interpolation: ported bulirsch-stoer rational algorithm

Signed-off-by: Christoph Ruegg <git@cdrnet.ch>

src/Managed.UnitTests/InterpolationTests/InterpolationContract.cs

@@ -40,6 +40,7 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
     {
         public Func<IList<double>, IList<double>, IInterpolation> Factory { get; set; }
         public int[] Order { get; set; }
+        public bool LinearBehavior { get; set; }
         public bool PolynomialBehavior { get; set; }
         public bool RationalBehavior { get; set; }
 
@@ -56,7 +57,11 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             yield return CreateConstructorInitShortcutTest("ConstructorInitShortcut");
             yield return CreateConsistentCapabilityBehaviorTest("ConsistentCapabilityBehavior");
             yield return CreateInterpolationMatchesNodePointsTest("InterpolationMatchesNodePoints");
-            yield return CreateLinearBehaviorTest("LinearBehavior");
+
+            if (LinearBehavior)
+            {
+                yield return CreateLinearBehaviorTest("LinearBehavior");
+            }
 
             if (PolynomialBehavior)
             {

src/Managed.UnitTests/InterpolationTests/InterpolationTest.cs

@@ -42,6 +42,7 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         {
             Factory = Interpolate.LinearBetweenPoints,
             Order = new[] { 2, 3, 6 },
+            LinearBehavior = true,
             PolynomialBehavior = false,
             RationalBehavior = false
         };
@@ -51,6 +52,7 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         {
             Factory = Interpolate.RationalWithoutPoles,
             Order = new[] { 1, 2, 6 },
+            LinearBehavior = true,
             PolynomialBehavior = true,
             RationalBehavior = true
         };
@@ -60,8 +62,19 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         {
             Factory = (t, x) => new NevillePolynomialInterpolation(t, x),
             Order = new[] { 1, 2, 6 },
+            LinearBehavior = true,
             PolynomialBehavior = true,
             RationalBehavior = false
         };
+
+        [VerifyContract]
+        public readonly IContract BulirschStoerRationalContractTests = new InterpolationContract<BulirschStoerRationalInterpolation>()
+        {
+            Factory = Interpolate.RationalWithPoles,
+            Order = new[] { 1, 2, 6 },
+            LinearBehavior = false,
+            PolynomialBehavior = true,
+            RationalBehavior = true
+        };
     }
 }

src/Managed/Interpolation/Algorithms/BulirschStoerRationalInterpolation.cs

@@ -0,0 +1,222 @@
+// <copyright file="BulirschStoerRationalInterpolation.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 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.Interpolation.Algorithms
+{
+    using System;
+    using System.Collections.Generic;
+
+    /// <summary>
+    /// Rational Interpolation (with poles) using Roland Bulirsch and Josef Stoer's Algorithm.
+    /// </summary>
+    /// <remarks>
+    /// <para>
+    /// This algorithm supports neither differentiation nor integration.
+    /// </para>
+    /// </remarks>
+    public class BulirschStoerRationalInterpolation : IInterpolation
+    {
+        /// <summary>
+        /// Sample Points t.
+        /// </summary>
+        private IList<double> _points;
+
+        /// <summary>
+        /// Spline Values x(t).
+        /// </summary>
+        private IList<double> _values;
+
+        /// <summary>
+        /// Initializes a new instance of the BulirschStoerRationalInterpolation class.
+        /// </summary>
+        public BulirschStoerRationalInterpolation()
+        {
+        }
+
+        /// <summary>
+        /// Initializes a new instance of the BulirschStoerRationalInterpolation class.
+        /// </summary>
+        /// <param name="samplePoints">Sample Points t</param>
+        /// <param name="sampleValues">Sample Values x(t)</param>
+        public BulirschStoerRationalInterpolation(
+            IList<double> samplePoints,
+            IList<double> sampleValues)
+        {
+            Initialize(samplePoints, sampleValues);
+        }
+
+        /// <summary>
+        /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
+        /// </summary>
+        /// <seealso cref="Differentiate(double)"/>
+        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        bool IInterpolation.SupportsDifferentiation
+        {
+            get { return false; }
+        }
+
+        /// <summary>
+        /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
+        /// </summary>
+        /// <seealso cref="Integrate"/>
+        bool IInterpolation.SupportsIntegration
+        {
+            get { return false; }
+        }
+
+        /// <summary>
+        /// Initialize the interpolation method with the given sample pairs.
+        /// </summary>
+        /// <param name="samplePoints">Sample Points t</param>
+        /// <param name="sampleValues">Sample Values x(t)</param>
+        public void Initialize(
+            IList<double> samplePoints,
+            IList<double> sampleValues)
+        {
+            if (null == samplePoints)
+            {
+                throw new ArgumentNullException("samplePoints");
+            }
+
+            if (null == sampleValues)
+            {
+                throw new ArgumentNullException("sampleValues");
+            }
+
+            if (samplePoints.Count != sampleValues.Count)
+            {
+                throw new ArgumentException(Properties.Resources.ArgumentVectorsSameLengths);
+            }
+
+            _points = samplePoints;
+            _values = sampleValues;
+        }
+
+        /// <summary>
+        /// Interpolate at point t.
+        /// </summary>
+        /// <param name="t">Point t to interpolate at.</param>
+        /// <returns>Interpolated value x(t).</returns>
+        public double Interpolate(double t)
+        {
+            const double Tiny = 1.0e-25;
+            int n = _points.Count;
+
+            double[] c = new double[n];
+            double[] d = new double[n];
+
+            int nearestIndex = 0;
+            double nearestDistance = Math.Abs(t - _points[0]);
+
+            for (int i = 0; i < n; i++)
+            {
+                double distance = Math.Abs(t - _points[i]);
+                if (distance.AlmostZero())
+                {
+                    return _values[i];
+                }
+
+                if (distance < nearestDistance)
+                {
+                    nearestIndex = i;
+                    nearestDistance = distance;
+                }
+
+                c[i] = _values[i];
+                d[i] = _values[i] + Tiny;
+            }
+
+            double x = _values[nearestIndex];
+
+            for (int level = 1; level < n; level++)
+            {
+                for (int i = 0; i < n - level; i++)
+                {
+                    double hp = _points[i + level] - t;
+                    double ho = (_points[i] - t) * d[i] / hp;
+
+                    double den = ho - c[i + 1];
+                    if (den.AlmostZero())
+                    {
+                        return double.NaN; // zero-div, singularity
+                    }
+
+                    den = (c[i + 1] - d[i]) / den;
+                    d[i] = c[i + 1] * den;
+                    c[i] = ho * den;
+                }
+
+                x += (2 * nearestIndex) < (n - level)
+                    ? c[nearestIndex]
+                    : d[--nearestIndex];
+            }
+
+            return x;
+        }
+
+        /// <summary>
+        /// Differentiate at point t.
+        /// </summary>
+        /// <param name="t">Point t to interpolate at.</param>
+        /// <returns>Interpolated first derivative at point t.</returns>
+        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
+        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        double IInterpolation.Differentiate(double t)
+        {
+            throw new NotSupportedException();
+        }
+
+        /// <summary>
+        /// Differentiate at point t.
+        /// </summary>
+        /// <param name="t">Point t to interpolate at.</param>
+        /// <param name="interpolatedValue">Interpolated value x(t)</param>
+        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
+        /// <returns>Interpolated first derivative at point t.</returns>
+        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
+        /// <seealso cref="Differentiate(double)"/>
+        double IInterpolation.Differentiate(
+            double t,
+            out double interpolatedValue,
+            out double secondDerivative)
+        {
+            throw new NotSupportedException();
+        }
+
+        /// <summary>
+        /// Integrate up to point t.
+        /// </summary>
+        /// <param name="t">Right bound of the integration interval [a,t].</param>
+        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
+        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        double IInterpolation.Integrate(double t)
+        {
+            throw new NotSupportedException();
+        }
+    }
+}

src/Managed/Interpolation/Algorithms/FloaterHormannRationalInterpolation.cs

@@ -32,7 +32,7 @@ namespace MathNet.Numerics.Interpolation.Algorithms
     using System.Collections.Generic;
 
     /// <summary>
-    /// Barycentric Rational Interpolation without poles, using Floater and Hormann's Algorithm.
+    /// Barycentric Rational Interpolation without poles, using Mike Floater and Kai Hormann's Algorithm.
     /// </summary>
     /// <remarks>
     /// This algorithm neither supports differentiation nor integration.

src/Managed/Interpolation/Algorithms/NevillePolynomialInterpolation.cs

@@ -95,7 +95,7 @@ namespace MathNet.Numerics.Interpolation.Algorithms
         }
 
         /// <summary>
-        /// Initialize the interpolation method with the given spline coefficients.
+        /// Initialize the interpolation method with the given sample pairs.
         /// </summary>
         /// <param name="samplePoints">Sample Points t</param>
         /// <param name="sampleValues">Sample Values x(t)</param>

src/Managed/Interpolation/Interpolate.cs

@@ -90,5 +90,24 @@ namespace MathNet.Numerics.Interpolation
             method.Initialize(points, values);
             return method;
         }
+
+        /// <summary>
+        /// Create a burlish stoer rational interpolation based on arbitrary points.
+        /// </summary>
+        /// <param name="points">The sample points t. Supports both lists and arrays.</param>
+        /// <param name="values">The sample point values x(t). Supports both lists and arrays.</param>
+        /// <returns>
+        /// An interpolation scheme optimized for the given sample points and values,
+        /// which can then be used to compute interpolations and extrapolations
+        /// on arbitrary points.
+        /// </returns>
+        public static IInterpolation RationalWithPoles(
+            IList<double> points,
+            IList<double> values)
+        {
+            BulirschStoerRationalInterpolation method = new BulirschStoerRationalInterpolation();
+            method.Initialize(points, values);
+            return method;
+        }
     }
 }

src/Managed/Managed.csproj

@@ -55,6 +55,7 @@
     <Compile Include="Distributions\IDiscreteDistribution.cs" />
     <Compile Include="Distributions\IDistribution.cs" />
     <Compile Include="Interpolation\Algorithms\BarycentricInterpolation.cs" />
+    <Compile Include="Interpolation\Algorithms\BulirschStoerRationalInterpolation.cs" />
     <Compile Include="Interpolation\Algorithms\FloaterHormannRationalInterpolation.cs" />
     <Compile Include="Interpolation\Algorithms\LinearSplineInterpolation.cs" />
     <Compile Include="Interpolation\Algorithms\NevillePolynomialInterpolation.cs" />

src/Native/Native.csproj

@@ -74,6 +74,9 @@
     <Compile Include="..\Managed\Interpolation\Algorithms\BarycentricInterpolation.cs">
       <Link>Interpolation\Algorithms\BarycentricInterpolation.cs</Link>
     </Compile>
+    <Compile Include="..\Managed\Interpolation\Algorithms\BulirschStoerRationalInterpolation.cs">
+      <Link>Interpolation\Algorithms\BulirschStoerRationalInterpolation.cs</Link>
+    </Compile>
     <Compile Include="..\Managed\Interpolation\Algorithms\FloaterHormannRationalInterpolation.cs">
       <Link>Interpolation\Algorithms\FloaterHormannRationalInterpolation.cs</Link>
     </Compile>