def get_eigendecomposition_report(D):
"""
@param D: a distance matrix
@return: a multi-line string
"""
out = StringIO()
# get some intermediate matrices and vectors
L = Euclid.edm_to_laplacian(D)
laplacian_fiedler = BuildTreeTopology.laplacian_to_fiedler(L)
distance_fiedler = BuildTreeTopology.edm_to_fiedler(D)
eigensplit = BuildTreeTopology.eigenvector_to_split(laplacian_fiedler)
# report the two eigenvalue lists that should be the same
HDH = MatrixUtil.double_centered(D)
HSH = -0.5 * HDH
w_distance, vt_distance = np.linalg.eigh(HSH)
print >> out, 'the laplacian-derived and distance-derived eigenvalues:'
w_laplacian, vt_laplacian = np.linalg.eigh(L)
for a, b in zip(sorted(w_laplacian), sorted(w_distance)):
print >> out, a, '\t', b
print >> out
# report the two fiedler vectors that should be the same
print >> out, 'the laplacian-derived and distance-derived fiedler vectors:'
for a, b in zip(laplacian_fiedler, distance_fiedler):
print >> out, a, '\t', b
return out.getvalue().strip()
def get_eigendecomposition_report(D):
"""
@param D: a distance matrix
@return: a multi-line string
"""
out = StringIO()
# get some intermediate matrices and vectors
L = Euclid.edm_to_laplacian(D)
laplacian_fiedler = BuildTreeTopology.laplacian_to_fiedler(L)
distance_fiedler = BuildTreeTopology.edm_to_fiedler(D)
eigensplit = BuildTreeTopology.eigenvector_to_split(laplacian_fiedler)
# report the two eigenvalue lists that should be the same
HDH = MatrixUtil.double_centered(D)
HSH = -0.5 * HDH
w_distance, vt_distance = np.linalg.eigh(HSH)
print >> out, 'the laplacian-derived and distance-derived eigenvalues:'
w_laplacian, vt_laplacian = np.linalg.eigh(L)
for a, b in zip(sorted(w_laplacian), sorted(w_distance)):
print >> out, a, '\t', b
print >> out
# report the two fiedler vectors that should be the same
print >> out, 'the laplacian-derived and distance-derived fiedler vectors:'
for a, b in zip(laplacian_fiedler, distance_fiedler):
print >> out, a, '\t', b
return out.getvalue().strip()
def spectral_split(D):
"""
@param D: numpy distance matrix
@return: a split of the indices of the distance matrix
"""
v = BuildTreeTopology.edm_to_fiedler(D)
split = BuildTreeTopology.eigenvector_to_split(v)
# if one side of the split is empty then there is a failure
if frozenset() in split:
raise ValueError('failed split')
return split
def get_subtree_messages(D, eigensplit, ordered_tip_names):
"""
@param D: the matrix of pairwise distances among tips of the tree
@param eigensplit: the split induced by the fiedler vector
@param ordered_tip_names: names of the tips of the tree conformant to v and D
@return: a multi-line string
"""
out = StringIO()
n = len(D)
ordered_label_sets = [set([i]) for i in range(n)]
all_labels = set(range(n))
for i, child in enumerate(eigensplit):
complement = all_labels - child
D_child = MatrixUtil.get_principal_submatrix(D, list(sorted(child)))
child_label_sets = SchurAlgebra.vdelete(ordered_label_sets, complement)
v_child = BuildTreeTopology.edm_to_fiedler(D_child)
print >> out, 'the Fiedler split of Schur complements of subtree', i + 1
for label_set, value in zip(child_label_sets, v_child):
s = label_set_to_string(label_set, ordered_tip_names)
print >> out, s, ':', value
print >> out
return out.getvalue().strip()
def get_subtree_messages(D, eigensplit, ordered_tip_names):
"""
@param D: the matrix of pairwise distances among tips of the tree
@param eigensplit: the split induced by the fiedler vector
@param ordered_tip_names: names of the tips of the tree conformant to v and D
@return: a multi-line string
"""
out = StringIO()
n = len(D)
ordered_label_sets = [set([i]) for i in range(n)]
all_labels = set(range(n))
for i, child in enumerate(eigensplit):
complement = all_labels - child
D_child = MatrixUtil.get_principal_submatrix(D, list(sorted(child)))
child_label_sets = SchurAlgebra.vdelete(ordered_label_sets, complement)
v_child = BuildTreeTopology.edm_to_fiedler(D_child)
print >> out, 'the Fiedler split of Schur complements of subtree', i+1
for label_set, value in zip(child_label_sets, v_child):
s = label_set_to_string(label_set, ordered_tip_names)
print >> out, s, ':', value
print >> out
return out.getvalue().strip()