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/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_mat.h"
void
acb_mat_exp_taylor_sum(acb_mat_t S, const acb_mat_t A, slong N, slong prec)
{
if (A == S)
{
acb_mat_t t;
acb_mat_init(t, acb_mat_nrows(A), acb_mat_nrows(A));
acb_mat_set(t, A);
acb_mat_exp_taylor_sum(S, t, N, prec);
acb_mat_clear(t);
}
else if (N <= 0)
{
acb_mat_zero(S);
}
else if (N == 1)
{
acb_mat_one(S);
}
else if (N == 2)
{
acb_mat_one(S);
acb_mat_add(S, S, A, prec);
}
else if (N == 3)
{
acb_mat_t T;
acb_mat_init(T, acb_mat_nrows(A), acb_mat_nrows(A));
acb_mat_sqr(T, A, prec);
acb_mat_scalar_mul_2exp_si(T, T, -1);
acb_mat_add(S, A, T, prec);
acb_mat_one(T);
acb_mat_add(S, S, T, prec);
acb_mat_clear(T);
}
else
{
slong i, lo, hi, m, w, dim;
acb_mat_struct * pows;
acb_mat_t T, U;
fmpz_t c, f;
dim = acb_mat_nrows(A);
m = n_sqrt(N);
w = (N + m - 1) / m;
fmpz_init(c);
fmpz_init(f);
pows = flint_malloc(sizeof(acb_mat_t) * (m + 1));
acb_mat_init(T, dim, dim);
acb_mat_init(U, dim, dim);
for (i = 0; i <= m; i++)
{
acb_mat_init(pows + i, dim, dim);
if (i == 0)
acb_mat_one(pows + i);
else if (i == 1)
acb_mat_set(pows + i, A);
else
acb_mat_mul(pows + i, pows + i - 1, A, prec);
}
acb_mat_zero(S);
fmpz_one(f);
for (i = w - 1; i >= 0; i--)
{
lo = i * m;
hi = FLINT_MIN(N - 1, lo + m - 1);
acb_mat_zero(T);
fmpz_one(c);
while (hi >= lo)
{
acb_mat_scalar_addmul_fmpz(T, pows + hi - lo, c, prec);
if (hi != 0)
fmpz_mul_ui(c, c, hi);
hi--;
}
acb_mat_mul(U, pows + m, S, prec);
acb_mat_scalar_mul_fmpz(S, T, f, prec);
acb_mat_add(S, S, U, prec);
fmpz_mul(f, f, c);
}
acb_mat_scalar_div_fmpz(S, S, f, prec);
fmpz_clear(c);
fmpz_clear(f);
for (i = 0; i <= m; i++)
acb_mat_clear(pows + i);
flint_free(pows);
acb_mat_clear(T);
acb_mat_clear(U);
}
}
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