Alglib: solving A * x = b in a least squares sense

Question

I have a somewhat complicated algorithm that requires the fitting of a quadric to a set of points. This quadric is given by its parametrization (u, v, f(u,v)), where f(u,v) = au^2+bv^2+cuv+du+ev+f. The coefficients of the f(u,v) function need to be found since I have a set of exactly 6 constraints this function should obey. The problem is that this set of constraints, although yielding a problem like A*x = b, is not completely well behaved to guarantee a unique solution.

Thus, to cut it short, I'd like to use alglib's facilities to somehow either determine A's pseudoinverse or directly find the best fit for the x vector.

Apart from computing the SVD, is there a more direct algorithm implemented in this library that can solve a system in a least squares sense (again, apart from the SVD or from using the naive inv(transpose(A)*A)*transpose(A)*b formula for general least squares problems where A is not a square matrix?

Answer 1

Found the answer through some careful documentation browsing:

rmatrixsolvels( A, noRows, noCols, b, singularValueThreshold, info, solverReport, x)

The documentation states the the singular value threshold is a clamping threshold that sets any singular value from the SVD decomposition S matrix to 0 if that value is below it. Thus it should be a scalar between 0 and 1.

Hopefully, it will help someone else too.