mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
127 lines
3.4 KiB
C
127 lines
3.4 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_airy_series(arb_ptr ai, arb_ptr ai_prime,
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arb_ptr bi, arb_ptr bi_prime, arb_srcptr z, slong zlen, slong len, slong prec)
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{
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arb_ptr t, u, v;
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slong tlen = len + ((ai_prime != NULL) || (bi_prime != NULL));
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zlen = FLINT_MIN(zlen, len);
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if (zlen <= 0)
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return;
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if (zlen == 1)
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{
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arb_hypgeom_airy(ai, ai_prime, bi, bi_prime, z, prec);
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return;
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}
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t = _arb_vec_init(tlen);
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u = _arb_vec_init(tlen);
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v = _arb_vec_init(len);
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arb_hypgeom_airy_jet((ai || ai_prime) ? t : NULL,
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(bi || bi_prime) ? u : NULL, z, tlen, prec);
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/* compose with nonconstant part */
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arb_zero(v);
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_arb_vec_set(v + 1, z + 1, zlen - 1);
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if (ai != NULL) _arb_poly_compose_series(ai, t, len, v, zlen, len, prec);
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if (bi != NULL) _arb_poly_compose_series(bi, u, len, v, zlen, len, prec);
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/* todo: use chain rule to avoid compositions for derivatives? */
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if (ai_prime != NULL)
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{
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_arb_poly_derivative(t, t, len + 1, prec);
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_arb_poly_compose_series(ai_prime, t, len, v, zlen, len, prec);
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}
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if (bi_prime != NULL)
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{
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_arb_poly_derivative(u, u, len + 1, prec);
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_arb_poly_compose_series(bi_prime, u, len, v, zlen, len, prec);
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}
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_arb_vec_clear(t, tlen);
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_arb_vec_clear(u, tlen);
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_arb_vec_clear(v, len);
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}
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void
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arb_hypgeom_airy_series(arb_poly_t ai, arb_poly_t ai_prime,
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arb_poly_t bi, arb_poly_t bi_prime, const arb_poly_t z, slong len, slong prec)
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{
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if (len == 0)
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{
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if (ai != NULL) arb_poly_zero(ai);
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if (ai_prime != NULL) arb_poly_zero(ai_prime);
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if (bi != NULL) arb_poly_zero(bi);
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if (bi_prime != NULL) arb_poly_zero(bi_prime);
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return;
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}
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if (z->length <= 1)
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len = 1;
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if (ai != NULL) arb_poly_fit_length(ai, len);
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if (ai_prime != NULL) arb_poly_fit_length(ai_prime, len);
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if (bi != NULL) arb_poly_fit_length(bi, len);
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if (bi_prime != NULL) arb_poly_fit_length(bi_prime, 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_airy_series(
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ai ? ai->coeffs : NULL, ai_prime ? ai_prime->coeffs : NULL,
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bi ? bi->coeffs : NULL, bi_prime ? bi_prime->coeffs : NULL,
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t, 1, 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_airy_series(
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ai ? ai->coeffs : NULL, ai_prime ? ai_prime->coeffs : NULL,
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bi ? bi->coeffs : NULL, bi_prime ? bi_prime->coeffs : NULL,
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z->coeffs, z->length, len, prec);
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}
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if (ai != NULL)
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{
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_arb_poly_set_length(ai, len);
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_arb_poly_normalise(ai);
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}
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if (ai_prime != NULL)
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{
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_arb_poly_set_length(ai_prime, len);
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_arb_poly_normalise(ai_prime);
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}
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if (bi != NULL)
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{
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_arb_poly_set_length(bi, len);
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_arb_poly_normalise(bi);
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}
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if (bi_prime != NULL)
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{
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_arb_poly_set_length(bi_prime, len);
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_arb_poly_normalise(bi_prime);
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}
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}
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