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20100816b.py
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20100816b.py
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"""Look at the eigendecomposition of an augmented Laplacian matrix.
"""
from StringIO import StringIO
import math
import numpy as np
from SnippetUtil import HandlingError
import Form
import FormOut
import NewickIO
import Euclid
import FelTree
import SchurAlgebra
import EigUtil
import const
g_tree_string = const.read('20100730g').rstrip()
def get_form():
"""
@return: a list of form objects
"""
# define the form objects
form_objects = [
Form.MultiLine('tree_string', 'newick tree',
g_tree_string),
Form.Float('strength', 'duplicate node connection strength', 100),
Form.Integer('ndups', 'add this many extra duplicates per tip', 3)]
return form_objects
def get_form_out():
return FormOut.Report()
def get_augmented_adjacency(A, ntips, ndups, strength):
"""
@param A: adjacency matrix
@param ntips: the number of tips of the tree defining the adjacency matrix
@param ndups: add this many extra duplicates per tip
@param strength: the strength of the duplicate connection
@return: a new adjacency matrix with tip extensions at the end
"""
n = len(A)
nnew = n + ntips*ndups
ninternal = n - ntips
P = np.zeros((nnew, nnew))
for i in range(nnew):
for j in range(nnew):
if i < n and j < n:
P[i,j] = A[i,j]
elif i < ntips and j >= n:
if (j - n) % ntips == i:
P[i,j] = strength
elif j < ntips and i >= n:
if (i - n) % ntips == j:
P[i,j] = strength
return P
def get_response_content(fs):
# build the newick tree from the string
tree = NewickIO.parse(fs.tree_string, FelTree.NewickTree)
nvertices = len(list(tree.preorder()))
nleaves = len(list(tree.gen_tips()))
# get ordered ids with the leaves first
ordered_ids = get_ordered_ids(tree)
# get the adjacency matrix and the augmented adjacency matrix
A = np.array(tree.get_affinity_matrix(ordered_ids))
A_aug = get_augmented_adjacency(A, nleaves, fs.ndups, fs.strength)
# get the laplacian matrices
L = Euclid.adjacency_to_laplacian(A)
L_aug = Euclid.adjacency_to_laplacian(A_aug)
# get the schur complement
R = SchurAlgebra.mschur(L, set(range(nleaves, nvertices)))
R_pinv = np.linalg.pinv(R)
vals, vecs = EigUtil.eigh(R_pinv)
# get the scaled Fiedler vector for the Schur complement
w, v = EigUtil.principal_eigh(R_pinv)
fiedler = v * math.sqrt(w)
# get the eigendecomposition of the augmented Laplacian
L_aug_pinv = np.linalg.pinv(L_aug)
vals_aug, vecs_aug = EigUtil.eigh(L_aug_pinv)
# get the scaled Fiedler vector for the augmented Laplacian
w_aug, v_aug = EigUtil.principal_eigh(L_aug_pinv)
fiedler_aug = v_aug * math.sqrt(w_aug)
# report the results
np.set_printoptions(linewidth=300)
out = StringIO()
print >> out, 'Laplacian matrix:'
print >> out, L
print >> out
print >> out, 'Schur complement of Laplacian matrix:'
print >> out, R
print >> out
print >> out, 'scaled Fiedler vector of Schur complement:'
print >> out, fiedler
print >> out
print >> out, 'eigenvalues of pinv of Schur complement:'
print >> out, vals
print >> out
print >> out, 'corresponding eigenvectors of pinv of Schur complement:'
print >> out, np.array(vecs).T
print >> out
print >> out
print >> out, 'augmented Laplacian matrix:'
print >> out, L_aug
print >> out
print >> out, 'scaled Fiedler vector of augmented Laplacian:'
print >> out, fiedler_aug
print >> out
print >> out, 'eigenvalues of pinv of augmented Laplacian:'
print >> out, vals_aug
print >> out
print >> out, 'rows are eigenvectors of pinv of augmented Laplacian:'
print >> out, np.array(vecs_aug)
return out.getvalue()
def get_ordered_ids(tree):
"""
Maybe I could use postorder here instead.
@param tree: a tree
@return: a list of ids beginning with the leaves
"""
ordered_ids = []
ordered_ids.extend(id(node) for node in tree.gen_tips())
ordered_ids.extend(id(node) for node in tree.gen_internal_nodes())
return ordered_ids