a></strong></code>
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<div class="block">The model parameters.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>double[][]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#paramSeries">paramSeries</a></strong></code>
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<div class="block">The model parameter distribution.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#pValue">pValue</a></strong></code>
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<div class="block">The goodness-of-fit <I>p</I>-value.</div>
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</td>
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</tr>
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</table>
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</li>
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<h3>Constructor Summary</h3>
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<caption><span>Constructors</span><span class="tabEnd"> </span></caption>
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<tr>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#RobustFit(edu.rit.numeric.ParameterizedFunction)">RobustFit</a></strong>(<a href="../../../edu/rit/numeric/ParameterizedFunction.html" title="interface in edu.rit.numeric">ParameterizedFunction</a> model)</code>
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<div class="block">Construct a new robust fitting object for the given model.</div>
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</td>
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</tr>
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</table>
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<h3>Method Summary</h3>
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<caption><span>Methods</span><span class="tabEnd"> </span></caption>
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<tr>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#fit(edu.rit.numeric.XYSeries)">fit</a></strong>(<a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a> data)</code>
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<div class="block">Fit the given data series to the model.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#fitWithDistribution(edu.rit.numeric.XYSeries, int, edu.rit.util.Random, double)">fitWithDistribution</a></strong>(<a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a> data,
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int T,
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<a href="../../../edu/rit/util/Random.html" title="class in edu.rit.util">Random</a> prng,
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double conf)</code>
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<div class="block">Fit the given data series to the model and compute the distribution of
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the model parameters.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>protected void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/RobustFit.html#initializeSimplex(edu.rit.numeric.MDMinimizationDownhillSimplex)">initializeSimplex</a></strong>(<a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html" title="class in edu.rit.numeric">MDMinimizationDownhillSimplex</a> minimizer)</code>
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<div class="block">Initialize the simplex in the given downhill simplex minimizer object.</div>
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</td>
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</tr>
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<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
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<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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</li>
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<h3>Field Detail</h3>
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<a name="model">
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<h4>model</h4>
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<pre>public final <a href="../../../edu/rit/numeric/ParameterizedFunction.html" title="interface in edu.rit.numeric">ParameterizedFunction</a> model</pre>
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<div class="block">The model function. When <TT>model.f()</TT> is called, the <TT>x</TT>
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argument is <I>x</I><SUB><I>i</I></SUB>, the <I>x</I> value of a data
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point; the <TT>p</TT> argument contains the model parameters; and the
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return value is
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<I>f</I> (<I>x</I><SUB><I>i</I></SUB>, parameters).</div>
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<h4>M</h4>
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<pre>public final int M</pre>
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<div class="block">The number of parameters in the model, <I>M</I>.</div>
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<pre>public <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a> metric</pre>
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<div class="block">The metric function. By default, this is <TT>CAUCHY</TT>. It can instead
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be set to <TT>NORMAL</TT>, <TT>EXPONENTIAL</TT>, or some other metric
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function.</div>
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<h4>param</h4>
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<pre>public final double[] param</pre>
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<div class="block">The model parameters. On input to the <TT>fit()</TT> and
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<TT>fitWithDistribution()</TT> methods, <TT>param</TT> contains the
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initial guess for the model parameters. On output from the <TT>fit()</TT>
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and <TT>fitWithDistribution()</TT> methods, <TT>param</TT> contains the
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fitted parameter values.</div>
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<h4>data</h4>
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<pre>public <a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a> data</pre>
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<div class="block">The data series. It contains the (<I>x,y</I>) data points to be fitted to
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the model. It is specified as an argument of the <TT>fit()</TT> and
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<TT>fitWithDistribution()</TT> methods.</div>
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<h4>metricValue</h4>
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<pre>public double metricValue</pre>
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<div class="block">The metric value. An output of the <TT>fit()</TT> and
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<TT>fitWithDistribution()</TT> methods. It is set to the value of the
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metric for the model with the fitted parameters stored in <TT>param</TT>.</div>
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<pre>public double[][] paramSeries</pre>
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<div class="block">The model parameter distribution. An output of the
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<TT>fitWithDistribution()</TT> method. <TT>paramSeries</TT> is a
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<I>T</I>-element array, where <I>T</I> is the number of trials. Each
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element of <TT>paramSeries</TT> is an <I>M</I>-element array giving the
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fitted parameter values for the corresponding trial.</div>
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<pre>public double[] metricSeries</pre>
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<div class="block">The metric values for the model parameter distribution. An output of the
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<TT>fitWithDistribution()</TT> method. <TT>metricSeries</TT> is a
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<I>T</I>-element array, where <I>T</I> is the number of trials. Each
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element of <TT>metricSeries</TT> gives the value of the metric for the
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model with the parameters stored in the corresponding element of
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<TT>paramSeries</TT>.</div>
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<pre>public double[] confidenceRegionLowerBound</pre>
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<div class="block">The lower bound of the confidence region for the model parameters. An
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output of the <TT>fitWithDistribution()</TT> method. The confidence level
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is specified as an argument of the <TT>fitWithDistribution()</TT> method;
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for example, 0.90 specifies a 90% confidence level. The confidence region
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is an <I>M</I>-dimensional rectangular hyperprism centered on the fitted
|
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parameters stored in <TT>param</TT>, such that the given fraction of the
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model parameter distribution stored in <TT>paramSeries</TT> falls within
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the hyperprism. <TT>confidenceRegionLowerBound</TT> gives the lower bound
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of each dimension of the confidence region hyperprism.</div>
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<h4>confidenceRegionUpperBound</h4>
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<pre>public double[] confidenceRegionUpperBound</pre>
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<div class="block">The upper bound of the confidence region for the model parameters. An
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output of the <TT>fitWithDistribution()</TT> method.
|
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<TT>confidenceRegionUpperBound</TT> gives the upper bound of each
|
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dimension of the confidence region hyperprism.</div>
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<h4>pValue</h4>
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<pre>public double pValue</pre>
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<div class="block">The goodness-of-fit <I>p</I>-value. An output of the
|
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<TT>fitWithDistribution()</TT> method. This gives the probability that a
|
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metric value greater than or equal to <TT>metricValue</TT> would occur by
|
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chance, even if the model with parameters <TT>params</TT> is correct.</div>
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<h4>NORMAL</h4>
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<pre>public static final <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a> NORMAL</pre>
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<div class="block">The normal metric function.</div>
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</li>
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<a name="EXPONENTIAL">
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<h4>EXPONENTIAL</h4>
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<pre>public static final <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a> EXPONENTIAL</pre>
|
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<div class="block">The exponential metric function.</div>
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</li>
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</ul>
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<a name="CAUCHY">
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<h4>CAUCHY</h4>
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<pre>public static final <a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a> CAUCHY</pre>
|
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<div class="block">The Cauchy metric function.</div>
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</li>
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<h3>Constructor Detail</h3>
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<a name="RobustFit(edu.rit.numeric.ParameterizedFunction)">
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<h4>RobustFit</h4>
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<pre>public RobustFit(<a href="../../../edu/rit/numeric/ParameterizedFunction.html" title="interface in edu.rit.numeric">ParameterizedFunction</a> model)</pre>
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<div class="block">Construct a new robust fitting object for the given model. The
|
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<TT>model</TT> field is set to the corresponding argument. The <TT>M</TT>
|
|
field is set by calling the model function's <TT>parameterLength()</TT>
|
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method. The <TT>param</TT> field is allocated with <I>M</I> elements;
|
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initially, the elements are 0.</div>
|
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>model</code> - Model function.</dd>
|
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<dt><span class="strong">Throws:</span></dt>
|
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>model</TT> is null.</dd></dl>
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<h4>fit</h4>
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<pre>public void fit(<a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a> data)</pre>
|
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<div class="block">Fit the given data series to the model. The data series is stored in the
|
|
<TT>data</TT> field. The model function was specified to the constructor,
|
|
and is also stored in the <TT>model</TT> field. On input to the
|
|
<TT>fit()</TT> method, <TT>param</TT> contains the initial guess for the
|
|
model parameters. On output from the <TT>fit()</TT> method,
|
|
<TT>param</TT> contains the fitted parameter values and
|
|
<TT>metricValue</TT> contains the value of the metric for the fitted
|
|
parameters.
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|
<P>
|
|
The <TT>fit()</TT> method uses the downhill simplex technique to find the
|
|
model parameters that minimize the metric. This involves initializing the
|
|
<I>simplex</I> in an <a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html" title="class in edu.rit.numeric">MDMinimizationDownhillSimplex</a> object.
|
|
The <TT>initializeSimplex()</TT> method is called to initialize the
|
|
simplex.</div>
|
|
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - Data series.</dd>
|
|
<dt><span class="strong">Throws:</span></dt>
|
|
<dd><code><a href="../../../edu/rit/numeric/TooManyIterationsException.html" title="class in edu.rit.numeric">TooManyIterationsException</a></code> - (unchecked exception) Thrown if too many iterations occurred without
|
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finding parameters that minimize the metric function.</dd></dl>
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</li>
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</ul>
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<a name="fitWithDistribution(edu.rit.numeric.XYSeries, int, edu.rit.util.Random, double)">
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<h4>fitWithDistribution</h4>
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<pre>public void fitWithDistribution(<a href="../../../edu/rit/numeric/XYSeries.html" title="class in edu.rit.numeric">XYSeries</a> data,
|
|
int T,
|
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<a href="../../../edu/rit/util/Random.html" title="class in edu.rit.util">Random</a> prng,
|
|
double conf)</pre>
|
|
<div class="block">Fit the given data series to the model and compute the distribution of
|
|
the model parameters. The data series is stored in the <TT>data</TT>
|
|
field. The bootstrapping technique with <I>T</I> trials using the given
|
|
pseudorandom number generator is used to compute the distribution. The
|
|
given confidence level is used to compute the confidence region; for
|
|
example, 0.90 specifies a 90% confidence level. The model function was
|
|
specified to the constructor, and is also stored in the <TT>model</TT>
|
|
field. On input to the <TT>fitWithDistribution()</TT> method,
|
|
<TT>param</TT> contains the initial guess for the model parameters. On
|
|
output from the <TT>fit()</TT> method, <TT>param</TT> contains the fitted
|
|
parameter values, <TT>metricValue</TT> contains the value of the metric
|
|
for the fitted parameters, <TT>paramSeries</TT> contains the series of
|
|
fitted parameter values from all the trials, <TT>metricSeries</TT>
|
|
contains the metric values from all the trials,
|
|
<TT>confidenceRegionLowerBound</TT> and
|
|
<TT>confidenceRegionUpperBound</TT> contain the lower and upper bounds of
|
|
the confidence region hyperprism, and <TT>pValue</TT> contains the
|
|
goodness-of-fit.
|
|
<P>
|
|
The <TT>fitWithDistribution()</TT> method uses the downhill simplex
|
|
technique to find the model parameters that minimize the metric. This
|
|
involves initializing the <I>simplex</I> in an <a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html" title="class in edu.rit.numeric">MDMinimizationDownhillSimplex</a> object. The <TT>initializeSimplex()</TT>
|
|
method is called to initialize the simplex.</div>
|
|
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - Data series.</dd><dd><code>T</code> - Number of trials.</dd><dd><code>prng</code> - Pseudorandom number generator.</dd><dd><code>conf</code> - Confidence level, in the range 0.0 .. 1.0.</dd>
|
|
<dt><span class="strong">Throws:</span></dt>
|
|
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>conf</TT> is out of bounds.</dd>
|
|
<dd><code><a href="../../../edu/rit/numeric/TooManyIterationsException.html" title="class in edu.rit.numeric">TooManyIterationsException</a></code> - (unchecked exception) Thrown if too many iterations occurred without
|
|
finding parameters that minimize the metric function.</dd></dl>
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</li>
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</ul>
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<a name="initializeSimplex(edu.rit.numeric.MDMinimizationDownhillSimplex)">
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</a>
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<h4>initializeSimplex</h4>
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<pre>protected void initializeSimplex(<a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html" title="class in edu.rit.numeric">MDMinimizationDownhillSimplex</a> minimizer)</pre>
|
|
<div class="block">Initialize the simplex in the given downhill simplex minimizer object.
|
|
The simplex points must be set based on the initial guess for the
|
|
parameter values stored in the <TT>param</TT> field. For further
|
|
information about initializing the simplex, see class <a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html" title="class in edu.rit.numeric">MDMinimizationDownhillSimplex</a>.
|
|
<P>
|
|
The default implementation of this method sets the first simplex point to
|
|
<TT>param</TT>, sets the second simplex point to <TT>param</TT> except
|
|
element 0 is set to perturb(<TT>param[0]</TT>), sets the third simplex
|
|
point to <TT>param</TT> except element 1 is set to
|
|
perturb(<TT>param[1]</TT>), and so on. perturb(<I>x</I>) = 1.01<I>x</I>
|
|
if <I>x</I> ≠ 0; perturb(0) = 0.01. This method can be overridden to
|
|
initialize the simplex differently.</div>
|
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</li>
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</ul>
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</li>
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</ul>
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<p class="legalCopy"><small><FONT SIZE="-2">Copyright © 2013–2016 by Alan Kaminsky. All rights reserved. Send comments to ark</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">@</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">cs.rit.edu.</FONT></small></p>
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