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180 lines
11 KiB
180 lines
11 KiB
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<li><a href="https://www.mathdotnet.com">Math.NET Project</a></li>
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<h3 class="muted">Math.NET Numerics</h3>
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<h1><a name="Interpolation" class="anchor" href="#Interpolation">Interpolation</a></h1>
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<p>Namespace: MathNet.Numerics.Interpolation</p>
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<p>Interpolation is a two-phased operation in Math.NET Numerics:</p>
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<ol>
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<li>Create an interpolation scheme for the chosen algorithm and optimized for the given sample points. You get back a class that implements the <em>IInterpolation</em> interface.</li>
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<li>Use this scheme to compute values at arbitrary points. Some interpolation algorithms also allow you to compute the derivative and the indefinite integral at that point.</li>
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</ol>
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<p>The static <code>Interpolate</code> class provides simple factory methods to create the interpolation scheme in a simple method call:</p>
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<ul>
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<li><em>RationalWithoutPoles</em>, creates a Floater-Hormann barycentric interpolation</li>
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<li><em>RationalWithPoles</em>, creates a Bulirsch & Stoer rational interpolation</li>
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<li><em>LinearBetweenPoints</em>, creates a linear spline interpolation</li>
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</ul>
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<p>If unsure, we recommend using <em>RationalWithoutPoles</em> for most cases.</p>
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<p>Alternatively you can also use the algorithms directly, they're publicly available in the <em>Algorithms</em> sub-namespace for those who want to use a specific algorithm. The following algorithms are available:</p>
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<h2><a name="Interpolation-on-equidistant-sample-points" class="anchor" href="#Interpolation-on-equidistant-sample-points">Interpolation on equidistant sample points</a></h2>
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<ul>
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<li><em>Polynomial</em>: Barycentric Algorithm</li>
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</ul>
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<h2><a name="Interpolation-on-arbitrary-sample-points" class="anchor" href="#Interpolation-on-arbitrary-sample-points">Interpolation on arbitrary sample points</a></h2>
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<ul>
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<li><em>Rational pole-free</em>: Barycentric Floater-Hormann Algorithm</li>
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<li><strong>Rational with poles</strong>: Bulirsch & Stoer Algorithm</li>
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<li><em>Neville Polynomial</em>: Neville Algorithm. Note that the Neville algorithm performs very badly on equidistant points. If you need to interpolate a polynomial on equidistant points, we recommend to use the barycentric algorithm instead.</li>
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<li><em>Linear Spline</em></li>
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<li><em>Cubic Spline</em> with boundary conditions</li>
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<li><em>Natural Cubic Spline</em></li>
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<li><em>Akima Cubic Spline</em></li>
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</ul>
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<h2><a name="Interpolation-with-additional-data" class="anchor" href="#Interpolation-with-additional-data">Interpolation with additional data</a></h2>
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<ul>
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<li><em>Generic Barycentric Interpolation</em>, requires barycentric weights</li>
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<li><em>Generic Spline</em>, requires spline coefficients</li>
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<li><em>Generic Cubic Hermite Spline</em>, requires the derivatives</li>
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