Simpler defaults without FiniteDifferences special cases #96
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IMO the AbstractFiniteDifference special cases in the default definitions are confusing (see #94...) and lead to code that is less idiomatic and more difficult to optimize.
With increasing dimensionality, avoiding one additional computation of the primal matters less and less, and hence this PR proposes to disentangle the computation of the primal and the jacobian/Hessian/etc. Moreover, also with these changes one can improve performance for individual backends, if possible and desired, by defining a more optimized
value_and_jacobian
etc.An additional advantage for higher-order calls
value_and_hessian
andvalue_gradient_and_hessian
is that it is sufficient to callgradient
instead ofvalue_and_gradient
.