C#，数值计算——积分方程与逆理论，构造n点等间隔求积的权重的计算方法与源程序

1 文本格式

using System;

namespace Legalsoft.Truffer
{
    ///

    /// 构造n点等间隔求积的权重
    /// Constructs weights for the n-point equal-interval quadrature
    /// from O to(n-1)h of a function f(x) times an arbitrary
    /// (possibly singular) weight function w(x). The indefinite-integral
    /// moments Fn(y) of w(x) are provided by the user-supplied function
    /// kermom in the quad object.
    ///

    public class Wwghts
    {
        private double h { get; set; }
        private int n { get; set; }
        //private Quad_matrix quad { get; set; }
        UniVarRealMultiValueFun quad;
        private double[] wghts { get; set; }

        public Wwghts(double hh, int nn, UniVarRealMultiValueFun q)
        {
            this.h = hh;
            this.n = nn;
            this.quad = q;
            this.wghts = new double[n];
        }

        public double[] weights()
        {
            double hi = 1.0 / h;
            for (int j = 0; j < n; j++)
            {
                wghts[j] = 0.0;
            }
            if (n >= 4)
            {
                double[] w = new double[4];
                double[] wold = quad.funk(0.0);
                double b = 0.0;
                for (int j = 0; j < n - 3; j++)
                {
                    double c = j;
                    double a = b;
                    b = a + h;
                    if (j == n - 4)
                    {
                        b = (n - 1) * h;
                    }
                    double[] wnew = quad.funk(b);
                    double fac = 1.0;
                    for (int k = 0; k < 4; k++, fac *= hi)
                    {
                        w[k] = (wnew[k] - wold[k]) * fac;
                    }
                    wghts[j] += (((c + 1.0) * (c + 2.0) * (c + 3.0) * w[0] - (11.0 + c * (12.0 + c * 3.0)) * w[1] + 3.0 * (c + 2.0) * w[2] - w[3]) / 6.0);
                    wghts[j + 1] += ((-c * (c + 2.0) * (c + 3.0) * w[0] + (6.0 + c * (10.0 + c * 3.0)) * w[1] - (3.0 * c + 5.0) * w[2] + w[3]) * 0.5);
                    wghts[j + 2] += ((c * (c + 1.0) * (c + 3.0) * w[0] - (3.0 + c * (8.0 + c * 3.0)) * w[1] + (3.0 * c + 4.0) * w[2] - w[3]) * 0.5);
                    wghts[j + 3] += ((-c * (c + 1.0) * (c + 2.0) * w[0] + (2.0 + c * (6.0 + c * 3.0)) * w[1] - 3.0 * (c + 1.0) * w[2] + w[3]) / 6.0);
                    for (int k = 0; k < 4; k++)
                    {
                        wold[k] = wnew[k];
                    }
                }
            }
            else if (n == 3)
            {
                double[] w = new double[3];
                double[] wold = quad.funk(0.0);
                double[] wnew = quad.funk(h + h);
                w[0] = wnew[0] - wold[0];
                w[1] = hi * (wnew[1] - wold[1]);
                w[2] = hi * hi * (wnew[2] - wold[2]);
                wghts[0] = w[0] - 1.5 * w[1] + 0.5 * w[2];
                wghts[1] = 2.0 * w[1] - w[2];
                wghts[2] = 0.5 * (w[2] - w[1]);
            }
            else if (n == 2)
            {
                double[] wold = quad.funk(0.0);
                double[] wnew = quad.funk(h);
                wghts[0] = wnew[0] - wold[0] - (wghts[1] = hi * (wnew[1] - wold[1]));
            }
            return wghts;
        }
    }
}
 

2 代码格式

using System;

namespace Legalsoft.Truffer
{
    /// 

    /// 构造n点等间隔求积的权重
    /// Constructs weights for the n-point equal-interval quadrature
    /// from O to(n-1)h of a function f(x) times an arbitrary
    /// (possibly singular) weight function w(x). The indefinite-integral
    /// moments Fn(y) of w(x) are provided by the user-supplied function
    /// kermom in the quad object.
    /// 
    public class Wwghts
    {
        private double h { get; set; }
        private int n { get; set; }
        //private Quad_matrix quad { get; set; }
        UniVarRealMultiValueFun quad;
        private double[] wghts { get; set; }

        public Wwghts(double hh, int nn, UniVarRealMultiValueFun q)
        {
            this.h = hh;
            this.n = nn;
            this.quad = q;
            this.wghts = new double[n];
        }

        public double[] weights()
        {
            double hi = 1.0 / h;
            for (int j = 0; j < n; j++)
            {
                wghts[j] = 0.0;
            }
            if (n >= 4)
            {
                double[] w = new double[4];
                double[] wold = quad.funk(0.0);
                double b = 0.0;
                for (int j = 0; j < n - 3; j++)
                {
                    double c = j;
                    double a = b;
                    b = a + h;
                    if (j == n - 4)
                    {
                        b = (n - 1) * h;
                    }
                    double[] wnew = quad.funk(b);
                    double fac = 1.0;
                    for (int k = 0; k < 4; k++, fac *= hi)
                    {
                        w[k] = (wnew[k] - wold[k]) * fac;
                    }
                    wghts[j] += (((c + 1.0) * (c + 2.0) * (c + 3.0) * w[0] - (11.0 + c * (12.0 + c * 3.0)) * w[1] + 3.0 * (c + 2.0) * w[2] - w[3]) / 6.0);
                    wghts[j + 1] += ((-c * (c + 2.0) * (c + 3.0) * w[0] + (6.0 + c * (10.0 + c * 3.0)) * w[1] - (3.0 * c + 5.0) * w[2] + w[3]) * 0.5);
                    wghts[j + 2] += ((c * (c + 1.0) * (c + 3.0) * w[0] - (3.0 + c * (8.0 + c * 3.0)) * w[1] + (3.0 * c + 4.0) * w[2] - w[3]) * 0.5);
                    wghts[j + 3] += ((-c * (c + 1.0) * (c + 2.0) * w[0] + (2.0 + c * (6.0 + c * 3.0)) * w[1] - 3.0 * (c + 1.0) * w[2] + w[3]) / 6.0);
                    for (int k = 0; k < 4; k++)
                    {
                        wold[k] = wnew[k];
                    }
                }
            }
            else if (n == 3)
            {
                double[] w = new double[3];
                double[] wold = quad.funk(0.0);
                double[] wnew = quad.funk(h + h);
                w[0] = wnew[0] - wold[0];
                w[1] = hi * (wnew[1] - wold[1]);
                w[2] = hi * hi * (wnew[2] - wold[2]);
                wghts[0] = w[0] - 1.5 * w[1] + 0.5 * w[2];
                wghts[1] = 2.0 * w[1] - w[2];
                wghts[2] = 0.5 * (w[2] - w[1]);
            }
            else if (n == 2)
            {
                double[] wold = quad.funk(0.0);
                double[] wnew = quad.funk(h);
                wghts[0] = wnew[0] - wold[0] - (wghts[1] = hi * (wnew[1] - wold[1]));
            }
            return wghts;
        }
    }
}