Sparse Matrix Eigenvector Computation

sparse_eigenvector.py

import numpy as np
import pandas as pd
from scipy.sparse import csr_matrix, linalg

data="""h_tract	w_tract	total
01001020100	01001020200	54
01001020400	01001020500	79
01001020200	01001020400	11
01001020100	01001020300	3
01001020400	01001020100	25
01001020500	01001020400	21
01001020400	01001020200	59
01001020100	01001020100	6
01001020100	01001020500	32
01001020500	01001020200	138
01001020400	01001020300	22
01001020500	01001020100	45
01001020300	01001020400	13
01001020400	01001020400	17
01001020300	01001020300	20
01001020300	01001020100	16
01001020500	01001020300	27
01001020200	01001020500	48
01001020500	01001020500	215
01001020200	01001020100	10
01001020200	01001020300	7
01001020300	01001020500	72
01001020200	01001020200	45
01001020100	01001020400	8
01001020300	01001020200	64"""

df = pd.read_csv(pd.compat.StringIO(data), sep='\t', dtype={'h_tract': str, 'w_tract': str, 's000': int})
print df.head()
w_tract_u = list(sorted(df.w_tract.unique()))
h_tract_u = list(sorted(df.h_tract.unique()))

data = df['total'].tolist()

row = df.w_tract.astype(pd.api.types.CategoricalDtype(categories=w_tract_u)).cat.codes
col = df.h_tract.astype(pd.api.types.CategoricalDtype(categories=h_tract_u)).cat.codes
sparse_matrix = csr_matrix((data, (row, col)), shape=(len(w_tract_u), len(h_tract_u)))

w_tracts = sparse_matrix.sum(axis=1, dtype=np.int64)
h_tracts = sparse_matrix.sum(axis=0, dtype=np.int64)
print "w_tracts", w_tracts
print "h_tracts", h_tracts
A = sparse_matrix.transpose()
print "A", A.todense()
S = np.true_divide(A.todense(), w_tracts)
print "S", S
w, v = linalg.eigs(S, k=2)
idx = w.argsort()[::-1]
eigenValues = w[idx]
eigenVectors = v[:,idx]
vector = eigenVectors[:, 0]
print eigenValues
print vector