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<a href="../MathNet.Numerics.Interpolation/Barycentric.htm">Barycentric</a>
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<div class="header">
<p class="class"><strong>Type</strong> CubicSpline</p>
<p><strong>Namespace</strong> MathNet.Numerics.Interpolation</p>
<p><strong>Interfaces</strong> <a href="../MathNet.Numerics.Interpolation/IInterpolation.htm">IInterpolation</a></p>
</div>
<div class="sub-header">
<div id="summary">Cubic Spline Interpolation. <blockquote class="remarks">
Supports both differentiation and integration.
</blockquote>
</div>
<h3 class="section">Constructors</h3>
<ul>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#.ctor">CubicSpline</a></li>
</ul>
<h3 class="section">Static Functions</h3>
<ul>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateAkima">InterpolateAkima</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateAkimaInplace">InterpolateAkimaInplace</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateAkimaSorted">InterpolateAkimaSorted</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateBoundaries">InterpolateBoundaries</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateBoundariesInplace">InterpolateBoundariesInplace</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateBoundariesSorted">InterpolateBoundariesSorted</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateHermite">InterpolateHermite</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateHermiteInplace">InterpolateHermiteInplace</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateHermiteSorted">InterpolateHermiteSorted</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateNatural">InterpolateNatural</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateNaturalInplace">InterpolateNaturalInplace</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolateNaturalSorted">InterpolateNaturalSorted</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolatePchip">InterpolatePchip</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolatePchipInplace">InterpolatePchipInplace</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#InterpolatePchipSorted">InterpolatePchipSorted</a></li>
</ul>
<h3 class="section">Methods</h3>
<ul>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#Differentiate">Differentiate</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#Differentiate2">Differentiate2</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#Equals">Equals</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#GetHashCode">GetHashCode</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#GetType">GetType</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#Integrate">Integrate</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#Integrate">Integrate</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#Interpolate">Interpolate</a></li>
<li><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm#ToString">ToString</a></li>
</ul>
</div>
<h3 class="section">Public Constructors</h3>
<div id=".ctor" class="method">
<h4> <strong>CubicSpline</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> c0, <span title="System.Double[]">Double[]</span> c1, <span title="System.Double[]">Double[]</span> c2, <span title="System.Double[]">Double[]</span> c3)</h4>
<div class="content">
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Double[]">Double[]</span></code> x</h6>
<p class="comments">sample points (N+1), sorted ascending </p>
<h6><code><span title="System.Double[]">Double[]</span></code> c0</h6>
<p class="comments">Zero order spline coefficients (N) </p>
<h6><code><span title="System.Double[]">Double[]</span></code> c1</h6>
<p class="comments">First order spline coefficients (N) </p>
<h6><code><span title="System.Double[]">Double[]</span></code> c2</h6>
<p class="comments">second order spline coefficients (N) </p>
<h6><code><span title="System.Double[]">Double[]</span></code> c3</h6>
<p class="comments">third order spline coefficients (N) </p>
</div>
</div>
</div>
<h3 class="section">Public Static Functions</h3>
<div id="InterpolateAkima" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateAkima</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> x, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> y)</h4>
<div class="content">Create an Akima cubic spline interpolation from an unsorted set of (x,y) value pairs.
Akima splines are robust to outliers.
</div>
</div>
<div id="InterpolateAkimaInplace" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateAkimaInplace</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y)</h4>
<div class="content">Create an Akima cubic spline interpolation from an unsorted set of (x,y) value pairs.
Akima splines are robust to outliers.
WARNING: Works in-place and can thus causes the data array to be reordered.
</div>
</div>
<div id="InterpolateAkimaSorted" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateAkimaSorted</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y)</h4>
<div class="content">Create an Akima cubic spline interpolation from a set of (x,y) value pairs, sorted ascendingly by x.
Akima splines are robust to outliers.
</div>
</div>
<div id="InterpolateBoundaries" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateBoundaries</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> x, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> y, <a href="../MathNet.Numerics.Interpolation/SplineBoundaryCondition.htm">SplineBoundaryCondition</a> leftBoundaryCondition, <span title="System.double">double</span> leftBoundary, <a href="../MathNet.Numerics.Interpolation/SplineBoundaryCondition.htm">SplineBoundaryCondition</a> rightBoundaryCondition, <span title="System.double">double</span> rightBoundary)</h4>
<div class="content">Create a cubic spline interpolation from an unsorted set of (x,y) value pairs and custom boundary/termination conditions.
</div>
</div>
<div id="InterpolateBoundariesInplace" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateBoundariesInplace</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y, <a href="../MathNet.Numerics.Interpolation/SplineBoundaryCondition.htm">SplineBoundaryCondition</a> leftBoundaryCondition, <span title="System.double">double</span> leftBoundary, <a href="../MathNet.Numerics.Interpolation/SplineBoundaryCondition.htm">SplineBoundaryCondition</a> rightBoundaryCondition, <span title="System.double">double</span> rightBoundary)</h4>
<div class="content">Create a cubic spline interpolation from an unsorted set of (x,y) value pairs and custom boundary/termination conditions.
WARNING: Works in-place and can thus causes the data array to be reordered.
</div>
</div>
<div id="InterpolateBoundariesSorted" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateBoundariesSorted</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y, <a href="../MathNet.Numerics.Interpolation/SplineBoundaryCondition.htm">SplineBoundaryCondition</a> leftBoundaryCondition, <span title="System.double">double</span> leftBoundary, <a href="../MathNet.Numerics.Interpolation/SplineBoundaryCondition.htm">SplineBoundaryCondition</a> rightBoundaryCondition, <span title="System.double">double</span> rightBoundary)</h4>
<div class="content">Create a cubic spline interpolation from a set of (x,y) value pairs, sorted ascendingly by x,
and custom boundary/termination conditions.
</div>
</div>
<div id="InterpolateHermite" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateHermite</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> x, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> y, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> firstDerivatives)</h4>
<div class="content">Create a Hermite cubic spline interpolation from an unsorted set of (x,y) value pairs and their slope (first derivative).
</div>
</div>
<div id="InterpolateHermiteInplace" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateHermiteInplace</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y, <span title="System.Double[]">Double[]</span> firstDerivatives)</h4>
<div class="content">Create a Hermite cubic spline interpolation from an unsorted set of (x,y) value pairs and their slope (first derivative).
WARNING: Works in-place and can thus causes the data array to be reordered.
</div>
</div>
<div id="InterpolateHermiteSorted" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateHermiteSorted</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y, <span title="System.Double[]">Double[]</span> firstDerivatives)</h4>
<div class="content">Create a Hermite cubic spline interpolation from a set of (x,y) value pairs and their slope (first derivative), sorted ascendingly by x.
</div>
</div>
<div id="InterpolateNatural" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateNatural</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> x, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> y)</h4>
<div class="content">Create a natural cubic spline interpolation from an unsorted set of (x,y) value pairs
and zero second derivatives at the two boundaries.
</div>
</div>
<div id="InterpolateNaturalInplace" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateNaturalInplace</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y)</h4>
<div class="content">Create a natural cubic spline interpolation from an unsorted set of (x,y) value pairs
and zero second derivatives at the two boundaries.
WARNING: Works in-place and can thus causes the data array to be reordered.
</div>
</div>
<div id="InterpolateNaturalSorted" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolateNaturalSorted</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y)</h4>
<div class="content">Create a natural cubic spline interpolation from a set of (x,y) value pairs
and zero second derivatives at the two boundaries, sorted ascendingly by x.
</div>
</div>
<div id="InterpolatePchip" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolatePchip</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> x, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> y)</h4>
<div class="content">Create a piecewise cubic Hermite interpolating polynomial from an unsorted set of (x,y) value pairs.
Monotone-preserving interpolation with continuous first derivative.
</div>
</div>
<div id="InterpolatePchipInplace" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolatePchipInplace</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y)</h4>
<div class="content">Create a piecewise cubic Hermite interpolating polynomial from an unsorted set of (x,y) value pairs.
Monotone-preserving interpolation with continuous first derivative.
WARNING: Works in-place and can thus causes the data array to be reordered.
</div>
</div>
<div id="InterpolatePchipSorted" class="method">
<h4><a href="../MathNet.Numerics.Interpolation/CubicSpline.htm">CubicSpline</a> <strong>InterpolatePchipSorted</strong>(<span title="System.Double[]">Double[]</span> x, <span title="System.Double[]">Double[]</span> y)</h4>
<div class="content">Create a piecewise cubic Hermite interpolating polynomial from an unsorted set of (x,y) value pairs.
Monotone-preserving interpolation with continuous first derivative.
</div>
</div>
<h3 class="section">Public Methods</h3>
<div id="Differentiate" class="method">
<h4><span title="System.double">double</span> <strong>Differentiate</strong>(<span title="System.double">double</span> t)</h4>
<div class="content">Differentiate at point t.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.double">double</span></code> t</h6>
<p class="comments">Point t to interpolate at. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>Interpolated first derivative at point t. </p>
</div>
</div>
</div>
<div id="Differentiate2" class="method">
<h4><span title="System.double">double</span> <strong>Differentiate2</strong>(<span title="System.double">double</span> t)</h4>
<div class="content">Differentiate twice at point t.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.double">double</span></code> t</h6>
<p class="comments">Point t to interpolate at. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>Interpolated second derivative at point t. </p>
</div>
</div>
</div>
<div id="Equals" class="method">
<h4><span title="System.bool">bool</span> <strong>Equals</strong>(<span title="System.object">object</span> obj)</h4>
<div class="content">
</div>
</div>
<div id="GetHashCode" class="method">
<h4><span title="System.int">int</span> <strong>GetHashCode</strong>()</h4>
<div class="content">
</div>
</div>
<div id="GetType" class="method">
<h4><span title="System.Type">Type</span> <strong>GetType</strong>()</h4>
<div class="content">
</div>
</div>
<div id="Integrate" class="method">
<h4><span title="System.double">double</span> <strong>Integrate</strong>(<span title="System.double">double</span> a, <span title="System.double">double</span> b)</h4>
<div class="content">Definite integral between points a and b.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.double">double</span></code> a</h6>
<p class="comments">Left bound of the integration interval [a,b]. </p>
<h6><code><span title="System.double">double</span></code> b</h6>
<p class="comments">Right bound of the integration interval [a,b]. </p>
</div>
</div>
</div>
<div id="Integrate" class="method">
<h4><span title="System.double">double</span> <strong>Integrate</strong>(<span title="System.double">double</span> t)</h4>
<div class="content">Indefinite integral at point t.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.double">double</span></code> t</h6>
<p class="comments">Point t to integrate at. </p>
</div>
</div>
</div>
<div id="Interpolate" class="method">
<h4><span title="System.double">double</span> <strong>Interpolate</strong>(<span title="System.double">double</span> t)</h4>
<div class="content">Interpolate at point t.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.double">double</span></code> t</h6>
<p class="comments">Point t to interpolate at. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>Interpolated value x(t). </p>
</div>
</div>
</div>
<div id="ToString" class="method">
<h4><span title="System.string">string</span> <strong>ToString</strong>()</h4>
<div class="content">
</div>
</div>
<div id="footer">
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