void
_arb_poly_log1p_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)
{
arb_t a;
flen = FLINT_MIN(flen, n);
arb_init(a);
arb_log1p(a, f, prec);
if (flen == 1)
{
_arb_vec_zero(res + 1, n - 1);
}
else if (n == 2)
{
arb_add_ui(res, f + 0, 1, prec);
arb_div(res + 1, f + 1, res + 0, prec);
}
else if (_arb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
slong i, j, d = flen - 1;
arb_add_ui(res, f + 0, 1, prec);
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
arb_div(res + j, f + d, res, prec);
else
arb_mul(res + j, res + j - d, res + d, prec);
_arb_vec_zero(res + j - d + 1, flen - 2);
}
_arb_vec_zero(res + j - d + 1, n - (j - d + 1));
for (i = 2, j = 2 * d; j < n; j += d, i++)
arb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
}
else
{
arb_ptr f_diff, f_inv;
slong alloc;
alloc = n + flen;
f_inv = _arb_vec_init(alloc);
f_diff = f_inv + n;
arb_add_ui(f_diff, f, 1, prec);
_arb_vec_set(f_diff + 1, f + 1, flen - 1);
_arb_poly_inv_series(f_inv, f_diff, flen, n, prec);
_arb_poly_derivative(f_diff, f, flen, prec);
_arb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_arb_poly_integral(res, res, n, prec);
_arb_vec_clear(f_inv, alloc);
}
arb_swap(res, a);
arb_clear(a);
}
void
custom_rate_mixture_expectation(arb_t rate, const custom_rate_mixture_t x, slong prec)
{
if (x->mode == RATE_MIXTURE_UNDEFINED)
{
flint_fprintf(stderr, "internal error: undefined rate mixture\n");
abort();
}
else if (x->mode == RATE_MIXTURE_NONE)
{
arb_one(rate);
}
else if (x->mode == RATE_MIXTURE_UNIFORM || x->mode == RATE_MIXTURE_CUSTOM)
{
slong i;
arb_t tmp, tmpb;
arb_init(tmp);
arb_init(tmpb);
arb_zero(rate);
if (x->mode == RATE_MIXTURE_UNIFORM)
{
for (i = 0; i < x->n; i++)
{
arb_set_d(tmp, x->rates[i]);
arb_add(rate, rate, tmp, prec);
}
arb_div_si(rate, rate, x->n, prec);
}
else if (x->mode == RATE_MIXTURE_CUSTOM)
{
for (i = 0; i < x->n; i++)
{
arb_set_d(tmp, x->rates[i]);
arb_set_d(tmpb, x->prior[i]);
arb_addmul(rate, tmp, tmpb, prec);
}
}
arb_clear(tmp);
arb_clear(tmpb);
}
else
{
flint_fprintf(stderr, "internal error: "
"unrecognized rate mixture mode\n");
abort();
}
}
void Lib_Arb_Div_Si(ArbPtr f, ArbPtr g, int32_t x, int32_t prec)
{
arb_div_si( (arb_ptr) f, (arb_ptr) g, x, prec);
}
int main()
{
long iter;
flint_rand_t state;
printf("div_si....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c, d;
long x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
x = z_randtest(state);
prec = 2 + n_randint(state, 2000);
arb_set_si(b, x);
arb_div_si(c, a, x, prec);
arb_div(d, a, b, prec);
if (!arb_equal(c, d))
{
printf("FAIL\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
printf("d = "); arb_print(d); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
/* aliasing */
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
long x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
x = z_randtest(state);
prec = 2 + n_randint(state, 2000);
arb_set_si(b, x);
arb_div_si(c, a, x, prec);
arb_div_si(a, a, x, prec);
if (!arb_equal(a, c))
{
printf("FAIL (aliasing)\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
gamma_rate_mixture_summarize(
arb_ptr rate_mix_prior, arb_ptr rate_mix_rates, arb_ptr rate_mix_expect,
const gamma_rate_mixture_t x, enum rate_mixture_mode mode, slong prec)
{
slong i;
arb_ptr r;
arb_t p, q;
arb_init(p);
arb_init(q);
arb_set_d(p, x->invariable_prior);
arb_sub_si(q, p, 1, prec);
arb_neg(q, q);
/* the expectation is designed to be 1 */
arb_one(rate_mix_expect);
/* probabilities corresponding to gamma rate categories */
for (i = 0; i < x->gamma_categories; i++)
{
r = rate_mix_prior + i;
arb_div_si(r, q, x->gamma_categories, prec);
}
/* optional probability corresponding to the invariable category */
if (x->invariable_prior)
{
r = rate_mix_prior + x->gamma_categories;
arb_set(r, p);
}
/* set the discretized gamma rates */
{
arb_t s;
arb_init(s);
arb_set_d(s, x->gamma_shape);
if (mode == RATE_MIXTURE_GAMMA)
{
gamma_rates(
rate_mix_rates, x->gamma_categories, s, prec);
}
else if (mode == RATE_MIXTURE_GAMMA_MEDIAN)
{
normalized_median_gamma_rates(
rate_mix_rates, x->gamma_categories, s, prec);
}
else
{
abort(); /* assert */
}
arb_clear(s);
}
/* normalize the rates to account for a possible invariable category */
for (i = 0; i < x->gamma_categories; i++)
{
r = rate_mix_rates + i;
arb_div(r, r, q, prec);
}
arb_clear(p);
arb_clear(q);
}
