Unit Tests: Interpolation III

src/UnitTests/InterpolationTests/FloaterHormannRationalTest.cs

@@ -0,0 +1,116 @@
+// <copyright file="FloaterHormannRationalTest.cs" company="Math.NET">
+// 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.
+// </copyright>
+
+namespace MathNet.Numerics.UnitTests.InterpolationTests
+{
+    using Interpolation;
+    using Interpolation.Algorithms;
+    using NUnit.Framework;
+
+    [TestFixture]
+    public class FloaterHormannRationalTest
+    {
+        readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 };
+        readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 };
+
+        /// <summary>
+        /// Verifies that the interpolation matches the given value at all the provided polynomial sample points.
+        /// </summary>
+        [Test]
+        public void PolyomnialFitsAtSamplePoints()
+        {
+            IInterpolation interpolation = new FloaterHormannRationalInterpolation(_t, _x);
+
+            for (int i = 0; i < _x.Length; i++)
+            {
+                Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that at points other than the provided polynomial sample points, the interpolation matches the one computed by Maple as a reference.
+        /// </summary>
+        /// <remarks>
+        /// Maple:
+        /// with(CurveFitting);
+        /// PolynomialInterpolation([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x);
+        /// </remarks>
+        [Test, Sequential]
+        public void PolynomialFitsAtArbitraryPointsWithMaple(
+            [Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t,
+            [Values(-4.5968, 1.65395, 0.21875, -0.84205, -1.10805, -1.1248, 0.5392, -4431.0, -5071.0)] double x,
+            [Values(1e-14, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-9, 1e-9)] double maxAbsoluteError)
+        {
+            IInterpolation interpolation = new EquidistantPolynomialInterpolation(_t, _x);
+
+            Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
+        }
+
+        /// <summary>
+        /// Verifies that the interpolation matches the given value at all the provided rational sample points.
+        /// </summary>
+        [Test]
+        public void RationalFitsAtSamplePoints()
+        {
+            var t = new double[40];
+            var x = new double[40];
+
+            const double step = 10.0 / 39.0;
+            for (int i = 0; i < t.Length; i++)
+            {
+                double tt = -5 + (i * step);
+                t[i] = tt;
+                x[i] = 1.0 / (1.0 + (tt * tt));
+            }
+
+            IInterpolation interpolation = new FloaterHormannRationalInterpolation(t, x);
+
+            for (int i = 0; i < x.Length; i++)
+            {
+                Assert.AreEqual(x[i], interpolation.Interpolate(t[i]), "A Exact Point " + i);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that the interpolation supports the linear case appropriately
+        /// </summary>
+        [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 FloaterHormannRationalInterpolation(x, y);
+            for (int i = 0; i < xtest.Length; i++)
+            {
+                Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-14, "Linear with {0} samples, sample {1}", samples, i);
+            }
+        }
+    }
+}

src/UnitTests/UnitTests.csproj

@@ -113,6 +113,7 @@
     <Compile Include="IntegralTransformsTests\MatchingNaiveTransformTest.cs" />
     <Compile Include="IntegralTransformsTests\ParsevalTheoremTest.cs" />
     <Compile Include="IntegrationTests\IntegrationTest.cs" />
+    <Compile Include="InterpolationTests\FloaterHormannRationalTest.cs" />
     <Compile Include="InterpolationTests\EquidistantPolynomialTest.cs" />
     <Compile Include="InterpolationTests\NevillePolynomialTest.cs" />
     <Compile Include="InterpolationTests\LinearInterpolationCase.cs" />