### comparison env/lib/python3.9/site-packages/networkx/algorithms/centrality/flow_matrix.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
comparison
equal inserted replaced
-1:000000000000 0:4f3585e2f14b
1 # Helpers for current-flow betweenness and current-flow closness
2 # Lazy computations for inverse Laplacian and flow-matrix rows.
3 import networkx as nx
4
5
6 def flow_matrix_row(G, weight=None, dtype=float, solver="lu"):
7 # Generate a row of the current-flow matrix
8 import numpy as np
9
10 solvername = {
11 "full": FullInverseLaplacian,
12 "lu": SuperLUInverseLaplacian,
13 "cg": CGInverseLaplacian,
14 }
15 n = G.number_of_nodes()
16 L = laplacian_sparse_matrix(
17 G, nodelist=range(n), weight=weight, dtype=dtype, format="csc"
18 )
19 C = solvername[solver](L, dtype=dtype) # initialize solver
20 w = C.w # w is the Laplacian matrix width
21 # row-by-row flow matrix
22 for u, v in sorted(sorted((u, v)) for u, v in G.edges()):
23 B = np.zeros(w, dtype=dtype)
24 c = G[u][v].get(weight, 1.0)
25 B[u % w] = c
26 B[v % w] = -c
27 # get only the rows needed in the inverse laplacian
28 # and multiply to get the flow matrix row
29 row = np.dot(B, C.get_rows(u, v))
30 yield row, (u, v)
31
32
33 # Class to compute the inverse laplacian only for specified rows
34 # Allows computation of the current-flow matrix without storing entire
35 # inverse laplacian matrix
36 class InverseLaplacian:
37 def __init__(self, L, width=None, dtype=None):
38 global np
39 import numpy as np
40
41 (n, n) = L.shape
42 self.dtype = dtype
43 self.n = n
44 if width is None:
45 self.w = self.width(L)
46 else:
47 self.w = width
48 self.C = np.zeros((self.w, n), dtype=dtype)
49 self.L1 = L[1:, 1:]
50 self.init_solver(L)
51
52 def init_solver(self, L):
53 pass
54
55 def solve(self, r):
56 raise nx.NetworkXError("Implement solver")
57
58 def solve_inverse(self, r):
59 raise nx.NetworkXError("Implement solver")
60
61 def get_rows(self, r1, r2):
62 for r in range(r1, r2 + 1):
63 self.C[r % self.w, 1:] = self.solve_inverse(r)
64 return self.C
65
66 def get_row(self, r):
67 self.C[r % self.w, 1:] = self.solve_inverse(r)
68 return self.C[r % self.w]
69
70 def width(self, L):
71 m = 0
72 for i, row in enumerate(L):
73 w = 0
74 x, y = np.nonzero(row)
75 if len(y) > 0:
76 v = y - i
77 w = v.max() - v.min() + 1
78 m = max(w, m)
79 return m
80
81
82 class FullInverseLaplacian(InverseLaplacian):
83 def init_solver(self, L):
84 self.IL = np.zeros(L.shape, dtype=self.dtype)
85 self.IL[1:, 1:] = np.linalg.inv(self.L1.todense())
86
87 def solve(self, rhs):
88 s = np.zeros(rhs.shape, dtype=self.dtype)
89 s = np.dot(self.IL, rhs)
90 return s
91
92 def solve_inverse(self, r):
93 return self.IL[r, 1:]
94
95
96 class SuperLUInverseLaplacian(InverseLaplacian):
97 def init_solver(self, L):
98 from scipy.sparse import linalg
99
100 self.lusolve = linalg.factorized(self.L1.tocsc())
101
102 def solve_inverse(self, r):
103 rhs = np.zeros(self.n, dtype=self.dtype)
104 rhs[r] = 1
105 return self.lusolve(rhs[1:])
106
107 def solve(self, rhs):
108 s = np.zeros(rhs.shape, dtype=self.dtype)
109 s[1:] = self.lusolve(rhs[1:])
110 return s
111
112
113 class CGInverseLaplacian(InverseLaplacian):
114 def init_solver(self, L):
115 global linalg
116 from scipy.sparse import linalg
117
118 ilu = linalg.spilu(self.L1.tocsc())
119 n = self.n - 1
120 self.M = linalg.LinearOperator(shape=(n, n), matvec=ilu.solve)
121
122 def solve(self, rhs):
123 s = np.zeros(rhs.shape, dtype=self.dtype)
124 s[1:] = linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]
125 return s
126
127 def solve_inverse(self, r):
128 rhs = np.zeros(self.n, self.dtype)
129 rhs[r] = 1
130 return linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]
131
132
133 # graph laplacian, sparse version, will move to linalg/laplacianmatrix.py
134 def laplacian_sparse_matrix(G, nodelist=None, weight=None, dtype=None, format="csr"):
135 import numpy as np
136 import scipy.sparse
137
138 A = nx.to_scipy_sparse_matrix(
139 G, nodelist=nodelist, weight=weight, dtype=dtype, format=format
140 )
141 (n, n) = A.shape
142 data = np.asarray(A.sum(axis=1).T)
143 D = scipy.sparse.spdiags(data, 0, n, n, format=format)
144 return D - A