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Sameer Agarwal
9064b4ed27
Before this change, the default step size for a function F(x) at x was step_size = |x| * relative_step_size if step_size was exactly zero, then to prevent division by zero we would fall back to relative_step_size. This however is not good enough, as values of x say 1e-64 would lead to step sizes ~ 1e-70 and dividing by such numbers leads to inaccurate results. For even smaller numbers, like 1e-300, which I have observed can occur as the optimization algorithm makes progress, this leads to NaNs. The key change in this CL is to change the fallback mechanism to be step_size = max(|x| * relative_step_size, min_step_size) where min_step_size = sqrt(DBL_EPSILON) This is the recommended minimum value for the step size for double precision arithmetic on the interwebs. This results in a small loss of precision in the transcendental functions test, but that is unavoidable as we are not taking sufficiently small steps anymore. On the whole though this will improve the numerical performance of the algorithm. To validate this approach, one of the parameter values for the EasyFunctorTest has been set to 1e-64, which causes the test to start failing without the corrected fallback logic. This change should also address some if not all of https://github.com/ceres-solver/ceres-solver/issues/121 Change-Id: I4a9013ef358626c1ba7b8abad60b3904163d63f6