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<BODY><PRE>// Random Number Generation & Useful subfunctions
// Written by Microsoft Visual C++
// Copyright by UTLab, Tsinghua University
// http://orsc.edu.cn/UTLab
double myu(double a, double b) // Uniform Distribution
{
double y;
if(a>b) {
printf("\nThe first parameter should be less than the second!");
exit(1);
}
y = (double)rand()/(RAND_MAX);
return (a+(b-a)*y);
}
double myexp(double beta) // Exponential Distribution
{
double u;
do {
u = myu(0,1);
} while(u<=0||u>=1);
return (-1*beta*log(u));
}
double myn(double mu, double sigma2) // Normal Distribution
{
double mu1, mu2, z;
do {
mu1 = myu(0,1);
mu2 = myu(0,1);
} while (mu1<=0||mu1>=1);
z = sqrt(-2*log(mu1))*sin(2*3.14159*mu2);
return (mu+sqrt(sigma2)*z);
}
double randomoptimistic(double *p, int samplenumber, double alpha)
{
int i, j;
double w;
for(i=1; i<=samplenumber; i++)
for(j=i+1; j<=samplenumber; j++)
if(*(p+i) < *(p+j)) {
w = *(p+j);
*(p+j) = *(p+i);
*(p+i) = w;
}
return *(p+(int)(alpha*samplenumber));
}
double randompessimistic(double *p, int samplenumber, double alpha)
{
int i, j;
double w;
for(i=1; i<=samplenumber; i++)
for(j=i+1; j<=samplenumber; j++)
if(*(p+i) > *(p+j)) {
w = *(p+j);
*(p+j) = *(p+i);
*(p+i) = w;
}
return *(p+(int)(alpha*samplenumber));
}
double triangle(double x, double a, double b, double c)
{
if(a<x&&x<b) return (x-a)/(b-a);
if(b<=x&&x<c) return (x-c)/(b-c);
return 0;
}
double trapezoidal(double x, double a, double b, double c, double d)
{
if(a<x&&x<b) return (x-a)/(b-a);
if(b<=x&&x<=c) return 1;
if(c<x&&x<d) return (x-d)/(c-d);
return 0;
}
double fuzzyoptimistic(double x[], double mu[], int samplenumber, double alpha)
{
double v1, v2, v, xx, min, max;
int i;
min=x[1];
max=x[1];
for(i=2; i<=samplenumber; i++) {
if(min>x[i]) min=x[i];
if(max<x[i]) max=x[i];
}
do {
xx=(min+max)/2;
v1=0;
v2=0;
for(i=1; i<=samplenumber; i++) {
if((x[i]>=xx)&&(v1<mu[i])) v1=mu[i];
if((x[i]<xx)&&(v2<mu[i])) v2=mu[i];
}
if(v1>v2) v1=1; else v2=1;
v=(v1+1-v2)/2;
if(v>=alpha) min=xx;
else max=xx;
}while((max-min)>0.0001);
return (max+min)/2;
}
double fuzzypessimistic(double x[], double mu[], int samplenumber, double alpha)
{
double v1, v2, v, xx, min, max;
int i;
min=x[1];
max=x[1];
for(i=2; i<=samplenumber; i++) {
if(min>x[i]) min=x[i];
if(max<x[i]) max=x[i];
}
do {
xx=(min+max)/2;
v1=0;
v2=0;
for(i=1; i<=samplenumber; i++) {
if((x[i]<=xx)&&(mu[i]>v1)) v1=mu[i];
if((x[i]>xx)&&(mu[i]>v2)) v2=mu[i];
}
if(v1>v2) v1=1; else v2=1;
v=(v1+1-v2)/2;
if(v>=alpha) max=xx;
else min=xx;
}while((max-min)>0.0001);
return (max+min)/2;
}
double credibility(double x[], double mu[], int samplenumber, char relation, double a)
{
double v1=0, v2=0;
int i;
if(relation=='<')
for(i=1; i<=samplenumber; i++) {
if((x[i]<=a)&&(v1<mu[i])) v1=mu[i];
if((x[i]>a)&&(v2<mu[i])) v2=mu[i];
}
if(relation=='>')
for(i=1; i<=samplenumber; i++) {
if((x[i]>=a)&&(v1<mu[i])) v1=mu[i];
if((x[i]<a)&&(v2<mu[i])) v2=mu[i];
}
if(v1>v2) v1=1; else v2=1;
return (v1+1-v2)/2;
}
double fuzzymean(double x[], double mu[], int samplenumber, int integralnumber=2000)
{
int i,k;
double Expect=0, left, right, b1, b2, r;
left=x[1];
right=x[1];
for(i=2;i<=samplenumber;i++) {
if(left>x[i]) left=x[i];
if(right<x[i]) right=x[i];
}
for(k=1; k<=integralnumber; k++) {
r=myu(left,right);
b1=0;
b2=0;
if(r>=0) {
for(i=1; i<=samplenumber; i++) {
if(x[i]>=r&&b1<mu[i]) b1 = mu[i];
if(x[i]<r&&b2<mu[i]) b2 = mu[i];
}
Expect = Expect+(b1+1-b2)/2.0;
}
else {
for(i=1; i<=samplenumber; i++) {
if(x[i]<=r&&b1<mu[i]) b1 = mu[i];
if(x[i]>r&&b2<mu[i]) b2 = mu[i];
}
Expect = Expect-(b1+1-b2)/2.0;
}
}
return Expect*(right-left)/integralnumber+((left>0)?left:0)+((right<0)?right:0);
}
////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////
void sortminmax(double *p,int min,int max)
{
int i,j;
double w;
for(i=min; i<max; i++)
for(j=i+1; j<=max; j++)
if(*(p+i) > *(p+j)) {
w = *(p+i);
*(p+i) = *(p+j);
*(p+j) = w;
}
}
void sortmaxmin(double *p,int min,int max)
{
int i, j;
double w;
for(i=min; i<max; i++)
for(j=i+1; j<=max; j++)
if(*(p+i) < *(p+j)) {
w = *(p+i);
*(p+i) = *(p+j);
*(p+j) = w;
}
}
double findmaxn(double *p,int min,int max,int n)
{
int i, j;
double w;
for(i=min; i<=n; i++)
for(j=i+1; j<=max; j++)
if(*(p+i) < *(p+j)) {
w = *(p+j);
*(p+j) = *(p+i);
*(p+i) = w;
}
return *(p+n);
}
double findminn(double *p,int min,int max,int n)
{
int i, j;
double w;
for(i=min; i<=n; i++)
for(j=i+1; j<=max; j++)
if(*(p+i) > *(p+j)) {
w = *(p+j);
*(p+j) = *(p+i);
*(p+i) = w;
}
return *(p+n);
}
int mybe(double p) // Bernoulli Distribution
{
if(p>1||p<0) {
printf("\nParameter is out of bound!\n");
exit(1);
}
if(myu(0,1)<=p) return 1;
else return 0;
}
int mybn(int n, double p)
{
int i, y=0;
for(i=1; i<=n; i++)
y=y+mybe(p);
return y;
}
double myc(double alpha, double beta)
{
double u;
do {
u = myu(0,1);
} while (u<=0);
return (alpha-beta/tan(3.14159*u));
}
double myemp(double *a,int n) // Empirical Distribution
{
int i,m;
double mu;
for(i=1;i<n;i++)
{
if(a[i-1]>a[i])
{
printf("\nThe observations should be ordered from small to large!\n");
exit(1);
}
}
mu=myu(0,1);
m=(int)((n-1)*mu+1);
return (a[m-1]+((n-1)*mu-m+1)*(a[m]-a[m-1]));
}
double mychi(int k)
{
int i;
double z,y=0;
if(k<1)
{
printf("\nThe parameter should be a integer larger than zero!\n");
exit(1);
}
for(i=1;i<=k;i++)
{
z=myn(0,1);
y=y+z*z;
}
return y;
}
double myf(int k1, int k2)
{
double y1, y2;
y1 = mychi(k1);
for(;;){
y2 = mychi(k2);
if(y2!=0) break;
}
return((y1/k1)/(y2/k2));
}
double mys(int k)
{
double y, z;
z = myn(0,1);
y = mychi(k);
return (z/sqrt(y/k));
}
double myer(int k,double beta)
{
int i;
double y;
y=0;
if(k<=0)
{
printf("\nThe first parameter should be a integer larger than zero!\n");
exit(1);
}
for(i=1;i<=k;i++)
y=y+myexp(beta);
return y;
}
double myg(double alpha, double beta)
{
double x, v;
x = 0;
if(alpha<=0||beta<=0)
{
printf("\nParameter should all larger than zero!\n");
exit(1);
}
mark:
v = myexp(1);
x = x + v;
if(alpha == 1) {
x = beta*x;
return x;
}
alpha = alpha -1;
goto mark;
}
double myb(int alpha, int beta)
{
double y1, y2;
y1 = myg(alpha,1);
y2 = myg(beta,1);
return (y1/(y1+y2));
}
double myw(double alpha, double beta)
{
double v;
if(alpha<=0||beta<=0)
{
printf("\nParameter should all larger than zero!\n");
exit(1);
}
v = myexp(1);
return (beta*pow(v,(1/alpha)));
}
int myge(double p)
{
int x;
double r;
if(p>=1||p<=0)
{
printf("\nParameter is out of bound!\n");
exit(1);
}
do {
r=myu(0,1);
} while (r<=0||r>=1);
x= (int)(log(r)/log(1-p));
return x;
}
int mynb(int k,double p)
{
int i,y;
if(k<=0)
{
printf("\nThe first parameter should be a integer larger than zero!\n");
exit(1);
}
y=0;
for(i=1;i<=k;i++)
y=y+myge(p);
return y;
}
double myl(double a,double b)
{
double mu;
do {
mu = myu(0,1);
} while (mu<=0||mu>=1);
return(a-b*log(1/mu-1));
}
int myp(double lamd) // Poisson Distribution
{
int x;
double b,u;
if(lamd<=0)
{
printf("\nThe parameter should be larger than zero!\n");
exit(1);
}
x=0;
b=1;
do
{
u=myu(0,1);
b=b*u;
x=x+1;
}while(b>=exp(-lamd));
return(x-1);
}
double mynormal(double x, double c, double w)
{
return(exp(-(x-c)*(x-c)/(w*w)));
}
double mylogn(double mu, double sigma2) // Lognormal Distribution
{
double z;
z = myn(mu,sigma2);
return (exp(z));
}
double myt(double a,double b,double m) // Triangular Distribution
{
double c,u,y;
if(a>=m||m>=b) {
printf("\nThe first parameter should be the smallest!");
printf("\nAnd the second one should be the largest!\n");
exit(1);
}
c=(m-a)/(b-a);
u=myu(0,1);
if(u<c)
y=sqrt(c*u);
else
y=1-sqrt((1-c)*(1-u));
return(a+(b-a)*y);
}
double randommean(double x[], int samplenumber)
{
int i;
double Expect=0;
for(i=1;i<=samplenumber;i++)
Expect=Expect+x[i];
return Expect/samplenumber;
}
</PRE></BODY></HTML>
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