Fix check_point for SPD

[mateuszbaran]

A small bugfix. eigvals returns complex eigenvalues in the provided test case, which are not comparable to 0. This, also, should be faster.

[kellertuer]

LGTM,
could you also remove those two lines since we are at fixing small things :)

Manifolds.jl/src/groups/rotation_action.jl

Lines 304 to 305 in 8ccd5d8

	is_point(A.manifold, p, true)
	is_point(A.manifold, q, true)

[codecov]

Codecov Report

Merging #593 (d6ebea0) into master (8ccd5d8) will decrease coverage by 0.01%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #593      +/-   ##
==========================================
- Coverage   98.90%   98.90%   -0.01%     
==========================================
  Files          98       98              
  Lines        9897     9896       -1     
==========================================
- Hits         9789     9788       -1     
  Misses        108      108              

Impacted Files	Coverage Δ
src/groups/rotation_action.jl	100.00% <100.00%> (ø)
src/manifolds/SymmetricPositiveDefinite.jl	100.00% <100.00%> (ø)
...tricPositiveDefiniteGeneralizedBuresWasserstein.jl	100.00% <100.00%> (ø)

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[mateuszbaran]

Sure, I will remove them.

[kellertuer]

The CI seems to indicate that you probably have to adapt tolerances?

[mateuszbaran]

I increased accuracy instead, I hope that's also fine 🙂

[dkarrasch]

How is this increasing accuracy? How do you know the error in q is "symmetric", and reduced by symmetrization? Also, I wonder if this is optimal with respect to memory consumption? Perhaps something like

temp = m * Y * p * Y * m
temp .= temp .+ p .+ X
copyto!(q, temp)
# or
# copyto!(q, Symmetric(temp))
# or 
# copyto!(q, (temp .+ temp') ./ 2) # which first allocates the result and then copies it to `q`
# or, starting from Julia v1.10
# hermitianpart!(q, temp)

?

[mateuszbaran]

Well, it's more accurate than the previous implementation in the sense that the result is numerically closer to the manifold. I should've made a better comment there.

Maybe taking either the upper or lower part instead of average would be a better idea, I didn't check that. I didn't care much about memory consumption here because previous lines are already quite expensive.