C#，数值计算——有理函数插值和外推（Rational_interp）的计算方法与源程序

1 文本格式
 

using System;

namespace Legalsoft.Truffer
{
    /// <summary>
    /// 有理函数插值和外推
    /// Rational Function Interpolation and Extrapolation
    /// Given a value x, and using pointers to data xx and yy, this routine returns
    /// an interpolated value y, and stores an error estimate dy. The returned value
    /// is obtained by mm-point polynomial interpolation on the subrange
    /// xx[jl..jl + mm - 1].
    /// </summary>
    public class Rational_interp : Base_interp
    {
        private double dy { get; set; }

        public Rational_interp(double[] xv, double[] yv, int m) : base(xv, yv[0], m)
        {
            this.dy = 0.0;
        }

        /// <summary>
        /// Given a value x, and using pointers to data xx and yy, this routine returns
        /// an interpolated value y, and stores an error estimate dy. The returned
        /// value is obtained by mm-point diagonal rational function interpolation on
        /// the subrange xx[jl..jl + mm - 1].
        /// </summary>
        /// <param name="jl"></param>
        /// <param name="x"></param>
        /// <returns></returns>
        /// <exception cref="Exception"></exception>
        public override double rawinterp(int jl, double x)
        {
            const double TINY = 1.0e-99;
            int ns = 0;
            double[] c = new double[mm];
            double[] d = new double[mm];
            double hh = Math.Abs(x - xx[jl + 0]);
            for (int i = 0; i < mm; i++)
            {
                double h = Math.Abs(x - xx[jl + i]);
                //if (h == 0.0)
                if (Math.Abs(h) <= float.Epsilon)
                {
                    dy = 0.0;
                    return yy[jl + i];
                }
                else if (h < hh)
                {
                    ns = i;
                    hh = h;
                }
                c[i] = yy[jl + i];
                d[i] = yy[jl + i] + TINY;
            }
            double y = yy[jl + ns--];
            for (int m = 1; m < mm; m++)
            {
                for (int i = 0; i < mm - m; i++)
                {
                    double w = c[i + 1] - d[i];
                    double h = xx[jl + i + m] - x;
                    double t = (xx[jl + i] - x) * d[i] / h;
                    double dd = t - c[i + 1];
                    //if (dd == 0.0)
                    if (Math.Abs(dd) <= float.Epsilon)
                    {
                        throw new Exception("Error in routine ratint");
                    }
                    dd = w / dd;
                    d[i] = c[i + 1] * dd;
                    c[i] = t * dd;
                }
                y += (dy = (2 * (ns + 1) < (mm - m) ? c[ns + 1] : d[ns--]));
            }
            return y;
        }
    }
}
 

2 代码格式

using System;

namespace Legalsoft.Truffer
{
    /// <summary>
    /// 有理函数插值和外推
    /// Rational Function Interpolation and Extrapolation
    /// Given a value x, and using pointers to data xx and yy, this routine returns
    /// an interpolated value y, and stores an error estimate dy. The returned value
    /// is obtained by mm-point polynomial interpolation on the subrange
    /// xx[jl..jl + mm - 1].
    /// </summary>
    public class Rational_interp : Base_interp
    {
        private double dy { get; set; }

        public Rational_interp(double[] xv, double[] yv, int m) : base(xv, yv[0], m)
        {
            this.dy = 0.0;
        }

        /// <summary>
        /// Given a value x, and using pointers to data xx and yy, this routine returns
        /// an interpolated value y, and stores an error estimate dy. The returned
        /// value is obtained by mm-point diagonal rational function interpolation on
        /// the subrange xx[jl..jl + mm - 1].
        /// </summary>
        /// <param name="jl"></param>
        /// <param name="x"></param>
        /// <returns></returns>
        /// <exception cref="Exception"></exception>
        public override double rawinterp(int jl, double x)
        {
            const double TINY = 1.0e-99;
            int ns = 0;
            double[] c = new double[mm];
            double[] d = new double[mm];
            double hh = Math.Abs(x - xx[jl + 0]);
            for (int i = 0; i < mm; i++)
            {
                double h = Math.Abs(x - xx[jl + i]);
                //if (h == 0.0)
                if (Math.Abs(h) <= float.Epsilon)
                {
                    dy = 0.0;
                    return yy[jl + i];
                }
                else if (h < hh)
                {
                    ns = i;
                    hh = h;
                }
                c[i] = yy[jl + i];
                d[i] = yy[jl + i] + TINY;
            }
            double y = yy[jl + ns--];
            for (int m = 1; m < mm; m++)
            {
                for (int i = 0; i < mm - m; i++)
                {
                    double w = c[i + 1] - d[i];
                    double h = xx[jl + i + m] - x;
                    double t = (xx[jl + i] - x) * d[i] / h;
                    double dd = t - c[i + 1];
                    //if (dd == 0.0)
                    if (Math.Abs(dd) <= float.Epsilon)
                    {
                        throw new Exception("Error in routine ratint");
                    }
                    dd = w / dd;
                    d[i] = c[i + 1] * dd;
                    c[i] = t * dd;
                }
                y += (dy = (2 * (ns + 1) < (mm - m) ? c[ns + 1] : d[ns--]));
            }
            return y;
        }
    }
}