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

author shellac Mon, 22 Mar 2021 18:12:50 +0000
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```
# 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)
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)

# 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
```