mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
75 lines
1.8 KiB
C
75 lines
1.8 KiB
C
/*
|
|
Copyright (C) 2016 Fredrik Johansson
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb is free software: you can redistribute it and/or modify it under
|
|
the terms of the GNU Lesser General Public License (LGPL) as published
|
|
by the Free Software Foundation; either version 2.1 of the License, or
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "arb_hypgeom.h"
|
|
|
|
void
|
|
_arb_hypgeom_erf_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
|
|
{
|
|
arb_t c;
|
|
arb_init(c);
|
|
|
|
arb_hypgeom_erf(c, h, prec);
|
|
|
|
hlen = FLINT_MIN(hlen, len);
|
|
|
|
if (hlen == 1)
|
|
{
|
|
_arb_vec_zero(g + 1, len - 1);
|
|
}
|
|
else
|
|
{
|
|
arb_ptr t, u;
|
|
slong ulen;
|
|
|
|
t = _arb_vec_init(len);
|
|
u = _arb_vec_init(len);
|
|
|
|
/* erf(h(x)) = integral(h'(x) exp(-h(x)^2)) * (2/sqrt(pi)) */
|
|
ulen = FLINT_MIN(len, 2 * hlen - 1);
|
|
|
|
_arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
|
|
_arb_vec_neg(u, u, ulen);
|
|
_arb_poly_exp_series(u, u, ulen, len, prec);
|
|
_arb_poly_derivative(t, h, hlen, prec);
|
|
_arb_poly_mullow(g, u, len, t, hlen - 1, len, prec);
|
|
_arb_poly_integral(g, g, len, prec);
|
|
|
|
arb_const_sqrt_pi(t, prec);
|
|
arb_inv(t, t, prec);
|
|
arb_mul_2exp_si(t, t, 1);
|
|
_arb_vec_scalar_mul(g, g, len, t, prec);
|
|
|
|
_arb_vec_clear(t, len);
|
|
_arb_vec_clear(u, len);
|
|
}
|
|
|
|
arb_swap(g, c);
|
|
arb_clear(c);
|
|
}
|
|
|
|
void
|
|
arb_hypgeom_erf_series(arb_poly_t g, const arb_poly_t h, slong len, slong prec)
|
|
{
|
|
slong hlen = h->length;
|
|
|
|
if (hlen == 0 || len == 0)
|
|
{
|
|
arb_poly_zero(g);
|
|
return;
|
|
}
|
|
|
|
arb_poly_fit_length(g, len);
|
|
_arb_hypgeom_erf_series(g->coeffs, h->coeffs, hlen, len, prec);
|
|
_arb_poly_set_length(g, len);
|
|
_arb_poly_normalise(g);
|
|
}
|
|
|