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using System;

namespace IStation.Numerics.Interpolation
{
    /// <summary>
    /// Quadratic Spline Interpolation.
    /// </summary>
    /// <remarks>Supports both differentiation and integration.</remarks>
    public class QuadraticSpline : IInterpolation
    {
        readonly double[] _x;
        readonly double[] _c0;
        readonly double[] _c1;
        readonly double[] _c2;
        readonly Lazy<double[]> _indefiniteIntegral;

        /// <param name="x">sample points (N+1), sorted ascending</param>
        /// <param name="c0">Zero order spline coefficients (N)</param>
        /// <param name="c1">First order spline coefficients (N)</param>
        /// <param name="c2">second order spline coefficients (N)</param>
        public QuadraticSpline(double[] x, double[] c0, double[] c1, double[] c2)
        {
            if (x.Length != c0.Length + 1 || x.Length != c1.Length + 1 || x.Length != c2.Length + 1)
            {
                throw new ArgumentException("All vectors must have the same dimensionality.");
            }

            if (x.Length < 2)
            {
                throw new ArgumentException("The given array is too small. It must be at least 2 long.", nameof(x));
            }

            _x = x;
            _c0 = c0;
            _c1 = c1;
            _c2 = c2;
            _indefiniteIntegral = new Lazy<double[]>(ComputeIndefiniteIntegral);
        }

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

        /// <summary>
        /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
        /// </summary>
        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)
        {
            int k = LeftSegmentIndex(t);
            var x = t - _x[k];
            return _c0[k] + x*(_c1[k] + x*_c2[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 k = LeftSegmentIndex(t);
            return _c1[k] + (t - _x[k])*2*_c2[k];
        }

        /// <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)
        {
            int k = LeftSegmentIndex(t);
            return 2*_c2[k];
        }

        /// <summary>
        /// Indefinite integral at point t.
        /// </summary>
        /// <param name="t">Point t to integrate at.</param>
        public double Integrate(double t)
        {
            int k = LeftSegmentIndex(t);
            var x = t - _x[k];
            return _indefiniteIntegral.Value[k] + x*(_c0[k] + x*(_c1[k]/2 + x*_c2[k]/3));
        }

        /// <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)
        {
            return Integrate(b) - Integrate(a);
        }

        double[] ComputeIndefiniteIntegral()
        {
            var integral = new double[_c1.Length];
            for (int i = 0; i < integral.Length - 1; i++)
            {
                double w = _x[i + 1] - _x[i];
                integral[i + 1] = integral[i] + w*(_c0[i] + w*(_c1[i]/2 + w*_c2[i]/3));
            }

            return integral;
        }

        /// <summary>
        /// Find the index of the greatest sample point smaller than t,
        /// or the left index of the closest segment for extrapolation.
        /// </summary>
        int LeftSegmentIndex(double t)
        {
            int index = Array.BinarySearch(_x, t);
            if (index < 0)
            {
                index = ~index - 1;
            }

            return Math.Min(Math.Max(index, 0), _x.Length - 2);
        }
    }
}