def left_eigenvector(matrix):
"""
Calculates the left eigenvector for a given matrix.
Arguments: matrix ([[float]]): The dampened, "Google" matrix.
Returns:
left_eigenvector ([float]): A vector of weights for each site.
"""
try:
evals, evecs = linalg.eig(a=matrix, left=True, right=False, overwrite_a=True, check_finite=False)
except LinAlgError as e:
return None
evec_ind = index_of(evals, lambda x: x > .99 and x < 1.01)
return evecs[:,evec_ind]
def create_matrix(self, cleaned_small_orgs):
"""
Convert the cleaned small_orgs to a matrix.
Arguments:
cleaned_small_orgs ([SmallOrganization]): The list of all organizations in the form of SmallOrganization
objects that has passed through the cleanup_data function.
Returns:
matrix [[float]]: A 2D matrix of floats on which to perform the PageRank algorithm.
"""
org_count = len(cleaned_small_orgs)
if org_count <= 0:
return None
default_val = 1 / float(org_count)
matrix = []
for org in cleaned_small_orgs:
# initialize row to zeros
row = [0] * org_count
total = 0.0
for ref in org.page_rank_info.references:
# don't count self for now...
if ref.org_domain == org.org_domain:
continue
# find index of the referenced organization in the list
index = index_of(cleaned_small_orgs, lambda x: x.org_domain == ref.org_domain)
if index != -1:
row[index] = ref.count / float(org.page_rank_info.total)
# track total to make sure this all adds to 1.0
total += row[index]
# if zero, org didn't referefence other organizations,
# set all values evenly to simulate random navigation behavior
if total == 0.0:
for i in range(0, org_count):
row[i] = default_val
total += default_val
# if our total doesn't add to exactly 1.0, compensate.
if total != 1.0:
# first, try to distribute equally
diff = 1.0 - total
refs_count = len(org.page_rank_info.references)
if refs_count == 0:
# set to org_count if no references
refs_count = org_count
diff_to_add = diff / refs_count
for i in range(0, org_count):
if row[i] != 0.0:
row[i] += diff_to_add
total += diff_to_add
# if still not perfect, just alter the first val that's big enough to not be a huge deal
if total != 1.0:
diff = 1.0 - total
first_val = index_of(row, lambda x: x > abs(diff_to_add))
row[first_val] += diff
total = 1.0
# add row to matrix
matrix.append(row)
# sanity check
if len(matrix) != org_count:
raise Exception("Error: The matrix constructed is not square in preprocessors.py - create_matrix().")
return matrix
