mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
113 lines
2.7 KiB
C
113 lines
2.7 KiB
C
/*
|
|
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);
|
|
}
|
|
}
|
|
|