> OK, I managed to implement this using the gsl_linalg_SV_decomp and
> gsl_linalg_SV_solve functions as following. In case it's useful to
> anyone else. It nicely picks up the case of points being colinear as well.

Looks good. On second thought it may not be appropriate to modify
gsl_multifit_linear for this problem. There does happen to be a
unique solution for your problem, however in general if you try to
solve X c = y, where X is singular then there could be infinitely many
solutions even if y = 0, so it may not be worth it to add in a special
case like this.


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