Changed DynamicAutoDiffCostFunction to handle multiple derivative
sections as opposed to just a single contiguous block.
In the previous implementation it was assumed that non-constant
parameters occur in a single contiguous block so that constant
parameters could NOT lie between non-constant parameters. Previously,
start_derivative_section was first set as soon as the first
non-constant parameter block (marked by jacobians[i] != NULL) was
encountered. After this, entries in input_jets[parameter_cursor].v were
accessed with `parameter_cursor - start_derivative_section`. For
contiguous non-constant parameter blocks this is fine, but if constant
parameter blocks fall between then this indexing is incorrect because
`parameter_cursor - start_derivative_section` can go out of bounds.
For a concrete example, take a cost function with three parameter
blocks, each of size 1 and with the center block fixed. Assume that
Stride=1 so that two passes are required. On the first pass
start_derivative_section=0, and the first variable block is handled
correctly. At the end of the first pass end_derivative_section=1, so
for the second pass start_derivative_section=1. Now comes the problem.
When parameter_cursor=1, parameter_cursor >= start_derivative_section
so jacobian[1] is checked to be NULL. Since it is NULL (second
parameter block is constant) then nothing is done and
active_parameter_count is NOT incremented. Next, when
parameter_cursor=2, parameter_cursor >= start_derivative_section and
jacobian[2] is checked. Since it is not NULL then
input_jets[parameter_cursor].v[parameter_cursor -
start_derivative_section] is set to 1.0, BUT parameter_cursor -
start_derivative_section = 2 - 1 = 1 which is out of bounds
(input_jets[parameter_cursor].v is only of size Stride=1).
The proposed solution records the start of each contiguous block of
non-constant parameters and indexing into
input_jets[parameter_cursor].v is independent of parameter_cursor.
Change-Id: I388ab6a0bafa35d317491135ec6fe980453ff888
Richard Stebbing