Multidimensional product spaces

[kohr-h]

Not a must-have, but certainly nice: a way to produce product spaces which are more than one-dimensional, i.e. the factors are stored in a multidimensional array rather than a list. With all the connected questions of norms, inner products etc.

We could follow a similar approach as in the case of FnBase vs. DiscreteLp: make the underlying storage linear (e.g. a NumPy array with dtype=object) and reshape to higher dimensions only on demand by some generalized Discretization class.

Of course, this will give a substantial speed penalty for a large number of member spaces compared to the situation where we have a discretization of a single large space, but I think we're going to need something like this in the long run, see e.g. #156.

[adler-j]

There is a age old issue on this on the old github.

A trivial way to do this is to implement this recursively, something like

>>> space1 = odl.ProductSpace(odl.Rn(3), [2, 2])
>>> space2 = odl.ProductSpace(odl.ProductSpace(odl.Rn(3), 2), 2)
>>> space1 == space2
True

[kohr-h]

As long as we don't need anything else than our good old weighted p-norms, this should be working. More thoughts necessary for more complicated things.

[kohr-h]

For power spaces, this will be trivial with #857. For the general case, I guess as long as there's no real need for it we don't do it?

[adler-j]

I agree. #857 solves the most common use cases and in other cases it's just a matter of somewhat clunky syntax that we can live with.