Materialize adjoint in mul with HermOrSym

[dkarrasch]

Fixes #850, at least the original issue. Promoting Bool to some BlasFloat seems to be very tricky in terms method ambiguities.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.90%. Comparing base (c9ad828) to head (d71f9b8).
Report is 16 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1191   +/-   ##
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  Coverage   91.89%   91.90%           
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  Files          34       34           
  Lines       15360    15366    +6     
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+ Hits        14115    14122    +7     
+ Misses       1245     1244    -1     

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[dkarrasch]

x-ref JuliaLang/julia#52787 for the Bool case.

[araujoms]

Why not implement @mcabbott 's suggestion, though? It is faster for small matrices and avoids a copy.

[dkarrasch]

We seem to avoid wrapping results in adjoint or transpose, or, better said, we materialize the final wrapper:

A' * Q = copy((Q' * A)')

We return wrapped results only when the first factor is an adjoint vector.

[araujoms]

Why, though? I don't see the problem with wrapping results in adjoint or transpose.

[dkarrasch]

@andreasnoack Do you remember why we typically materialize products that we compute by the adjoint formula, except for AdjOrTransAbsVec?

[andreasnoack]

I don't remember the specifics here. Only that the wrapped versions can sometimes lead to performance issues because they wrappers sometimes causes dispatch to slow fallback definitions for AbstractMatrix.

[dkarrasch]

Another reason for going with this as is is that this currently returns a Matrix, and not an Adjoint. I suggest we go with it, and if we consider returning Adjoints, we should do this in several other places consistently, and we would need to evaluate the effect on the ecosystem. Perhaps now is a good idea, early in the release cycle, or would this be generally regarded as "breaking", because it changes return types?