double
nb_est_alpha
(
tab_t *tab
)
{
// Find upper and lower bouds for a(lpha).
double a = 1.0;
double a_lo;
double a_hi;
if (eval_nb_f(a, tab) < 0) {
a /= 2;
while (eval_nb_f(a, tab) < 0) a /= 2;
a_lo = a;
a_hi = a*2;
}
else {
a *= 2;
while (eval_nb_f(a, tab) > 0) a *= 2;
a_lo = a/2;
a_hi = a;
}
// Input is pathological.
if (a_lo > 128) return -1.0;
double new_a = (a_lo + a_hi) / 2;
for (int i = 0 ; i < ZINM_MAXITER ; i++) {
a = (new_a < a_lo || new_a > a_hi) ?
(a_lo + a_hi) / 2 :
new_a;
double f = eval_nb_f(a, tab);
if (f < 0) a_hi = a; else a_lo = a;
if ((a_hi - a_lo) < ZINM_TOL) break;
double dfda = eval_nb_dfda(a, tab);
new_a = a - f / dfda;
}
return a;
}
void
test_eval_nb_f
(void)
{
// 0:14, 1:5, 2:4, 3:1, 5:1
int x[25] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,1,1,1,1,2,2,2,2,3,5 };
tab_t *tab = tabulate(x, 25);
test_assert(fabs(eval_nb_f(1.0, tab)+0.12747262) < 1e-6);
test_assert(fabs(eval_nb_f(1.1, tab)+0.24215981) < 1e-6);
test_assert(fabs(eval_nb_f(1.2, tab)+0.31636395) < 1e-6);
test_assert(fabs(eval_nb_f(1.3, tab)+0.36350700) < 1e-6);
test_assert(fabs(eval_nb_f(1.4, tab)+0.39225466) < 1e-6);
test_assert(fabs(eval_nb_f(1.5, tab)+0.40834322) < 1e-6);
test_assert(fabs(eval_nb_f(2.0, tab)+0.39975512) < 1e-6);
free(tab);
return;
}
