mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
114 lines
2.8 KiB
C
114 lines
2.8 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_beta_lower_series(arb_ptr res,
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const arb_t a, const arb_t b, arb_srcptr z, slong zlen, int regularized,
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slong len, slong prec)
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{
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arb_ptr t, u, v;
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arb_t c, d, e;
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zlen = FLINT_MIN(zlen, len);
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if (zlen == 1)
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{
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arb_hypgeom_beta_lower(res, a, b, z, regularized, prec);
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_arb_vec_zero(res + 1, len - 1);
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return;
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}
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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(zlen - 1);
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arb_init(c);
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arb_init(d);
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arb_init(e);
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arb_hypgeom_beta_lower(d, a, b, z, regularized, prec);
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if (regularized)
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{
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/* todo: except in special cases, we already compute a bunch of
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gamma functions in beta_lower, so we could avoid recomputing them */
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arb_add(e, a, b, prec);
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arb_gamma(e, e, prec);
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arb_rgamma(c, a, prec);
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arb_mul(e, e, c, prec);
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arb_rgamma(c, b, prec);
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arb_mul(e, e, c, prec);
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}
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/* u = (1-z)^(b-1) */
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_arb_vec_neg(t, z, zlen);
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arb_add_ui(t, t, 1, prec);
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arb_sub_ui(c, b, 1, prec);
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_arb_poly_pow_arb_series(u, t, FLINT_MIN(zlen, len - 1), c, len - 1, prec);
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/* t = z^(a-1) */
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arb_sub_ui(c, a, 1, prec);
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_arb_poly_pow_arb_series(t, z, FLINT_MIN(zlen, len - 1), c, len - 1, prec);
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/* v = z' */
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_arb_poly_derivative(v, z, zlen, prec);
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_arb_poly_mullow(res, t, len - 1, u, len - 1, len - 1, prec);
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_arb_poly_mullow(t, res, len - 1, v, zlen - 1, len - 1, prec);
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_arb_poly_integral(res, t, len, prec);
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if (regularized)
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{
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_arb_vec_scalar_mul(res, res, len, e, prec);
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}
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arb_set(res, d);
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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, zlen - 1);
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arb_clear(c);
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arb_clear(d);
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arb_clear(e);
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}
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void arb_hypgeom_beta_lower_series(arb_poly_t res,
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const arb_t a, const arb_t b, const arb_poly_t z, int regularized,
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slong len, slong prec)
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{
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if (len == 0)
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{
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arb_poly_zero(res);
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return;
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}
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arb_poly_fit_length(res, len);
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if (z->length == 0)
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{
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arb_t t;
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arb_init(t);
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_arb_hypgeom_beta_lower_series(res->coeffs, a, b, t, 1,
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regularized, len, prec);
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arb_clear(t);
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}
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else
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{
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_arb_hypgeom_beta_lower_series(res->coeffs, a, b, z->coeffs,
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z->length, regularized, len, prec);
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}
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_arb_poly_set_length(res, len);
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_arb_poly_normalise(res);
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}
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