C#，数值计算——函数计算，Dfridr的计算方法与源程序

1 文本格式

using System;

namespace Legalsoft.Truffer
{
    ///

    /// 通过Ridders的多项式外推方法返回函数func在点x处的导数。
    /// 输入值h作为估计的初始步长；它不需要很小，而是应为x上的增量，
    /// 在此增量上func将发生实质性变化。误差估计导数返回为err。
    /// Returns the derivative of a function func at a point x by Ridders' method of polynomial extrap-
    /// olation.The value h is input as an estimated initial stepsize; it need not be small, but rather
    /// should be an increment in x over which func changes substantially.An estimate of the error in
    /// the derivative is returned as err.
    ///

    public class Dfridr
    {
        public Dfridr()
        {
        }

        public static double dfridr(UniVarRealValueFun func, double x, double h, ref double err)
        {
            const int ntab = 10;
            const double con = 1.4;
            const double con2 = (con * con);
            const double big = double.MaxValue;
            const double safe = 2.0;

            double ans = 0.0;
            double[,] a = new double[ntab, ntab];
            //if (h == 0.0)
            if (Math.Abs(h) <= float.Epsilon)
            {
                throw new Exception("h must be nonzero in dfridr.");
            }
            double hh = h;
            a[0, 0] = (func.funk(x + hh) - func.funk(x - hh)) / (2.0 * hh);
            err = big;
            for (int i = 1; i < ntab; i++)
            {
                hh /= con;
                a[0, i] = (func.funk(x + hh) - func.funk(x - hh)) / (2.0 * hh);
                double fac = con2;
                for (int j = 1; j <= i; j++)
                {
                    a[j, i] = (a[j - 1, i] * fac - a[j - 1, i - 1]) / (fac - 1.0);
                    fac = con2 * fac;
                    double errt = Math.Max(Math.Abs(a[j, i] - a[j - 1, i]), Math.Abs(a[j, i] - a[j - 1, i - 1]));
                    if (errt <= err)
                    {
                        err = errt;
                        ans = a[j, i];
                    }
                }
                if (Math.Abs(a[i, i] - a[i - 1, i - 1]) >= safe * err)
                {
                    break;
                }
            }
            return ans;
        }
    }
}
 

2 代码格式

using System;

namespace Legalsoft.Truffer
{
    /// 

    /// 通过Ridders的多项式外推方法返回函数func在点x处的导数。
    /// 输入值h作为估计的初始步长；它不需要很小，而是应为x上的增量，
    /// 在此增量上func将发生实质性变化。误差估计导数返回为err。
    /// Returns the derivative of a function func at a point x by Ridders' method of polynomial extrap-
    /// olation.The value h is input as an estimated initial stepsize; it need not be small, but rather
    /// should be an increment in x over which func changes substantially.An estimate of the error in
    /// the derivative is returned as err.
    /// 
    public class Dfridr
    {
        public Dfridr()
        {
        }

        public static double dfridr(UniVarRealValueFun func, double x, double h, ref double err)
        {
            const int ntab = 10;
            const double con = 1.4;
            const double con2 = (con * con);
            const double big = double.MaxValue;
            const double safe = 2.0;

            double ans = 0.0;
            double[,] a = new double[ntab, ntab];
            //if (h == 0.0)
            if (Math.Abs(h) <= float.Epsilon)
            {
                throw new Exception("h must be nonzero in dfridr.");
            }
            double hh = h;
            a[0, 0] = (func.funk(x + hh) - func.funk(x - hh)) / (2.0 * hh);
            err = big;
            for (int i = 1; i < ntab; i++)
            {
                hh /= con;
                a[0, i] = (func.funk(x + hh) - func.funk(x - hh)) / (2.0 * hh);
                double fac = con2;
                for (int j = 1; j <= i; j++)
                {
                    a[j, i] = (a[j - 1, i] * fac - a[j - 1, i - 1]) / (fac - 1.0);
                    fac = con2 * fac;
                    double errt = Math.Max(Math.Abs(a[j, i] - a[j - 1, i]), Math.Abs(a[j, i] - a[j - 1, i - 1]));
                    if (errt <= err)
                    {
                        err = errt;
                        ans = a[j, i];
                    }
                }
                if (Math.Abs(a[i, i] - a[i - 1, i - 1]) >= safe * err)
                {
                    break;
                }
            }
            return ans;
        }
    }
}