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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 "arb_poly.h"
void
_arb_poly_interpolate_barycentric(arb_ptr poly,
arb_srcptr xs, arb_srcptr ys, slong n, slong prec)
{
arb_ptr P, Q, w;
arb_t t;
slong i, j;
if (n == 1)
{
arb_set(poly, ys);
return;
}
P = _arb_vec_init(n + 1);
Q = _arb_vec_init(n);
w = _arb_vec_init(n);
arb_init(t);
_arb_poly_product_roots(P, xs, n, prec);
for (i = 0; i < n; i++)
{
arb_one(w + i);
for (j = 0; j < n; j++)
{
if (i != j)
{
arb_sub(t, xs + i, xs + j, prec);
arb_mul(w + i, w + i, t, prec);
}
}
arb_inv(w + i, w + i, prec);
}
_arb_vec_zero(poly, n);
for (i = 0; i < n; i++)
{
_arb_poly_div_root(Q, t, P, n + 1, xs + i, prec);
arb_mul(t, w + i, ys + i, prec);
_arb_vec_scalar_addmul(poly, Q, n, t, prec);
}
_arb_vec_clear(P, n + 1);
_arb_vec_clear(Q, n);
_arb_vec_clear(w, n);
arb_clear(t);
}
void
arb_poly_interpolate_barycentric(arb_poly_t poly,
arb_srcptr xs, arb_srcptr ys, slong n, slong prec)
{
if (n == 0)
{
arb_poly_zero(poly);
}
else
{
arb_poly_fit_length(poly, n);
_arb_poly_set_length(poly, n);
_arb_poly_interpolate_barycentric(poly->coeffs,
xs, ys, n, prec);
_arb_poly_normalise(poly);
}
}
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