d13r10.cpp

使用VC++编写的大量数学算法的源代码

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

double ran1(long& idum)
{
    int j,iff=-1;
	static long ix1,ix2,ix3;
	static double r[98];
    long m1 = 259200; long m2 = 134456; long m3 = 243000;
	long ia1 = 7141; long ia2 = 8121; long ia3 = 4561;
	long ic1 = 54773; long ic2 = 28411; long ic3 = 51349;
	double rm1 = 0.0000038580247; double rm2 = 0.0000074373773;    
    if (idum < 0 || iff == 0)
	{
        iff = 1;
        ix1 = (ic1 - idum) % m1;
        ix1 = (ia1 * ix1 + ic1) % m1;
        ix2 = ix1 % m2;
        ix1 = (ia1 * ix1 + ic1) % m1;
        ix3 = ix1 % m3;
        for (j = 1; j<=97; j++)
		{
            ix1 = (ia1 * ix1 + ic1) % m1;
            ix2 = (ia2 * ix2 + ic2) % m2;
            r[j] = (double(ix1) + double(ix2) * rm2) * rm1;
        }
        idum = 1;
    }
    ix1 = (ia1 * ix1 + ic1) % m1;
    ix2 = (ia2 * ix2 + ic2) % m2;
    ix3 = (ia3 * ix3 + ic3) % m3;
    j = 1 + int((97 * ix3) / m3);
    if (j > 97 || j < 1)
	{
		cout<<"abnormal exit in ran1"<<endl;
		exit(1);
	}
	double temp=r[j];
    r[j] = (double(ix1) + double(ix2) * rm2) * rm1;
	return temp;
}

double gasdev(long& idum)
{
    static int iset;
	static double gset;
	double v1,v2,r,fac;
    if (iset == 0)
	{
		do
		{
			v1 = 2.0 * ran1(idum) - 1.0;
			v2 = 2.0 * ran1(idum) - 1.0;
			r = v1 * v1 + v2 * v2;
		}while (r >= 1.0 || r == 0);
		fac = sqrt(-2.0 * log(r) / r);
		gset = v1 * fac;
		iset = 1;
		return v2 * fac;
	}
    else
	{
		iset = 0;
		return gset;
    }
}

double gammln(double xx)
{
	double cof[7];
	cof[1] = 76.18009173;
	cof[2] = -86.50532033;
	cof[3] = 24.01409822;
	cof[4] = -1.231739516;
	cof[5] = 0.00120858003;
	cof[6] = -0.00000536382;
	double ser,x,tmp,stp = 2.50662827465;
	double half = 0.5;
	double one = 1.0;
	double fpf = 5.5;
	int j;
	x = xx - one;
	tmp = x + fpf;
	tmp = (x + half) * log(tmp) - tmp;
	ser = one;
	for (j = 1; j<=6; j++)
	{
		x = x + one;
		ser = ser + cof[j] / x;
	}
	return tmp + log(stp * ser);
}
void gcf(double& gammcf, double a, double x, double& gln)
{
	int an,n,itmax = 100;
	double anf,g,ana,eps = 0.0000003;
	gln = gammln(a);
	double gold = 0.0;
	double a1,a0 = 1.0;
	a1 = x;
	double b0 = 0.0;
	double b1 = 1.0;
	double fac = 1.0;
	for (n = 1; n<=itmax; n++)
	{
		an = n;
		ana = an - a;
		a0 = (a1 + a0 * ana) * fac;
		b0 = (b1 + b0 * ana) * fac;
		anf = an * fac;
		a1 = x * a0 + anf * a1;
		b1 = x * b0 + anf * b1;
		if (a1 != 0.0)
		{
			fac = 1.0 / a1;
			g = b1 * fac;
			if (fabs((g - gold) / g) < eps)
			{
				gammcf = exp(-x + a * log(x) - gln) * g;
				return;
			}
			gold = g;
		}
	}
	cout<< "a too large, itmax too small"<<endl;
	gammcf = exp(-x + a * log(x) - gln) * g;
}
void gser(double& gamser, double a, double x, double& gln)
{
	int n,itmax = 100;
	double ap,sum,del,eps = 0.0000003;
	gln = gammln(a);
	if (x <= 0.0)
	{
		if (x < 0.0)
		{
			cout<<"pause in gser"<<endl;
			return;
		}
		gamser = 0.0;
		return;
	}
	ap = a;
	sum = 1.0 / a;
	del = sum;
	for (n = 1; n<=itmax; n++)
	{
		ap = ap + 1.0;
		del = del * x / ap;
		sum = sum + del;
		if (fabs(del) < fabs(sum) * eps)
		{
			gamser = sum * exp(-x + a * log(x) - gln);
			return;
		}
	}
	cout<< "a too large, itmax too small";
	gamser = sum * exp(-x + a * log(x) - gln);
}
double  gammp(double a, double x)
{
	double gln;
	if (x < 0.0 || a <= 0.0)
	{
		cout<< "pause in gammp"<<endl;
		exit(1);
	}
	if (x < a + 1.0)
	{
		double gamser;
		gser(gamser, a, x, gln);
		return gamser;
	}
	else
	{
		double gammcf;
		gcf(gammcf, a, x, gln);
		return  1.0 - gammcf;
	}
}

void sort(int n, double ra[])
{
	int i,j,l,ir;
	double rra;
	l = n / 2 + 1;
	ir = n;
	do
	{
		if (l > 1)
		{
			l = l - 1;
			rra = ra[l];
		}
		else
		{
			rra = ra[ir];
			ra[ir] = ra[1];
			ir = ir - 1;
			if (ir == 1)
			{
				ra[1] = rra;
				return;
			}
		}
		i = l;
		j = l + l;
		while (j <= ir)
		{		
			if (j < ir)
			{
				if (ra[j] < ra[j + 1])
				{
					j = j + 1;
				}
			}
			if (rra < ra[j])
			{
				ra[i] = ra[j];
				i = j;
				j = j + j;
			}
			else
			{
				j = ir + 1;
			}
		}
		ra[i] = rra;
	}while(1);
}

double probks(double alam)
{
	double eps1 = 0.001;
    double eps2 = 0.00000001;
    double a2 = -2.0 * alam * alam;
    double fac = 2.0;
    double aaa,temp = 0.0;
    double term,termbf = 0.0;
    for (int j = 1; j<=100; j++)
	{
        term = fac * exp(a2 * j * j);
        temp = temp + term;
        aaa = fabs(term);
        if (aaa < eps1 * termbf || aaa < eps2 * temp)
		{
			return temp;
        }
        fac = -fac;
        termbf = fabs(term);
    }
    return 1.0;
}

double erf(double x)
{
	if (x < 0.0)
	{
		return -gammp(0.5, x * x);
	}
    else
	{
        return gammp(0.5, x * x);
    }
}

double func(double x)
{
	double y;
    y = x / sqrt(2.0);
    return erf(y);
}


void ksone(double data[], int n, double& d, double& prob)
{
    sort(n, data);
    int en = n;
    d = 0.0;
    double fq,ff,dt,fo = 0.0;
    for (int j = 1; j<=n; j++)
	{
        fq = (double)j /(double)en;
        ff = func(data[j]);
        dt = fabs(fo - ff);
        if (fabs(fq - ff) > dt)
		{
			dt = fabs(fq - ff);
		}
        if (dt > d)
		{
			d = dt;
		}
        fo = fq;
    }
    prob = probks(sqrt(en) * d);
}

void main()
{
    //program d13r10
    //driver for routine ksone
    int i,j,npts = 1000;
    double var,factr,d,prob,eps = 0.1;
    double data[1001];
    long idum = -5;
    cout<<endl;
    cout<<"Variance ratio  K-S statistic   Probability"<<endl;
	cout.setf(ios::fixed|ios::left);
	cout.precision(4);
    for (i = 1; i<=11; i++)
	{
        var = 1.0 + (i - 1) * eps;
        factr = sqrt(var);
        for (j = 1; j<=npts; j++)
		{
            data[j] = factr * fabs(gasdev(idum));
        }
        ksone(data, npts, d, prob);
		cout<<"    ";
		cout.width(14);
        cout<<var;
		cout.width(14);
        cout<<d;
		cout.width(14);
		cout.unsetf(ios::fixed);
		cout.setf(ios::scientific);
        cout<<prob<<endl;
		cout.unsetf(ios::scientific);
		cout.setf(ios::fixed);
    }
}