BulirschStoerRationalInterpolation.cs

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using System;
using System.Collections.Generic;
using System.Linq;

namespace MathNet.Numerics.Interpolation
{
    /// <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
    {
        readonly double[] _x;
        readonly double[] _y;

        /// <param name="x">Sample Points t, sorted ascendingly.</param>
        /// <param name="y">Sample Values x(t), sorted ascendingly by x.</param>
        public BulirschStoerRationalInterpolation(double[] x, double[] y)
        {
            if (x.Length != y.Length)
            {
                throw new ArgumentException("All vectors must have the same dimensionality.");
            }

            if (x.Length < 1)
            {
                throw new ArgumentException("The given array is too small. It must be at least 1 long.", nameof(x));
            }

            _x = x;
            _y = y;
        }

        /// <summary>
        /// Create a Bulirsch-Stoer rational interpolation from a set of (x,y) value pairs, sorted ascendingly by x.
        /// </summary>
        public static BulirschStoerRationalInterpolation InterpolateSorted(double[] x, double[] y)
        {
            return new BulirschStoerRationalInterpolation(x, y);
        }

        /// <summary>
        /// Create a Bulirsch-Stoer rational interpolation from an unsorted set of (x,y) value pairs.
        /// WARNING: Works in-place and can thus causes the data array to be reordered.
        /// </summary>
        public static BulirschStoerRationalInterpolation InterpolateInplace(double[] x, double[] y)
        {
            if (x.Length != y.Length)
            {
                throw new ArgumentException("All vectors must have the same dimensionality.");
            }

            Sorting.Sort(x, y);
            return InterpolateSorted(x, y);
        }

        /// <summary>
        /// Create a Bulirsch-Stoer rational interpolation from an unsorted set of (x,y) value pairs.
        /// </summary>
        public static BulirschStoerRationalInterpolation Interpolate(IEnumerable<double> x, IEnumerable<double> y)
        {
            // note: we must make a copy, even if the input was arrays already
            return InterpolateInplace(x.ToArray(), y.ToArray());
        }

        /// <summary>
        /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
        /// </summary>
        bool IInterpolation.SupportsDifferentiation => false;

        /// <summary>
        /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
        /// </summary>
        bool IInterpolation.SupportsIntegration => false;

        /// <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 = _x.Length;

            var c = new double[n];
            var d = new double[n];

            int nearestIndex = 0;
            double nearestDistance = Math.Abs(t - _x[0]);

            for (int i = 0; i < n; i++)
            {
                double distance = Math.Abs(t - _x[i]);
                if (distance.AlmostEqual(0.0))
                {
                    return _y[i];
                }

                if (distance < nearestDistance)
                {
                    nearestIndex = i;
                    nearestDistance = distance;
                }

                c[i] = _y[i];
                d[i] = _y[i] + tiny;
            }

            double x = _y[nearestIndex];

            for (int level = 1; level < n; level++)
            {
                for (int i = 0; i < n - level; i++)
                {
                    double hp = _x[i + level] - t;
                    double ho = (_x[i] - t)*d[i]/hp;

                    double den = ho - c[i + 1];
                    if (den.AlmostEqual(0.0))
                    {
                        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. NOT SUPPORTED.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated first derivative at point t.</returns>
        double IInterpolation.Differentiate(double t) => throw new NotSupportedException();

        /// <summary>
        /// Differentiate twice at point t. NOT SUPPORTED.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated second derivative at point t.</returns>
        double IInterpolation.Differentiate2(double t) => throw new NotSupportedException();

        /// <summary>
        /// Differentiate three times at point t. NOT SUPPORTED.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated third derivative at point t.</returns>
        double IInterpolation.Differentiate3(double t) => throw new NotSupportedException();

        /// <summary>
        /// Indefinite integral at point t. NOT SUPPORTED.
        /// </summary>
        /// <param name="t">Point t to integrate at.</param>
        double IInterpolation.Integrate(double t) => throw new NotSupportedException();

        /// <summary>
        /// Definite integral between points a and b. NOT SUPPORTED.
        /// </summary>
        /// <param name="a">Left bound of the integration interval [a,b].</param>
        /// <param name="b">Right bound of the integration interval [a,b].</param>
        double IInterpolation.Integrate(double a, double b) => throw new NotSupportedException();
    }
}