d11r1.cpp

数值计算c++源代码,包括各种算法。很有用的。

#include "iostream.h"
#include "math.h"

double bessj0(double x)
{
	double p1,p2,p3,p4,p5,q1,q2,q3,q4,q5;
	double r1,r2,r3,r4,r5,r6,s1,s2,s3,s4,s5,s6;
	double y,bbb,ccc,aaa,temp,eee,ddd,ax,xx,z;
    p1 = 1.0;                 p2 = -0.001098628627;
    p3 = 0.00002734510407;    p4 = -0.000002073370639;
    p5 = 2.093887211e-07;
    q1 = -0.01562499995;      q2 = 0.0001430488765;
    q3 = -0.000006911147651;  q4 = 7.621095161e-07;
    q5 = -9.34945152e-08;
    r1 = 57568490574.0;       r2 = -13362590354.0;
    r3 = 651619640.7;         r4 = -11214424.18;
    r5 = 77392.33017;         r6 = -184.9052456;
    s1 = 57568490411.0;       s2 = 1029532985.0;
    s3 = 9494680.718;         s4 = 59272.64853;
    s5 = 267.8532712;         s6 = 1.0;
    if (fabs(x) < 8.0)
	{
       y = x * x;
       bbb = y * (r4 + y * (r5 + y * r6));
       aaa = r1 + y * (r2 + y * (r3 + bbb));
       ccc = y * (s3 + y * (s4 + y * (s5 + y * s6)));
       temp = aaa / (s1 + y * (s2 + ccc));
	}
    else
	{
       ax = fabs(x);
       z = 8.0 / ax;
       y = z * z;
       xx = ax - 0.785398164;
       ccc = y * (p3 + y * (p4 + y * p5));
       aaa = p1 + y * (p2 + ccc);
       ddd = y * (q3 + y * (q4 + y * q5));
       eee = z * sin(xx) * (q1 + y * (q2 + ddd));
       temp = sqrt(0.636619772 / ax) * (cos(xx) * aaa - eee);
	}
	return temp;
}

double func(double x)
{
    return bessj0(x);
}

void mnbrak(double& ax, double& bx, double& cx, double& fa, double& fb, double& fc)
{
    double r,q,dum,gold = 1.618034;
    int glimit = 100;
    double u,ulim,fu,tiny = 1e-20;
    fa = func(ax);
    fb = func(bx);
    if (fb > fa)
	{
        dum = ax;
        ax = bx;
        bx = dum;
        dum = fb;
        fb = fa;
        fa = dum;
    }
    cx = bx + gold * (bx - ax);
    fc = func(cx);
	while (fb >= fc)
	{
        r = (bx - ax) * (fb - fc);
        q = (bx - cx) * (fb - fa);
        dum = q - r;
        if (fabs(dum) < tiny)
		{
			dum = tiny;
		}
        u = bx - ((bx - cx) * q - (bx - ax) * r) / (2 * dum);
        ulim = bx + glimit * (cx - bx);
        if ((bx - u) * (u - cx) > 0)
		{
            fu = func(u);
            if (fu < fc)
			{
                ax = bx;
                fa = fb;
                bx = u;
                fb = fu;
                return;
			}
            else
			{
				if (fu > fb)
				{
					cx = u;
					fc = fu;
					return;
				}
            }
            u = cx + gold * (cx - bx);
            fu = func(u);
		}
        else
		{
			if ((cx - u) * (u - ulim) > 0)
			{
				fu = func(u);
				if (fu < fc)
				{
					bx = cx;
					cx = u;
					u = cx + gold * (cx - bx);
					fb = fc;
					fc = fu;
					fu = func(u);
				}
            }
			else
			{
				if ((u - ulim) * (ulim - cx) >= 0)
				{
					u = ulim;
					fu = func(u);
				}
				else
				{
					u = cx + gold * (cx - bx);
					fu = func(u);
				}
			}
		}
		ax = bx;
		bx = cx;
		cx = u;
		fa = fb;
		fb = fc;
		fc = fu;
	}
}

void main()
{
    //program d11r1
    //driver for routine mnbrak
	double ax,bx,cx,fa,fb,fc;
	cout.setf(ios::fixed);
	cout.precision(6);
    for (int i = 1; i<=10; i++)
	{
        ax = i * 0.5;
        bx = (i + 1) * 0.5;
        mnbrak(ax, bx, cx, fa, fb, fc);
        cout<<"        a           b            c"<<endl;
        cout<<"x";
		cout.width(12);        cout<<ax;
		cout.width(12);        cout<<bx;
		cout.width(12);        cout<<cx<<endl;
        cout<<"f";	   
		cout.width(12);        cout<<fa;
		cout.width(12);        cout<<fb;
		cout.width(12);        cout<<fc;
		cout<<endl;
    }
}