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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html">CubicSplineInterpolation</a></div>
<h1>CubicSplineInterpolation Class Reference</h1><!-- doxytag: class="QuantLib::CubicSplineInterpolation" --><!-- doxytag: inherits="QuantLib::Interpolation" --><code>#include <ql/math/interpolations/cubicspline.hpp></code>
<p>
<div class="dynheader">
Inheritance diagram for CubicSplineInterpolation:</div>
<div class="dynsection">
<p><center><img src="class_quant_lib_1_1_cubic_spline_interpolation__inherit__graph.png" border="0" usemap="#_cubic_spline_interpolation__inherit__map" alt="Inheritance graph"></center>
<map name="_cubic_spline_interpolation__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_monotonic_cubic_spline.html" title="Cubic spline with monotonicity constraint" alt="" coords="5,161,168,188"><area shape="rect" href="class_quant_lib_1_1_natural_cubic_spline.html" title="Cubic spline with null second derivative at end points" alt="" coords="192,161,336,188"><area shape="rect" href="class_quant_lib_1_1_natural_monotonic_cubic_spline.html" title="Natural cubic spline with monotonicity constraint." alt="" coords="360,161,571,188"><area shape="rect" href="class_quant_lib_1_1_interpolation.html" title="base class for 1-D interpolations." alt="" coords="213,7,315,33"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
<p>
<a href="class_quant_lib_1_1_cubic_spline_interpolation-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Cubic spline interpolation between discrete points.
<p>
It implements different type of end conditions: not-a-knot, first derivative value, second derivative value.<p>
It also implements Hyman's monotonicity constraint filter which ensures that in the regions of monotoniticity of the input (so, three successive increasing or decreasing values) the interpolating spline remains monotonic at the expense of the second derivative of the curve which will no longer be continuous where the filter has been applied. If the interpolating spline is already monotonic, the Hyman filter leaves it unchanged.<p>
See R. L. Dougherty, A. Edelman, and J. M. Hyman, "Nonnegativity-, Monotonicity-, or Convexity-Preserving <a class="el" href="class_quant_lib_1_1_cubic_spline.html" title="Cubic spline interpolation factory and traits">CubicSpline</a> and Quintic Hermite Interpolation" Mathematics Of Computation, v. 52, n. 186, April 1989, pp. 471-494.<p>
<dl compact><dt><b><a class="el" href="test.html#_test000032">Tests:</a></b></dt><dd>the correctness of the returned values is tested by reproducing results available in literature. </dd></dl>
<table border="0" cellpadding="0" cellspacing="0">
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<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">enum </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555">BoundaryCondition</a> { <br>
<a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b265557922e3c8bf97083083c9261300dcfedf">NotAKnot</a>,
<a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555af8392865aea8f24355012391183d9e9">FirstDerivative</a>,
<a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b2655523de8c854eb282410ba10963837c94b5">SecondDerivative</a>,
<a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b265556db09e3bc054df6f996a45de2ccfeacd">Periodic</a>,
<br>
<a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b265551e1c27164b52b5cdf7df7f110dbb0fd3">Lagrange</a>
<br>
}</td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memTemplParams" nowrap colspan="2">template<class I1, class I2> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#115a1dcad0d263e8258147fb397b565f">CubicSplineInterpolation</a> (const I1 &xBegin, const I1 &xEnd, const I2 &yBegin, <a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555">CubicSplineInterpolation::BoundaryCondition</a> leftCondition, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> leftConditionValue, <a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555">CubicSplineInterpolation::BoundaryCondition</a> rightCondition, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> rightConditionValue, bool monotonicityConstraint)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="294c76c9e77213bbb3da550152033826"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::primitiveConstants" ref="294c76c9e77213bbb3da550152033826" args="() const " -->
const std::vector< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>primitiveConstants</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4119d6ba4d3f11be628a129a7a2bfe6f"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::aCoefficients" ref="4119d6ba4d3f11be628a129a7a2bfe6f" args="() const " -->
const std::vector< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>aCoefficients</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="aca6dd10570ae2dbc6e5ea6ab8a7e9bb"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::bCoefficients" ref="aca6dd10570ae2dbc6e5ea6ab8a7e9bb" args="() const " -->
const std::vector< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>bCoefficients</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7746999062e0736bd067da1e60548069"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::cCoefficients" ref="7746999062e0736bd067da1e60548069" args="() const " -->
const std::vector< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>cCoefficients</b> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7f8698aec8c4a956e68c3a9d6b19f23a"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::monotonicityAdjustments" ref="7f8698aec8c4a956e68c3a9d6b19f23a" args="() const " -->
const std::vector< bool > & </td><td class="memItemRight" valign="bottom"><b>monotonicityAdjustments</b> () const </td></tr>
</table>
<hr><h2>Member Enumeration Documentation</h2>
<a class="anchor" name="f3393571fa8a8daa4ee5c06613b26555"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::BoundaryCondition" ref="f3393571fa8a8daa4ee5c06613b26555" args="" -->
<div class="memitem">
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<td class="memname">enum <a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555">BoundaryCondition</a> </td>
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<p>
<dl compact><dt><b>Enumerator: </b></dt><dd>
<table border="0" cellspacing="2" cellpadding="0">
<tr><td valign="top"><em><a class="anchor" name="f3393571fa8a8daa4ee5c06613b265557922e3c8bf97083083c9261300dcfedf"></a><!-- doxytag: member="NotAKnot" ref="f3393571fa8a8daa4ee5c06613b265557922e3c8bf97083083c9261300dcfedf" args="" -->NotAKnot</em> </td><td>
Make second(-last) point an inactive knot. </td></tr>
<tr><td valign="top"><em><a class="anchor" name="f3393571fa8a8daa4ee5c06613b26555af8392865aea8f24355012391183d9e9"></a><!-- doxytag: member="FirstDerivative" ref="f3393571fa8a8daa4ee5c06613b26555af8392865aea8f24355012391183d9e9" args="" -->FirstDerivative</em> </td><td>
Match value of end-slope. </td></tr>
<tr><td valign="top"><em><a class="anchor" name="f3393571fa8a8daa4ee5c06613b2655523de8c854eb282410ba10963837c94b5"></a><!-- doxytag: member="SecondDerivative" ref="f3393571fa8a8daa4ee5c06613b2655523de8c854eb282410ba10963837c94b5" args="" -->SecondDerivative</em> </td><td>
Match value of second derivative at end. </td></tr>
<tr><td valign="top"><em><a class="anchor" name="f3393571fa8a8daa4ee5c06613b265556db09e3bc054df6f996a45de2ccfeacd"></a><!-- doxytag: member="Periodic" ref="f3393571fa8a8daa4ee5c06613b265556db09e3bc054df6f996a45de2ccfeacd" args="" -->Periodic</em> </td><td>
Match first and second derivative at either end. </td></tr>
<tr><td valign="top"><em><a class="anchor" name="f3393571fa8a8daa4ee5c06613b265551e1c27164b52b5cdf7df7f110dbb0fd3"></a><!-- doxytag: member="Lagrange" ref="f3393571fa8a8daa4ee5c06613b265551e1c27164b52b5cdf7df7f110dbb0fd3" args="" -->Lagrange</em> </td><td>
Match end-slope to the slope of the cubic that matches the first four data at the respective end </td></tr>
</table>
</dl>
</div>
</div><p>
<hr><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" name="115a1dcad0d263e8258147fb397b565f"></a><!-- doxytag: member="QuantLib::CubicSplineInterpolation::CubicSplineInterpolation" ref="115a1dcad0d263e8258147fb397b565f" args="(const I1 &xBegin, const I1 &xEnd, const I2 &yBegin, CubicSplineInterpolation::BoundaryCondition leftCondition, Real leftConditionValue, CubicSplineInterpolation::BoundaryCondition rightCondition, Real rightConditionValue, bool monotonicityConstraint)" -->
<div class="memitem">
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<table class="memname">
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<td class="memname"><a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html">CubicSplineInterpolation</a> </td>
<td>(</td>
<td class="paramtype">const I1 & </td>
<td class="paramname"> <em>xBegin</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const I1 & </td>
<td class="paramname"> <em>xEnd</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const I2 & </td>
<td class="paramname"> <em>yBegin</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555">CubicSplineInterpolation::BoundaryCondition</a> </td>
<td class="paramname"> <em>leftCondition</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>leftConditionValue</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_quant_lib_1_1_cubic_spline_interpolation.html#f3393571fa8a8daa4ee5c06613b26555">CubicSplineInterpolation::BoundaryCondition</a> </td>
<td class="paramname"> <em>rightCondition</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>rightConditionValue</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">bool </td>
<td class="paramname"> <em>monotonicityConstraint</em></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"></td>
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<div class="memdoc">
<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>the <img class="formulaInl" alt="$ x $" src="form_138.png"> values must be sorted. </dd></dl>
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