124 lines
3.1 KiB
C
124 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) 2011 Fredrik Johansson
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "fmpz_poly.h"
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#include "fmpq_poly.h"
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void
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_fmpq_poly_interpolate_fmpz_vec(fmpz * poly, fmpz_t den,
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const fmpz * xs, const fmpz * ys, slong n)
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{
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fmpz *P, *Q, *w;
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fmpz_t t;
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slong i, j;
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/* Constant */
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if (n == 1)
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{
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fmpz_set(poly, ys);
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fmpz_one(den);
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return;
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}
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/* Linear */
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if (n == 2)
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{
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fmpz_sub(den, xs, xs + 1);
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fmpz_sub(poly + 1, ys, ys + 1);
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fmpz_mul(poly, xs, ys + 1);
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fmpz_submul(poly, xs + 1, ys);
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return;
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}
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fmpz_init(t);
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P = _fmpz_vec_init(n + 1);
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Q = _fmpz_vec_init(n);
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w = _fmpz_vec_init(n);
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/* P = (x-x[0])*(x-x[1])*...*(x-x[n-1]) */
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_fmpz_poly_product_roots_fmpz_vec(P, xs, n);
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/* Weights */
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for (i = 0; i < n; i++)
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{
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fmpz_one(w + i);
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for (j = 0; j < n; j++)
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{
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if (i != j)
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{
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fmpz_sub(t, xs + i, xs + j);
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fmpz_mul(w + i, w + i, t);
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}
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}
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}
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_fmpz_vec_zero(poly, n);
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_fmpz_vec_lcm(den, w, n);
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for (i = 0; i < n; i++)
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{
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/* Q = P / (x - x[i]) */
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_fmpz_poly_div_root(Q, P, n + 1, xs + i);
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/* result += Q * weight(i) */
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fmpz_divexact(t, den, w + i);
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fmpz_mul(t, t, ys + i);
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_fmpz_vec_scalar_addmul_fmpz(poly, Q, n, t);
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}
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_fmpz_vec_clear(P, n + 1);
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_fmpz_vec_clear(Q, n);
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_fmpz_vec_clear(w, n);
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fmpz_clear(t);
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}
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void
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fmpq_poly_interpolate_fmpz_vec(fmpq_poly_t poly,
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const fmpz * xs, const fmpz * ys, slong n)
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{
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if (n == 0)
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{
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fmpq_poly_zero(poly);
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}
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else if (n == 1)
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{
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fmpq_poly_set_fmpz(poly, ys);
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}
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else
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{
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fmpq_poly_fit_length(poly, n);
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_fmpq_poly_interpolate_fmpz_vec(poly->coeffs, poly->den, xs, ys, n);
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_fmpq_poly_set_length(poly, n);
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fmpq_poly_canonicalise(poly);
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}
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}
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