From 2529512a856129e8e496289b28a2df453b66ae8a Mon Sep 17 00:00:00 2001 From: Christoph Ruegg Date: Mon, 28 Feb 2011 16:54:26 +0100 Subject: [PATCH] Unit Tests: Interpolation I --- .../LinearInterpolationCase.cs | 75 +++++++++++++ .../NevillePolynomialTest.cs | 102 ++++++++++++++++++ src/UnitTests/UnitTests.csproj | 2 + 3 files changed, 179 insertions(+) create mode 100644 src/UnitTests/InterpolationTests/LinearInterpolationCase.cs create mode 100644 src/UnitTests/InterpolationTests/NevillePolynomialTest.cs diff --git a/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs b/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs new file mode 100644 index 00000000..37bbcda2 --- /dev/null +++ b/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs @@ -0,0 +1,75 @@ +// +// Math.NET Numerics, part of the Math.NET Project +// http://numerics.mathdotnet.com +// http://github.com/mathnet/mathnet-numerics +// http://mathnetnumerics.codeplex.com +// +// Copyright (c) 2002-2011 Math.NET +// +// Permission is hereby granted, free of charge, to any person +// obtaining a copy of this software and associated documentation +// files (the "Software"), to deal in the Software without +// restriction, including without limitation the rights to use, +// copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following +// conditions: +// +// The above copyright notice and this permission notice shall be +// included in all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +// OTHER DEALINGS IN THE SOFTWARE. +// + +namespace MathNet.Numerics.UnitTests.InterpolationTests +{ + using Distributions; + using Numerics.Random; + + internal static class LinearInterpolationCase + { + 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) + { + // Fixed-seed "random" distribution to ensure we always test with the same data + var uniform = new ContinuousUniform + { + RandomSource = new MersenneTwister(42) + }; + + // build linear samples + x = new double[samples]; + y = new double[samples]; + for (int i = 0; i < x.Length; i++) + { + x[i] = i + sampleOffset; + y[i] = x[i] * slope + intercept; + } + + // build linear test vectors randomly between the sample points + xtest = new double[samples + 1]; + ytest = new double[samples + 1]; + if (samples == 1) + { + // y = const + xtest[0] = sampleOffset - uniform.Sample(); + xtest[1] = sampleOffset + uniform.Sample(); + ytest[0] = ytest[1] = sampleOffset * slope + intercept; + } + else + { + for (int i = 0; i < xtest.Length; i++) + { + xtest[i] = (i - 1) + sampleOffset + uniform.Sample(); + ytest[i] = xtest[i] * slope + intercept; + } + } + } + } +} diff --git a/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs b/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs new file mode 100644 index 00000000..bb8ce994 --- /dev/null +++ b/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs @@ -0,0 +1,102 @@ +// +// Math.NET Numerics, part of the Math.NET Project +// http://numerics.mathdotnet.com +// http://github.com/mathnet/mathnet-numerics +// http://mathnetnumerics.codeplex.com +// +// Copyright (c) 2002-2011 Math.NET +// +// Permission is hereby granted, free of charge, to any person +// obtaining a copy of this software and associated documentation +// files (the "Software"), to deal in the Software without +// restriction, including without limitation the rights to use, +// copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following +// conditions: +// +// The above copyright notice and this permission notice shall be +// included in all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +// OTHER DEALINGS IN THE SOFTWARE. +// + +namespace MathNet.Numerics.UnitTests.InterpolationTests +{ + using Interpolation; + using Interpolation.Algorithms; + using NUnit.Framework; + + [TestFixture] + public class NevillePolynomialTest + { + readonly double[] _t = new[] { 0.0, 1.0, 3.0, 4.0 }; + readonly double[] _x = new[] { 0.0, 3.0, 1.0, 3.0 }; + + /// + /// Verifies that the interpolation matches the given value at all the provided sample points. + /// + [Test] + public void FitsAtSamplePoints() + { + IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x); + + for (int i = 0; i < _t.Length; i++) + { + // verify the interpolated values exactly at the sample points. + Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); + + double interpolatedValue; + double secondDerivative; + interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); + Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); + } + } + + /// + /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference. + /// + /// + /// Maple: + /// with(CurveFitting); + /// evalf(subs({x=0.1},PolynomialInterpolation([[0,0],[1,3],[3,1],[4,3]], x)),20); + /// + [Test, Sequential] + public void FitsAtArbitraryPointsWithMaple( + [Values(0.1, 0.4, 1.1, 3.2, 4.5, 10.0, -10.0)] double t, + [Values(.57225, 1.884, 3.0314166666666666667, 1.034666666666666667, 6.28125, 277.5, -1010.8333333333333333)] double x, + [Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12)] double maxAbsoluteError) + { + IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x); + + Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); + + double interpolatedValue; + double secondDerivative; + interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); + Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); + } + + /// + /// Verifies that the interpolation supports the linear case appropriately + /// + [Test] + public void SupportsLinearCase([Values(2, 4, 12)] int samples) + { + double[] x, y, xtest, ytest; + LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples); + IInterpolation interpolation = new NevillePolynomialInterpolation(x, y); + for (int i = 0; i < xtest.Length; i++) + { + Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-13, "Linear with {0} samples, sample {1}", samples, i); + } + } + } +} diff --git a/src/UnitTests/UnitTests.csproj b/src/UnitTests/UnitTests.csproj index 081bfb36..7ca5578b 100644 --- a/src/UnitTests/UnitTests.csproj +++ b/src/UnitTests/UnitTests.csproj @@ -113,6 +113,8 @@ + + Code