block_triangularize

(function from pyomo.contrib.incidence_analysis.triangularize)

pyomo.contrib.incidence_analysis.triangularize.block_triangularize(matrix, matching=None)[source]

Compute ordered partitions of the matrix’s rows and columns that permute the matrix to block lower triangular form

Subsets in the partition correspond to diagonal blocks in the block triangularization. The order is topological, with ties broken “lexicographically”.

Parameters:

  • matrix (scipy.sparse.coo_matrix) – Matrix whose rows and columns will be permuted

  • matching (dict) – A perfect matching. Maps rows to columns and columns back to rows.

Returns:

  • row_partition (list of lists) – A partition of rows. The inner lists hold integer row coordinates.

  • col_partition (list of lists) – A partition of columns. The inner lists hold integer column coordinates.

Note

Breaking change in Pyomo 6.5.0

The pre-6.5.0 block_triangularize function returned maps from each row or column to the index of its block in a block lower triangularization as the original intent of this function was to identify when coordinates do or don’t share a diagonal block in this partition. Since then, the dominant use case of block_triangularize has been to partition variables and constraints into these blocks and inspect or solve each block individually. A natural return type for this functionality is the ordered partition of rows and columns, as lists of lists. This functionality was previously available via the get_diagonal_blocks method, which was confusing as it did not capture that the partition was the diagonal of a block triangularization (as opposed to diagonalization). The pre-6.5.0 functionality of block_triangularize is still available via the map_coords_to_block_triangular_indices function.