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
Since Ceres is moving to using GitHub for issues, and the Google
Code URL in the current copyright header will soon become invalid,
update all the headers.
Change-Id: I1fce70375d1bcf098591f07b4d8f01a5c1e0789c
A wrapper class that takes a variadic functor evaluating a
function, numerically differentiates it and makes it available as a
templated functor so that it can be easily used as part of Ceres'
automatic differentiation framework.
The tests for NumericDiffCostFunction and NumericDiffFunctor have
a lot of stuff that is common, so refactor them to reduce code.
Change-Id: I83b01e58b05e575fb2530d15cbd611928298646a
Sameer Agarwal