mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
74 lines
1.8 KiB
C
74 lines
1.8 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_erfi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
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{
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arb_t c;
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arb_init(c);
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arb_hypgeom_erfi(c, h, prec);
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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_vec_zero(g + 1, len - 1);
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}
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else
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{
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arb_ptr t, u;
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slong ulen;
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t = _arb_vec_init(len);
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u = _arb_vec_init(len);
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/* erfi(h(x)) = integral(h'(x) exp(h(x)^2)) * (2/sqrt(pi)) */
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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_poly_exp_series(u, u, ulen, len, prec);
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_arb_poly_derivative(t, h, hlen, prec);
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_arb_poly_mullow(g, u, len, t, hlen - 1, len, prec);
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_arb_poly_integral(g, g, len, prec);
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arb_const_sqrt_pi(t, prec);
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arb_inv(t, t, prec);
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arb_mul_2exp_si(t, t, 1);
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_arb_vec_scalar_mul(g, g, len, t, prec);
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_arb_vec_clear(t, len);
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_arb_vec_clear(u, len);
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}
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arb_swap(g, c);
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arb_clear(c);
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}
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void
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arb_hypgeom_erfi_series(arb_poly_t g, const arb_poly_t h, 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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arb_poly_zero(g);
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return;
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}
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arb_poly_fit_length(g, len);
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_arb_hypgeom_erfi_series(g->coeffs, h->coeffs, hlen, len, prec);
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_arb_poly_set_length(g, len);
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_arb_poly_normalise(g);
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}
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