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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_solver1_d.html">Solver1D</a></div>
<h1>Solver1D Class Template Reference</h1><!-- doxytag: class="QuantLib::Solver1D" --><!-- doxytag: inherits="QuantLib::CuriouslyRecurringTemplate" --><code>#include <ql/math/solver1d.hpp></code>
<p>
<div class="dynheader">
Inheritance diagram for Solver1D:</div>
<div class="dynsection">
<p><center><img src="class_quant_lib_1_1_solver1_d__inherit__graph.png" border="0" usemap="#_solver1_d__inherit__map" alt="Inheritance graph"></center>
<map name="_solver1_d__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_bisection.html" title="Bisection 1-D solver" alt="" coords="468,5,700,32"><area shape="rect" href="class_quant_lib_1_1_brent.html" title="Brent 1-D solver" alt="" coords="489,56,679,83"><area shape="rect" href="class_quant_lib_1_1_false_position.html" title="False position 1-D solver." alt="" coords="443,107,725,133"><area shape="rect" href="class_quant_lib_1_1_newton.html" title="Newton 1-D solver" alt="" coords="475,157,693,184"><area shape="rect" href="class_quant_lib_1_1_newton_safe.html" title="safe Newton 1-D solver" alt="" coords="444,208,724,235"><area shape="rect" href="class_quant_lib_1_1_ridder.html" title="Ridder 1-D solver" alt="" coords="484,259,684,285"><area shape="rect" href="class_quant_lib_1_1_secant.html" title="Secant 1-D solver" alt="" coords="480,309,688,336"><area shape="rect" href="class_quant_lib_1_1_curiously_recurring_template.html" title="Support for the curiously recurring template pattern." alt="" coords="7,157,263,184"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
<p>
<a href="class_quant_lib_1_1_solver1_d-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
<h3>template<class Impl><br>
class QuantLib::Solver1D< Impl ></h3>
Base class for 1-D solvers.
<p>
The implementation of this class uses the so-called "Barton-Nackman trick", also known as "the curiously recurring template pattern". Concrete solvers will be declared as: <div class="fragment"><pre class="fragment"> <span class="keyword">class </span>Foo : <span class="keyword">public</span> Solver1D<Foo> {
<span class="keyword">public</span>:
...
<span class="keyword">template</span> <<span class="keyword">class</span> F>
<a class="code" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> solveImpl(<span class="keyword">const</span> F& f, <a class="code" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a> accuracy)<span class="keyword"> const </span>{
...
}
};
</pre></div> Before calling <code>solveImpl</code>, the base class will set its protected data members so that:<ul>
<li><code>xMin_</code> and <code>xMax_</code> form a valid bracket;</li><li><code>fxMin_</code> and <code>fxMax_</code> contain the values of the function in <code>xMin_</code> and <code>xMax_</code>;</li><li><code>root_</code> is a valid initial guess. The implementation of <code>solveImpl</code> can safely assume all of the above.</li></ul>
<p>
<dl compact><dt><b><a class="el" href="todo.html#_todo000026">Possible enhancements:</a></b></dt><dd><ul>
<li>clean up the interface so that it is clear whether the accuracy is specified for <img class="formulaInl" alt="$ x $" src="form_138.png"> or <img class="formulaInl" alt="$ f(x) $" src="form_162.png">.</li><li>add target value (now the target value is 0.0) </li></ul>
</dd></dl>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">Modifiers</div></td></tr>
<tr><td class="memTemplParams" nowrap colspan="2">template<class F> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_solver1_d.html#a3e4a1cb8d3a75698d6b05672b878c79">solve</a> (const F &f, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> accuracy, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> guess, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> step) const </td></tr>
<tr><td class="memTemplParams" nowrap colspan="2">template<class F> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_solver1_d.html#af1d825631e53bada873867a0d66dd8a">solve</a> (const F &f, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> accuracy, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> guess, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> xMin, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> xMax) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_solver1_d.html#5cd4ab37661635dfaf1b58f547f4223f">setMaxEvaluations</a> (<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> evaluations)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6a9af21bb68e575c5616e2902a4788af"></a><!-- doxytag: member="QuantLib::Solver1D::setLowerBound" ref="6a9af21bb68e575c5616e2902a4788af" args="(Real lowerBound)" -->
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_solver1_d.html#6a9af21bb68e575c5616e2902a4788af">setLowerBound</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> lowerBound)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">sets the lower bound for the function domain <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="96c5f418c69b6d88109d2ad8097694f0"></a><!-- doxytag: member="QuantLib::Solver1D::setUpperBound" ref="96c5f418c69b6d88109d2ad8097694f0" args="(Real upperBound)" -->
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_solver1_d.html#96c5f418c69b6d88109d2ad8097694f0">setUpperBound</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> upperBound)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">sets the upper bound for the function domain <br></td></tr>
<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="89fa88b509db30a8647975af216f813e"></a><!-- doxytag: member="QuantLib::Solver1D::root_" ref="89fa88b509db30a8647975af216f813e" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>root_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="40f1875e76a0018adeb7d900d0afe1a0"></a><!-- doxytag: member="QuantLib::Solver1D::xMin_" ref="40f1875e76a0018adeb7d900d0afe1a0" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>xMin_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="baa9fa4e15bfef5dff0636efb04b948f"></a><!-- doxytag: member="QuantLib::Solver1D::xMax_" ref="baa9fa4e15bfef5dff0636efb04b948f" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>xMax_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="70b291b7f51aba1fd2d1b0e952b05eff"></a><!-- doxytag: member="QuantLib::Solver1D::fxMin_" ref="70b291b7f51aba1fd2d1b0e952b05eff" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>fxMin_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b1a3629c843b1a45743e0b3f4de5e127"></a><!-- doxytag: member="QuantLib::Solver1D::fxMax_" ref="b1a3629c843b1a45743e0b3f4de5e127" args="" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>fxMax_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d1fbba98763c2a0de29a5700ad331942"></a><!-- doxytag: member="QuantLib::Solver1D::maxEvaluations_" ref="d1fbba98763c2a0de29a5700ad331942" args="" -->
<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>maxEvaluations_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2a155adc5fe7e5242e59c1d9e059f0c9"></a><!-- doxytag: member="QuantLib::Solver1D::evaluationNumber_" ref="2a155adc5fe7e5242e59c1d9e059f0c9" args="" -->
<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>evaluationNumber_</b></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="a3e4a1cb8d3a75698d6b05672b878c79"></a><!-- doxytag: member="QuantLib::Solver1D::solve" ref="a3e4a1cb8d3a75698d6b05672b878c79" args="(const F &f, Real accuracy, Real guess, Real step) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> solve </td>
<td>(</td>
<td class="paramtype">const F & </td>
<td class="paramname"> <em>f</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>accuracy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>guess</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>step</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
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<p>
This method returns the zero of the function <img class="formulaInl" alt="$ f $" src="form_41.png">, determined with the given accuracy <img class="formulaInl" alt="$ \epsilon $" src="form_137.png">; depending on the particular solver, this might mean that the returned <img class="formulaInl" alt="$ x $" src="form_138.png"> is such that <img class="formulaInl" alt="$ |f(x)| < \epsilon $" src="form_171.png">, or that <img class="formulaInl" alt="$ |x-\xi| < \epsilon $" src="form_172.png"> where <img class="formulaInl" alt="$ \xi $" src="form_173.png"> is the real zero.<p>
This method contains a bracketing routine to which an initial guess must be supplied as well as a step used to scan the range of the possible bracketing values.
</div>
</div><p>
<a class="anchor" name="af1d825631e53bada873867a0d66dd8a"></a><!-- doxytag: member="QuantLib::Solver1D::solve" ref="af1d825631e53bada873867a0d66dd8a" args="(const F &f, Real accuracy, Real guess, Real xMin, Real xMax) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> solve </td>
<td>(</td>
<td class="paramtype">const F & </td>
<td class="paramname"> <em>f</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>accuracy</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>guess</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>xMin</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>xMax</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const</td>
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<p>
This method returns the zero of the function <img class="formulaInl" alt="$ f $" src="form_41.png">, determined with the given accuracy <img class="formulaInl" alt="$ \epsilon $" src="form_137.png">; depending on the particular solver, this might mean that the returned <img class="formulaInl" alt="$ x $" src="form_138.png"> is such that <img class="formulaInl" alt="$ |f(x)| < \epsilon $" src="form_171.png">, or that <img class="formulaInl" alt="$ |x-\xi| < \epsilon $" src="form_172.png"> where <img class="formulaInl" alt="$ \xi $" src="form_173.png"> is the real zero.<p>
An initial guess must be supplied, as well as two values <img class="formulaInl" alt="$ x_\mathrm{min} $" src="form_174.png"> and <img class="formulaInl" alt="$ x_\mathrm{max} $" src="form_175.png"> which must bracket the zero (i.e., either <img class="formulaInl" alt="$ f(x_\mathrm{min}) \leq 0 \leq f(x_\mathrm{max}) $" src="form_176.png">, or <img class="formulaInl" alt="$ f(x_\mathrm{max}) \leq 0 \leq f(x_\mathrm{min}) $" src="form_177.png"> must be true).
</div>
</div><p>
<a class="anchor" name="5cd4ab37661635dfaf1b58f547f4223f"></a><!-- doxytag: member="QuantLib::Solver1D::setMaxEvaluations" ref="5cd4ab37661635dfaf1b58f547f4223f" args="(Size evaluations)" -->
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<td class="memname">void setMaxEvaluations </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> </td>
<td class="paramname"> <em>evaluations</em> </td>
<td> ) </td>
<td width="100%"></td>
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<p>
This method sets the maximum number of function evaluations for the bracketing routine. An error is thrown if a bracket is not found after this number of evaluations.
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