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<p>Non-linear least-square method.
<a href="class_quant_lib_1_1_non_linear_least_square.html#details">More...</a></p>
<p><code>#include <ql/math/optimization/leastsquare.hpp></code></p>
<p><a href="class_quant_lib_1_1_non_linear_least_square-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a97ef06e4c5f0246dc4628a5e4d397444"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::NonLinearLeastSquare" ref="a97ef06e4c5f0246dc4628a5e4d397444" args="(Constraint &c, Real accuracy=1e-4, Size maxiter=100)" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a97ef06e4c5f0246dc4628a5e4d397444">NonLinearLeastSquare</a> (<a class="el" href="class_quant_lib_1_1_constraint.html">Constraint</a> &c, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> accuracy=1e-4, Size maxiter=100)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a55fdd63d7f7096f711f7b26bc52b543e"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::NonLinearLeastSquare" ref="a55fdd63d7f7096f711f7b26bc52b543e" args="(Constraint &c, Real accuracy, Size maxiter, boost::shared_ptr< OptimizationMethod > om)" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a55fdd63d7f7096f711f7b26bc52b543e">NonLinearLeastSquare</a> (<a class="el" href="class_quant_lib_1_1_constraint.html">Constraint</a> &c, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> accuracy, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> maxiter, boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_optimization_method.html">OptimizationMethod</a> > om)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a20fd9ab60a7cce2d6c0acad31c0038ce"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::~NonLinearLeastSquare" ref="a20fd9ab60a7cce2d6c0acad31c0038ce" args="()" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a20fd9ab60a7cce2d6c0acad31c0038ce">~NonLinearLeastSquare</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Destructor. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a067968a223168798fa3f64b6051f4354"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::perform" ref="a067968a223168798fa3f64b6051f4354" args="(LeastSquareProblem &lsProblem)" -->
<a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a067968a223168798fa3f64b6051f4354">perform</a> (<a class="el" href="class_quant_lib_1_1_least_square_problem.html">LeastSquareProblem</a> &lsProblem)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve least square problem using numerix solver. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a3332be4ffb31e7777ad8797ddaf803a9"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::setInitialValue" ref="a3332be4ffb31e7777ad8797ddaf803a9" args="(const Array &initialValue)" -->
void </td><td class="memItemRight" valign="bottom"><b>setInitialValue</b> (const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &initialValue)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a1cbd190434a8924319877d9a566a7362"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::results" ref="a1cbd190434a8924319877d9a566a7362" args="()" -->
<a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a1cbd190434a8924319877d9a566a7362">results</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">return the results <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a3f311cedd53bc1947d0cbf7846bf2778"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::residualNorm" ref="a3f311cedd53bc1947d0cbf7846bf2778" args="()" -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a3f311cedd53bc1947d0cbf7846bf2778">residualNorm</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">return the least square residual norm <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a424fb70e9f6bd717d1ebaeef27266237"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::lastValue" ref="a424fb70e9f6bd717d1ebaeef27266237" args="()" -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a424fb70e9f6bd717d1ebaeef27266237">lastValue</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">return last function value <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac91e0c85dd8c6275c6fb8da8de811dcc"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::exitFlag" ref="ac91e0c85dd8c6275c6fb8da8de811dcc" args="()" -->
<a class="el" href="group__types.html#gab9c87440c314438e51a899a03d2442d0">Integer</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#ac91e0c85dd8c6275c6fb8da8de811dcc">exitFlag</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">return exit flag <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a39cd20d97f356086d2c033b0bad60caf"></a><!-- doxytag: member="QuantLib::NonLinearLeastSquare::iterationsNumber" ref="a39cd20d97f356086d2c033b0bad60caf" args="()" -->
<a class="el" href="group__types.html#gab9c87440c314438e51a899a03d2442d0">Integer</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_non_linear_least_square.html#a39cd20d97f356086d2c033b0bad60caf">iterationsNumber</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">return the performed number of iterations <br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Non-linear least-square method. </p>
<p>Using a given optimization algorithm (default is conjugate gradient),</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ min \{ r(x) : x in R^n \} \]" src="form_228.png"/>
</p>
<p>where <img class="formulaInl" alt="$ r(x) = |f(x)|^2 $" src="form_229.png"/> is the Euclidean norm of <img class="formulaInl" alt="$ f(x) $" src="form_230.png"/> for some vector-valued function <img class="formulaInl" alt="$ f $" src="form_37.png"/> from <img class="formulaInl" alt="$ R^n $" src="form_231.png"/> to <img class="formulaInl" alt="$ R^m $" src="form_232.png"/>, </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ f = (f_1, ..., f_m) \]" src="form_233.png"/>
</p>
<p> with <img class="formulaInl" alt="$ f_i(x) = b_i - \phi(x,t_i) $" src="form_234.png"/> where <img class="formulaInl" alt="$ b $" src="form_48.png"/> is the vector of target data and <img class="formulaInl" alt="$ phi $" src="form_235.png"/> is a scalar function.</p>
<p>Assuming the differentiability of <img class="formulaInl" alt="$ f $" src="form_37.png"/>, the gradient of <img class="formulaInl" alt="$ r $" src="form_65.png"/> is defined by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ grad r(x) = f'(x)^t.f(x) \]" src="form_236.png"/>
</p>
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