mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
117 lines
2.7 KiB
C
117 lines
2.7 KiB
C
/*
|
|
Copyright (C) 2018 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 "arb_mat.h"
|
|
|
|
static void _stirling_number_1u_vec_next(arb_ptr row,
|
|
arb_srcptr prev, slong n, slong klen, slong prec)
|
|
{
|
|
slong k;
|
|
|
|
if (klen > n) arb_one(row + n);
|
|
if (n != 0 && klen != 0) arb_zero(row);
|
|
|
|
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
|
|
{
|
|
arb_mul_ui(row + k, prev + k, n - 1, prec);
|
|
arb_add(row + k, prev + k - 1, row + k, prec);
|
|
}
|
|
|
|
for (k = n + 1; k < klen; k++)
|
|
arb_zero(row + k);
|
|
}
|
|
|
|
static void _stirling_number_1_vec_next(arb_ptr row,
|
|
arb_srcptr prev, slong n, slong klen, slong prec)
|
|
{
|
|
slong k;
|
|
|
|
if (klen > n) arb_one(row + n);
|
|
if (n != 0 && klen != 0) arb_zero(row);
|
|
|
|
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
|
|
{
|
|
arb_mul_ui(row + k, prev + k, n - 1, prec);
|
|
arb_sub(row + k, prev + k - 1, row + k, prec);
|
|
}
|
|
|
|
for (k = n + 1; k < klen; k++)
|
|
arb_zero(row + k);
|
|
}
|
|
|
|
static void _stirling_number_2_vec_next(arb_ptr row,
|
|
arb_srcptr prev, slong n, slong klen, slong prec)
|
|
{
|
|
slong k;
|
|
|
|
if (klen > n) arb_one(row + n);
|
|
if (n != 0 && klen != 0) arb_zero(row);
|
|
|
|
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
|
|
{
|
|
arb_mul_ui(row + k, prev + k, k, prec);
|
|
arb_add(row + k, prev + k - 1, row + k, prec);
|
|
}
|
|
|
|
for (k = n + 1; k < klen; k++)
|
|
arb_zero(row + k);
|
|
}
|
|
|
|
static void
|
|
_stirling_matrix_1u(arb_mat_t mat, slong prec)
|
|
{
|
|
slong n;
|
|
|
|
if (arb_mat_is_empty(mat))
|
|
return;
|
|
|
|
for (n = 0; n < mat->r; n++)
|
|
_stirling_number_1u_vec_next(mat->rows[n],
|
|
mat->rows[n - (n != 0)], n, mat->c, prec);
|
|
}
|
|
|
|
static void
|
|
_stirling_matrix_1(arb_mat_t mat, slong prec)
|
|
{
|
|
slong n;
|
|
|
|
if (arb_mat_is_empty(mat))
|
|
return;
|
|
|
|
for (n = 0; n < mat->r; n++)
|
|
_stirling_number_1_vec_next(mat->rows[n],
|
|
mat->rows[n - (n != 0)], n, mat->c, prec);
|
|
}
|
|
|
|
static void
|
|
_stirling_matrix_2(arb_mat_t mat, slong prec)
|
|
{
|
|
slong n;
|
|
|
|
if (arb_mat_is_empty(mat))
|
|
return;
|
|
|
|
for (n = 0; n < mat->r; n++)
|
|
_stirling_number_2_vec_next(mat->rows[n],
|
|
mat->rows[n - (n != 0)], n, mat->c, prec);
|
|
}
|
|
|
|
void
|
|
arb_mat_stirling(arb_mat_t mat, int kind, slong prec)
|
|
{
|
|
if (kind == 0)
|
|
_stirling_matrix_1u(mat, prec);
|
|
else if (kind == 1)
|
|
_stirling_matrix_1(mat, prec);
|
|
else
|
|
_stirling_matrix_2(mat, prec);
|
|
}
|
|
|