Coercion operator(s)

[adler-j]

There are many cases in mathematics where a user "inteprets an X as an Y", often very subtly or unstated. Nonetheless, this needs to be made explicit at times. Some examples in odl include

• Overlook FnBase details,
  • Rn(10) as CudaRn(10)
  • Rn(10) as `Rn(10, dtype='float32')
• Interpret elements in ProductSpace(X, 1) as in X, or the inverse of this
• Overlooking discretization details. uniform_discr(FunctionSpace(Interval(0, 1)), 10) as uniform_discr(FunctionSpace(Interval(0, 3.1415)), 10)
• Overlook dspace of Discretization according to the above

To solve this we should implement some kind of CoerceOperator, example below for most simple FnBase case

class CoerceOperator(odl.Operator):
    def __init__(self, dom, ran):
        super().__init__(dom, ran, True)

    def _call(self, x):
        return self.ran.element(x.asarray())

    def _apply(self, x, out):
        out[:] = x

[kohr-h]

This is definitely useful. "Coerce" is more of a computer science notion AFAIK, this makes sense if changing only data type within the same "family", or changing implementation. In math one would rather speak of an embedding.

[adler-j]

From the discussion in #49 i found another case:

• ProductSpaces of FnBase spaces (possibly only of the same kind) as a single space: ProductSpace(Rn(3), Rn(2)) <--> Rn(5) this would solve many of the problems in #49 aswell.

[adler-j]

Suggested programming of this:

• Make a new file under operator, call it coercion or embedding if we prefer that. (@ozanoktem ?)
• Add classes for the cases we have above.
• make a coerce/embed "entry point" function, so users can call

>>> embed(Rn(10), CudaRn(10))
FnBaseEmbedding(Rn(10), CudaRn(10))
>>> embed(uniform_discr(FunctionSpace(Interval(0, 3.1415)), 10), 
          uniform_discr(FunctionSpace(Interval(0, 1)), 10))
USpaceEmbedding(uniform_discr(FunctionSpace(Interval(0, 3.1415)), 10), 
                uniform_discr(FunctionSpace(Interval(0, 1)), 10))

etc...

[adler-j]

Followup, it seems coerce is already taken, embed it is then!