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<div class="subTitle">org.apache.commons.math3.stat.correlation</div>
<h2 title="Class Covariance" class="title">Class Covariance</h2>
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<dl>
<dt>Direct Known Subclasses:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/stat/correlation/StorelessCovariance.html" title="class in org.apache.commons.math3.stat.correlation">StorelessCovariance</a></dd>
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<pre>public class <span class="strong">Covariance</span>
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>
<div class="block">Computes covariances for pairs of arrays or columns of a matrix.
<p>The constructors that take <code>RealMatrix</code> or
<code>double[][]</code> arguments generate covariance matrices. The
columns of the input matrices are assumed to represent variable values.</p>
<p>The constructor argument <code>biasCorrected</code> determines whether or
not computed covariances are bias-corrected.</p>
<p>Unbiased covariances are given by the formula</p>
<code>cov(X, Y) = Σ[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / (n - 1)</code>
where <code>E(X)</code> is the mean of <code>X</code> and <code>E(Y)</code>
is the mean of the <code>Y</code> values.
<p>Non-bias-corrected estimates use <code>n</code> in place of <code>n - 1</code></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.0</dd></dl>
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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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<th class="colOne" scope="col">Constructor and Description</th>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance()">Covariance</a></strong>()</code>
<div class="block">Create a Covariance with no data</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance(double[][])">Covariance</a></strong>(double[][] data)</code>
<div class="block">Create a Covariance matrix from a rectangular array
whose columns represent covariates.</div>
</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance(double[][],%20boolean)">Covariance</a></strong>(double[][] data,
boolean biasCorrected)</code>
<div class="block">Create a Covariance matrix from a rectangular array
whose columns represent covariates.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance(org.apache.commons.math3.linear.RealMatrix)">Covariance</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</code>
<div class="block">Create a covariance matrix from a matrix whose columns
represent covariates.</div>
</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance(org.apache.commons.math3.linear.RealMatrix,%20boolean)">Covariance</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix,
boolean biasCorrected)</code>
<div class="block">Create a covariance matrix from a matrix whose columns
represent covariates.</div>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#computeCovarianceMatrix(double[][])">computeCovarianceMatrix</a></strong>(double[][] data)</code>
<div class="block">Create a covariance matrix from a rectangular array whose columns represent
covariates.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#computeCovarianceMatrix(double[][],%20boolean)">computeCovarianceMatrix</a></strong>(double[][] data,
boolean biasCorrected)</code>
<div class="block">Compute a covariance matrix from a rectangular array whose columns represent
covariates.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#computeCovarianceMatrix(org.apache.commons.math3.linear.RealMatrix)">computeCovarianceMatrix</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</code>
<div class="block">Create a covariance matrix from a matrix whose columns represent
covariates.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#computeCovarianceMatrix(org.apache.commons.math3.linear.RealMatrix,%20boolean)">computeCovarianceMatrix</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix,
boolean biasCorrected)</code>
<div class="block">Compute a covariance matrix from a matrix whose columns represent
covariates.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#covariance(double[],%20double[])">covariance</a></strong>(double[] xArray,
double[] yArray)</code>
<div class="block">Computes the covariance between the two arrays, using the bias-corrected
formula.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#covariance(double[],%20double[],%20boolean)">covariance</a></strong>(double[] xArray,
double[] yArray,
boolean biasCorrected)</code>
<div class="block">Computes the covariance between the two arrays.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#getCovarianceMatrix()">getCovarianceMatrix</a></strong>()</code>
<div class="block">Returns the covariance matrix</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#getN()">getN</a></strong>()</code>
<div class="block">Returns the number of observations (length of covariate vectors)</div>
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<h3>Constructor Detail</h3>
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<h4>Covariance</h4>
<pre>public Covariance()</pre>
<div class="block">Create a Covariance with no data</div>
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<h4>Covariance</h4>
<pre>public Covariance(double[][] data,
boolean biasCorrected)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Create a Covariance matrix from a rectangular array
whose columns represent covariates.
<p>The <code>biasCorrected</code> parameter determines whether or not
covariance estimates are bias-corrected.</p>
<p>The input array must be rectangular with at least one column
and two rows.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - rectangular array with columns representing covariates</dd><dd><code>biasCorrected</code> - true means covariances are bias-corrected</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the input data array is not
rectangular with at least two rows and one column.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if the input data array is not
rectangular with at least one row and one column.</dd></dl>
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<h4>Covariance</h4>
<pre>public Covariance(double[][] data)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Create a Covariance matrix from a rectangular array
whose columns represent covariates.
<p>The input array must be rectangular with at least one column
and two rows</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - rectangular array with columns representing covariates</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the input data array is not
rectangular with at least two rows and one column.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if the input data array is not
rectangular with at least one row and one column.</dd></dl>
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<h4>Covariance</h4>
<pre>public Covariance(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix,
boolean biasCorrected)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Create a covariance matrix from a matrix whose columns
represent covariates.
<p>The <code>biasCorrected</code> parameter determines whether or not
covariance estimates are bias-corrected.</p>
<p>The matrix must have at least one column and two rows</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing covariates</dd><dd><code>biasCorrected</code> - true means covariances are bias-corrected</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the input matrix does not have
at least two rows and one column</dd></dl>
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<h4>Covariance</h4>
<pre>public Covariance(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Create a covariance matrix from a matrix whose columns
represent covariates.
<p>The matrix must have at least one column and two rows</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing covariates</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the input matrix does not have
at least two rows and one column</dd></dl>
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<h3>Method Detail</h3>
<a name="getCovarianceMatrix()">
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<h4>getCovarianceMatrix</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getCovarianceMatrix()</pre>
<div class="block">Returns the covariance matrix</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>covariance matrix</dd></dl>
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<pre>public int getN()</pre>
<div class="block">Returns the number of observations (length of covariate vectors)</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>number of observations</dd></dl>
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<h4>computeCovarianceMatrix</h4>
<pre>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> computeCovarianceMatrix(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix,
boolean biasCorrected)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Compute a covariance matrix from a matrix whose columns represent
covariates.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - input matrix (must have at least one column and two rows)</dd><dd><code>biasCorrected</code> - determines whether or not covariance estimates are bias-corrected</dd>
<dt><span class="strong">Returns:</span></dt><dd>covariance matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the matrix does not contain sufficient data</dd></dl>
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<pre>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> computeCovarianceMatrix(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Create a covariance matrix from a matrix whose columns represent
covariates. Covariances are computed using the bias-corrected formula.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - input matrix (must have at least one column and two rows)</dd>
<dt><span class="strong">Returns:</span></dt><dd>covariance matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if matrix does not contain sufficient data</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance(org.apache.commons.math3.linear.RealMatrix)"><code>Covariance(org.apache.commons.math3.linear.RealMatrix)</code></a></dd></dl>
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<pre>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> computeCovarianceMatrix(double[][] data,
boolean biasCorrected)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Compute a covariance matrix from a rectangular array whose columns represent
covariates.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - input array (must have at least one column and two rows)</dd><dd><code>biasCorrected</code> - determines whether or not covariance estimates are bias-corrected</dd>
<dt><span class="strong">Returns:</span></dt><dd>covariance matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the data array does not contain sufficient
data</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if the input data array is not
rectangular with at least one row and one column.</dd></dl>
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<pre>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> computeCovarianceMatrix(double[][] data)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Create a covariance matrix from a rectangular array whose columns represent
covariates. Covariances are computed using the bias-corrected formula.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - input array (must have at least one column and two rows)</dd>
<dt><span class="strong">Returns:</span></dt><dd>covariance matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the data array does not contain sufficient data</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if the input data array is not
rectangular with at least one row and one column.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/stat/correlation/Covariance.html#Covariance(org.apache.commons.math3.linear.RealMatrix)"><code>Covariance(org.apache.commons.math3.linear.RealMatrix)</code></a></dd></dl>
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<h4>covariance</h4>
<pre>public double covariance(double[] xArray,
double[] yArray,
boolean biasCorrected)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Computes the covariance between the two arrays.
<p>Array lengths must match and the common length must be at least 2.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>xArray</code> - first data array</dd><dd><code>yArray</code> - second data array</dd><dd><code>biasCorrected</code> - if true, returned value will be bias-corrected</dd>
<dt><span class="strong">Returns:</span></dt><dd>returns the covariance for the two arrays</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the arrays lengths do not match or
there is insufficient data</dd></dl>
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<h4>covariance</h4>
<pre>public double covariance(double[] xArray,
double[] yArray)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Computes the covariance between the two arrays, using the bias-corrected
formula.
<p>Array lengths must match and the common length must be at least 2.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>xArray</code> - first data array</dd><dd><code>yArray</code> - second data array</dd>
<dt><span class="strong">Returns:</span></dt><dd>returns the covariance for the two arrays</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the arrays lengths do not match or
there is insufficient data</dd></dl>
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