mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
95 lines
2.3 KiB
C
95 lines
2.3 KiB
C
/*
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Copyright (C) 2017 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_poly.h"
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void _acb_poly_lambertw_series(acb_ptr res,
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acb_srcptr z, slong zlen, const fmpz_t k, int flags, slong len, slong prec)
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{
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acb_ptr w, ew, t, u;
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acb_t ew0;
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zlen = FLINT_MIN(zlen, len);
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if (zlen == 1)
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{
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acb_lambertw(res, z, k, flags, prec);
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_acb_vec_zero(res + 1, len - 1);
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return;
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}
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w = _acb_vec_init(len);
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ew = _acb_vec_init(len);
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t = _acb_vec_init(len);
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u = _acb_vec_init(len);
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acb_init(ew0);
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acb_lambertw(w, z, k, flags, prec);
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if (acb_contains_zero(w))
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acb_exp(ew0, w, prec);
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else
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acb_div(ew0, z, w, prec);
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acb_add(t, ew0, z, prec);
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acb_div(w + 1, z + 1, t, prec);
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NEWTON_INIT(2, len)
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NEWTON_LOOP(m, n)
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/* _acb_poly_exp_series(ew, w, m, n, prec); */
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acb_zero(t);
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_acb_vec_set(t + 1, w + 1, m - 1);
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_acb_poly_exp_series(ew, t, m, n, prec);
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_acb_vec_scalar_mul(ew, ew, n, ew0, prec);
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_acb_poly_mullow(t, ew, n, w, m, n, prec);
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_acb_poly_sub(u, t, n, z, FLINT_MIN(zlen, n), prec);
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_acb_vec_add(t, t, ew, n, prec);
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_acb_poly_div_series(ew, u, n, t, n, n, prec);
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_acb_vec_neg(w + m, ew + m, n - m);
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NEWTON_END_LOOP
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NEWTON_END
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_acb_vec_set(res, w, len);
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_acb_vec_clear(w, len);
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_acb_vec_clear(ew, len);
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_acb_vec_clear(t, len);
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_acb_vec_clear(u, len);
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acb_clear(ew0);
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}
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void
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acb_poly_lambertw_series(acb_poly_t res,
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const acb_poly_t z, const fmpz_t k, int flags, slong len, slong prec)
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{
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if (len == 0 || (fmpz_is_zero(k) && z->length == 0))
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{
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acb_poly_zero(res);
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return;
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}
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if (z->length == 0)
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{
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acb_poly_fit_length(res, len);
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_acb_vec_indeterminate(res->coeffs, len);
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_acb_poly_set_length(res, len);
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return;
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}
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acb_poly_fit_length(res, len);
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_acb_poly_lambertw_series(res->coeffs, z->coeffs, z->length, k, flags, len, prec);
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_acb_poly_set_length(res, len);
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_acb_poly_normalise(res);
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}
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