Functor

Functor#

class discopy.tensor.Functor(ob_map, ar_map, dom=None, dtype=<class 'float'>, optimize='greedy', **params)[source]#

Bases: discopy.frobenius.Functor

A tensor functor is a frobenius functor with a domain category dom and Tensor[dtype] as codomain for a given dtype.

Calling it on a diagram converts it to a CMap and contracts the network in a single einsum call under the active backend(), passing any optional einsum parameters through.

Parameters:

  • ob_map (dict[cat.Ob, Dim]) – The object mapping.

  • ar_map (dict[cat.Box, list]) – The arrow mapping.

  • dom (type) – The domain of the functor, i.e. the class of diagrams it evaluates, the class attribute dom by default.

  • dtype (type) – The datatype for the codomain Tensor[dtype].

  • optimize – The contraction path, passed verbatim to the backend einsum, e.g. "greedy", "optimal" or an explicit path.

  • params – Any other optional parameter of the backend einsum method, passed verbatim.

Example

>>> n, s = map(rigid.Ty, "ns")
>>> Alice = rigid.Box('Alice', rigid.Ty(), n)
>>> loves = rigid.Box('loves', rigid.Ty(), n.r @ s @ n.l)
>>> Bob = rigid.Box('Bob', rigid.Ty(), n)
>>> diagram = Alice @ loves @ Bob\
...     >> rigid.Cup(n, n.r) @ s @ rigid.Cup(n.l, n)

>>> F = Functor(
...     ob_map={s: 1, n: 2},
...     ar_map={Alice: [0, 1], loves: [0, 1, 1, 0], Bob: [1, 0]},
...     dom=rigid.Diagram, dtype=bool)
>>> F(diagram)
Tensor[bool]([True], dom=Dim(1), cod=Dim(1))

>>> rewrite = diagram\
...     .transpose_box(2).transpose_box(0, left=True).normal_form()
>>> Equation(diagram, rewrite).draw(
...     figsize=(8, 3), path='docs/_static/tensor/rewrite.svg')
../_images/rewrite.svg
>>> assert F(diagram) == F(rewrite)
dom#

alias of Diagram

cod#

alias of Tensor

contract(other)[source]#

Contract the image of a combinatorial map in a single einsum call under the active backend().

The map is Einstein notation: the 2-cycles of its edges involution are the summed indices, boxes are the tensors and the boundary ports are the free indices, with integer labels. A wire is one index of the size of its object’s image. Networks with more than config.MAX_EINSUM_INDICES indices are contracted with the optional opt_einsum package instead.

Parameters:

other (CMap) – The combinatorial map to contract.

Return type:

Tensor

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