virtual int ComputeModel(ModelSet& models, const Data& data, const std::set<int>& samples)
{
double meanX = 0, meanY = 0, meanXX = 0, meanYY = 0, meanXY = 0;
for (std::set<int>::const_iterator it = samples.begin();it != samples.end(); it++)
{
const Datum& p = data[*it];
meanX += p.x;
meanY += p.y;
meanXX += p.x * p.x;
meanYY += p.y * p.y;
meanXY += p.x * p.y;
}
int M = static_cast<int>(samples.size());
meanX /= M;
meanY /= M;
meanXX /= M;
meanYY /= M;
meanXY /= M;
double a = meanXX - meanX*meanX;
double b = meanXY - meanX*meanY;
double d = meanYY - meanY*meanY;
Model model;
if (fabs(b) > DBL_EPSILON)
{
// Calculate the first eigen vector of A = [a, b; b, d]
// Ref. http://www.math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html
double T2 = (a + d) / 2;
double lambda = T2 - sqrt(T2 * T2 - (a * d - b * b));
double v1 = lambda - d, v2 = b;
double norm = sqrt(v1 * v1 + v2 * v2);
model.a = v1 / norm;
model.b = v2 / norm;
}
else
{
model.a = 1;
model.b = 0;
}
model.c = -model.a * meanX - model.b * meanY;
models.push_back(model);
return 1;
}
