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import sklearn
import sklearn.metrics
import scipy.sparse, scipy.sparse.linalg # scipy.spatial.distance
import numpy as np
def grid_graph(grid_side,number_edges,metric):
"""Generate graph of a grid"""
z = grid(grid_side)
dist, idx = distance_sklearn_metrics(z, k=number_edges, metric=metric)
A = adjacency(dist, idx)
print("nb edges: ",A.nnz)
return A
def grid(m, dtype=np.float32):
"""Return coordinates of grid points"""
M = m**2
x = np.linspace(0,1,m, dtype=dtype)
y = np.linspace(0,1,m, dtype=dtype)
xx, yy = np.meshgrid(x, y)
z = np.empty((M,2), dtype)
z[:,0] = xx.reshape(M)
z[:,1] = yy.reshape(M)
return z
def distance_sklearn_metrics(z, k=4, metric='euclidean'):
"""Compute pairwise distances"""
d = sklearn.metrics.pairwise.pairwise_distances(z, metric=metric, n_jobs=1)
# k-NN
idx = np.argsort(d)[:,1:k+1]
d.sort()
d = d[:,1:k+1]
return d, idx
def adjacency(dist, idx):
"""Return adjacency matrix of a kNN graph"""
M, k = dist.shape
assert M, k == idx.shape
assert dist.min() >= 0
assert dist.max() <= 1
# Pairwise distances
sigma2 = np.mean(dist[:,-1])**2
dist = np.exp(- dist**2 / sigma2)
# Weight matrix
I = np.arange(0, M).repeat(k)
J = idx.reshape(M*k)
V = dist.reshape(M*k)
W = scipy.sparse.coo_matrix((V, (I, J)), shape=(M, M))
# No self-connections
W.setdiag(0)
# Undirected graph
bigger = W.T > W
W = W - W.multiply(bigger) + W.T.multiply(bigger)
assert W.nnz % 2 == 0
assert np.abs(W - W.T).mean() < 1e-10
assert type(W) is scipy.sparse.csr.csr_matrix
return W
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