Dimension overhaul

[Ericgig]

Description

This is an overhaul of the dimensions based on the proposition by @jakelishman in #1476.
As proposed, dimension objects singleton instances composed of map and spaces.

Dimensions used by Qobj are all represented by a map between 2 spaces:

• ket: Dimensions(Field, Space)
• bra: Dimensions(Space, Field)
• oper: Dimensions(Space, Space)
  ...

This Dimension is the Map proposed by Jake, but ket are map from Field to Space and not Spacethemselves. Spaces come into multiple sub classes as proposed :Space, SuperSpace, Field, Compound, and EnrSpace. Splitting maps and spaces simplify spaces by not needing to have a dummy 2nd dims : Space()[1]` does exist.

Dimensions can be initiated from a list and converted back to one. Field are automatically contracted: Compound(Field, Field) is a Field, same for maps. With the exceptions that Qobj with a shape of (1,1) with be a Dimensions(Field, Field) and not a Field.

Some previously valid and used list format are no longer accepted. Playing with of tensor of super operators, permute and reshuffle, you could make object with dims as [[[2, 2], [3, 3], [4, 4]], [[2, 2], [3, 3], [4, 4]]] which can be interpreted as the tensor of 3 super operators. But then [[[2, 2], [3, 3]], [[2, 2],[3, 3]]] can both be interpreted as tensor of super operator or super operator of tensor spaces, so :

• [[[2, 2], [3, 3], [4, 4]], [[2, 2], [3, 3], [4, 4]]]: Error
• [[[2, 2], [4, 4]], [[2, 2], [4, 4]]]: list representation of dimensions of to_super(tensor(oper, oper))
• [[[2], [2], [3], [3]], [[2], [2], [3], [3]]]: list representation of dimensions of tensor(to_super(oper), to_super(oper))

Dimensions object have a type and shape set a initialization. There is a check when creating/ modifying a Qobj with between the data's shape and dims's shape and an error is raise when they are not matching.

Since operator-ket have a superrep, I added the superrep parameter to the Superspace instead of the dimensions, for now. But a better look at super operator representation is needed.

At the present state, Qobj.dims take and return a list, keeping the dimension object internally. From there, minimal adjustment were made so test pass.

The eigenstate fix in #1820 is already merged since it would create Qobj which dims and shape did not match.

ToDo:

• Tensor using dimension directly instead of list.
• QobjEvo.dims use dimension object.
• state and operator accept dimension.
• Super operator representation.
• Ptrace, partial_transpose and permute use dimension object (supported with enr states).
• Flags / new types for rectangular operator?
• List dimension manipulation function in dimension.py should support the class/ be integrated in it / removed.

Related issues or PRs
#1476

Changelog

[coveralls]

Coverage increased (+0.3%) to 65.978% when pulling 0af50ac on Ericgig:dimension into d240c4c on qutip:dev.major.