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diff --git a/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html new file mode 100644 index 0000000..7289715 --- /dev/null +++ b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html @@ -0,0 +1,396 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<!-- NewPage --> +<html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<title>BracketedRealFieldUnivariateSolver (Apache Commons Math 3.6.1 API)</title> +<link rel="stylesheet" type="text/css" href="../../../../../../stylesheet.css" title="Style"> +</head> +<body> +<script type="text/javascript"><!-- + if (location.href.indexOf('is-external=true') == -1) { + parent.document.title="BracketedRealFieldUnivariateSolver (Apache Commons Math 3.6.1 API)"; 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+ if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li>Field | </li> +<li>Constr | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li>Field | </li> +<li>Constr | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_top"> +<!-- --> +</a></div> +<!-- ========= END OF TOP NAVBAR ========= --> +<!-- ======== START OF CLASS DATA ======== --> +<div class="header"> +<div class="subTitle">org.apache.commons.math3.analysis.solvers</div> +<h2 title="Interface BracketedRealFieldUnivariateSolver" class="title">Interface BracketedRealFieldUnivariateSolver<T extends <a href="../../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></h2> +</div> +<div class="contentContainer"> +<div class="description"> +<ul class="blockList"> +<li class="blockList"> +<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd></dl> +<dl> +<dt>All Known Implementing Classes:</dt> +<dd><a href="../../../../../../org/apache/commons/math3/dfp/BracketingNthOrderBrentSolverDFP.html" title="class in org.apache.commons.math3.dfp">BracketingNthOrderBrentSolverDFP</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/FieldBracketingNthOrderBrentSolver.html" title="class in org.apache.commons.math3.analysis.solvers">FieldBracketingNthOrderBrentSolver</a></dd> +</dl> +<hr> +<br> +<pre>public interface <span class="strong">BracketedRealFieldUnivariateSolver<T extends <a href="../../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a><T>></span></pre> +<div class="block">Interface for <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers"><code>(univariate real) root-finding + algorithms</code></a> that maintain a bracketed solution. There are several advantages + to having such root-finding algorithms: + <ul> + <li>The bracketed solution guarantees that the root is kept within the + interval. As such, these algorithms generally also guarantee + convergence.</li> + <li>The bracketed solution means that we have the opportunity to only + return roots that are greater than or equal to the actual root, or + are less than or equal to the actual root. That is, we can control + whether under-approximations and over-approximations are + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers"><code>allowed solutions</code></a>. Other root-finding + algorithms can usually only guarantee that the solution (the root that + was found) is around the actual root.</li> + </ul> + + <p>For backwards compatibility, all root-finding algorithms must have + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html#ANY_SIDE"><code>ANY_SIDE</code></a> as default for the allowed + solutions.</p></div> +<dl><dt><span class="strong">Since:</span></dt> + <dd>3.6</dd> +<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers"><code>AllowedSolution</code></a></dd></dl> +</li> +</ul> +</div> +<div class="summary"> +<ul class="blockList"> +<li class="blockList"> +<!-- ========== METHOD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_summary"> +<!-- --> +</a> +<h3>Method Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> +<caption><span>Methods</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Modifier and Type</th> +<th class="colLast" scope="col">Method and Description</th> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#getAbsoluteAccuracy()">getAbsoluteAccuracy</a></strong>()</code> +<div class="block">Get the absolute accuracy of the solver.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>int</code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#getEvaluations()">getEvaluations</a></strong>()</code> +<div class="block">Get the number of evaluations of the objective function.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#getFunctionValueAccuracy()">getFunctionValueAccuracy</a></strong>()</code> +<div class="block">Get the function value accuracy of the solver.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>int</code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#getMaxEvaluations()">getMaxEvaluations</a></strong>()</code> +<div class="block">Get the maximum number of function evaluations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#getRelativeAccuracy()">getRelativeAccuracy</a></strong>()</code> +<div class="block">Get the relative accuracy of the solver.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#solve(int,%20org.apache.commons.math3.analysis.RealFieldUnivariateFunction,%20T,%20T,%20org.apache.commons.math3.analysis.solvers.AllowedSolution)">solve</a></strong>(int maxEval, + <a href="../../../../../../org/apache/commons/math3/analysis/RealFieldUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">RealFieldUnivariateFunction</a><<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a>> f, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> min, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> max, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers">AllowedSolution</a> allowedSolution)</code> +<div class="block">Solve for a zero in the given interval.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#solve(int,%20org.apache.commons.math3.analysis.RealFieldUnivariateFunction,%20T,%20T,%20T,%20org.apache.commons.math3.analysis.solvers.AllowedSolution)">solve</a></strong>(int maxEval, + <a href="../../../../../../org/apache/commons/math3/analysis/RealFieldUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">RealFieldUnivariateFunction</a><<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a>> f, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> min, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> max, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> startValue, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers">AllowedSolution</a> allowedSolution)</code> +<div class="block">Solve for a zero in the given interval, start at <code>startValue</code>.</div> +</td> +</tr> +</table> +</li> +</ul> +</li> +</ul> +</div> +<div class="details"> +<ul class="blockList"> +<li class="blockList"> +<!-- ============ METHOD DETAIL ========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_detail"> +<!-- --> +</a> +<h3>Method Detail</h3> +<a name="getMaxEvaluations()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getMaxEvaluations</h4> +<pre>int getMaxEvaluations()</pre> +<div class="block">Get the maximum number of function evaluations.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>the maximum number of function evaluations.</dd></dl> +</li> +</ul> +<a name="getEvaluations()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getEvaluations</h4> +<pre>int getEvaluations()</pre> +<div class="block">Get the number of evaluations of the objective function. + The number of evaluations corresponds to the last call to the + <code>optimize</code> method. It is 0 if the method has not been + called yet.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>the number of evaluations of the objective function.</dd></dl> +</li> +</ul> +<a name="getAbsoluteAccuracy()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getAbsoluteAccuracy</h4> +<pre><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> getAbsoluteAccuracy()</pre> +<div class="block">Get the absolute accuracy of the solver. Solutions returned by the + solver should be accurate to this tolerance, i.e., if ε is the + absolute accuracy of the solver and <code>v</code> is a value returned by + one of the <code>solve</code> methods, then a root of the function should + exist somewhere in the interval (<code>v</code> - ε, <code>v</code> + ε).</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>the absolute accuracy.</dd></dl> +</li> +</ul> +<a name="getRelativeAccuracy()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getRelativeAccuracy</h4> +<pre><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> getRelativeAccuracy()</pre> +<div class="block">Get the relative accuracy of the solver. The contract for relative + accuracy is the same as <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html#getAbsoluteAccuracy()"><code>getAbsoluteAccuracy()</code></a>, but using + relative, rather than absolute error. If ρ is the relative accuracy + configured for a solver and <code>v</code> is a value returned, then a root + of the function should exist somewhere in the interval + (<code>v</code> - ρ <code>v</code>, <code>v</code> + ρ <code>v</code>).</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>the relative accuracy.</dd></dl> +</li> +</ul> +<a name="getFunctionValueAccuracy()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getFunctionValueAccuracy</h4> +<pre><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> getFunctionValueAccuracy()</pre> +<div class="block">Get the function value accuracy of the solver. If <code>v</code> is + a value returned by the solver for a function <code>f</code>, + then by contract, <code>|f(v)|</code> should be less than or equal to + the function value accuracy configured for the solver.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>the function value accuracy.</dd></dl> +</li> +</ul> +<a name="solve(int,org.apache.commons.math3.analysis.RealFieldUnivariateFunction,org.apache.commons.math3.RealFieldElement,org.apache.commons.math3.RealFieldElement,org.apache.commons.math3.analysis.solvers.AllowedSolution)"> +<!-- --> +</a><a name="solve(int, org.apache.commons.math3.analysis.RealFieldUnivariateFunction, T, T, org.apache.commons.math3.analysis.solvers.AllowedSolution)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>solve</h4> +<pre><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> solve(int maxEval, + <a href="../../../../../../org/apache/commons/math3/analysis/RealFieldUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">RealFieldUnivariateFunction</a><<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a>> f, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> min, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> max, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers">AllowedSolution</a> allowedSolution)</pre> +<div class="block">Solve for a zero in the given interval. + A solver may require that the interval brackets a single zero root. + Solvers that do require bracketing should be able to handle the case + where one of the endpoints is itself a root.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>maxEval</code> - Maximum number of evaluations.</dd><dd><code>f</code> - Function to solve.</dd><dd><code>min</code> - Lower bound for the interval.</dd><dd><code>max</code> - Upper bound for the interval.</dd><dd><code>allowedSolution</code> - The kind of solutions that the root-finding algorithm may + accept as solutions.</dd> +<dt><span class="strong">Returns:</span></dt><dd>A value where the function is zero.</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 arguments do not satisfy the requirements specified by the solver.</dd> +<dd><code><a href="../../../../../../org/apache/commons/math3/exception/TooManyEvaluationsException.html" title="class in org.apache.commons.math3.exception">TooManyEvaluationsException</a></code> - if + the allowed number of evaluations is exceeded.</dd></dl> +</li> +</ul> +<a name="solve(int,org.apache.commons.math3.analysis.RealFieldUnivariateFunction,org.apache.commons.math3.RealFieldElement,org.apache.commons.math3.RealFieldElement,org.apache.commons.math3.RealFieldElement,org.apache.commons.math3.analysis.solvers.AllowedSolution)"> +<!-- --> +</a><a name="solve(int, org.apache.commons.math3.analysis.RealFieldUnivariateFunction, T, T, T, org.apache.commons.math3.analysis.solvers.AllowedSolution)"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>solve</h4> +<pre><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> solve(int maxEval, + <a href="../../../../../../org/apache/commons/math3/analysis/RealFieldUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">RealFieldUnivariateFunction</a><<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a>> f, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> min, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> max, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" title="type parameter in BracketedRealFieldUnivariateSolver">T</a> startValue, + <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers">AllowedSolution</a> allowedSolution)</pre> +<div class="block">Solve for a zero in the given interval, start at <code>startValue</code>. + A solver may require that the interval brackets a single zero root. + Solvers that do require bracketing should be able to handle the case + where one of the endpoints is itself a root.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>maxEval</code> - Maximum number of evaluations.</dd><dd><code>f</code> - Function to solve.</dd><dd><code>min</code> - Lower bound for the interval.</dd><dd><code>max</code> - Upper bound for the interval.</dd><dd><code>startValue</code> - Start value to use.</dd><dd><code>allowedSolution</code> - The kind of solutions that the root-finding algorithm may + accept as solutions.</dd> +<dt><span class="strong">Returns:</span></dt><dd>A value where the function is zero.</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 arguments do not satisfy the requirements specified by the solver.</dd> +<dd><code><a href="../../../../../../org/apache/commons/math3/exception/TooManyEvaluationsException.html" title="class in org.apache.commons.math3.exception">TooManyEvaluationsException</a></code> - if + the allowed number of evaluations is exceeded.</dd></dl> +</li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +</div> +<!-- ========= END OF CLASS DATA ========= --> +<!-- ======= START OF BOTTOM NAVBAR ====== --> +<div class="bottomNav"><a name="navbar_bottom"> +<!-- --> +</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/BracketedRealFieldUnivariateSolver.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BisectionSolver.html" title="class in org.apache.commons.math3.analysis.solvers"><span class="strong">Prev Class</span></a></li> +<li><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedUnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers"><span class="strong">Next Class</span></a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../../index.html?org/apache/commons/math3/analysis/solvers/BracketedRealFieldUnivariateSolver.html" target="_top">Frames</a></li> +<li><a href="BracketedRealFieldUnivariateSolver.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_bottom"> +<li><a href="../../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_bottom"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li>Field | </li> +<li>Constr | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li>Field | </li> +<li>Constr | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_bottom"> +<!-- --> +</a></div> +<!-- ======== END OF BOTTOM NAVBAR ======= --> +<p class="legalCopy"><small>Copyright © 2003–2016 <a href="http://www.apache.org/">The Apache Software Foundation</a>. 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