Fully mutating linear solver

[gdalle]

At the moment, AbstractDifferentiation does not have a fully mutating API, and benchmarks show allocations are non-negligible when multiplying by A and B. Opening this to track JuliaDiff/AbstractDifferentiation.jl#14 and see what we can do

[mohamed82008]

The problem is that most AD packages don't actually support mutation.

[gdalle]

Yeah I know, it would be useless for ChainRules, but not for ForwardDiff?

[gdalle]

Trying to solve this with https://github.com/gdalle/DifferentiationInterface.jl

[gdalle]

This is now possible with DifferentiationInterface but

• it won't work with every outer backend
• it requires a mutating version of the conditions conditions!(c, x, y)

I hope to make it part of v0.7