mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
113 lines
2.7 KiB
C
113 lines
2.7 KiB
C
/*
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Copyright (C) 2013 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_mat.h"
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void
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arb_mat_exp_taylor_sum(arb_mat_t S, const arb_mat_t A, slong N, slong prec)
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{
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if (A == S)
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{
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arb_mat_t t;
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arb_mat_init(t, arb_mat_nrows(A), arb_mat_nrows(A));
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arb_mat_set(t, A);
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arb_mat_exp_taylor_sum(S, t, N, prec);
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arb_mat_clear(t);
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}
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else if (N <= 0)
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{
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arb_mat_zero(S);
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}
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else if (N == 1)
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{
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arb_mat_one(S);
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}
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else if (N == 2)
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{
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arb_mat_one(S);
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arb_mat_add(S, S, A, prec);
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}
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else if (N == 3)
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{
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arb_mat_t T;
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arb_mat_init(T, arb_mat_nrows(A), arb_mat_nrows(A));
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arb_mat_sqr(T, A, prec);
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arb_mat_scalar_mul_2exp_si(T, T, -1);
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arb_mat_add(S, A, T, prec);
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arb_mat_one(T);
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arb_mat_add(S, S, T, prec);
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arb_mat_clear(T);
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}
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else
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{
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slong i, lo, hi, m, w, dim;
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arb_mat_struct * pows;
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arb_mat_t T, U;
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fmpz_t c, f;
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dim = arb_mat_nrows(A);
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m = n_sqrt(N);
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w = (N + m - 1) / m;
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fmpz_init(c);
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fmpz_init(f);
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pows = flint_malloc(sizeof(arb_mat_t) * (m + 1));
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arb_mat_init(T, dim, dim);
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arb_mat_init(U, dim, dim);
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for (i = 0; i <= m; i++)
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{
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arb_mat_init(pows + i, dim, dim);
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if (i == 0)
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arb_mat_one(pows + i);
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else if (i == 1)
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arb_mat_set(pows + i, A);
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else
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arb_mat_mul(pows + i, pows + i - 1, A, prec);
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}
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arb_mat_zero(S);
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fmpz_one(f);
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for (i = w - 1; i >= 0; i--)
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{
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lo = i * m;
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hi = FLINT_MIN(N - 1, lo + m - 1);
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arb_mat_zero(T);
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fmpz_one(c);
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while (hi >= lo)
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{
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arb_mat_scalar_addmul_fmpz(T, pows + hi - lo, c, prec);
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if (hi != 0)
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fmpz_mul_ui(c, c, hi);
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hi--;
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}
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arb_mat_mul(U, pows + m, S, prec);
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arb_mat_scalar_mul_fmpz(S, T, f, prec);
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arb_mat_add(S, S, U, prec);
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fmpz_mul(f, f, c);
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}
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arb_mat_scalar_div_fmpz(S, S, f, prec);
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fmpz_clear(c);
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fmpz_clear(f);
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for (i = 0; i <= m; i++)
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arb_mat_clear(pows + i);
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flint_free(pows);
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arb_mat_clear(T);
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arb_mat_clear(U);
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}
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}
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