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135 lines
4.2 KiB
Python
135 lines
4.2 KiB
Python
# Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
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# Jake Vanderplas <vanderplas@astro.washington.edu>
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# License: BSD
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import numpy as np
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from numpy.testing import assert_allclose, assert_array_almost_equal
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from pytest import raises as assert_raises
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from scipy import sparse
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from scipy.sparse import csgraph
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def _explicit_laplacian(x, normed=False):
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if sparse.issparse(x):
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x = x.todense()
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x = np.asarray(x)
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y = -1.0 * x
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for j in range(y.shape[0]):
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y[j,j] = x[j,j+1:].sum() + x[j,:j].sum()
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if normed:
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d = np.diag(y).copy()
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d[d == 0] = 1.0
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y /= d[:,None]**.5
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y /= d[None,:]**.5
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return y
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def _check_symmetric_graph_laplacian(mat, normed):
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if not hasattr(mat, 'shape'):
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mat = eval(mat, dict(np=np, sparse=sparse))
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if sparse.issparse(mat):
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sp_mat = mat
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mat = sp_mat.todense()
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else:
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sp_mat = sparse.csr_matrix(mat)
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laplacian = csgraph.laplacian(mat, normed=normed)
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n_nodes = mat.shape[0]
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if not normed:
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assert_array_almost_equal(laplacian.sum(axis=0), np.zeros(n_nodes))
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assert_array_almost_equal(laplacian.T, laplacian)
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assert_array_almost_equal(laplacian,
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csgraph.laplacian(sp_mat, normed=normed).todense())
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assert_array_almost_equal(laplacian,
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_explicit_laplacian(mat, normed=normed))
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def test_laplacian_value_error():
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for t in int, float, complex:
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for m in ([1, 1],
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[[[1]]],
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[[1, 2, 3], [4, 5, 6]],
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[[1, 2], [3, 4], [5, 5]]):
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A = np.array(m, dtype=t)
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assert_raises(ValueError, csgraph.laplacian, A)
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def test_symmetric_graph_laplacian():
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symmetric_mats = ('np.arange(10) * np.arange(10)[:, np.newaxis]',
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'np.ones((7, 7))',
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'np.eye(19)',
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'sparse.diags([1, 1], [-1, 1], shape=(4,4))',
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'sparse.diags([1, 1], [-1, 1], shape=(4,4)).todense()',
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'np.asarray(sparse.diags([1, 1], [-1, 1], shape=(4,4)).todense())',
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'np.vander(np.arange(4)) + np.vander(np.arange(4)).T')
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for mat_str in symmetric_mats:
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for normed in True, False:
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_check_symmetric_graph_laplacian(mat_str, normed)
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def _assert_allclose_sparse(a, b, **kwargs):
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# helper function that can deal with sparse matrices
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if sparse.issparse(a):
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a = a.toarray()
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if sparse.issparse(b):
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b = a.toarray()
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assert_allclose(a, b, **kwargs)
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def _check_laplacian(A, desired_L, desired_d, normed, use_out_degree):
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for arr_type in np.array, sparse.csr_matrix, sparse.coo_matrix:
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for t in int, float, complex:
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adj = arr_type(A, dtype=t)
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L = csgraph.laplacian(adj, normed=normed, return_diag=False,
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use_out_degree=use_out_degree)
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_assert_allclose_sparse(L, desired_L, atol=1e-12)
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L, d = csgraph.laplacian(adj, normed=normed, return_diag=True,
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use_out_degree=use_out_degree)
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_assert_allclose_sparse(L, desired_L, atol=1e-12)
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_assert_allclose_sparse(d, desired_d, atol=1e-12)
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def test_asymmetric_laplacian():
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# adjacency matrix
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A = [[0, 1, 0],
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[4, 2, 0],
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[0, 0, 0]]
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# Laplacian matrix using out-degree
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L = [[1, -1, 0],
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[-4, 4, 0],
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[0, 0, 0]]
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d = [1, 4, 0]
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_check_laplacian(A, L, d, normed=False, use_out_degree=True)
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# normalized Laplacian matrix using out-degree
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L = [[1, -0.5, 0],
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[-2, 1, 0],
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[0, 0, 0]]
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d = [1, 2, 1]
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_check_laplacian(A, L, d, normed=True, use_out_degree=True)
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# Laplacian matrix using in-degree
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L = [[4, -1, 0],
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[-4, 1, 0],
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[0, 0, 0]]
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d = [4, 1, 0]
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_check_laplacian(A, L, d, normed=False, use_out_degree=False)
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# normalized Laplacian matrix using in-degree
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L = [[1, -0.5, 0],
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[-2, 1, 0],
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[0, 0, 0]]
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d = [2, 1, 1]
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_check_laplacian(A, L, d, normed=True, use_out_degree=False)
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def test_sparse_formats():
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for fmt in ('csr', 'csc', 'coo', 'lil', 'dok', 'dia', 'bsr'):
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mat = sparse.diags([1, 1], [-1, 1], shape=(4,4), format=fmt)
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for normed in True, False:
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_check_symmetric_graph_laplacian(mat, normed)
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