Add functions to copy data between Function(s) and PETSc Vecs

[jhale]

This PR adds functions that can copy data between function(s) and standard/blocked/nested PETSc Vecs. Dispatch to correct function is performed through weak typing, always duck-typing through to standard routine.

This work was based on #3648 by @jorgensd

[jhale]

Some outstanding points:

• Use localForm in _copy_vec_to_function
• Should we assume x and vector underlying u enters in a consistent state?
• Are all of the ghost updates necessary?

[jorgensd]

Some outstanding points:

* Use localForm in `_copy_vec_to_function`

* Should we assume `x` and vector underlying `u` enters in a consistent state?

* Are all of the ghost updates necessary?

They do not do not always come in as a consistent state (observed in the SNESSolver).

[garth-wells]

I've reduced the number of functions and made them much simpler, and demonstrated usage in the SNES tests.

The functions should not have ghost updates. Copying the ghost values eliminates any need for a 'post' update. Any 'pre' ghost update should be performed by the caller. Throwing in mis-guided ghost updates is something we have eliminated in DOLFINx.

If we go with this, the 'assign' functions that are 'linear algebra' only should probably move to a dolfinx.la.petsc module, or be made private.

[jorgensd]

Only minor things to consider.

Should we move it into dolfinx.la.petsc right away?

[jorgensd]

Shouldn't the typing also include np.complexfloating for complex values?

[jhale]

From my reading of the numpy documentation this concept is expressed as np.inexact. https://numpy.org/doc/stable/reference/arrays.scalars.html#inexact-types

I suspect we're making a number of issues overtyping/undertyping/incorrectly typing throughout the codebase. This could be looked at in another PR.

[jhale]

Clearly we should get this one agreed on so we can look elsewhere!

[jorgensd]

Suggested change

	of ``Functions``s, values in ``x`` are assigned block-wise ro the
	of ``Functions``s, values in ``x`` are assigned block-wise to the

[jorgensd]

Suggested change

	"""Assign vector entries to :class:`.Function` degrees-of-freedom.
	"""Assign vector entries to :class:`Function` degrees-of-freedom.

Should there really be a . here?

[garth-wells]

Should we move it into dolfinx.la.petsc right away?

We don't have a dolfinx.ls.petsc.py file at the moment, so rather than creating one it might be better to make the linear algebra functions private.

[jorgensd]

Should we move it into dolfinx.la.petsc right away?

We don't have a dolfinx.ls.petsc.py file at the moment, so rather than creating one it might be better to make the linear algebra functions private.

The assign vec<->function are very useful, even for experienced programmers. This was pointed out by @jhale in the snes-problem PR. I don’t understand the reason for making them if you want them to be private.

[jhale]

Should we move it into dolfinx.la.petsc right away?

We don't have a dolfinx.ls.petsc.py file at the moment, so rather than creating one it might be better to make the linear algebra functions private.

The assign vec<->function are very useful, even for experienced programmers. This was pointed out by @jhale in the snes-problem PR. I don’t understand the reason for making them if you want them to be private.

My interpretation of @garth-wells comment was that the lower-level routine should be made private, rather than putting it in a new location la.petsc (which would be the strictly correct placement). The routines that take Functions belong in fem.petsc.

[garth-wells]

My interpretation of @garth-wells comment was that the lower-level routine should be made private, rather than putting it in a new location la.petsc (which would be the strictly correct placement). The routines that take Functions belong in fem.petsc.

Correct.

[jhale]

I've done the legwork to split la into a native and PETSc part in a manner consistent with the rest of our interface. This creates an API change dolfinx.la.create_petsc_vector -> dolfinx.la.petsc.create_petsc_vector. The second petsc now seems redundant. Should it be renamed e.g. dolfinx.la.petsc.create_vector and dolfinx.la.petsc.create_vector_wrap?

https://github.com/FEniCS/dolfinx/tree/jhale/refactor-la-petsc

[jhale]

Closed in favour of #3659