tensor

The category of matrices with the Kronecker product as monoidal product.

Summary

Dim	A dimension is a tuple of integers greater than one seen as a type.
Tensor	A tensor is a Matrix with dimensions as domain and codomain and the Kronecker product as tensor.
Functor	A tensor functor is a frobenius functor with a domain category dom and Tensor[dtype] as codomain for a given dtype.
Diagram	A tensor diagram is a frobenius diagram with tensor boxes.
CMap	alias of CMap[Diagram]
Box	A tensor box is a frobenius box with an array as data.
Swap	A tensor swap is a frobenius swap in a tensor diagram.
Cup	A tensor cup is a frobenius cup in a tensor diagram.
Cap	A tensor cap is a frobenius cap in a tensor diagram.
Spider	A tensor spider is a frobenius spider in a tensor diagram.
Sum	A formal sum of tensor diagrams with the same domain and codomain.
Bubble	Bubble in a tensor diagram, applies a function elementwise.

Tensor combinatorial maps

A CMap is a tensor network stored as a combinatorial map, whose boxes are tensors, edges are summed indices and boundary ports are free indices. Swaps, cups and caps become wiring while spiders stay as boxes.

>>> vector = Box('vector', Dim(1), Dim(2), [0, 1])
>>> assert (vector >> vector[::-1]).to_map().eval().array == 1

>>> with backend('jax'):  
...     import jax, jax.numpy as jnp
...     b = lambda x: Box[float]('v', Dim(1), Dim(2), x * jnp.ones(2))
...     f = lambda x: (b(x) >> b(x)[::-1]).to_map().eval().array
...     assert jax.grad(f)(1.) == 4.