//--------------------------------------------------------------------------------
double binomial(unsigned long n, unsigned long k)
{
{
NTA_ASSERT(k <= n)
<< "binomial: Wrong arguments: n= " << n << " k= " << k;
}
if (n < 171)
return floor(0.5 + fact(n) / (fact(k) * fact(n-k)));
else
return floor(0.5 + exp(lfact(n) - lfact(k) - lfact(n-k)));
}
/* generates a success * trials table of bionomial probability densities (log transformed) */
static double* logbinomial_table( const int n_size )
{
/* prob distribution for binom var is p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k} */
/* this calcs p(k) = {log(n!) - log(k!) - log((n-k)!) */
int k, n;
double *logbinom = (double*)calloc(n_size * n_size, sizeof(double));
for (n = 1; n < n_size; ++n) {
double lfn = lfact(n);
for (k = 1; k <= n; ++k)
logbinom[n<<8|k] = lfn - lfact(k) - lfact(n-k);
}
return logbinom;
}
/*
* Computes the hypergeometric function 1F1(a;b;z1,z2) in canonical form (z1 > z2 > 0)
*/
static double compute_1F1_2d_canon(double a, double b, double z1, double z2, int iter)
{
int i, j;
double g, F = 0.0, logz1 = log(z1), logz2 = log(z2);
for (i = 0; i < iter; i++) {
for (j = 0; j < iter; j++) {
g = lgamma(i+a) + lgamma(j+a) - lgamma(i+j+b) + i*logz1 + j*logz2 - lfact(i) - lfact(j);
if ((i > z1 || j > z2) && exp(g) < EPSILON * F) // exp(g) < 2e-9
break;
F += exp(g);
}
}
return 2*sqrt(M_PI)*F;
}
long lfact ( int n )
{
if ( n < 0 )
return -1 ;
if ( n < 1 )
return 1 ;
return n * lfact ( n - 1 ) ;
}
/*
* Computes the hypergeometric function 1F1(a;b;z) in canonical form (z > 0)
*/
static double compute_1F1_1d_canon(double a, double b, double z, int iter)
{
//printf("compute_1F1_1d_canon(%f, %f, %f, %d)\n", a, b, z, iter);
int i;
double g, F = 0.0, logz = log(z);
for (i = 0; i < iter; i++) {
g = lgamma(i+a) - lgamma(i+b) + i*logz - lfact(i);
if (i > z && exp(g) < EPSILON * F) // exp(g) < 1e-8 * F
break;
F += exp(g);
}
return 2*sqrt(M_PI)*F;
}
/*
* Computes the hypergeometric function 1F1(a;b;z1,z2,z3) in canonical form (z1 > z2 > z3 > 0)
*/
static double compute_1F1_3d_canon(double a, double b, double z1, double z2, double z3, int iter)
{
int i, j, k;
double g, F = 0.0, logz1 = log(z1), logz2 = log(z2), logz3 = log(z3);
for (i = 0; i < iter; i++) {
for (j = 0; j < iter; j++) {
for (k = 0; k < iter; k++) {
g = lgamma(i+a) + lgamma(j+a) + lgamma(k+a) - lgamma(i+j+k+b) + i*logz1 + j*logz2 + k*logz3 - lfact(i) - lfact(j) - lfact(k);
if ((i > z1 || j > z2 || k > z3) && exp(g) < EPSILON * F) // exp(g) < 2e-9
break;
F += exp(g);
}
}
}
return 2*sqrt(M_PI)*F;
}
