Some additions to forward mode Ad_array

[vlipovac]

Hei,

I have some ideas for the Ad_array class, which would simplify some algorithms (at least for me 😄 )

1. Slicing

By overloading
Ad_array.__getitem__
and
Ad_array.__getslice__

we could allow for a more unified treatment of PorePy's custom AD arays and numpy arrays, i.e.
A = Ad_array(some_vector, some_matrix)
B = A[1:10]
where the slicing would return a row-wise slicing for both value and Jacobian. It would be equivalent to
B = Ad_array(some_vector[1:10], some_matrix[1:10])

This is motivated by the fact that PorePy's AD framework vectorizes the DOFs, so row-wise slicing would be DOF-wise slicing.

2. Logical comparison

I am sure this was already discussed at some point, but again motivated by simpler, unified treatment, it would be nice to have logical comparison.
It seems natural to me to provide a comparison for the values of an Ad_array.
A < B would be then A.val < B.val.

Why

This would remove many type checks and if clauses in the code, making code compatible for both numpy arrays and Ad_array instances as arguments.

I think its justified to give the val priority over jac in both suggestions, considering that vals is the numerical representation of whatever quantitiy the Ad_array represents, and jac is kind of "secondary" (if I may say so).

[IvarStefansson]

Interesting ideas! I agree on prioritising val over jac, although I'm not entirely sure what that implies in your first suggestion?

[vlipovac]

Interesting ideas! I agree on prioritising val over jac, although I'm not entirely sure what that implies in your first suggestion?

As I see it, an Ad_array can be seen as a vector-valued function and the slicing as above would apply that certain components of that
vector-valued function are accessed, together with all their derivatives (row in Jacobian)

If we think of an Ad_array as a representation of a linearized system and its residual, then above slicing is basically an accessing of a row block and its residual.

[keileg]

I think this makes sense.

[vlipovac]

This is been resolved with the introduction of EquationSystem