## Data types for the Grand Unification

```
Space:
structured or unstructured set of points (current NIFTy's "Domain")
SpaceTuple:
external product of zero or more Spaces (current NIFTy's "DomainTuple")
SpaceTuple = (Space, Space, ...)
SpaceTupleDict:
dictionary (with string keys) of one or more SpaceTuples
SpaceTupleDict = {name1: SpaceTuple1, name2: SpaceTuple2, ...}
(current NIFTy's "MultiDomain")
Domain:
This is an abstract concept. Can currently be represented by SpaceTuple or SpaceTupleDict
Special domains:
ScalarDomain: empty SpaceTuple
Operator:
- Operators take an Operand defined on an input domain, transform it in some way
and return a new Operand defined on a (possibly different) target domain.
- Operators can be concatenated, as long as the domains at the interface are
identical. The result is another Operator.
Operand:
- Operand objects represent fields and potentially their Jacobians and metrics.
- an Operand object can be asked for its "value" and (if configured accordingly)
its Jacobian. If the target domain of an Operand object is scalar, a metric
may also be available.
- Applying an Operator to an Operand object will always return another Operand object.
class Operator(object):
@property
def domain(self):
# return input domain
@property
def target(self):
# return output domain
def __call__(self, other):
# if isinstance(other, Operand) return an Operand object
# else return an Operator object
def __matmul__(self, other):
return self(other)
class LinearOperator(Operator):
# more or less analogous to the current LinearOperator
class Operand(object):
# this unifies current NIFTy's Field, MultiField, and Linearization classes
@property
def domain(self):
# if no Jacobian is present, return None, else the Jacobian's domain.
@property
def target(self):
# return the domain on which the value of the Operand is defined. This is
# also the Jacobian's target (if a Jacobian is defined)
@property
def val(self):
# return a low level data structure holding the actual values (currently numpy.ndarray
# or dictionary of numpy.ndarrays. Read-only.
def val_rw(self):
# return a writeable copy of `val`
def fld(self):
# return am Operand that only contains the value content of this object. Its Jacobian and
# potential higher derivatives will be `None`.
@property
def jac(self):
return a Jacobian LinearOperator if possible, else None
@property
def want_metric(self):
return True or False
@property
def metric(self):
if self.jacobian is None, raise an exception
if self.target is not ScalarDomain, raise an exception
if not self.want_metric, raise an exception
if metric cannot be computed, raise an exception
return metric
```

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