test_katz fails in CI

[rafguns]

On both 3.8 and 3.11. Here's the output for 3.11:

 =================================== FAILURES ===================================
  __________________________________ test_katz ___________________________________
  
      def test_katz():
          G = nx.Graph()
          G.add_weighted_edges_from(
              [(1, 2, 1), (0, 2, 5), (2, 3, 1), (0, 4, 2), (1, 4, 1), (3, 5, 1), (4, 5, 3)]
          )
      
          beta = 0.01
          I = np.identity(6)
          for weight in ("weight", None):
              katz = Katz(G).predict(beta=beta, weight=weight)
      
              nodes = list(G.nodes())
              M = nx.to_numpy_array(G, nodelist=nodes, weight=weight)
              K = np.linalg.matrix_power(I - beta * M, -1) - I
      
              x, y = np.asarray(K).nonzero()
              for i, j in zip(x, y):
                  if i == j:
                      continue
                  u, v = nodes[i], nodes[j]
  >               assert K[i, j] == pytest.approx(katz[(u, v)], abs=1e-5)
  E               assert 0.010038160831933126 == 0.010101010100000004 ± 1.0e-05
  E                 comparison failed
  E                 Obtained: 0.010038160831933126
  E                 Expected: 0.010101010100000004 ± 1.0e-05
  
  tests/test_predictors_path.py:28: AssertionError
  ----------------------------- Captured stdout call -----------------------------
  Computing matrix powers: [............................................................] 0/5
  Computing matrix powers: [############................................................] 1/5
  Computing matrix powers: [########################....................................] 2/5
  Computing matrix powers: [####################################........................] 3/5
  Computing matrix powers: [################################################............] 4/5
  Computing matrix powers: [############################################################] 5/5

Weirdly enough, this test passes on my computer. Perhaps this is due to a differnece in version of some package, like numpy?

[rafguns]

Seems like the difference is in the output of Katz.predict. On my computer, this yields 0.010038160200000002, whereas in CI it gives 0.010101010100000004.

Given this test case:

G.add_weighted_edges_from(
    [(1, 2, 1), (0, 2, 5), (2, 3, 1), (0, 4, 2), (1, 4, 1), (3, 5, 1), (4, 5, 3)]
)

the difference happens for nodes 1 and 2.

[rafguns]

Hmm, looks like it's not due to numpy or networkx version...

[rafguns]

Minimal testcase:

import networkx as nx
from linkpred.predictors import Katz


G = nx.Graph()
G.add_weighted_edges_from(
    [(1, 2, 1), (0, 2, 5), (2, 3, 1), (0, 4, 2), (1, 4, 1), (3, 5, 1), (4, 5, 3)]
)

katz = Katz(G).predict(beta=beta, weight="weight", dtype=int)
assert katz[(1, 2)] == 0.010038160200000002

[rafguns]

Seems like the difference is between scipy 1.9 and 1.10.

[rafguns]

Matrix multiplication in scipy.sparse 1.10 is fundamentally different! It does element-wise multiplication.

In 1.9:

[9]: adj.todense()

array([[0, 1, 0, 0, 1, 0],
       [1, 0, 5, 1, 0, 0],
       [0, 5, 0, 0, 2, 0],
       [0, 1, 0, 0, 0, 1],
       [1, 0, 2, 0, 0, 3],
       [0, 0, 0, 1, 3, 0]], dtype=int32)

[10]: (adj**2).todense()

array([[ 2,  0,  7,  1,  0,  3],
       [ 0, 27,  0,  0, 11,  1],
       [ 7,  0, 29,  5,  0,  6],
       [ 1,  0,  5,  2,  3,  0],
       [ 0, 11,  0,  3, 14,  0],
       [ 3,  1,  6,  0,  0, 10]], dtype=int32)

In 1.10:

[10]: (adj**2).todense()

array([[ 0,  1,  0,  0,  1,  0],
       [ 1,  0, 25,  1,  0,  0],
       [ 0, 25,  0,  0,  4,  0],
       [ 0,  1,  0,  0,  0,  1],
       [ 1,  0,  4,  0,  0,  9],
       [ 0,  0,  0,  1,  9,  0]], dtype=int32)

[rafguns]

This is presumably related to this note from the scipy.sparse documentation:

x * y no longer performs matrix multiplication, but element-wise multiplication (just like with NumPy arrays). To make code work with both arrays and matrices, use x @ y for matrix multiplication.