topobench.nn.backbones.graph.nsd_utils.laplace module#

Utilities for computing Laplacian indices and operations.

This module provides efficient functions for computing indices required for sheaf Laplacian construction and sparse matrix operations.

compute_learnable_diag_laplacian_indices(size, edge_index, learned_d, total_d)#

Compute sparse indices for a learnable Laplacian with diagonal matrices.

Generates indices for both diagonal and non-diagonal blocks of a block-structured Laplacian matrix where each block is diagonal (learned_d x learned_d).

Parameters:

sizeint: Number of nodes in the graph.
edge_indextorch.Tensor: Edge indices of shape [2, num_edges] where edge_index[0] < edge_index[1].
learned_dint: Dimension of each learned diagonal block.
total_dint: Total dimension per node (typically equal to learned_d).

Returns:

diag_indicestorch.Tensor: Sparse indices for diagonal blocks, shape [2, size * learned_d].
non_diag_indicestorch.Tensor: Sparse indices for non-diagonal blocks, shape [2, num_edges * learned_d].

compute_learnable_laplacian_indices(size, edge_index, learned_d, total_d)#

Compute sparse indices for a learnable Laplacian with full matrices.

Generates indices for both diagonal and non-diagonal blocks of a block-structured Laplacian matrix where each block is learned_d x learned_d.

Parameters:

sizeint: Number of nodes in the graph.
edge_indextorch.Tensor: Edge indices of shape [2, num_edges] where edge_index[0] < edge_index[1].
learned_dint: Dimension of each learned block matrix.
total_dint: Total dimension per node (typically equal to learned_d).

Returns:

diag_indicestorch.Tensor: Sparse indices for diagonal blocks, shape [2, size * learned_d * learned_d].
non_diag_indicestorch.Tensor: Sparse indices for non-diagonal blocks, shape [2, num_edges * learned_d * learned_d].

compute_left_right_map_index(edge_index, full_matrix=False)#

Compute indices for mapping edges to their reverse edges.

For each edge in the lower triangular part (source < target) or all edges, find the index of its corresponding reverse edge in the original edge list.

Parameters:

edge_indextorch.Tensor: Edge indices of shape [2, num_edges] representing directed edges.
full_matrixbool, optional: If True, use all edges. If False, only use edges where source < target. Default is False.

Returns:

left_right_indextorch.Tensor: Indices of shape [2, num_selected_edges] where first row contains indices of selected edges and second row contains indices of their reverse edges.
new_edge_indextorch.Tensor: Edge indices of selected edges, shape [2, num_selected_edges].

mergesp(index1, value1, index2, value2)#

Merge two sparse matrices with disjoint indices into one.

Concatenates two sets of sparse matrix indices and values, assuming the indices are disjoint (no overlapping entries).

Parameters:

index1torch.Tensor: First set of sparse indices, shape [2, num_entries1].
value1torch.Tensor: First set of values, shape [num_entries1].
index2torch.Tensor: Second set of sparse indices, shape [2, num_entries2].
value2torch.Tensor: Second set of values, shape [num_entries2].

Returns:

indextorch.Tensor: Merged sparse indices, shape [2, num_entries1 + num_entries2].
valtorch.Tensor: Merged values, shape [num_entries1 + num_entries2].