120 lines
3.1 KiB
C
120 lines
3.1 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010, 2013 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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void arith_stirling_number_1u_vec_next(fmpz * row,
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const fmpz * prev, slong n, slong klen)
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{
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slong k;
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if (klen > n) fmpz_one(row + n);
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if (n != 0 && klen != 0) fmpz_zero(row);
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for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
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{
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fmpz_mul_ui(row + k, prev + k, n - UWORD(1));
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fmpz_add(row + k, prev + k - 1, row + k);
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}
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for (k = n + 1; k < klen; k++)
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fmpz_zero(row + k);
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}
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void arith_stirling_number_1_vec_next(fmpz * row,
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const fmpz * prev, slong n, slong klen)
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{
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slong k;
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if (klen > n) fmpz_one(row + n);
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if (n != 0 && klen != 0) fmpz_zero(row);
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for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
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{
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fmpz_mul_ui(row + k, prev + k, n - UWORD(1));
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fmpz_sub(row + k, prev + k - 1, row + k);
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}
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for (k = n + 1; k < klen; k++)
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fmpz_zero(row + k);
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}
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void arith_stirling_number_2_vec_next(fmpz * row,
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const fmpz * prev, slong n, slong klen)
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{
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slong k;
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if (klen > n) fmpz_one(row + n);
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if (n != 0 && klen != 0) fmpz_zero(row);
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for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
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{
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fmpz_mul_ui(row + k, prev + k, k);
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fmpz_add(row + k, prev + k - 1, row + k);
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}
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for (k = n + 1; k < klen; k++)
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fmpz_zero(row + k);
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}
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void
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arith_stirling_matrix_1u(fmpz_mat_t mat)
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{
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slong n;
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if (fmpz_mat_is_empty(mat))
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return;
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for (n = 0; n < mat->r; n++)
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arith_stirling_number_1u_vec_next(mat->rows[n],
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mat->rows[n - (n != 0)], n, mat->c);
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}
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void
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arith_stirling_matrix_1(fmpz_mat_t mat)
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{
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slong n;
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if (fmpz_mat_is_empty(mat))
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return;
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for (n = 0; n < mat->r; n++)
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arith_stirling_number_1_vec_next(mat->rows[n],
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mat->rows[n - (n != 0)], n, mat->c);
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}
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void
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arith_stirling_matrix_2(fmpz_mat_t mat)
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{
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slong n;
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if (fmpz_mat_is_empty(mat))
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return;
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for (n = 0; n < mat->r; n++)
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arith_stirling_number_2_vec_next(mat->rows[n],
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mat->rows[n - (n != 0)], n, mat->c);
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}
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