def assign_laplacian_matrix(self, laplacian_matrix, laplacian_type = "unknown"):
laplacian_matrix = check_array(laplacian_matrix, accept_sparse = sparse_formats)
(a, b) = laplacian_matrix.shape
if a != b:
raise ValueError("Laplacian matrix is not square")
else:
self.laplacian_matrix = laplacian_matrix
self.laplacian_type = laplacian_type;
def assign_distance_matrix(self, distance_mat, neighborhood_radius = None):
distance_mat = check_array(distance_mat, accept_sparse = sparse_formats)
(a, b) = distance_mat.shape
if a != b:
raise ValueError("distance matrix is not square")
else:
self.distance_matrix = distance_mat
if neighborhood_radius is not None:
self.neighborhood_radius = neighborhood_radius
def assign_affinity_matrix(self, affinity_matrix, affinity_radius = None):
affinity_matrix = check_array(affinity_matrix, accept_sparse = sparse_formats)
(a, b) = affinity_matrix.shape
if a != b:
raise ValueError("affinity matrix is not square")
else:
self.affinity_matrix = affinity_matrix
if affinity_radius is not None:
self.affinity_radius = affinity_radius
self.default_affinity = False
def assign_data_matrix(self, X):
X = check_array(X, accept_sparse = sparse_formats)
self.X = X
def __init__(self, X, neighborhood_radius = None, affinity_radius = None,
distance_method = 'auto', input_type = 'data',
laplacian_type = None, path_to_flann = None):
self.distance_method = distance_method
self.input_type = input_type
self.path_to_flann = path_to_flann
self.laplacian_type = laplacian_type
if self.distance_method not in distance_methods:
raise ValueError("invalid distance method.")
if neighborhood_radius is None:
self.neighborhood_radius = 1/X.shape[1]
else:
try:
neighborhood_radius = np.float(neighborhood_radius)
self.neighborhood_radius = neighborhood_radius
except ValueError:
raise ValueError("neighborhood_radius must be convertable to float")
if affinity_radius is None:
self.affinity_radius = self.neighborhood_radius
self.default_affinity = True
else:
try:
affinity_radius = np.float(affinity_radius)
self.affinity_radius = affinity_radius
self.default_affinity = False
except ValueError:
raise ValueError("affinity_radius must be convertable to float")
if self.input_type == 'distance':
X = check_array(X, accept_sparse = sparse_formats)
a, b = X.shape
if a != b:
raise ValueError("input_type is distance but input matrix is not square")
self.X = None
self.distance_matrix = X
self.affinity_matrix = None
self.laplacian_matrix = None
elif self.input_type == 'affinity':
X = check_array(X, accept_sparse = sparse_formats)
a, b = X.shape
if a != b:
raise ValueError("input_type is affinity but input matrix is not square")
self.X = None
self.distance_matrix = None
self.affinity_matrix = X
self.laplacian_matrix = None
elif self.input_type == 'data':
X = check_array(X, accept_sparse = sparse_formats)
self.X = X
self.distance_matrix = None
self.affinity_matrix = None
self.laplacian_matrix = None
else:
raise ValueError('input_type must be one of: data, distance, affinity.')
if distance_method == 'cython':
if input_type == 'data':
try:
from Mmani.geometry.cyflann.index import Index
self.cyindex = Index(X)
except ImportError:
raise ValueError("distance_method set to cython but cyflann_index cannot be imported.")
else:
self.cyindex = None
if distance_method == 'pyflann':
if self.path_to_flann is not None:
# FLANN is installed in specific location
sys.path.insert(0, self.path_to_flann)
try:
import pyflann as pyf
self.flindex = pyf.FLANN()
self.flparams = self.flindex.build_index(X, algorithm = 'kmeans',
target_precision = 0.9)
except ImportError:
raise ValueError("distance_method is set to pyflann but pyflann is "
"not available.")
else:
self.flindex = None
self.flparams = None
def eigen_decomposition(G, n_components=8, eigen_solver=None,
random_state=None, eigen_tol=0.0,
drop_first=True, largest = True):
"""
G : 2d numpy/scipy array. Potentially sparse.
The matrix to find the eigendecomposition of
n_components : integer, optional
The number of eigenvectors to return
eigen_solver : {'auto', 'dense', 'arpack', 'lobpcg', or 'amg'}
auto : algorithm will attempt to choose the best method for input data
dense : use standard dense matrix operations for the eigenvalue
decomposition. For this method, M must be an array
or matrix type. This method should be avoided for
large problems.
arpack : use arnoldi iteration in shift-invert mode.
For this method, M may be a dense matrix, sparse matrix,
or general linear operator.
Warning: ARPACK can be unstable for some problems. It is
best to try several random seeds in order to check results.
lobpcg : Locally Optimal Block Preconditioned Conjugate Gradient Method.
a preconditioned eigensolver for large symmetric positive definite
(SPD) generalized eigenproblems.
amg : AMG requires pyamg to be installed. It can be faster on very large,
sparse problems, but may also lead to instabilities.
random_state : int seed, RandomState instance, or None (default)
A pseudo random number generator used for the initialization of the
lobpcg eigen vectors decomposition when eigen_solver == 'amg'.
By default, arpack is used.
eigen_tol : float, optional, default=0.0
Stopping criterion for eigendecomposition when using arpack eigen_solver
Returns
-------
lambdas, diffusion_map : eigenvalues, eigenvectors
"""
n_nodes = G.shape[0]
if eigen_solver is None:
eigen_solver = 'auto'
elif not eigen_solver in eigen_solvers:
raise ValueError("Unknown value for eigen_solver: '%s'."
"Should be: '%s'"
% eigen_solver, eigen_solvers)
if eigen_solver == 'auto':
if G.shape[0] > 200:
eigen_solver = 'arpack'
else:
eigen_solver = 'dense'
# Check eigen_solver method
try:
from pyamg import smoothed_aggregation_solver
except ImportError:
if eigen_solver == "amg":
raise ValueError("The eigen_solver was set to 'amg', but pyamg is "
"not available.")
# Check input values
if not isinstance(largest, bool):
raise ValueError("largest should be True if you want largest eigenvalues otherwise False")
random_state = check_random_state(random_state)
if drop_first:
n_components = n_components + 1
# Check for symmetry
is_symmetric = _is_symmetric(G)
# Convert G to best type for eigendecomposition
if sparse.issparse(G):
if G.getformat() is not 'csr':
G.tocsr()
G = G.astype(np.float)
if ((eigen_solver == 'lobpcg') and (n_nodes < 5 * n_components + 1)):
warnings.warn("lobpcg has problems with small number of nodes. Using dense eigh")
eigen_solver = 'dense'
# Try Eigen Methods:
if eigen_solver == 'arpack':
if is_symmetric:
if largest:
which = 'LM'
else:
which = 'SM'
lambdas, diffusion_map = eigsh(G, k=n_components, which=which,tol=eigen_tol)
else:
if largest:
which = 'LR'
else:
which = 'SR'
lambdas, diffusion_map = eigs(G, k=n_components, which=which,tol=eigen_tol)
lambdas = np.real(lambdas)
diffusion_map = np.real(diffusion_map)
elif eigen_solver == 'amg':
if not is_symmetric:
raise ValueError("lobpcg requires symmetric matrices.")
if not sparse.issparse(G):
warnings.warn("AMG works better for sparse matrices")
# Use AMG to get a preconditioner and speed up the eigenvalue problem.
ml = smoothed_aggregation_solver(check_array(G, accept_sparse = ['csr']))
M = ml.aspreconditioner()
n_find = min(n_nodes, 5 + 2*n_components)
X = random_state.rand(n_nodes, n_find)
X[:, 0] = (G.diagonal()).ravel()
lambdas, diffusion_map = lobpcg(G, X, M=M, largest=largest)
sort_order = np.argsort(lambdas)
if largest:
lambdas = lambdas[sort_order[::-1]]
diffusion_map = diffusion_map[:, sort_order[::-1]]
else:
lambdas = lambdas[sort_order]
diffusion_map = diffusion_map[:, sort_order]
lambdas = lambdas[:n_components]
diffusion_map = diffusion_map[:, :n_components]
elif eigen_solver == "lobpcg":
if not is_symmetric:
raise ValueError("lobpcg requires symmetric matrices.")
n_find = min(n_nodes, 5 + 2*n_components)
X = random_state.rand(n_nodes, n_find)
lambdas, diffusion_map = lobpcg(G, X, largest=largest)
sort_order = np.argsort(lambdas)
if largest:
lambdas = lambdas[sort_order[::-1]]
diffusion_map = diffusion_map[:, sort_order[::-1]]
else:
lambdas = lambdas[sort_order]
diffusion_map = diffusion_map[:, sort_order]
lambdas = lambdas[:n_components]
diffusion_map = diffusion_map[:, :n_components]
elif eigen_solver == 'dense':
if sparse.isspmatrix(G):
G = G.todense()
if is_symmetric:
lambdas, diffusion_map = eigh(G)
else:
lambdas, diffusion_map = eig(G)
if largest:# eigh always returns eigenvalues in ascending order
lambdas = lambdas[::-1] # reverse order the e-values
diffusion_map = diffusion_map[:, ::-1] # reverse order the vectors
lambdas = lambdas[:n_components]
diffusion_map = diffusion_map[:, :n_components]
return (lambdas, diffusion_map)
def test_check_array():
# accept_sparse == None
# raise error on sparse inputs
X = [[1, 2], [3, 4]]
X_csr = sp.csr_matrix(X)
assert_raises(TypeError, check_array, X_csr)
# ensure_2d
assert_warns(DeprecationWarning, check_array, [0, 1, 2])
X_array = check_array([0, 1, 2])
assert_equal(X_array.ndim, 2)
X_array = check_array([0, 1, 2], ensure_2d=False)
assert_equal(X_array.ndim, 1)
# don't allow ndim > 3
X_ndim = np.arange(8).reshape(2, 2, 2)
assert_raises(ValueError, check_array, X_ndim)
check_array(X_ndim, allow_nd=True) # doesn't raise
# force_all_finite
X_inf = np.arange(4).reshape(2, 2).astype(np.float)
X_inf[0, 0] = np.inf
assert_raises(ValueError, check_array, X_inf)
check_array(X_inf, force_all_finite=False) # no raise
# nan check
X_nan = np.arange(4).reshape(2, 2).astype(np.float)
X_nan[0, 0] = np.nan
assert_raises(ValueError, check_array, X_nan)
check_array(X_inf, force_all_finite=False) # no raise
# dtype and order enforcement.
X_C = np.arange(4).reshape(2, 2).copy("C")
X_F = X_C.copy("F")
X_int = X_C.astype(np.int)
X_float = X_C.astype(np.float)
Xs = [X_C, X_F, X_int, X_float]
dtypes = [np.int32, np.int, np.float, np.float32, None, np.bool, object]
orders = ['C', 'F', None]
copys = [True, False]
for X, dtype, order, copy in product(Xs, dtypes, orders, copys):
X_checked = check_array(X, dtype=dtype, order=order, copy=copy)
if dtype is not None:
assert_equal(X_checked.dtype, dtype)
else:
assert_equal(X_checked.dtype, X.dtype)
if order == 'C':
assert_true(X_checked.flags['C_CONTIGUOUS'])
assert_false(X_checked.flags['F_CONTIGUOUS'])
elif order == 'F':
assert_true(X_checked.flags['F_CONTIGUOUS'])
assert_false(X_checked.flags['C_CONTIGUOUS'])
if copy:
assert_false(X is X_checked)
else:
# doesn't copy if it was already good
if (X.dtype == X_checked.dtype and
X_checked.flags['C_CONTIGUOUS'] == X.flags['C_CONTIGUOUS']
and X_checked.flags['F_CONTIGUOUS'] == X.flags['F_CONTIGUOUS']):
assert_true(X is X_checked)
# allowed sparse != None
X_csc = sp.csc_matrix(X_C)
X_coo = X_csc.tocoo()
X_dok = X_csc.todok()
X_int = X_csc.astype(np.int)
X_float = X_csc.astype(np.float)
Xs = [X_csc, X_coo, X_dok, X_int, X_float]
accept_sparses = [['csr', 'coo'], ['coo', 'dok']]
for X, dtype, accept_sparse, copy in product(Xs, dtypes, accept_sparses,
copys):
with warnings.catch_warnings(record=True) as w:
X_checked = check_array(X, dtype=dtype,
accept_sparse=accept_sparse, copy=copy)
if (dtype is object or sp.isspmatrix_dok(X)) and len(w):
message = str(w[0].message)
messages = ["object dtype is not supported by sparse matrices",
"Can't check dok sparse matrix for nan or inf."]
assert_true(message in messages)
else:
assert_equal(len(w), 0)
if dtype is not None:
assert_equal(X_checked.dtype, dtype)
else:
assert_equal(X_checked.dtype, X.dtype)
if X.format in accept_sparse:
# no change if allowed
assert_equal(X.format, X_checked.format)
else:
# got converted
assert_equal(X_checked.format, accept_sparse[0])
if copy:
assert_false(X is X_checked)
else:
# doesn't copy if it was already good
if (X.dtype == X_checked.dtype and X.format == X_checked.format):
assert_true(X is X_checked)
# other input formats
# convert lists to arrays
X_dense = check_array([[1, 2], [3, 4]])
assert_true(isinstance(X_dense, np.ndarray))
# raise on too deep lists
assert_raises(ValueError, check_array, X_ndim.tolist())
check_array(X_ndim.tolist(), allow_nd=True) # doesn't raise
def test_check_array_dtype_stability():
# test that lists with ints don't get converted to floats
X = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
assert_equal(check_array(X).dtype.kind, "i")
assert_equal(check_array(X, ensure_2d=False).dtype.kind, "i")