This method numerically computes function derivatives in different
scales, extrapolating between intermediate results to conserve function
evaluations. Adaptive differentiation is essential to produce accurate
results for functions with noisy derivatives.
Full changelist:
-Created a new type of NumericDiffMethod (RIDDERS).
-Implemented EvaluateRiddersJacobianColumn in NumericDiff.
-Created unit tests with f(x) = x^2 + [random noise] and
f(x) = exp(x).
Change-Id: I2d6e924d7ff686650272f29a8c981351e6f72091
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
If the parameter block size is 1, asking Eigen to create
a row-major matrix triggers a compile time error. Previously
we were handling the case where the number of rows in the
jacobian block was known statically, but the problem is present
when the nummber of rows is dynamic.
This CL fixes this problem.
Thanks to Dominik Reitzle for reporting this.
Change-Id: I99c3eec3558e66ebf4efa51c4dee8ce292ffe0c1
1. Update AutoDiffCostFunction template parameters to be consistent
with NumericDiffCostFunction.
2. Update the documentation for NumericDiffCostFunction and
AutoDiffCostFunction.
Change-Id: I113038abb5bedebb0f6f326f2a4ac31480d785fc
The interface for NumericDiffCostFunction and AutoDiffCostFunction
are not comparable. They both accept variadic functors.
The change is backward compatible, as it still supports numeric
differentiation of CostFunction objects.
Some refactoring of documentation and code in auto_diff_cost_function
and its relatives was also done to make things consistent.
Change-Id: Ib5f230a1d4a85738eb187803b9c1cd7166bb3b92
Keir Mierle