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interpolate_newton.c
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interpolate_newton.c
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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"
static void
_interpolate_newton(arb_ptr ys, arb_srcptr xs, slong n, slong prec)
{
arb_t p, q, t;
slong i, j;
arb_init(p);
arb_init(q);
arb_init(t);
for (i = 1; i < n; i++)
{
arb_set(t, ys + i - 1);
for (j = i; j < n; j++)
{
arb_sub(p, ys + j, t, prec);
arb_sub(q, xs + j, xs + j - i, prec);
arb_set(t, ys + j);
arb_div(ys + j, p, q, prec);
}
}
arb_clear(p);
arb_clear(q);
arb_clear(t);
}
static void
_newton_to_monomial(arb_ptr ys, arb_srcptr xs, slong n, slong prec)
{
arb_t t, u;
slong i, j;
arb_init(t);
arb_init(u);
for (i = n - 2; i >= 0; i--)
{
arb_set(t, ys + i);
arb_set(ys + i, ys + i + 1);
for (j = i + 1; j < n - 1; j++)
{
arb_mul(u, ys + j, xs + i, prec);
arb_sub(ys + j, ys + j + 1, u, prec);
}
arb_mul(u, ys + n - 1, xs + i, prec);
arb_sub(ys + n - 1, t, u, prec);
}
_arb_poly_reverse(ys, ys, n, n);
arb_clear(t);
arb_clear(u);
}
void
_arb_poly_interpolate_newton(arb_ptr poly, arb_srcptr xs,
arb_srcptr ys, slong n, slong prec)
{
if (n == 1)
{
arb_set(poly, ys);
}
else
{
_arb_vec_set(poly, ys, n);
_interpolate_newton(poly, xs, n, prec);
while (n > 0 && arb_is_zero(poly + n - 1)) n--;
_newton_to_monomial(poly, xs, n, prec);
}
}
void
arb_poly_interpolate_newton(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_newton(poly->coeffs,
xs, ys, n, prec);
_arb_poly_normalise(poly);
}
}