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20090413a.py
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20090413a.py
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"""Given a Laplacian matrix, Schur complement out a set of taxa.
"""
from StringIO import StringIO
import numpy as np
from SnippetUtil import HandlingError
import SnippetUtil
import Util
import MatrixUtil
import Euclid
import SchurAlgebra
import Form
import FormOut
def get_form():
"""
@return: the body of a form
"""
# define the default matrix
upper_matrix = np.array([
[0, 0, 0, 0, 0, 0, 0, 0, 1/.05, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 1/.05, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1/.2, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/.05, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/.05, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/.2],
[0, 0, 0, 0, 0, 0, 0, 0.65245955, 0, 0.72801183, 0, -0.48410939],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0.72801183, 0, -0.48410939],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1/0.15, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.78713969],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/0.15],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
labels = ['a', 'b', 'c', 'm', 'n', 'p', 'x', 'y', 'ab', 'abc', 'mn', 'mnp']
n = len(labels)
L = [[0]*n for i in range(n)]
for i in range(n):
for j in range(n):
L[i][j] = -(upper_matrix[i][j] + upper_matrix[j][i])
row_sums = [sum(row) for row in L]
for i in range(n):
L[i][i] = -row_sums[i]
# define some default strings
ordered_label_string = '\n'.join(labels)
selected_label_string = '\n'.join(['ab', 'abc', 'mn', 'mnp'])
# define the sequence of form objects
form_objects = [
Form.Matrix('laplacian', 'laplacian matrix',
L, MatrixUtil.assert_symmetric),
Form.MultiLine('labels', 'ordered taxa',
ordered_label_string),
Form.MultiLine('selection', 'taxa to be schur complemented out',
selected_label_string)]
# return the sequence of form objects
return form_objects
def get_form_out():
return FormOut.Report()
def get_response_content(fs):
# read the matrix
L = fs.laplacian
# read the ordered labels
ordered_labels = Util.get_stripped_lines(StringIO(fs.labels))
if not ordered_labels:
raise HandlingError('no ordered taxa were provided')
if len(ordered_labels) != len(set(ordered_labels)):
raise HandlingError('the ordered taxa should be unique')
# get the label selection and its complement
min_selected_labels = 2
min_unselected_labels = 1
selected_labels = set(Util.get_stripped_lines(StringIO(fs.selection)))
if len(selected_labels) < min_selected_labels:
raise HandlingError('at least %d taxa should be selected to be grouped' % min_selected_labels)
# get the set of labels in the complement
unselected_labels = set(ordered_labels) - selected_labels
if len(unselected_labels) < min_unselected_labels:
raise HandlingError('at least %d taxa should remain outside the selected group' % min_unselected_labels)
# assert that no bizarre labels were selected
weird_labels = selected_labels - set(ordered_labels)
if weird_labels:
raise HandlingError('some selected taxa are invalid: ' + str(weird_labels))
# assert that the size of the distance matrix is compatible with the number of ordered labels
if len(L) != len(ordered_labels):
raise HandlingError('the number of listed taxa does not match the number of rows in the distance matrix')
# get the set of selected indices and its complement
n = len(L)
index_selection = set(i for i, label in enumerate(ordered_labels) if label in selected_labels)
index_complement = set(range(n)) - index_selection
# begin the response
out = StringIO()
# calculate the new laplacian matrix
L_small = SchurAlgebra.mschur(L, index_selection)
D_small = Euclid.laplacian_to_edm(L_small)
# print the matrices and the labels of its rows
print >> out, 'new laplacian matrix:'
print >> out, MatrixUtil.m_to_string(L_small)
print >> out
print >> out, 'new distance matrix:'
print >> out, MatrixUtil.m_to_string(D_small)
print >> out
print >> out, 'new taxon labels:'
for index in sorted(index_complement):
print >> out, ordered_labels[index]
# write the response
return out.getvalue()