// <copyright file="Interpolate.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System.Collections.Generic;
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using IStation.Numerics.Interpolation;
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namespace IStation.Numerics
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{
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/// <summary>
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/// Interpolation Factory.
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/// </summary>
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public static class Interpolate
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{
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/// <summary>
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/// Creates an interpolation based on arbitrary points.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.Barycentric.InterpolateRationalFloaterHormannSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation Common(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Barycentric.InterpolateRationalFloaterHormann(points, values);
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}
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/// <summary>
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/// Create a Floater-Hormann rational pole-free interpolation based on arbitrary points.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.Barycentric.InterpolateRationalFloaterHormannSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation RationalWithoutPoles(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Barycentric.InterpolateRationalFloaterHormann(points, values);
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}
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/// <summary>
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/// Create a Bulirsch Stoer rational interpolation based on arbitrary points.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.BulirschStoerRationalInterpolation.InterpolateSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation RationalWithPoles(IEnumerable<double> points, IEnumerable<double> values)
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{
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return BulirschStoerRationalInterpolation.Interpolate(points, values);
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}
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/// <summary>
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/// Create a barycentric polynomial interpolation where the given sample points are equidistant.
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/// </summary>
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/// <param name="points">The sample points t, must be equidistant.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.Barycentric.InterpolatePolynomialEquidistantSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation PolynomialEquidistant(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Barycentric.InterpolatePolynomialEquidistant(points, values);
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}
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/// <summary>
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/// Create a Neville polynomial interpolation based on arbitrary points.
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/// If the points happen to be equidistant, consider to use the much more robust PolynomialEquidistant instead.
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/// Otherwise, consider whether RationalWithoutPoles would not be a more robust alternative.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.NevillePolynomialInterpolation.InterpolateSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation Polynomial(IEnumerable<double> points, IEnumerable<double> values)
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{
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return NevillePolynomialInterpolation.Interpolate(points, values);
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}
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/// <summary>
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/// Create a piecewise linear interpolation based on arbitrary points.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.LinearSpline.InterpolateSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation Linear(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Interpolation.LinearSpline.Interpolate(points, values);
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}
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/// <summary>
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/// Create piecewise log-linear interpolation based on arbitrary points.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.LogLinear.InterpolateSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation LogLinear(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Interpolation.LogLinear.Interpolate(points, values);
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}
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/// <summary>
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/// Create an piecewise natural cubic spline interpolation based on arbitrary points,
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/// with zero secondary derivatives at the boundaries.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.CubicSpline.InterpolateNaturalSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation CubicSpline(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Interpolation.CubicSpline.InterpolateNatural(points, values);
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}
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/// <summary>
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/// Create a piecewise cubic Akima spline interpolation based on arbitrary points.
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/// Akima splines are robust to outliers.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.CubicSpline.InterpolateAkimaSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation CubicSplineRobust(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Interpolation.CubicSpline.InterpolateAkima(points, values);
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}
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/// <summary>
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/// Create a piecewise cubic monotone spline interpolation based on arbitrary points.
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/// This is a shape-preserving spline with continuous first derivative.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.CubicSpline.InterpolatePchipSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation CubicSplineMonotone(IEnumerable<double> points, IEnumerable<double> values)
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{
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return Interpolation.CubicSpline.InterpolatePchip(points, values);
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}
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/// <summary>
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/// Create a piecewise cubic Hermite spline interpolation based on arbitrary points
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/// and their slopes/first derivative.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <param name="firstDerivatives">The slope at the sample points. Optimized for arrays.</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.CubicSpline.InterpolateHermiteSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation CubicSplineWithDerivatives(IEnumerable<double> points, IEnumerable<double> values, IEnumerable<double> firstDerivatives)
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{
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return Interpolation.CubicSpline.InterpolateHermite(points, values, firstDerivatives);
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}
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/// <summary>
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/// Create a step-interpolation based on arbitrary points.
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/// </summary>
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/// <param name="points">The sample points t.</param>
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/// <param name="values">The sample point values x(t).</param>
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/// <returns>
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/// An interpolation scheme optimized for the given sample points and values,
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/// which can then be used to compute interpolations and extrapolations
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/// on arbitrary points.
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/// </returns>
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/// <remarks>
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/// if your data is already sorted in arrays, consider to use
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/// IStation.Numerics.Interpolation.StepInterpolation.InterpolateSorted
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/// instead, which is more efficient.
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/// </remarks>
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public static IInterpolation Step(IEnumerable<double> points, IEnumerable<double> values)
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{
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return StepInterpolation.Interpolate(points, values);
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}
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}
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}
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