Add pagerank example

examples/pagerank_example.py

@@ -0,0 +1,79 @@
+import time
+
+import sparse
+
+import networkx as nx
+from networkx.algorithms.link_analysis.pagerank_alg import _pagerank_scipy
+
+import numpy as np
+import scipy.sparse as sp
+
+
+def pagerank(G, alpha=0.85, max_iter=100, tol=1e-6) -> dict:
+    N = len(G)
+    if N == 0:
+        return {}
+
+    alpha = sparse.asarray(alpha)
+    nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, dtype=float, format="csc")
+    A = sparse.asarray(A)
+    S = sparse.sum(A, axis=1)
+    S = sparse.where(sparse.asarray(0.0) != S, sparse.asarray(1.0) / S, S)
+
+    # TODO: spdiags https://github.com/willow-ahrens/Finch.jl/issues/499
+    Q = sparse.asarray(sp.csc_array(sp.spdiags(S.todense(), 0, *A.shape)))
+    A = Q @ A
+
+    # initial vector
+    x = sparse.full((1, N), fill_value=1.0 / N)
+
+    # personalization vector
+    p = sparse.full((1, N), fill_value=1.0 / N)
+
+    # Dangling nodes
+    dangling_weights = p
+
+    # power iteration: make up to max_iter iterations
+    for _ in range(max_iter):
+        xlast = x
+        x_dangling = sparse.where(S[None, :] == sparse.asarray(0.0), x, sparse.asarray(0.0))
+        x = (
+            alpha * (x @ A + sparse.asarray(sparse.sum(x_dangling)) * dangling_weights)
+            + (sparse.asarray(1) - alpha) * p
+        )
+        # check convergence, l1 norm
+        err = sparse.sum(sparse.abs(x - xlast))
+        if err < N * tol:
+            return dict(zip(nodelist, map(float, x[0, :]), strict=False))
+
+    raise nx.PowerIterationFailedConvergence(max_iter)
+
+
+if __name__ == "__main__":
+    G = nx.DiGraph(nx.path_graph(4))
+    ITERS = 3
+
+    # compile
+    pagerank(G)
+    print("compiled")
+
+    # finch
+    start = time.time()
+    for i in range(ITERS):
+        print(f"finch iter: {i}")
+        pr = pagerank(G)
+    elapsed = time.time() - start
+    print(f"Finch took {elapsed / ITERS} s.")
+
+    # scipy
+    start = time.time()
+    for i in range(ITERS):
+        print(f"scipy iter: {i}")
+        scipy_pr = _pagerank_scipy(G)
+    elapsed = time.time() - start
+    print(f"SciPy took {elapsed / ITERS} s.")
+
+    np.testing.assert_almost_equal(list(pr.values()), list(scipy_pr.values()))
+    print(f"finch: {pr}")
+    print(f"scipy: {scipy_pr}")