StepInterpolation.cs

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

namespace MathNet.Numerics.Interpolation
{
    /// <summary>
    /// A step function where the start of each segment is included, and the last segment is open-ended.
    /// Segment i is [x_i, x_i+1) for i &lt; N, or [x_i, infinity] for i = N.
    /// The domain of the function is all real numbers, such that y = 0 where x &lt;.
    /// </summary>
    /// <remarks>Supports both differentiation and integration.</remarks>
    public class StepInterpolation : IInterpolation
    {
        readonly double[] _x;
        readonly double[] _y;
        readonly Lazy<double[]> _indefiniteIntegral;

        /// <param name="x">Sample points (N), sorted ascending</param>
        /// <param name="sy">Samples values (N) of each segment starting at the corresponding sample point.</param>
        public StepInterpolation(double[] x, double[] sy)
        {
            if (x.Length != sy.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 = sy;
            _indefiniteIntegral = new Lazy<double[]>(ComputeIndefiniteIntegral);
        }

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

        /// <summary>
        /// Create a linear spline 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 StepInterpolation 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 linear spline interpolation from an unsorted set of (x,y) value pairs.
        /// </summary>
        public static StepInterpolation 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());
        }

        bool IInterpolation.SupportsDifferentiation => true;

        bool IInterpolation.SupportsIntegration => true;

        /// <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)
        {
            if (t < _x[0])
            {
                return 0.0;
            }

            int k = LeftBracketIndex(t);
            return _y[k];
        }

        /// <summary>
        /// Differentiate at point t.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated first derivative at point t.</returns>
        public double Differentiate(double t)
        {
            int index = Array.BinarySearch(_x, t);
            if (index >= 0)
            {
                return double.NaN;
            }

            return 0d;
        }

        /// <summary>
        /// Differentiate twice at point t.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated second derivative at point t.</returns>
        public double Differentiate2(double t) => Differentiate(t);

        /// <summary>
        /// Differentiate three times at point t.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated third derivative at point t.</returns>
        public double Differentiate3(double t) => Differentiate2(t);

        /// <summary>
        /// Indefinite integral at point t.
        /// </summary>
        /// <param name="t">Point t to integrate at.</param>
        public double Integrate(double t)
        {
            if (t <= _x[0])
            {
                return 0.0;
            }

            int k = LeftBracketIndex(t);
            var x = t - _x[k];
            return _indefiniteIntegral.Value[k] + x*_y[k];
        }

        /// <summary>
        /// Definite integral between points a and b.
        /// </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>
        public double Integrate(double a, double b) => Integrate(b) - Integrate(a);

        double[] ComputeIndefiniteIntegral()
        {
            var integral = new double[_x.Length];
            for (int i = 0; i < integral.Length - 1; i++)
            {
                integral[i + 1] = integral[i] + (_x[i + 1] - _x[i])*_y[i];
            }

            return integral;
        }

        /// <summary>
        /// Find the index of the greatest sample point smaller than t.
        /// </summary>
        int LeftBracketIndex(double t)
        {
            int index = Array.BinarySearch(_x, t);
            return index >= 0 ? index : ~index - 1;
        }
    }
}