Unit Tests: Interpolation V

16 years ago · c271cea4cc
4 changed files with 388 additions and 0 deletions
--- a/src/UnitTests/InterpolationTests/AkimaSplineTest.cs
+++ b/src/UnitTests/InterpolationTests/AkimaSplineTest.cs
@ -0,0 +1,97 @@
+// <copyright file="AkimaSplineTest.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 AkimaSplineTest
+    {
+        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 sample points.
+        /// </summary>
+        [Test]
+        public void FitsAtSamplePoints()
+        {
+            IInterpolation interpolation = new AkimaSplineInterpolation(_t, _x);
+
+            for (int i = 0; i < _x.Length; i++)
+            {
+                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);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
+        /// </summary>
+        [Test, Sequential]
+        public void FitsAtArbitraryPointsWithMaple(
+            [Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t,
+            [Values(-0.52, 1.826, 0.25, -1.006, -0.9, -0.6, 0.2, 9, -151)] double x,
+            [Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15)] double maxAbsoluteError)
+        {
+            IInterpolation interpolation = new AkimaSplineInterpolation(_t, _x);
+
+            // TODO: Verify the expected values (that they are really the expected ones)
+            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);
+        }
+
+        /// <summary>
+        /// Verifies that the interpolation supports the linear case appropriately
+        /// </summary>
+        [Test]
+        public void SupportsLinearCase([Values(5, 7, 15)] int samples)
+        {
+            double[] x, y, xtest, ytest;
+            LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples);
+            IInterpolation interpolation = new AkimaSplineInterpolation(x, y);
+            for (int i = 0; i < xtest.Length; i++)
+            {
+                Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
+            }
+        }
+    }
+}
--- a/src/UnitTests/InterpolationTests/CubicSplineTest.cs
+++ b/src/UnitTests/InterpolationTests/CubicSplineTest.cs
@ -0,0 +1,187 @@
+// <copyright file="CubicSplineTest.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 CubicSplineTest
+    {
+        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 sample points.
+        /// </summary>
+        [Test]
+        public void NaturalFitsAtSamplePoints()
+        {
+            IInterpolation interpolation = new CubicSplineInterpolation(_t, _x);
+
+            for (int i = 0; i < _x.Length; i++)
+            {
+                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);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
+        /// </summary>
+        /// <remarks>
+        /// Maple:
+        /// with(CurveFitting);
+        /// evalf(subs({x=-2.4},Spline([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x, degree=3, endpoints='natural')),20);
+        /// </remarks>
+        [Test, Sequential]
+        public void NaturalFitsAtArbitraryPointsWithMaple(
+            [Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t,
+            [Values(.144, 1.7906428571428571429, .47321428571428571431, -.80992857142857142857, -1.1089285714285714286, -1.0285714285714285714, .30285714285714285716, 189, 677)] double x,
+            [Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12)] double maxAbsoluteError)
+        {
+            IInterpolation interpolation = new CubicSplineInterpolation(_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);
+        }
+
+        /// <summary>
+        /// Verifies that the interpolation matches the given value at all the provided sample points.
+        /// </summary>
+        [Test]
+        public void FixedFirstDerivativeFitsAtSamplePoints()
+        {
+            IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0);
+
+            for (int i = 0; i < _x.Length; i++)
+            {
+                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);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
+        /// </summary>
+        /// <remarks>
+        /// Maple:
+        /// with(CurveFitting);
+        /// evalf(subs({x=-2.4},Spline([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x, degree=3, endpoints=[1,-1])),20);
+        /// </remarks>
+        [Test, Sequential]
+        public void FixedFirstDerivativeFitsAtArbitraryPointsWithMaple(
+            [Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t,
+            [Values(1.12, 1.8243928571428571428, .54910714285714285715, -.78903571428571428572, -1.1304642857142857143, -1.1040000000000000000, .4148571428571428571, -608.14285714285714286, 1330.1428571428571429)] double x,
+            [Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12, 1e-12)] double maxAbsoluteError)
+        {
+            IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0);
+
+            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);
+        }
+
+        /// <summary>
+        /// Verifies that the interpolation matches the given value at all the provided sample points.
+        /// </summary>
+        [Test]
+        public void FixedSecondDerivativeFitsAtSamplePoints()
+        {
+            IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0);
+
+            for (int i = 0; i < _x.Length; i++)
+            {
+                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);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
+        /// </summary>
+        /// <remarks>
+        /// Maple:
+        /// with(CurveFitting);
+        /// evalf(subs({x=-2.4},Spline([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x, degree=3, endpoints=Matrix(2,13,{(1,3)=1,(1,13)=-5,(2,10)=1,(2,13)=-1}))),20);
+        /// </remarks>
+        [Test, Sequential]
+        public void FixedSecondDerivativeFitsAtArbitraryPointsWithMaple(
+            [Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t,
+            [Values(-.8999999999999999993, 1.7590357142857142857, .41517857142857142854, -.82010714285714285714, -1.1026071428571428572, -1.0211428571428571429, .31771428571428571421, 39, -37)] double x,
+            [Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-13, 1e-12)] double maxAbsoluteError)
+        {
+            IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0);
+
+            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);
+        }
+
+        /// <summary>
+        /// Verifies that the interpolation supports the linear case appropriately
+        /// </summary>
+        [Test]
+        public void NaturalSupportsLinearCase([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 CubicSplineInterpolation(x, y);
+            for (int i = 0; i < xtest.Length; i++)
+            {
+                Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
+            }
+        }
+    }
+}
--- a/src/UnitTests/InterpolationTests/LinearSplineTest.cs
+++ b/src/UnitTests/InterpolationTests/LinearSplineTest.cs
@ -0,0 +1,101 @@
+// <copyright file="LinearSplineTest.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 LinearSplineTest
+    {
+        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 sample points.
+        /// </summary>
+        [Test]
+        public void FitsAtSamplePoints()
+        {
+            IInterpolation interpolation = new LinearSplineInterpolation(_t, _x);
+
+            for (int i = 0; i < _x.Length; i++)
+            {
+                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);
+            }
+        }
+
+        /// <summary>
+        /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
+        /// </summary>
+        /// <remarks>
+        /// Maple:
+        /// f := x -> piecewise(x&lt;-1,3+x,x&lt;0,-1-3*x,x&lt;1,-1+x,-1+x);
+        /// f(x)
+        /// </remarks>
+        [Test, Sequential]
+        public void FitsAtArbitraryPointsWithMaple(
+            [Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t,
+            [Values(.6, 1.7, .5, -.7, -.9, -.6, .2, 9.0, -7.0)] double x,
+            [Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15)] double maxAbsoluteError)
+        {
+            IInterpolation interpolation = new LinearSplineInterpolation(_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);
+        }
+
+        /// <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 LinearSplineInterpolation(x, y);
+            for (int i = 0; i < xtest.Length; i++)
+            {
+                Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
+            }
+        }
+    }
+}
--- a/src/UnitTests/UnitTests.csproj
+++ b/src/UnitTests/UnitTests.csproj
@ -114,6 +114,9 @@
    <Compile Include="IntegralTransformsTests\ParsevalTheoremTest.cs" />
    <Compile Include="IntegrationTests\IntegrationTest.cs" />
    <Compile Include="InterpolationTests\BulirschStoerRationalTest.cs" />
+    <Compile Include="InterpolationTests\AkimaSplineTest.cs" />
+    <Compile Include="InterpolationTests\CubicSplineTest.cs" />
+    <Compile Include="InterpolationTests\LinearSplineTest.cs" />
    <Compile Include="InterpolationTests\FloaterHormannRationalTest.cs" />
    <Compile Include="InterpolationTests\EquidistantPolynomialTest.cs" />
    <Compile Include="InterpolationTests\NevillePolynomialTest.cs" />