isotypic_signal2irreducible_subspaces

isotypic_signal2irreducible_subspaces(x, rep_x)

Flatten an isotypic signal into its irreducible-subspace coordinates.

This function assumes \(\mathcal{X}\) is a single isotypic subspace of type \(k\), i.e.

\[\rho_{\mathcal{X}} = \bigoplus_{i\in[1,n_k]} \hat{\rho}_k.\]

For an input \(\mathbf{x}\) of shape \((n, n_k \cdot d_k)\), where \(d_k=\dim(\hat{\rho}_k)\), the output rearranges coordinates to shape \((n \cdot d_k, n_k)\) so each column stores one irrep copy across the sample axis.

\[\mathbf{z}[:, i] = [x_{1,i,1}, \ldots, x_{1,i,d_k}, x_{2,i,1}, \ldots, x_{n,i,d_k}]^\top.\]

Parameters:

• x (Tensor) – Shape \((n, n_k \cdot d_k)\).

• rep_x (Representation) – Representation in isotypic basis with a single active irrep type.

Returns:

Flattened irreducible-subspace signal of shape \((n \cdot d_k, n_k)\).

Return type:

Tensor

Shape:

\((n \cdot d_k, n_k)\).