escnn_representation_form_mapping

escnn_representation_form_mapping(group, rep, name='reconstructed')

Reconstruct a representation from a map \(\mathbb{G}\to\mathrm{GL}(\mathcal{X})\).

Given a representation map \(\rho: \mathbb{G}\to\mathrm{GL}(\mathcal{X})\), this function identifies the irreducible ESCNN decomposition and returns an equivalent Representation object.

Parameters:

• group (Group) – Symmetry group of the representation.

• rep (dict | collections.abc.Callable) – A Union-style input. Either a dict or a collections.abc.Callable returning the matrix \(\rho(g)\) for each GroupElement g.

• name (str, optional) – Name of the representation. Defaults to ‘reconstructed’.

Returns:

Reconstructed ESCNN representation

instance.

Return type:

representation (Representation)

Note

Matrices must define a valid representation (invertible and group-consistent). If a dictionary is provided, keys must be ESCNN’s group elements from group.elements.

Example

>>> from escnn.group import CyclicGroup
>>> G = CyclicGroup(4)
>>> rep_map = {g: G.regular_representation(g) for g in G.elements}
>>> rep = escnn_representation_form_mapping(G, rep_map, name="C4-regular-rec")