seemps.analysis.mesh.mps_to_mesh_matrix

seemps.analysis.mesh.mps_to_mesh_matrix(sites_per_dimension: list[int], permutation: TypeAliasForwardRef('~seemps.typing.Vector') | None = None, base: int = 2) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

Returns a transformation matrix T that maps between MPS indices and multi-dimensional mesh coordinates.

For a mesh with m dimensions and n = sum(sites_per_dimension) sites, T is a matrix of shape (n, m). Row r corresponds to an MPS site while column i contains the contribution of that site to dimension i, such that the integer mesh coordinates read:

x_i = sum_r physical_indices[r] * T[r, i].

Each dimension i uses sites_per_dimension[i] consecutive sites given by decreasing powers of base. If permutation is provided, the rows of T are reordered accordinglyy.

Parameters:

sites_per_dimensionlist[int]

Number of sites allocated to each dimension.

permutationVector | None

Optional row permutation. Defaults to None (no permutation).

baseint

Local physical dimension per site.

Returns:

Matrix

Linear mapping of shape (N, m) with integer base^k weights.

Examples

sites_per_dimension = [2, 3] with base 2 yields:

T = [[2, 0], # site 0 → x contributes base^1

[1, 0], # site 1 → x contributes base^0 [0, 4], # site 2 → y contributes base^2 [0, 2], # site 3 → y contributes base^1 [0, 1]] # site 4 → y contributes base^0