/*
Sample-based estimate of Normalization constant
Assume the normalized distribution P(x), and a sample-generating
distribution p(x), such that:
P(x) = zp(x)
We would like to find z.
The domain of x here is the 4-simplex with volume V. Each sample
point is centered around a sub-volume, where all N sub-volumes
constitute V (a 'tesselation' if you like). One notional definition
of "fair sample points" is that one can estimate the total mass of the
density in the sub-volume as volume times density, where the estimate
of the density over that subvolume is taken to be constant and having
the value of the density at that point.
Taking total mass to be 1, each sub-volume contributes 1/N mass. And,
volume = mass/density, so by summing over sub-volumes, we have:
sum_i{(1/N) / P(x_i)} = V
sum_i{(1/N) / (zp(x_i)} = V
(1/Nz) sum_i{1/p(x_i)} = V
z = (1/NV) sum_i{1/p(x_i)}
~ (1/N) sum_i{1/p(x_i)}
*/
void populate_points(struct wpoint *points, unsigned npoints,
double *alpha_dist, double *alpha_weights,
gsl_rng *rand,
const char *name,
double *dist_norm)
{
struct wpoint *s, *se = points + npoints;
/* double ln_dist_norm = NAN; */
double dn = 0;
for (s = points; s != se; ++s)
{
gsl_ran_dirichlet(rand, NUCS, alpha_dist, s->x);
s->d = gsl_ran_dirichlet_pdf(NUCS, alpha_dist, s->x);
s->o = gsl_ran_dirichlet_pdf(NUCS, alpha_weights, s->x);
s->ln_d = gsl_ran_dirichlet_lnpdf(NUCS, alpha_dist, s->x);
s->ln_o = gsl_ran_dirichlet_lnpdf(NUCS, alpha_weights, s->x);
strcpy(s->dist, name);
s->num_samples = npoints;
dn += 1.0 / s->d;
/* ln_dist_norm = safe_sum(ln_dist_norm, -s->ln_d); */
}
/* ln_dist_norm -= gsl_sf_log(npoints); */
/* *dist_norm = gsl_sf_exp(ln_dist_norm); */
dn /= (double)npoints;
*dist_norm = dn;
}
void test_dirichlet(void){
double alpha[SIZE] = { .4, .9, .4, .2 };
double theta[SIZE] = { 0.0, 0.0, 0.0, 0.0 };
double prob;
int i;
gsl_ran_dirichlet (rng, SIZE, alpha, theta);
printf("gsl_ran_dirichlet\t");
print_double_array(alpha, SIZE);
printf("\t");
print_double_array(theta, SIZE);
printf("\n");
theta[0] = 0.107873072217;
theta[1] = 0.518033738502;
theta[2] = 0.220000000209;
theta[3] = 0.154093189072;
/* theta and alpha flipped in perl interface */
prob = gsl_ran_dirichlet_pdf (SIZE, alpha, theta);
printf("gsl_ran_dirichlet_pdf\t");
print_double_array(theta, SIZE);
printf("\t");
print_double_array(alpha, SIZE);
printf("\t%.12f\n", prob);
prob = gsl_ran_dirichlet_lnpdf (SIZE, alpha, theta);
printf("gsl_ran_dirichlet_lnpdf\t");
print_double_array(theta, SIZE);
printf("\t");
print_double_array(alpha, SIZE);
printf("\t%.12f\n", prob);
}
CAMLprim value ml_gsl_ran_dirichlet_pdf(value alpha, value theta)
{
const size_t K = Double_array_length(alpha);
double r ;
if(Double_array_length(theta) != K)
GSL_ERROR("alpha and theta must have same size", GSL_EBADLEN);
r = gsl_ran_dirichlet_pdf(K, Double_array_val(alpha),
Double_array_val(theta));
return copy_double(r);
}
double
test_dirichlet_pdf (double x)
{
size_t K = 2;
double alpha[2] = { 2.5, 5.0 };
double theta[2];
if (x <= 0.0 || x >= 1.0)
return 0.0; /* Out of range */
theta[0] = x;
theta[1] = 1.0 - x;
return gsl_ran_dirichlet_pdf (K, alpha, theta);
}
double pdf_Dirichlet(long n, double *a, double *x) { return gsl_ran_dirichlet_pdf(n, a, x); }
