double rndgamma2 (double s)
{
double r ,d, f, g, x;
static double b, h, ss=0;
if (s!=ss)
{
b = s-1.0;
h = sqrt(3.0*s-0.75);
ss = s;
}
for (;;)
{
r = rndu();
g = r-r*r;
f = (r-0.5)*h/sqrt(g);
x = b+f;
if (x <= 0.0)
continue;
r = rndu();
d = 64*r*r*g*g*g;
if (d*x < x-2.0*f*f || log(d) < 2*(b*log(x/b)-f))
break;
}
return (x);
}
double rndgamma1 (double s)
{
double r, x=0.0, small=1e-37, w;
static double a, p, uf, ss=10.0, d;
if (s!=ss)
{
a = 1.0-s;
p = a/(a+s*exp(-a));
uf = p*pow(small/a,s);
d = a*log(a);
ss = s;
}
for (;;)
{
r = rndu();
if (r > p)
x = a-log((1.0-r)/(1.0-p)), w=a*log(x)-d;
else if (r>uf)
x = a*pow(r/p,1/s), w=x;
else
return (0.0);
r = rndu();
if (1.0-r <= w && r > 0.0)
if (r*(w+1.0) >= 1.0 || -log(r) <= w)
continue;
break;
}
return (x);
}
int main(void)
{
int n=400, noisy=0, i,j;
int nr=10, ir, TimeSquare=10, algorithm; /* TimeSquare should be larger for large t */
double t=5, *Q, *pi, *space, s;
char timestr[96], *AlgStr[2]={"repeated squaring", "eigensolution"};
if((Q=(double*)malloc(n*n*5*sizeof(double))) ==NULL) error2("oom");
pi=Q+n*n; space=pi+n;
for(algorithm=0; algorithm<2; algorithm++) {
starttime();
SetSeed(1234567);
for (i=0; i<n; i++) pi[i]=rndu();
s=sum(pi,n);
for (i=0; i<n; i++) pi[i]/=s;
for(ir=0; ir<nr; ir++) {
printf("Replicate %d/%d ", ir+1,nr);
for (i=0; i<n; i++)
for (j=0,Q[i*n+i]=0; j<i; j++)
Q[i*n+j]=Q[j*n+i] = square(rndu());
for (i=0; i<n; i++)
for (j=0; j<n; j++)
Q[i*n+j] *= pi[j];
for(i=0,s=0; i<n; i++) { /* rescaling Q so that average rate is 1 */
Q[i*n+i]=0; Q[i*n+i]=-sum(Q+i*n, n);
s-=pi[i]*Q[i*n+i];
}
if(noisy) {
matout(stdout, pi, 1, n);
matout(stdout, Q, n, n);
}
if(algorithm==0)
matexp(Q, 1, n, TimeSquare, space);
else
PMatQRev(Q, pi, 1, n, space);
printf("%s, time: %s\n", AlgStr[algorithm], printtime(timestr));
if(noisy)
matout(stdout, Q, n, n);
}
}
return (0);
}
double rndgamma (double s)
{
double r=0.0;
if (s <= 0.0)
return 0;
else if (s < 1.0)
r = rndgamma1 (s);
else if (s > 1.0)
r = rndgamma2 (s);
else
r =- log(rndu());
return (r);
}
int GetTreeI (int itree, int ns, int rooted)
{
/* get the i_th tree. Trees are ordered according to the algorithm of
adding species.
returns a random tree if itree==-1, in which case ns can be large
*/
int i, M[NS-2], nM=ns-3+rooted, Ib[NS-2];
for (i=0; i<nM-1; i++) M[i]=2*i+5;
for (i=0,M[nM-1]=1; i<nM-2; i++) M[nM-1-i-2]*=M[nM-1-i-1];
if (itree==-1) for (i=0; i<nM; i++) Ib[i]=(int)((2*i+3)*rndu());
else for (i=0; i<nM; i++) {Ib[i]=itree/M[i]; itree%=M[i]; }
/*
if (noisy>3) {
FOR (i, nM) printf ("%5d ", M[i]); FPN (F0);
FOR (i, nM) printf ("%5d ", Ib[i]); FPN (F0);
}
*/
MakeTreeIb (ns, Ib, rooted);
return (0);
}