d9r7f.java

解具有导数的多元函数的无约束极小值点或具有导数的非线性方程组的近似解

public class d9r7F
{
	double plgndr(double l, double m, double x)
	{
        int ll, i;
        double pmm, somx2, fact, temp, pmmp1, pll=0;
        if (m < 0 || m > l || Math.abs(x) > 1.0)
		{
			System.out.println("bad arguments");
			System.exit(1);
		}
		pmm = 1.0;
        if (m > 0)
		{
            somx2 = Math.sqrt((1.0 - x) * (1.0 + x));
            fact = 1.0;
            for (i = 1; i <= m; i++)
			{
                pmm = -pmm * fact * somx2;
                fact = fact + 2.0;
            }
        }
        if (l == m)
		{
            temp = pmm;
		}
        else
		{
            pmmp1 = x * (2 * m + 1) * pmm;
            if (l == m + 1)
			{
                temp = pmmp1;
			}
            else
			{
                for (ll = (int)m + 2; ll <= l; ll++)
				{
                    pll = x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm;
                    pll = pll / (ll - m);
                    pmm = pmmp1;
                    pmmp1 = pll;
                }
                temp = pll;
            }
        }
		return temp;
	}

	void fleg(double x, double pl[], int nl)
	{
		pl[1] = 1.0;
		pl[2] = x;
		if (nl > 2)
		{
			double twox = 2.0 * x;
			double f2 = x;
			double d = 1.0;
            for (int j = 3; j <= nl; j++)
			{
				double f1 = d;
				f2 = f2 + twox;
				d = d + 1.0;
				pl[j] = (f2 * pl[j - 1] - f1 * pl[j - 2]) / d;
			}
		}
	}
}