forked from tsai/mathnet-numerics
Christoph Ruegg
16 years ago
3 changed files with 179 additions and 0 deletions
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// <copyright file="LinearInterpolationCase.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) 2002-2011 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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namespace MathNet.Numerics.UnitTests.InterpolationTests |
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{ |
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using Distributions; |
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using Numerics.Random; |
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internal static class LinearInterpolationCase |
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{ |
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public static void Build(out double[] x, out double[] y, out double[] xtest, out double[] ytest, int samples = 3, double sampleOffset = -0.5, double slope = 2.0, double intercept = -1.0) |
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{ |
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// Fixed-seed "random" distribution to ensure we always test with the same data
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var uniform = new ContinuousUniform |
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{ |
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RandomSource = new MersenneTwister(42) |
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}; |
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// build linear samples
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x = new double[samples]; |
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y = new double[samples]; |
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for (int i = 0; i < x.Length; i++) |
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{ |
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x[i] = i + sampleOffset; |
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y[i] = x[i] * slope + intercept; |
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} |
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// build linear test vectors randomly between the sample points
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xtest = new double[samples + 1]; |
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ytest = new double[samples + 1]; |
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if (samples == 1) |
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{ |
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// y = const
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xtest[0] = sampleOffset - uniform.Sample(); |
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xtest[1] = sampleOffset + uniform.Sample(); |
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ytest[0] = ytest[1] = sampleOffset * slope + intercept; |
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} |
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else |
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{ |
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for (int i = 0; i < xtest.Length; i++) |
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{ |
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xtest[i] = (i - 1) + sampleOffset + uniform.Sample(); |
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ytest[i] = xtest[i] * slope + intercept; |
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} |
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} |
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} |
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} |
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} |
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// <copyright file="InterpolationTest.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) 2002-2011 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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namespace MathNet.Numerics.UnitTests.InterpolationTests |
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{ |
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using Interpolation; |
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using Interpolation.Algorithms; |
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using NUnit.Framework; |
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[TestFixture] |
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public class NevillePolynomialTest |
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{ |
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readonly double[] _t = new[] { 0.0, 1.0, 3.0, 4.0 }; |
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readonly double[] _x = new[] { 0.0, 3.0, 1.0, 3.0 }; |
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/// <summary>
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/// Verifies that the interpolation matches the given value at all the provided sample points.
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/// </summary>
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[Test] |
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public void FitsAtSamplePoints() |
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{ |
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IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x); |
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for (int i = 0; i < _t.Length; i++) |
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{ |
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// verify the interpolated values exactly at the sample points.
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Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); |
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double interpolatedValue; |
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double secondDerivative; |
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interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); |
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Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); |
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} |
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} |
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/// <summary>
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/// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
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/// </summary>
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/// <remarks>
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/// Maple:
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/// with(CurveFitting);
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/// evalf(subs({x=0.1},PolynomialInterpolation([[0,0],[1,3],[3,1],[4,3]], x)),20);
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/// </remarks>
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[Test, Sequential] |
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public void FitsAtArbitraryPointsWithMaple( |
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[Values(0.1, 0.4, 1.1, 3.2, 4.5, 10.0, -10.0)] double t, |
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[Values(.57225, 1.884, 3.0314166666666666667, 1.034666666666666667, 6.28125, 277.5, -1010.8333333333333333)] double x, |
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[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12)] double maxAbsoluteError) |
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{ |
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IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x); |
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Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); |
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double interpolatedValue; |
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double secondDerivative; |
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interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); |
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Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); |
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} |
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/// <summary>
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/// Verifies that the interpolation supports the linear case appropriately
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/// </summary>
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[Test] |
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public void SupportsLinearCase([Values(2, 4, 12)] int samples) |
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{ |
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double[] x, y, xtest, ytest; |
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LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples); |
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IInterpolation interpolation = new NevillePolynomialInterpolation(x, y); |
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for (int i = 0; i < xtest.Length; i++) |
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{ |
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Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-13, "Linear with {0} samples, sample {1}", samples, i); |
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} |
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} |
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} |
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} |
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