mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
112 lines
3 KiB
C
112 lines
3 KiB
C
/*
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Copyright (C) 2016 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "arb_hypgeom.h"
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void
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_arb_hypgeom_fresnel_series(arb_ptr s, arb_ptr c,
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arb_srcptr h, slong hlen, int normalized, slong len, slong prec)
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{
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hlen = FLINT_MIN(hlen, len);
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if (hlen == 1)
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{
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arb_hypgeom_fresnel(s, c, h, normalized, prec);
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if (s != NULL) _arb_vec_zero(s + 1, len - 1);
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if (c != NULL) _arb_vec_zero(c + 1, len - 1);
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}
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else
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{
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arb_t s0, c0;
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arb_ptr t, u, v;
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slong ulen;
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arb_init(s0);
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arb_init(c0);
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arb_hypgeom_fresnel((s != NULL) ? s0 : NULL,
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(c != NULL) ? c0 : NULL, h, normalized, prec);
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t = _arb_vec_init(len);
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u = _arb_vec_init(len);
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v = _arb_vec_init(len);
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/* normalized: */
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/* C(h(x)) = integral(h'(x) cos(-(pi/2) h(x)^2)) */
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/* S(h(x)) = -integral(h'(x) sin(-(pi/2) h(x)^2)) */
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ulen = FLINT_MIN(len, 2 * hlen - 1);
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_arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
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_arb_vec_neg(u, u, ulen);
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if (normalized)
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{
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_arb_vec_scalar_mul_2exp_si(u, u, ulen, -1);
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_arb_poly_sin_cos_pi_series(u, v, u, ulen, len, prec);
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}
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else
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{
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_arb_poly_sin_cos_series(u, v, u, ulen, len, prec);
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}
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_arb_poly_derivative(t, h, hlen, prec);
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if (s != NULL)
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{
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_arb_poly_mullow(s, u, len, t, hlen - 1, len, prec);
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_arb_poly_integral(s, s, len, prec);
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_arb_vec_neg(s, s, len);
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arb_swap(s, s0);
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}
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if (c != NULL)
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{
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_arb_poly_mullow(c, v, len, t, hlen - 1, len, prec);
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_arb_poly_integral(c, c, len, prec);
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arb_swap(c, c0);
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}
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_arb_vec_clear(t, len);
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_arb_vec_clear(u, len);
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_arb_vec_clear(v, len);
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arb_clear(s0);
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arb_clear(c0);
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}
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}
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void
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arb_hypgeom_fresnel_series(arb_poly_t s, arb_poly_t c,
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const arb_poly_t h, int normalized, slong len, slong prec)
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{
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slong hlen = h->length;
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if (hlen == 0 || len == 0)
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{
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if (s != NULL) arb_poly_zero(s);
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if (c != NULL) arb_poly_zero(c);
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return;
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}
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if (s != NULL) arb_poly_fit_length(s, len);
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if (c != NULL) arb_poly_fit_length(c, len);
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_arb_hypgeom_fresnel_series((s != NULL) ? s->coeffs : NULL,
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(c != NULL) ? c->coeffs : NULL,
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h->coeffs, hlen, normalized, len, prec);
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if (s != NULL) _arb_poly_set_length(s, len);
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if (c != NULL) _arb_poly_set_length(c, len);
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if (s != NULL) _arb_poly_normalise(s);
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if (c != NULL) _arb_poly_normalise(c);
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}
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