static
cmsFloat64Number RootOfLeastSquaresFitQuadraticCurve(int n, cmsFloat64Number x[], cmsFloat64Number y[])
{
double sum_x = 0, sum_x2 = 0, sum_x3 = 0, sum_x4 = 0;
double sum_y = 0, sum_yx = 0, sum_yx2 = 0;
double d, a, b, c;
int i;
cmsMAT3 m;
cmsVEC3 v, res;
if (n < 4) return 0;
for (i=0; i < n; i++) {
double xn = x[i];
double yn = y[i];
sum_x += xn;
sum_x2 += xn*xn;
sum_x3 += xn*xn*xn;
sum_x4 += xn*xn*xn*xn;
sum_y += yn;
sum_yx += yn*xn;
sum_yx2 += yn*xn*xn;
}
_cmsVEC3init(&m.v[0], n, sum_x, sum_x2);
_cmsVEC3init(&m.v[1], sum_x, sum_x2, sum_x3);
_cmsVEC3init(&m.v[2], sum_x2, sum_x3, sum_x4);
_cmsVEC3init(&v, sum_y, sum_yx, sum_yx2);
if (!_cmsMAT3solve(&res, &m, &v)) return 0;
a = res.n[2];
b = res.n[1];
c = res.n[0];
if (fabs(a) < 1.0E-10) {
return cmsmin(0, cmsmax(50, -c/b ));
}
else {
d = b*b - 4.0 * a * c;
if (d <= 0) {
return 0;
}
else {
double rt = (-b + sqrt(d)) / (2.0 * a);
return cmsmax(0, cmsmin(50, rt));
}
}
}
static
cmsFloat64Number VertexOfLeastSquaresFitQuadraticCurve(int n, cmsFloat64Number x[], cmsFloat64Number y[])
{
double sum_x = 0, sum_x2 = 0, sum_x3 = 0, sum_x4 = 0;
double sum_y = 0, sum_yx = 0, sum_yx2 = 0;
double disc;
int i;
cmsMAT3 m;
cmsVEC3 v, res;
if (n < 4) return 0;
for (i=0; i < n; i++) {
double xn = x[i];
double yn = y[i];
sum_x += xn;
sum_x2 += xn*xn;
sum_x3 += xn*xn*xn;
sum_x4 += xn*xn*xn*xn;
sum_y += yn;
sum_yx += yn*xn;
sum_yx2 += yn*xn*xn;
}
_cmsVEC3init(&m.v[0], n, sum_x, sum_x2);
_cmsVEC3init(&m.v[1], sum_x, sum_x2, sum_x3);
_cmsVEC3init(&m.v[2], sum_x2, sum_x3, sum_x4);
_cmsVEC3init(&v, sum_y, sum_yx, sum_yx2);
if (!_cmsMAT3solve(&res, &m, &v)) return 0;
// y = t x2 + u x + c
// x = ( - u + Sqrt( u^2 - 4 t c ) ) / ( 2 t )
disc = res.n[1]*res.n[1] - 4.0 * res.n[0] * res.n[2];
if (disc < 0) return -1;
return ( -1.0 * res.n[1] + sqrt( disc )) / (2.0 * res.n[0]);
}
