/*
 * Copyright 2014-2015 Anton Khirnov <anton@khirnov.net>
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

/**
 * @file
 * definitions of the basis functions for the spectral method
 */

#include <math.h>

#include "internal.h"

static double sb_even_eval(double coord, int idx, double sf)
{
    double val = atan2(sf, coord);

    idx *= 2;   // even only

    return sin((idx + 1) * val);
}

static double sb_even_eval_diff1(double coord, int idx, double sf)
{
    double val = atan2(sf, coord);

    idx *= 2;   // even only

    return - sf * (idx + 1) * cos((idx + 1) * val) / (SQR(sf) + SQR(coord));
}

static double sb_even_eval_diff2(double coord, int idx, double sf)
{
    double val = atan2(sf, coord);

    idx *= 2;   // even only

    return sf * (idx + 1) * (2 * coord * cos((idx + 1) * val) - sf * (idx + 1) * sin((idx + 1) * val)) / SQR(SQR(sf) + SQR(coord));
}

static double sb_even_colloc_point(int order, int idx, double sf)
{
    double t;

    idx = order - idx - 1;

    t = (idx + 2) * M_PI / (2 * order + 2);
    return sf / tan(t);
}

/*
 * The basis of even (n = 2 * idx) SB functions (Boyd 2000, Ch 17.9)
 * SB(x, n) = sin((n + 1) arccot(|x| / L))
 * They are symmetric wrt origin and decay as odd powers of x in infinity.
 */
const BasisSet bdi_sb_even_basis = {
    .eval         = sb_even_eval,
    .eval_diff1   = sb_even_eval_diff1,
    .eval_diff2   = sb_even_eval_diff2,
    .colloc_point = sb_even_colloc_point,
};