def plotjson(fn):
"""
plotjson: make plots from json output of fiedler.py
fn: the filename of the json file
"""
fo=open(fn)
data=json.load(fo)
fo.close()
if "adj" in data:
(A,adj,Npts) = fiedler.adj_mat(data["adj"])
#A = (A.T - A)/2
A=A.tocoo()
pos=A.data!=0
skew = numpy.column_stack((A.row[pos],A.col[pos],A.data[pos])).tolist()
# method from ranking driver.py
asc = abstract_simplicial_complex([numpy.column_stack((A.row[pos],A.col[pos])).tolist()])
B1 = asc.chain_complex()[1] # boundary matrix
rank = lsqr(B1.T, A.data[pos])[0] # solve least squares problem
# sc = simplicial_complex(([[el] for el in range(0,A.shape[0])],numpy.column_stack((A.row[pos],A.col[pos])).tolist()))
# omega = sc.get_cochain(1)
# omega.v[:] = A.data[pos]
# p = omega.k
# alpha = sc.get_cochain(p - 1)
#
# alpha.v = rank
# v = A.data[pos]-d(alpha).v
#
# cyclic_adj_list=numpy.column_stack((A.row[pos],A.col[pos],v)).tolist()
# div_adj_list=numpy.column_stack((A.row[pos],A.col[pos],d(alpha).v)).tolist()
data["hodge"]=list(rank)
data["hodgerank"]=list(numpy.argsort(numpy.argsort(rank)))
print "Adding hodge results to %s"%(os.path.abspath(fn))
fo = open(fn,"w")
json.dump(data,fo, indent=2)
fo.close()
def rate(self, mutate=True):
'''Least squares ranking on graphs. This method is adapted from the
example given by Hirani et al. Set mutate to False to prevent the
calculation from being saved on each Squad instance. No commits
are performed.
See also
* A. N. Hirani, K. Kalyanaraman, S. Watts
arXiv:1011.1716v1 [cs.NA] on http://arxiv.org/abs/1011.1716'''
data = self.distances
# Find edges
edges = data[:, :2]
# Create abstract simplicial complex from edges
asc = abstract_simplicial_complex([edges])
# Pairwise comparisons
omega = data[:, -1]
# Find boundary matrix of abs. simplicial complex
B = asc.chain_complex()[1]
# Solve least squares problem
alpha = lsqr(B.T, omega)[0]
# Normalize minimum
alpha = alpha - alpha.min()
# Convert enumerated IDs back into SIDs
ret = {}
for eid, aval in enumerate(alpha):
ret[self._squadmap['eid2sid'][eid]] = aval
if mutate:
for squad in self.squads:
squad.lsalpha = ret[squad.id]
return ret
Least Squares Ranking on Graphs, Hodge Laplacians, Time Optimality,
and Iterative Methods
A. N. Hirani, K. Kalyanaraman, S. Watts
See arXiv:1011.1716v1 [cs.NA] on http://arxiv.org/abs/1011.1716
"""
from numpy import loadtxt
from pydec import abstract_simplicial_complex
from scipy.sparse.linalg import lsqr
# Load graph and edge values
data = loadtxt('data.txt').astype(int)
edges = data[:,:2]
# Create abstract simplicial complex from edges
asc = abstract_simplicial_complex([edges])
omega = data[:,-1] # pairwise comparisons
B1 = asc.chain_complex()[1] # boundary matrix
alpha = lsqr(B1.T, omega)[0] # solve least squares problem
# Set the minimum to 0
alpha = alpha - alpha.min()
print alpha
Least Squares Ranking on Graphs, Hodge Laplacians, Time Optimality,
and Iterative Methods
A. N. Hirani, K. Kalyanaraman, S. Watts
See arXiv:1011.1716v1 [cs.NA] on http://arxiv.org/abs/1011.1716
"""
from numpy import loadtxt
from pydec import abstract_simplicial_complex
from scipy.sparse.linalg import lsqr
# Load graph and edge values
data = loadtxt('data.txt').astype(int)
edges = data[:,:2]
# Create abstract simplicial complex from edges
asc = abstract_simplicial_complex([edges])
omega = data[:,-1] # pairwise comparisons
B1 = asc.chain_complex()[1] # boundary matrix
alpha = lsqr(B1.T, omega)[0] # solve least squares problem
# Set the minimum to 0
alpha = alpha - alpha.min()
print(alpha)
def plotjson(fn):
"""
plotjson: make plots from json output of fiedler.py
fn: the filename of the json file
"""
fo=open(fn)
data=json.load(fo)
fo.close()
if "adj" in data:
(A,adj,Npts) = fiedler.adj_mat(data["adj"])
#scew symetricise
A = (A.T - A)/2
A=A.tocoo()
pos=A.data>0
skew = numpy.column_stack((A.row[pos],A.col[pos],A.data[pos])).tolist()
# #method from hodge decomposition driver.py
# sc = simplicial_complex(([[el] for el in range(0,A.shape[0])],numpy.column_stack((A.row[pos],A.col[pos])).tolist()))
# omega = sc.get_cochain(1)
# omega.v[:] = A.data[pos]
# p = omega.k
# alpha = sc.get_cochain(p - 1)
# #beta = sc.get_cochain(p + 1)
# # Solve for alpha
# A2 = delta(d(sc.get_cochain_basis(p - 1))).v
# b = delta(omega).v
# rank=cg( A2, b, tol=1e-8 )[0]
# method from ranking driver.py
asc = abstract_simplicial_complex([numpy.column_stack((A.row[pos],A.col[pos])).tolist()])
B1 = asc.chain_complex()[1] # boundary matrix
rank = lsqr(B1.T, A.data[pos])[0] # solve least squares problem
sc = simplicial_complex(([[el] for el in range(0,A.shape[0])],numpy.column_stack((A.row[pos],A.col[pos])).tolist()))
omega = sc.get_cochain(1)
omega.v[:] = A.data[pos]
p = omega.k
alpha = sc.get_cochain(p - 1)
alpha.v = rank
v = A.data[pos]-d(alpha).v
cyclic_adj_list=numpy.column_stack((A.row[pos],A.col[pos],v)).tolist()
div_adj_list=numpy.column_stack((A.row[pos],A.col[pos],d(alpha).v)).tolist()
data["hodge"]=list(rank)
data["hodgerank"]=list(numpy.argsort(numpy.argsort(rank)))
fo = open(fn,"w")
json.dump(data,fo, indent=2)
fo.close()
fn=fn+".abstract"
#fiedler.doPlots(numpy.array(data["f1"]),numpy.array(data["f2"]),numpy.array(data["d"]),cyclic_adj_list,fn+".decomp.cyclic.",widths=[6],vsdeg=False,nByi=data["nByi"],directed=True)
#fiedler.doPlots(numpy.array(data["f1"]),numpy.array(data["f2"]),numpy.array(data["d"]),div_adj_list,fn+".decomp.acyclic.",widths=[6],vsdeg=False,nByi=data["nByi"],directed=True)
#fiedler.doPlots(numpy.array(data["f1"]),numpy.array(data["f2"]),numpy.array(data["d"]),data["adj"],fn+".decomp.acyclic.over.all.",widths=[6],vsdeg=False,nByi=data["nByi"],adj_list2=div_adj_list,directed=True)
#fiedler.doPlots(numpy.array(data["f1"]),-1*numpy.array(rank),numpy.array(data["d"]),cyclic_adj_list,fn+".decomp.harmonic.v.grad.",widths=[6],heights=[2],vsdeg=False,nByi=data["nByi"],directed=True)
#fiedler.doPlots(numpy.array(data["f1"]),-1*numpy.array(rank),numpy.array(data["d"]),skew,fn+".decomp.skew.v.grad.",widths=[6],heights=[2],vsdeg=False,nByi=data["nByi"],directed=True)
#fiedler.doPlots(numpy.array(data["f1"]),-1*numpy.array(rank),numpy.array(data["d"]),data["adj"],fn+".decomp.acyclic.over.all.v.grad.",widths=[6],heights=[2],vsdeg=False,nByi=data["nByi"],adj_list2=div_adj_list,directed=True)
fiedler.doPlots(numpy.array(data["f1"]),-1*numpy.array(rank),numpy.array(data["d"]),data["adj"],fn+".all.v.grad.",widths=[24],heights=[6],vsdeg=False,nByi=data["nByi"],directed=False)
col_span = list(remainder(
range(block_location[1], (block_location[1] + block_size[1])),
matrix_size))
for r, c in product(row_span, col_span):
M[r, c] = 1
Mcsr = csr_matrix(M); Mcsc = csc_matrix(M)
# The complex formation is ugly for readability but IMHO elegant for
# getting the job done !
row_complex = map(list, list(set(filter(None, [tuple(
Mcsr.indices[Mcsr.indptr[i]:Mcsr.indptr[i + 1]]
) for i in range(len(Mcsr.indptr) - 1)]))))
## row_complex += [[vertex] for vertex in list(set(list(chain(*row_complex))))]
row_vertex_set = [vertex for vertex in list(set(list(chain(*row_complex))))]
row_complex += [[v] for v in row_vertex_set]
row_complex = abstract_simplicial_complex(row_complex)
col_complex = map(list, list(set(filter(None, [tuple(
Mcsc.indices[Mcsc.indptr[i]:Mcsc.indptr[i + 1]]
) for i in range(len(Mcsc.indptr) - 1)]))))
## col_complex += [[vertex] for vertex in list(set(list(chain(*col_complex))))]
col_vertex_set = [vertex for vertex in list(set(list(chain(*col_complex))))]
col_complex += [[v] for v in col_vertex_set]
col_complex = abstract_simplicial_complex(col_complex)
evals_row_complex = []; evals_col_complex = []
for p in range(row_complex.complex_dimension()):
B_p = row_complex.chain_complex()[p]
B_pplus1 = row_complex.chain_complex()[p + 1]
laplacian_p = (B_p.T * B_p + B_pplus1 * B_pplus1.T)
evals_row_complex.append(eigvalsh(laplacian_p.todense()))
# Define the tolerance for determining when an eigenvale is "zero enough."
tol = 1e-7
# Now that we have the master data matrix assembled, we filter it, and at
# each level construct the user- and movie-complex, upon which we compute
# dim(ker(Laplacian_k)) for k ranging from 0 through top dimension.
print "Filtering data and computing Betti numbers..."
M_0 = 1*(M > 0) # used to filter out the non-rated films
for stars in [1,2,3,4,5]:
print stars
# Filter M and create filtered complexes.
M_filt = 1*(M <= stars) * M_0
user_tuple, movie_tuple = get_complexes(M_filt)
user_complex = abstract_simplicial_complex(user_tuple)
movie_complex = abstract_simplicial_complex(movie_tuple)
# Perform calculations on user complex Lalacians.
for k in range(user_complex.complex_dimension()):
b_low = user_complex.chain_complex()[k]
b_high = user_complex.chain_complex()[k+1]
Laplacian_k = (b_low.T * b_low + b_high * b_high.T).todense()
betti_k = get_dim_ker(Laplacian_k, tol)
user_results[k, stars-1] = betti_k
k = user_complex.complex_dimension()
b_low = user_complex.chain_complex()[k]
Laplacian_k = (b_low.T * b_low).todense()
betti_k = get_dim_ker(Laplacian_k, tol)
user_results[k, stars-1] = betti_k
