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


i have complicated algorithm requires fitting of quadric set of points. quadric given parametrization (u, v, f(u,v)), f(u,v) = au^2+bv^2+cuv+du+ev+f. coefficients of f(u,v) function need found since have set of 6 constraints function should obey. problem set of constraints, although yielding problem a*x = b, not behaved guarantee unique solution.

thus, cut short, i'd use alglib's facilities somehow either determine a's pseudoinverse or directly find best fit x vector.

apart computing svd, there more direct algorithm implemented in library can solve system in least squares sense (again, apart svd or using naive inv(transpose(a)*a)*transpose(a)*b formula general least squares problems not square matrix?

found answer through careful documentation browsing:

rmatrixsolvels( a, norows, nocols, b, singularvaluethreshold, info, solverreport, x)

the documentation states the singular value threshold clamping threshold sets singular value svd decomposition s matrix 0 if value below it. should scalar between 0 , 1.

hopefully, else too.


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