Improve optimisers for +R models

[iqtree]

Improve optimisers for +R models

[bqminh]

This is done already, i.e. R4 parameters are initialised from the R3. In the code it's this function: RateFree::initFromCatMinusOne() of model/ratefree.cpp,

iqtree2/model/ratefree.cpp

Line 138 in c8be3c3

void RateFree::initFromCatMinusOne() {

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However, this is only one way of initialisation. Happy to chat if you have 'better' suggestions. Anyway, a lot of testings will be needed...

[roblanf]

My suggestion is not quite the same. It's that we initially hold the CatMinusOne parameters constant, and only optimise the new parameter. Once that's done, we optimise all of them.

E.g. if R2 gave: 0.1, 2.0

Then we initialise R3 with 0.1, 2.0, New

And we hold 0.1, 2.0 constant while finding the optimum value of New (allowing it to be anything from the minimum to maximum bound, i.e. smaller than 0.1, between 0.1 and 2.0, and larger than 2.0).

This might give e.g.

R3: New=0.08, 0.1, 2.0; 0.1, New=0.5, 2.0; 0.1, 2.0, New=3.2 etc.

It should be simple to find a better likelihood like this, because we are optimising a single parameter.

The final step is to optimise all parameters at once, using the values from the prior step as the initialisation.

Happy to test this if someone can implement it.