mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
74 lines
1.7 KiB
C
74 lines
1.7 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 "acb_hypgeom.h"
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void
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_acb_hypgeom_shi_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec)
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{
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acb_t c;
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acb_init(c);
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acb_hypgeom_shi(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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_acb_vec_zero(g + 1, len - 1);
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}
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else if (len == 2)
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{
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acb_mul_onei(g, h);
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acb_sinc(g, g, prec);
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acb_mul(g + 1, g, h + 1, prec);
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}
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else
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{
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acb_ptr t, u;
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slong i;
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t = _acb_vec_init(len - 1);
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u = _acb_vec_init(hlen);
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/* Shi(h(x)) = integral(h'(x) sinc(i h(x))) */
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for (i = 0; i < hlen; i++)
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acb_mul_onei(u + i, h + i);
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_acb_poly_sinc_series(t, u, hlen, len - 1, prec);
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_acb_poly_derivative(u, h, hlen, prec);
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_acb_poly_mullow(g, t, len - 1, u, hlen - 1, len - 1, prec);
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_acb_poly_integral(g, g, len, prec);
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_acb_vec_clear(t, len - 1);
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_acb_vec_clear(u, hlen);
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}
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acb_swap(g, c);
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acb_clear(c);
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}
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void
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acb_hypgeom_shi_series(acb_poly_t g, const acb_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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acb_poly_zero(g);
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return;
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}
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acb_poly_fit_length(g, len);
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_acb_hypgeom_shi_series(g->coeffs, h->coeffs, hlen, len, prec);
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_acb_poly_set_length(g, len);
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_acb_poly_normalise(g);
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}
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