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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_cubic_interpolation.html">CubicInterpolation</a></li> </ul>
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<a href="#pub-types">Public Types</a> |
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<div class="title">CubicInterpolation Class Reference<div class="ingroups"><a class="el" href="group__math.html">Math tools</a> » <a class="el" href="group__interpolations.html">1-D Interpolations and corresponding traits</a></div></div> </div>
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<p>Cubic interpolation between discrete points.
<a href="class_quant_lib_1_1_cubic_interpolation.html#details">More...</a></p>
<p><code>#include <ql/math/interpolations/cubicinterpolation.hpp></code></p>
<div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for CubicInterpolation:</div>
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<map name="_cubic_interpolation_inherit__map" id="a_cubic_interpolation_inherit__map">
<area shape="rect" title="Cubic interpolation between discrete points." alt="" coords="5,155,132,181"/>
<area shape="rect" href="class_quant_lib_1_1_interpolation.html" title="base class for 1-D interpolations." alt="" coords="22,80,115,107"/>
<area shape="rect" href="class_quant_lib_1_1_extrapolator.html" title="base class for classes possibly allowing extrapolation" alt="" coords="23,5,115,32"/>
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<table class="memberdecls">
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Public Types</h2></td></tr>
<tr class="memitem:aeccb633d9226f37b800589483ea2f0f6"><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6">DerivativeApprox</a> { <br />
  <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6a73a1396ca8adb89d7ff481ff55974c1e">Spline</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6aace9569c3a723c414afe7e6332958312">SplineOM1</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6a5230bf2465bab97aecd7087ee1a8ce1e">SplineOM2</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6a8908df67d5fb494d1799a270564789f8">FourthOrder</a>,
<br />
  <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6a6c56130d695e3aea964232dacfa2c298">Parabolic</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6ac194b4cb0838c7c484b13eb6d6dc0010">FritschButland</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6ab1ddc152184a0f96b8f6e9be8168e708">Akima</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6a065fa14c1b83af108fdae0c713695951">Kruger</a>,
<br />
  <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6a82e4e48ee59fde0b536296be56d2365f">Harmonic</a>
<br />
}</td></tr>
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<tr class="memitem:af3393571fa8a8daa4ee5c06613b26555"><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555">BoundaryCondition</a> { <br />
  <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555a7922e3c8bf97083083c9261300dcfedf">NotAKnot</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555aaf8392865aea8f24355012391183d9e9">FirstDerivative</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555a23de8c854eb282410ba10963837c94b5">SecondDerivative</a>,
<a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555a6db09e3bc054df6f996a45de2ccfeacd">Periodic</a>,
<br />
  <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555a1e1c27164b52b5cdf7df7f110dbb0fd3">Lagrange</a>
<br />
}</td></tr>
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<tr class="inherit_header pub_types_class_quant_lib_1_1_interpolation"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_quant_lib_1_1_interpolation')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_quant_lib_1_1_interpolation.html">Interpolation</a></td></tr>
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typedef <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>argument_type</b></td></tr>
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typedef <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>result_type</b></td></tr>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a4660490e94d17a41507f676a5eb41a15"><td class="memTemplParams" colspan="2">template<class I1 , class I2 > </td></tr>
<tr class="memitem:a4660490e94d17a41507f676a5eb41a15"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#a4660490e94d17a41507f676a5eb41a15">CubicInterpolation</a> (const I1 &xBegin, const I1 &xEnd, const I2 &yBegin, <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6">CubicInterpolation::DerivativeApprox</a> da, bool monotonic, <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555">CubicInterpolation::BoundaryCondition</a> leftCond, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> leftConditionValue, <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555">CubicInterpolation::BoundaryCondition</a> rightCond, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> rightConditionValue)</td></tr>
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const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>primitiveConstants</b> () const</td></tr>
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const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>aCoefficients</b> () const</td></tr>
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const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>bCoefficients</b> () const</td></tr>
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const std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > & </td><td class="memItemRight" valign="bottom"><b>cCoefficients</b> () const</td></tr>
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const std::vector< bool > & </td><td class="memItemRight" valign="bottom"><b>monotonicityAdjustments</b> () const</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_interpolation"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_interpolation')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_interpolation.html">Interpolation</a></td></tr>
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bool </td><td class="memItemRight" valign="bottom"><b>empty</b> () const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>operator()</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x, bool allowExtrapolation=false) const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>primitive</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x, bool allowExtrapolation=false) const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>derivative</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x, bool allowExtrapolation=false) const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>secondDerivative</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x, bool allowExtrapolation=false) const</td></tr>
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<tr class="memitem:a5efece7d663758ca3990448aa8e69bc7 inherit pub_methods_class_quant_lib_1_1_interpolation"><td class="memItemLeft" align="right" valign="top"><a id="a5efece7d663758ca3990448aa8e69bc7"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>xMin</b> () const</td></tr>
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<tr class="memitem:a7f70132c816636eee187ed4022f7c6c7 inherit pub_methods_class_quant_lib_1_1_interpolation"><td class="memItemLeft" align="right" valign="top"><a id="a7f70132c816636eee187ed4022f7c6c7"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>xMax</b> () const</td></tr>
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bool </td><td class="memItemRight" valign="bottom"><b>isInRange</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const</td></tr>
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void </td><td class="memItemRight" valign="bottom"><b>update</b> ()</td></tr>
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<tr class="inherit_header pub_methods_class_quant_lib_1_1_extrapolator"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_extrapolator')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_extrapolator.html">Extrapolator</a></td></tr>
<tr class="memitem:ae60e793a77f44a9c022b103458fa993c inherit pub_methods_class_quant_lib_1_1_extrapolator"><td class="memItemLeft" align="right" valign="top"><a id="ae60e793a77f44a9c022b103458fa993c"></a>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extrapolator.html#ae60e793a77f44a9c022b103458fa993c">enableExtrapolation</a> (bool b=true)</td></tr>
<tr class="memdesc:ae60e793a77f44a9c022b103458fa993c inherit pub_methods_class_quant_lib_1_1_extrapolator"><td class="mdescLeft"> </td><td class="mdescRight">enable extrapolation in subsequent calls <br /></td></tr>
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<tr class="memitem:abab5047522a68771f2b1d51d1ac78383 inherit pub_methods_class_quant_lib_1_1_extrapolator"><td class="memItemLeft" align="right" valign="top"><a id="abab5047522a68771f2b1d51d1ac78383"></a>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extrapolator.html#abab5047522a68771f2b1d51d1ac78383">disableExtrapolation</a> (bool b=true)</td></tr>
<tr class="memdesc:abab5047522a68771f2b1d51d1ac78383 inherit pub_methods_class_quant_lib_1_1_extrapolator"><td class="mdescLeft"> </td><td class="mdescRight">disable extrapolation in subsequent calls <br /></td></tr>
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<tr class="memitem:a323f875818fddd62a1c56c25ddaee418 inherit pub_methods_class_quant_lib_1_1_extrapolator"><td class="memItemLeft" align="right" valign="top"><a id="a323f875818fddd62a1c56c25ddaee418"></a>
bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extrapolator.html#a323f875818fddd62a1c56c25ddaee418">allowsExtrapolation</a> () const</td></tr>
<tr class="memdesc:a323f875818fddd62a1c56c25ddaee418 inherit pub_methods_class_quant_lib_1_1_extrapolator"><td class="mdescLeft"> </td><td class="mdescRight">tells whether extrapolation is enabled <br /></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pro_methods_class_quant_lib_1_1_interpolation"><td colspan="2" onclick="javascript:toggleInherit('pro_methods_class_quant_lib_1_1_interpolation')"><img src="closed.png" alt="-"/> Protected Member Functions inherited from <a class="el" href="class_quant_lib_1_1_interpolation.html">Interpolation</a></td></tr>
<tr class="memitem:af7f8e2474e4f230aa86ecf714b9d87d4 inherit pro_methods_class_quant_lib_1_1_interpolation"><td class="memItemLeft" align="right" valign="top"><a id="af7f8e2474e4f230aa86ecf714b9d87d4"></a>
void </td><td class="memItemRight" valign="bottom"><b>checkRange</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x, bool extrapolate) const</td></tr>
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<tr class="inherit_header pro_attribs_class_quant_lib_1_1_interpolation"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_interpolation')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_interpolation.html">Interpolation</a></td></tr>
<tr class="memitem:ac29a938cdc70db8abcde7a84fe62f9b4 inherit pro_attribs_class_quant_lib_1_1_interpolation"><td class="memItemLeft" align="right" valign="top"><a id="ac29a938cdc70db8abcde7a84fe62f9b4"></a>
ext::shared_ptr< <a class="el" href="class_quant_lib_1_1_interpolation_1_1_impl.html">Impl</a> > </td><td class="memItemRight" valign="bottom"><b>impl_</b></td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Cubic interpolation between discrete points. </p>
<p><a class="el" href="class_quant_lib_1_1_cubic.html" title="Cubic interpolation factory and traits">Cubic</a> interpolation is fully defined when the ${f_i}$ function values at points ${x_i}$ are supplemented with ${f^'_i}$ function derivative values.</p>
<p>Different type of first derivative approximations are implemented, both local and non-local. Local schemes (Fourth-order, Parabolic, Modified Parabolic, Fritsch-Butland, Akima, Kruger) use only $f$ values near $x_i$ to calculate each $f^'_i$. Non-local schemes (Spline with different boundary conditions) use all ${f_i}$ values and obtain ${f^'_i}$ by solving a linear system of equations. Local schemes produce $C^1$ interpolants, while the spline schemes generate $C^2$ interpolants.</p>
<p>Hyman's monotonicity constraint filter is also implemented: it can be applied to all schemes to ensure that in the regions of local monotoniticity of the input (three successive increasing or decreasing values) the interpolating cubic remains monotonic. If the interpolating cubic is already monotonic, the Hyman filter leaves it unchanged preserving all its original features.</p>
<p>In the case of $C^2$ interpolants the Hyman filter ensures local monotonicity at the expense of the second derivative of the interpolant which will no longer be continuous in the points where the filter has been applied.</p>
<p>While some non-linear schemes (Modified Parabolic, Fritsch-Butland, Kruger) are guaranteed to be locally monotonic in their original approximation, all other schemes must be filtered according to the Hyman criteria at the expense of their linearity.</p>
<p>See R. L. Dougherty, A. Edelman, and J. M. Hyman, "Nonnegativity-, Monotonicity-, or Convexity-Preserving CubicSpline and
Quintic Hermite Interpolation" Mathematics Of Computation, v. 52, n. 186, April 1989, pp. 471-494.</p>
<dl class="test"><dt><b><a class="el" href="test.html#_test000050">Tests:</a></b></dt><dd>to be adapted from old ones.</dd></dl>
<dl class="caveats"><dt><b><a class="el" href="caveats.html#_caveats000088">Warning:</a></b></dt><dd>See the <a class="el" href="class_quant_lib_1_1_interpolation.html" title="base class for 1-D interpolations.">Interpolation</a> class for information about the required lifetime of the underlying data. </dd></dl>
</div><h2 class="groupheader">Member Enumeration Documentation</h2>
<a id="aeccb633d9226f37b800589483ea2f0f6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aeccb633d9226f37b800589483ea2f0f6">◆ </a></span>DerivativeApprox</h2>
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<div class="memproto">
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<td class="memname">enum <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#aeccb633d9226f37b800589483ea2f0f6">DerivativeApprox</a></td>
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<table class="fieldtable">
<tr><th colspan="2">Enumerator</th></tr><tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6a73a1396ca8adb89d7ff481ff55974c1e"></a>Spline </td><td class="fielddoc"><p>Spline approximation (non-local, non-monotonic, linear[?]). Different boundary conditions can be used on the left and right boundaries: see <a class="el" href="class_quant_lib_1_1_boundary_condition.html" title="Abstract boundary condition class for finite difference problems.">BoundaryCondition</a>. </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6aace9569c3a723c414afe7e6332958312"></a>SplineOM1 </td><td class="fielddoc"><p>Overshooting minimization 1st derivative. </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6a5230bf2465bab97aecd7087ee1a8ce1e"></a>SplineOM2 </td><td class="fielddoc"><p>Overshooting minimization 2nd derivative. </p>
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<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6a8908df67d5fb494d1799a270564789f8"></a>FourthOrder </td><td class="fielddoc"><p>Fourth-order approximation (local, non-monotonic, linear) </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6a6c56130d695e3aea964232dacfa2c298"></a>Parabolic </td><td class="fielddoc"><p>Parabolic approximation (local, non-monotonic, linear) </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6ac194b4cb0838c7c484b13eb6d6dc0010"></a>FritschButland </td><td class="fielddoc"><p>Fritsch-Butland approximation (local, monotonic, non-linear) </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6ab1ddc152184a0f96b8f6e9be8168e708"></a>Akima </td><td class="fielddoc"><p>Akima approximation (local, non-monotonic, non-linear) </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6a065fa14c1b83af108fdae0c713695951"></a>Kruger </td><td class="fielddoc"><p>Kruger approximation (local, monotonic, non-linear) </p>
</td></tr>
<tr><td class="fieldname"><a id="aeccb633d9226f37b800589483ea2f0f6a82e4e48ee59fde0b536296be56d2365f"></a>Harmonic </td><td class="fielddoc"><p>Weighted harmonic mean approximation (local, monotonic, non-linear) </p>
</td></tr>
</table>
</div>
</div>
<a id="af3393571fa8a8daa4ee5c06613b26555"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af3393571fa8a8daa4ee5c06613b26555">◆ </a></span>BoundaryCondition</h2>
<div class="memitem">
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<td class="memname">enum <a class="el" href="class_quant_lib_1_1_cubic_interpolation.html#af3393571fa8a8daa4ee5c06613b26555">BoundaryCondition</a></td>
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<table class="fieldtable">
<tr><th colspan="2">Enumerator</th></tr><tr><td class="fieldname"><a id="af3393571fa8a8daa4ee5c06613b26555a7922e3c8bf97083083c9261300dcfedf"></a>NotAKnot </td><td class="fielddoc"><p>Make second(-last) point an inactive knot. </p>
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<tr><td class="fieldname"><a id="af3393571fa8a8daa4ee5c06613b26555aaf8392865aea8f24355012391183d9e9"></a>FirstDerivative </td><td class="fielddoc"><p>Match value of end-slope. </p>
</td></tr>
<tr><td class="fieldname"><a id="af3393571fa8a8daa4ee5c06613b26555a23de8c854eb282410ba10963837c94b5"></a>SecondDerivative </td><td class="fielddoc"><p>Match value of second derivative at end. </p>
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<tr><td class="fieldname"><a id="af3393571fa8a8daa4ee5c06613b26555a6db09e3bc054df6f996a45de2ccfeacd"></a>Periodic </td><td class="fielddoc"><p>Match first and second derivative at either end. </p>
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<tr><td class="fieldname"><a id="af3393571fa8a8daa4ee5c06613b26555a1e1c27164b52b5cdf7df7f110dbb0fd3"></a>Lagrange </td><td class="fielddoc"><p>Match end-slope to the slope of the cubic that matches the first four data at the respective end </p>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
<a id="a4660490e94d17a41507f676a5eb41a15"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4660490e94d17a41507f676a5eb41a15">◆ </a></span>CubicInterpolation()</h2>
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<td class="memname"><a class="el" href="class_quant_lib_1_1_cubic_interpolation.html">CubicInterpolation</a> </td>
<td>(</td>
<td class="paramtype">const I1 & </td>
<td class="paramname"><em>xBegin</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">const I1 & </td>
<td class="paramname"><em>xEnd</em>, </td>
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<td class="paramkey"></td>
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<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_interpolation.html#aeccb633d9226f37b800589483ea2f0f6">CubicInterpolation::DerivativeApprox</a> </td>
<td class="paramname"><em>da</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">bool </td>
<td class="paramname"><em>monotonic</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_interpolation.html#af3393571fa8a8daa4ee5c06613b26555">CubicInterpolation::BoundaryCondition</a> </td>
<td class="paramname"><em>leftCond</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">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_interpolation.html#af3393571fa8a8daa4ee5c06613b26555">CubicInterpolation::BoundaryCondition</a> </td>
<td class="paramname"><em>rightCond</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>rightConditionValue</em> </td>
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<td>)</td>
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<dl class="section pre"><dt>Precondition</dt><dd>the \( x \) values must be sorted. </dd></dl>
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