double ranpoiss1(double xm)
/* poisson variable conditioned on x>0 */
/** xm should be small here
ranpoissx is the driver.
Don't call this directly
*/
{
double t, tc, s, y ;
int k ;
t = exp(-xm) ;
tc = 1.0-t ;
if (tc==0.0) return 1 ;
y = t ;
s = tc*DRAND2() ;
/* s uniform [0, tc] */
k = 1 ;
y *= xm / (double) k ;
for (;;) {
if (s<y) return (double) k ;
s -= y ;
++k ;
y *= xm / (double) k ;
if (k>=100) {
fprintf(stderr,"(ranpoiss1) bug? xm: %12.6f\n", xm) ;
return k ;
}
}
}
double samppow(double e, double a, double b)
// sample x^e in range (a,b)
// uses cdf method since integral is analytic
// care taken to prevent underflow
{
double ztot, rhs, zlog, ee, x ;
double y1, y2, u ;
ee = e+1.0 ;
if (ee<0.0) fatalx("e must be > -1 \n") ; // fixable if integral finite
if (b<a) return samppow(e, b, a) ;
if (a==b) return a ;
u = DRAND2() ; if (u==0.0) u = 0.5 ; // tiny hack
y1 = ee*log(b) + log(u) ;
if (a==0.0) zlog = y1 ;
else {
y2 = ee*log(a) + log(1.0-u) ;
zlog = addlog(y1, y2) ;
}
/**
ztot = pow(b, ee) - pow(a, ee) ;
rhs = ztot*DRAND() + pow(a, ee) ;
zlog = log(rhs) ;
*/
x = exp(zlog/ee) ;
return x ;
}
double
ranexp( void)
{
/**
exponential mean 1
*/
double x, t;
t = DRAND2();
x = -log(1.0 - t);
return x;
}
int prob1(double p)
// return YES with probability p
{
double z ;
if ((p<0) || (p>1)) fatalx("bad p %12.6f\n", p) ;
z = DRAND2() ;
if (z<p) return YES ;
return NO ;
}
double rantruncnorm(double T, int upper)
{
double u ;
if (upper==0) return -rantruncnorm(-T, 1) ;
u = DRAND2() ; if (u==0.0) u = 0.5 ; // tiny hack
u *= ntail(T) ;
if (u==0.0) return MAX(T, 50.0) ;
return zprob(u) ;
}
double uniform(double lo, double hi)
{
double x, width ;
width = hi - lo ;
if (width < 0)
return uniform(hi, lo) ;
x = DRAND2() * width ;
return x + lo ;
}
double poidev(double xm)
/**
NUM REC pp 293 ff (modified)
*/
{
static double sq,alxm,g,oldm=(-1.0);
double em,t,y;
if (xm < 12.0) {
if (xm != oldm) {
oldm=xm;
g=exp(-xm);
}
em = -1;
t=1.0;
do {
++em;
t *= DRAND2();
} while (t > g);
} else {
if (xm != oldm) {
oldm=xm;
sq=sqrt(2.0*xm);
alxm=log(xm);
g=xm*alxm-lgamma(xm+1.0);
}
do {
do {
y=tan(PI*DRAND2());
em=sq*y+xm;
} while (em < 0.0);
em=floor(em);
t=0.9*(1.0+y*y)*exp(em*alxm-lgamma(em+1.0)-g);
} while (DRAND2() > t);
}
return em;
}
static int ranb1 (int n, double p)
/**
binomial dis.
Naive routine
*/
{
int cnt = 0, i ;
for (i=0 ; i< n ; i++) {
if (DRAND2() <= p) ++ cnt ;
}
return cnt ;
}
void ewens(int *a, int n, double theta)
/**
implements the Ewens sampler. Categories 1...K
*/
{
int i, k, maxcat=0 ;
double t, x ;
if (n==0) return ;
a[0] = maxcat = 1 ;
for (i=1 ; i< n ; i++) {
t = theta/ ((double) i + theta) ;
x = DRAND2() ;
if (x > t) {
k = ranmod(i) ;
a[i] = a[k] ;
}
else {
++maxcat ;
a[i] = maxcat ;
}
}
}
int randis(double *a, int n)
{
/* a should be prob dis summing to 1 */
int i ;
double t, y ;
static int nfirst=0 ;
t = DRAND2() ;
for (i=0; i<n; i++) {
t -= a[i] ;
if (t<=0.0) return i ;
}
if (nfirst==0) {
printf("pos t: %15.9f\n",t) ;
for (i=0; i<n ; i++) {
printf("zzrand %4d %9.3f\n",i, a[i]) ;
}
}
++nfirst ;
fprintf(stderr, "probable bug (randis)\n") ;
return n-1 ;
}
