I'll make a new release tomorrow (I hope) which contains new matrix optimization refinement feature; it will make it much easier than before to control tradeoffs in patch matching, which may be desirable especially for matrix-only profiles. As a LUT when relaxed closes in on the matrix it may be useful also for LUT profiles, for the perfectionist.
I've attached an example for the common CC24 target. First the normal matrix, where DCamProf without any refinement parameters and thus generates a matrix as before, trying to make total sum of errors as small as possible. As you can see the D02 patch has 0 error, as D02 is the most neutral patch in a CC24 and is assigned "D50 white", and as DCamProf's matrices are always "white point preserving" it will always have 0 error, that cannot be changed. DNG profiles require it by definition, and it's a good idea in any case so it can't be turned off.
Then I've added manual refinements using the new feature, to make the following adjustments: exact match on the light skin-tone patch, make sure that blues are not darkened for more stable behavior, and make sure colors are rather pulled away from purples than towards it (reds rather orange than purple, blues rather cyan than purple). It's specified like this:
dcamprof make-profile -L -v A02 0 -v C01 0,2,-1,1,-2,0 -v C03 -3,3,-3,3,0,3 -r dump1 cc24.ti3 test-profile.json
A02 0: exact match, DE 0.
C01 0,2 lightness range (up to 2DE lighter, but no darker), chroma range -1,1 and hue rather counter-clockwise (towards cyan) and absolutely not towards purple, same for red.
The tricky thing with matrices is that everything is interconnected, so if you make one patch match better, someone else must become worse. Quite easily you refine too hard so there's no solution possible, and then DCamProf will fail with an error, so it's a trial and error process. A quite simple one though.