Christoph Ruegg
13 years ago
5 changed files with 247 additions and 32 deletions
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// <copyright file="Barycentric.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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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2013 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; |
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using System.Collections.Generic; |
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using System.Linq; |
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using MathNet.Numerics.Properties; |
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namespace MathNet.Numerics.Interpolation |
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{ |
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/// <summary>
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/// Barycentric Interpolation Algorithm.
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/// </summary>
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/// <remarks>Supports neither differentiation nor integration.</remarks>
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public class Barycentric : IInterpolation |
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{ |
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readonly double[] _x; |
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readonly double[] _y; |
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readonly double[] _w; |
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/// <param name="x">Sample points (N), no sorting assumed.</param>
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/// <param name="y">Sample values (N).</param>
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/// <param name="w">Barycentric weights (N).</param>
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public Barycentric(double[] x, double[] y, double[] w) |
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{ |
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if (x.Length != y.Length || x.Length != w.Length) |
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{ |
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throw new ArgumentException(Resources.ArgumentVectorsSameLength); |
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} |
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if (x.Length < 1) |
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{ |
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throw new ArgumentOutOfRangeException("x"); |
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} |
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_x = x; |
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_y = y; |
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_w = w; |
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} |
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/// <summary>
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/// Create a barycentric polynomial interpolation from a set of (x,y) value pairs with equidistant x. No sorting is assumed.
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/// </summary>
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/// <remarks>
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/// The value pairs do not have to be sorted, but if they are not sorted ascendingly
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/// and the passed x and y arguments are arrays, they will be sorted inplace and thus modified.
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/// </remarks>
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public static Barycentric InterpolatePolynomialEquidistant(IEnumerable<double> x, IEnumerable<double> y) |
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{ |
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var xx = (x as double[]) ?? x.ToArray(); |
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var yy = (y as double[]) ?? y.ToArray(); |
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if (xx.Length != yy.Length) |
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{ |
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throw new ArgumentException(Resources.ArgumentVectorsSameLength); |
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} |
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if (xx.Length < 1) |
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{ |
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throw new ArgumentOutOfRangeException("x"); |
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} |
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Sorting.Sort(xx, yy); |
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var weights = new double[xx.Length]; |
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weights[0] = 1.0; |
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for (int i = 1; i < weights.Length; i++) |
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{ |
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weights[i] = -(weights[i - 1]*(weights.Length - i))/i; |
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} |
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return new Barycentric(xx, yy, weights); |
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} |
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/// <summary>
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/// Create a barycentric polynomial interpolation from a set of values related to linearly/equidistant spaced points within an interval.
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/// </summary>
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/// <remarks>
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/// The value pairs do not have to be sorted, but if they are not sorted ascendingly
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/// and the passed x and y arguments are arrays, they will be sorted inplace and thus modified.
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/// </remarks>
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public static Barycentric InterpolatePolynomialEquidistant(double leftBound, double rightBound, IEnumerable<double> y) |
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{ |
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var yy = (y as double[]) ?? y.ToArray(); |
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var xx = Generate.LinearSpaced(yy.Length, leftBound, rightBound); |
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return InterpolatePolynomialEquidistant(xx, yy); |
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} |
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/// <summary>
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/// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
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/// </summary>
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bool IInterpolation.SupportsDifferentiation |
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{ |
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get { return false; } |
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} |
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/// <summary>
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/// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
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/// </summary>
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bool IInterpolation.SupportsIntegration |
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{ |
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get { return false; } |
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} |
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public double Interpolate(double t) |
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{ |
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// trivial case: only one sample?
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if (_x.Length == 1) |
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{ |
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return _y[0]; |
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} |
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// evaluate closest point and offset from that point (no sorting assumed)
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int closestPoint = 0; |
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double offset = t - _x[0]; |
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for (int i = 1; i < _x.Length; i++) |
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{ |
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if (Math.Abs(t - _x[i]) < Math.Abs(offset)) |
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{ |
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offset = t - _x[i]; |
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closestPoint = i; |
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} |
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} |
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// trivial case: on a known sample point?
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if (offset == 0.0) |
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{ |
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// NOTE (cdrnet, 200908) not offset.AlmostZero() by design
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return _y[closestPoint]; |
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} |
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if (Math.Abs(offset) > 1e-150) |
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{ |
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// no need to guard against overflow, so use fast formula
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closestPoint = -1; |
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offset = 1.0; |
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} |
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double s1 = 0.0; |
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double s2 = 0.0; |
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for (int i = 0; i < _x.Length; i++) |
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{ |
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if (i != closestPoint) |
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{ |
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double v = offset*_w[i]/(t - _x[i]); |
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s1 = s1 + (v*_y[i]); |
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s2 = s2 + v; |
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} |
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else |
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{ |
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double v = _w[i]; |
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s1 = s1 + (v*_y[i]); |
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s2 = s2 + v; |
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} |
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} |
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return s1/s2; |
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} |
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/// <summary>
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/// Differentiate at point t. NOT SUPPORTED.
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/// </summary>
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/// <param name="t">Point t to interpolate at.</param>
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/// <returns>Interpolated first derivative at point t.</returns>
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double IInterpolation.Differentiate(double t) |
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{ |
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throw new NotSupportedException(); |
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} |
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/// <summary>
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/// Differentiate twice at point t. NOT SUPPORTED.
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/// </summary>
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/// <param name="t">Point t to interpolate at.</param>
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/// <returns>Interpolated second derivative at point t.</returns>
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double IInterpolation.Differentiate2(double t) |
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{ |
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throw new NotSupportedException(); |
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} |
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/// <summary>
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/// Indefinite integral at point t. NOT SUPPORTED.
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/// </summary>
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/// <param name="t">Point t to integrate at.</param>
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double IInterpolation.Integrate(double t) |
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{ |
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throw new NotSupportedException(); |
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} |
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/// <summary>
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/// Definite integral between points a and b. NOT SUPPORTED.
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/// </summary>
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/// <param name="a">Left bound of the integration interval [a,b].</param>
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/// <param name="b">Right bound of the integration interval [a,b].</param>
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double IInterpolation.Integrate(double a, double b) |
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{ |
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throw new NotSupportedException(); |
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} |
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} |
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} |
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