def test_lloyd_cluster(self):
np.random.seed(2099568097)
for G in self.cases:
G.data = np.random.rand(G.nnz) + 1.0j * np.random.rand(G.nnz)
for n_seeds in [5]:
if n_seeds > G.shape[0]:
continue
distances, clusters, centers = lloyd_cluster(G, n_seeds)
def test_lloyd_cluster(self):
numpy.random.seed(0)
for G in self.cases:
G.data = rand(G.nnz)
for n_seeds in [5]:
if n_seeds > G.shape[0]:
continue
distances, clusters, centers = lloyd_cluster(G, n_seeds)
def test_lloyd_cluster(self):
numpy.random.seed(0)
for G in self.cases:
G.data = rand(G.nnz) + 1.0j*rand(G.nnz)
for n_seeds in [5]:
if n_seeds > G.shape[0]:
continue
distances, clusters, centers = lloyd_cluster(G, n_seeds)
def lloyd_aggregation(C, ratio=0.03, distance='unit', maxiter=10):
"""Aggregate nodes using Lloyd Clustering.
Parameters
----------
C : csr_matrix
strength of connection matrix
ratio : scalar
Fraction of the nodes which will be seeds.
distance : ['unit','abs','inv',None]
Distance assigned to each edge of the graph G used in Lloyd clustering
For each nonzero value C[i,j]:
======= ===========================
'unit' G[i,j] = 1
'abs' G[i,j] = abs(C[i,j])
'inv' G[i,j] = 1.0/abs(C[i,j])
'same' G[i,j] = C[i,j]
'sub' G[i,j] = C[i,j] - min(C)
======= ===========================
maxiter : int
Maximum number of iterations to perform
Returns
-------
AggOp : csr_matrix
aggregation operator which determines the sparsity pattern
of the tentative prolongator
seeds : array
array of Cpts, i.e., Cpts[i] = root node of aggregate i
See Also
--------
amg_core.standard_aggregation
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from pyamg.gallery import poisson
>>> from pyamg.aggregation.aggregate import lloyd_aggregation
>>> A = poisson((4,), format='csr') # 1D mesh with 4 vertices
>>> A.toarray()
matrix([[ 2., -1., 0., 0.],
[-1., 2., -1., 0.],
[ 0., -1., 2., -1.],
[ 0., 0., -1., 2.]])
>>> lloyd_aggregation(A)[0].toarray() # one aggregate
matrix([[1],
[1],
[1],
[1]], dtype=int8)
>>> # more seeding for two aggregates
>>> Agg = lloyd_aggregation(A,ratio=0.5)[0].toarray()
"""
if ratio <= 0 or ratio > 1:
raise ValueError('ratio must be > 0.0 and <= 1.0')
if not (isspmatrix_csr(C) or isspmatrix_csc(C)):
raise TypeError('expected csr_matrix or csc_matrix')
if distance == 'unit':
data = np.ones_like(C.data).astype(float)
elif distance == 'abs':
data = abs(C.data)
elif distance == 'inv':
data = 1.0 / abs(C.data)
elif distance == 'same':
data = C.data
elif distance == 'min':
data = C.data - C.data.min()
else:
raise ValueError('unrecognized value distance=%s' % distance)
if C.dtype == complex:
data = np.real(data)
assert (data.min() >= 0)
G = C.__class__((data, C.indices, C.indptr), shape=C.shape)
num_seeds = int(min(max(ratio * G.shape[0], 1), G.shape[0]))
distances, clusters, seeds = lloyd_cluster(G, num_seeds, maxiter=maxiter)
row = (clusters >= 0).nonzero()[0]
col = clusters[row]
data = np.ones(len(row), dtype='int8')
AggOp = coo_matrix((data, (row, col)),
shape=(G.shape[0], num_seeds)).tocsr()
return AggOp, seeds
def lloyd_aggregation(C, ratio=0.03, distance='unit', maxiter=10):
"""Aggregated nodes using Lloyd Clustering
Parameters
----------
C : csr_matrix
strength of connection matrix
ratio : scalar
Fraction of the nodes which will be seeds.
distance : ['unit','abs','inv',None]
Distance assigned to each edge of the graph G used in Lloyd clustering
For each nonzero value C[i,j]:
======= ===========================
'unit' G[i,j] = 1
'abs' G[i,j] = abs(C[i,j])
'inv' G[i,j] = 1.0/abs(C[i,j])
'same' G[i,j] = C[i,j]
'sub' G[i,j] = C[i,j] - min(C)
======= ===========================
maxiter : int
Maximum number of iterations to perform
Returns
-------
AggOp : csr_matrix
aggregation operator which determines the sparsity pattern
of the tentative prolongator
seeds : array
array of Cpts, i.e., Cpts[i] = root node of aggregate i
See Also
--------
amg_core.standard_aggregation
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from pyamg.gallery import poisson
>>> from pyamg.aggregation.aggregate import lloyd_aggregation
>>> A = poisson((4,), format='csr') # 1D mesh with 4 vertices
>>> A.todense()
matrix([[ 2., -1., 0., 0.],
[-1., 2., -1., 0.],
[ 0., -1., 2., -1.],
[ 0., 0., -1., 2.]])
>>> lloyd_aggregation(A)[0].todense() # one aggregate
matrix([[1],
[1],
[1],
[1]], dtype=int8)
>>> # more seeding for two aggregates
>>> Agg = lloyd_aggregation(A,ratio=0.5)[0].todense()
"""
if ratio <= 0 or ratio > 1:
raise ValueError('ratio must be > 0.0 and <= 1.0')
if not (isspmatrix_csr(C) or isspmatrix_csc(C)):
raise TypeError('expected csr_matrix or csc_matrix')
if distance == 'unit':
data = np.ones_like(C.data).astype(float)
elif distance == 'abs':
data = abs(C.data)
elif distance == 'inv':
data = 1.0/abs(C.data)
elif distance is 'same':
data = C.data
elif distance is 'min':
data = C.data - C.data.min()
else:
raise ValueError('unrecognized value distance=%s' % distance)
if C.dtype == complex:
data = np.real(data)
assert(data.min() >= 0)
G = C.__class__((data, C.indices, C.indptr), shape=C.shape)
num_seeds = int(min(max(ratio * G.shape[0], 1), G.shape[0]))
distances, clusters, seeds = lloyd_cluster(G, num_seeds, maxiter=maxiter)
row = (clusters >= 0).nonzero()[0]
col = clusters[row]
data = np.ones(len(row), dtype='int8')
AggOp = coo_matrix((data, (row, col)),
shape=(G.shape[0], num_seeds)).tocsr()
return AggOp, seeds
