new test on issue with partial product of SE(2)

[dehann]

cc @Affie , this new test shows the problem, a product of two densities: one full and one partial SE(2) mkd gives the wrong result. A separate product of two partials over the same TranslationGroup(2) submanifold produces the correct result, but when one density is increased to a full SE(2), the product components on the submanifold is incorrect.

xref JuliaRobotics/RoME.jl#504 (comment)

[codecov-commenter]

Codecov Report

Merging #159 (ccb25b9) into master (b8cf601) will decrease coverage by 1.31%.
The diff coverage is 59.09%.

@@            Coverage Diff             @@
##           master     #159      +/-   ##
==========================================
- Coverage   50.13%   48.81%   -1.32%     
==========================================
  Files          16       16              
  Lines         740      760      +20     
==========================================
  Hits          371      371              
- Misses        369      389      +20     

Impacted Files	Coverage Δ
src/ApproxManifoldProducts.jl	100.00% <ø> (ø)
src/Legacy.jl	54.83% <ø> (-3.90%)	⬇️
src/services/ManifoldKernelDensity.jl	62.01% <41.93%> (+0.72%)	⬆️
src/API.jl	86.44% <100.00%> (-7.04%)	⬇️
src/KernelHilbertEmbeddings.jl	86.20% <0.00%> (-6.90%)	⬇️
src/services/CircularUtils.jl	64.91% <0.00%> (-5.27%)	⬇️
src/Interface.jl	63.63% <0.00%> (-4.55%)	⬇️
src/services/ManifoldPartials.jl	71.21% <0.00%> (-2.64%)	⬇️
... and 2 more

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[dehann]

okay, trail leads here in "the bad" case. By checking which labels from incoming densities multiply -- i.e.

red*green = blue # (these dots are Gaussian kernels centers).  

Looking at one posterior label set, I expect (when addEntropy=false) blue dot to be somewhere between and co-linear with red and green dots, but instead get this:

This is on coord dims [1;2] of two SE(2)s as described above (one full and one partial on [1;2]).

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EDIT, although the "good" dims=[1;2] product only (which does get the right posterior) also has blue dot not co-linear similar to above (not what I expected..)? Must be an indexing, visualization, or some other error -- investigation continues...

[dehann]

new test is still broken, but there are several general upgrades that are useful beyond this PR. So going to merge this with a @test_broken and then start a new PR towards fixing the partial product on SE2 issue.