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#include <math.h>
#include "maximal_slicing_axi.h"
static double sb_even_eval(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
idx *= 2; // even only
return sin((idx + 1) * val);
}
static double sb_even_eval_diff1(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
idx *= 2; // even only
return - SCALE_FACTOR * (idx + 1) * SGN(coord) * cos((idx + 1) * val) / (SQR(SCALE_FACTOR) + SQR(coord));
}
static double sb_even_eval_diff2(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
idx *= 2; // even only
return SCALE_FACTOR * (idx + 1) * SGN(coord) * (2 * fabs(coord) * cos((idx + 1) * val) - SCALE_FACTOR * (idx + 1) * sin((idx + 1) * val)) / SQR(SQR(SCALE_FACTOR) + SQR(coord));
}
static double sb_even_colloc_point(int order, int idx)
{
double t;
idx = order - idx - 1;
//order *= 2;
//t = (idx + 2) * M_PI / (order + 4);
t = (idx + 2) * M_PI / (2 * order + 2);
return SCALE_FACTOR / tan(t);
}
const BasisSet msa_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,
};
static double tb_even_eval(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
idx++;
idx *= 2; // even only
return cos(idx * val) - 1.0;
}
static double tb_even_eval_diff1(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
idx++;
idx *= 2; // even only
return SCALE_FACTOR * idx * SGN(coord) * sin(idx * val) / (SQR(SCALE_FACTOR) + SQR(coord));
}
static double tb_even_eval_diff2(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
idx++;
idx *= 2; // even only
return -SCALE_FACTOR * idx * SGN(coord) * (2 * fabs(coord) * sin(idx * val) + SCALE_FACTOR * idx * cos(idx * val)) / SQR(SQR(SCALE_FACTOR) + SQR(coord));
}
static double tb_even_colloc_point(int order, int idx)
{
double t;
idx = order - idx - 1;
//order *= 2;
//t = (idx + 2) * M_PI / (order + 4);
t = (idx + 3) * M_PI / (2 * (order + 2));
return SCALE_FACTOR / tan(t);
}
const BasisSet msa_tb_even_basis = {
.eval = tb_even_eval,
.eval_diff1 = tb_even_eval_diff1,
.eval_diff2 = tb_even_eval_diff2,
.colloc_point = tb_even_colloc_point,
};
static double full_eval(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
int flag = idx & 1;
idx /= 2;
if (flag) return sin((2 * idx + 1) * 4 * val);
else return cos((2 * idx + 2) * 4 * val) - 1;
}
static double full_eval_diff1(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
int flag = idx & 1;
idx /= 2;
if (flag) {
idx = 2 * idx + 1;
return -4 * idx * SCALE_FACTOR * cos(idx * 4 * val) / (SQR(SCALE_FACTOR) + SQR(coord));
} else {
idx = 2 * (idx + 1);
return 4 * idx * SCALE_FACTOR * sin(idx * 4 * val) / (SQR(SCALE_FACTOR) + SQR(coord));
}
}
static double full_eval_diff2(double coord, int idx)
{
double val = (coord == 0.0) ? M_PI_2 : atan(SCALE_FACTOR / fabs(coord));
int flag = idx & 1;
idx /= 2;
if (flag) {
idx = 2 * idx + 1;
return (16 * SQR(idx * SCALE_FACTOR) * cos(idx * 4 * val) - 4 * idx * SCALE_FACTOR * sin(idx * 4 * val) * 2 * coord) / SQR(SQR(SCALE_FACTOR) + SQR(coord));
} else {
idx = 2 * (idx + 1);
return (-16 * SQR(idx * SCALE_FACTOR) * sin(idx * 4 * val) - 4 * idx * SCALE_FACTOR * cos(idx * 4 * val) * 2 * coord) / SQR(SQR(SCALE_FACTOR) + SQR(coord));
}
}
static double full_colloc_point(int order, int idx)
{
double t;
idx = order - idx - 1;
t = (idx + 0.5) * M_PI / (2 * order);
return SCALE_FACTOR / tan(t);
}
const BasisSet msa_full_basis = {
.eval = full_eval,
.eval_diff1 = full_eval_diff1,
.eval_diff2 = full_eval_diff2,
.colloc_point = full_colloc_point,
};
static double cheb_eval(double coord, int idx)
{
return cos(2 * idx * acos(coord / SCALE_FACTOR));
}
static double cheb_eval_diff1(double coord, int idx)
{
return 2 * idx * sin(2 * idx * acos(coord / SCALE_FACTOR)) / sqrt(SQR(SCALE_FACTOR) - SQR(coord));
}
static double cheb_eval_diff2(double coord, int idx)
{
double t = acos(coord / SCALE_FACTOR);
return 2 * idx * (cos(2 * idx * t) * 2 * idx / (SQR(SCALE_FACTOR) - SQR(coord)) + sin(2 * idx * t) * coord / pow(SQR(SCALE_FACTOR) - SQR(coord), 1.5));
}
static double cheb_colloc_point(int order, int idx)
{
return SCALE_FACTOR * cos((idx + 0.01) * M_PI / (4 * order + 4));
}
const BasisSet msa_cheb_basis = {
.eval = cheb_eval,
.eval_diff1 = cheb_eval_diff1,
.eval_diff2 = cheb_eval_diff2,
.colloc_point = cheb_colloc_point,
};
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