diff env/lib/python3.9/site-packages/networkx/algorithms/centrality/flow_matrix.py @ 0:4f3585e2f14b draft default tip

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/env/lib/python3.9/site-packages/networkx/algorithms/centrality/flow_matrix.py	Mon Mar 22 18:12:50 2021 +0000
@@ -0,0 +1,144 @@
+# Helpers for current-flow betweenness and current-flow closness
+# Lazy computations for inverse Laplacian and flow-matrix rows.
+import networkx as nx
+
+
+def flow_matrix_row(G, weight=None, dtype=float, solver="lu"):
+    # Generate a row of the current-flow matrix
+    import numpy as np
+
+    solvername = {
+        "full": FullInverseLaplacian,
+        "lu": SuperLUInverseLaplacian,
+        "cg": CGInverseLaplacian,
+    }
+    n = G.number_of_nodes()
+    L = laplacian_sparse_matrix(
+        G, nodelist=range(n), weight=weight, dtype=dtype, format="csc"
+    )
+    C = solvername[solver](L, dtype=dtype)  # initialize solver
+    w = C.w  # w is the Laplacian matrix width
+    # row-by-row flow matrix
+    for u, v in sorted(sorted((u, v)) for u, v in G.edges()):
+        B = np.zeros(w, dtype=dtype)
+        c = G[u][v].get(weight, 1.0)
+        B[u % w] = c
+        B[v % w] = -c
+        # get only the rows needed in the inverse laplacian
+        # and multiply to get the flow matrix row
+        row = np.dot(B, C.get_rows(u, v))
+        yield row, (u, v)
+
+
+# Class to compute the inverse laplacian only for specified rows
+# Allows computation of the current-flow matrix without storing entire
+# inverse laplacian matrix
+class InverseLaplacian:
+    def __init__(self, L, width=None, dtype=None):
+        global np
+        import numpy as np
+
+        (n, n) = L.shape
+        self.dtype = dtype
+        self.n = n
+        if width is None:
+            self.w = self.width(L)
+        else:
+            self.w = width
+        self.C = np.zeros((self.w, n), dtype=dtype)
+        self.L1 = L[1:, 1:]
+        self.init_solver(L)
+
+    def init_solver(self, L):
+        pass
+
+    def solve(self, r):
+        raise nx.NetworkXError("Implement solver")
+
+    def solve_inverse(self, r):
+        raise nx.NetworkXError("Implement solver")
+
+    def get_rows(self, r1, r2):
+        for r in range(r1, r2 + 1):
+            self.C[r % self.w, 1:] = self.solve_inverse(r)
+        return self.C
+
+    def get_row(self, r):
+        self.C[r % self.w, 1:] = self.solve_inverse(r)
+        return self.C[r % self.w]
+
+    def width(self, L):
+        m = 0
+        for i, row in enumerate(L):
+            w = 0
+            x, y = np.nonzero(row)
+            if len(y) > 0:
+                v = y - i
+                w = v.max() - v.min() + 1
+                m = max(w, m)
+        return m
+
+
+class FullInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        self.IL = np.zeros(L.shape, dtype=self.dtype)
+        self.IL[1:, 1:] = np.linalg.inv(self.L1.todense())
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s = np.dot(self.IL, rhs)
+        return s
+
+    def solve_inverse(self, r):
+        return self.IL[r, 1:]
+
+
+class SuperLUInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        from scipy.sparse import linalg
+
+        self.lusolve = linalg.factorized(self.L1.tocsc())
+
+    def solve_inverse(self, r):
+        rhs = np.zeros(self.n, dtype=self.dtype)
+        rhs[r] = 1
+        return self.lusolve(rhs[1:])
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s[1:] = self.lusolve(rhs[1:])
+        return s
+
+
+class CGInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        global linalg
+        from scipy.sparse import linalg
+
+        ilu = linalg.spilu(self.L1.tocsc())
+        n = self.n - 1
+        self.M = linalg.LinearOperator(shape=(n, n), matvec=ilu.solve)
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s[1:] = linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]
+        return s
+
+    def solve_inverse(self, r):
+        rhs = np.zeros(self.n, self.dtype)
+        rhs[r] = 1
+        return linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]
+
+
+# graph laplacian, sparse version, will move to linalg/laplacianmatrix.py
+def laplacian_sparse_matrix(G, nodelist=None, weight=None, dtype=None, format="csr"):
+    import numpy as np
+    import scipy.sparse
+
+    A = nx.to_scipy_sparse_matrix(
+        G, nodelist=nodelist, weight=weight, dtype=dtype, format=format
+    )
+    (n, n) = A.shape
+    data = np.asarray(A.sum(axis=1).T)
+    D = scipy.sparse.spdiags(data, 0, n, n, format=format)
+    return D - A