Hi Christian, On 2018-03-06, Christian Stump <christian.st...@gmail.com> wrote: > Let me add that the situations I care about are n,m <= 20, the entries are ><=5 and the matrices are sparsely filled. An random and typical example is

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That matrix seems far too small to say anything substantial about timings. However, profiling the hash computation in a loop, it seems that the method add_edge is called quite frequently. However, I don't really see where the time spent in the function _matrix_to_digraph (which seems to be the bottle neck here) is spent. I haven't really been able to work around the bottle neck, but got a minor improvement (4%) as follows: add_edges is frequently used, so, I tried to not create an empty graph and then add edges to it, but instead create the list of vertices and edges and then create the graph from these lists. However, there is no gain at all, as DiGraph.__init__ calls add_edges basically in the same way as you do. I changed the use of the list edge_labels. You basically use it to tell at what point an edge label has been created, and do this by frequently computing the index. It seems slightly better to me to to store the same information in a dict. So, replace edge_labels.index((i,j)) and the error catching by edge_labels.setdefault((i,j), ...). Also, it seems slightly faster to obtain the hash of a frozen set than of a sorted tuple: sage: dg_canon = dg.canonical_label(partition=partition, algorithm="bliss", return_graph=False) sage: %timeit hash(frozenset(dg_canon)) 100000 loops, best of 3: 2.79 µs per loop sage: %timeit hash(tuple(sorted(dg_canon))) 100000 loops, best of 3: 4.57 µs per loop And of course using cython helps as well. With the following Cython code, I am down to 272 µs per loop, while your original Python code gave me 325 µs per loop: ################## def matrix_canonical_hash(M, n, m): dg,partition = _matrix_to_digraph(M, n, m) dg_canon = dg.canonical_label(partition=partition, algorithm="bliss", return_graph=False) return hash(frozenset(dg_canon)) from sage.matrix.matrix0 cimport Matrix from sage.all import matrix, DiGraph cpdef _matrix_to_digraph(Matrix M, int n, int m): cdef dict edge_labels = dict() cdef int n_labels = 0 cdef int new_vertex = n+m cdef list Edges = [] cdef list new_partition = [] cdef int i,j for i,j in M.nonzero_positions(): a = M.get_unsafe(i,j) if i < n: b = M.get_unsafe(j,i) else: b = -M.get_unsafe(i, j) if a > 0: if a == 1 and b == -1: Edges.append((i,j)) else: x = edge_labels.setdefault((a,b), n_labels) if n_labels < len(edge_labels): new_partition.append([]) n_labels += 1 Edges.append((i,new_vertex)) Edges.append((new_vertex,j)) new_partition[x].append(new_vertex) new_vertex += 1 elif i >= n: if a == -1 and b == 1: Edges.append((j,i)) else: a = -a b = -b x = edge_labels.setdefault((a,b), n_labels) if n_labels < len(edge_labels): new_partition.append([]) n_labels += 1 Edges.append((j,new_vertex)) Edges.append((new_vertex,i)) new_partition[x].append(new_vertex) new_vertex += 1 cdef list partition = [list(range(n))] if m > 0: partition.append(list(range(n,n+m))) if new_partition: partition.extend(new_partition) return DiGraph([range(new_vertex),Edges],sparse=True), partition M = matrix([(0, -1, 0, 0, 0, 0, 0, 1), (1, 0, 1, 0, 0, 0, 0, 0), (0, -1, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0), (0, 0, -1, 0, 0, 0, 1, 0), (0, 0, 0, -1, 0, 0, -1, 0), (0, 0, 0, 0, -1, 1, 0, 0), (-2, 0, 0, 0, 0, 0, 0, 0), (-1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0, -1), (0, 1, 0, 1, 0, -1, 0, -1), (0, 2, -1, 1, 0, -1, 0, -1), (0, 2, -1, 0, 0, -1, 0, -1), (0, 2, 0, 0, -1, -1, 0, -1), (0, 2, 0, 0, -1, 0, -1, -1), (0, 2, 0, 0, 0, 0, -2, -1)] ) ############### Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.