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 MDS(adj_list):
(A,adj,Npts) = fiedler.adj_mat(adj_list)
D = A.todense()
#converting to distance...may not work for importance scores
D = np.sqrt(1-np.abs(D))
#from Ryan Tasseff's cmdsAnalysis
[n,m] = D.shape
eps = 1E-21
if n!=m:
raise ValueError('Wrong size matrix')
# Construct an n x n centering matrix
# The form is P = I - (1/n) U where U is a matrix of all ones
P = np.eye(n) - (1/float(n) * np.ones((n,n)))
# center the data
B = np.dot(np.dot(P,-.5*D**2),P)
# if len(w)>0:
# W = np.diag(np.sqrt(w))
# B = np.dot(np.dot(W,B),W)
# Calculate the eigenvalues/vectors
[E, V] = linalg.eig((B+B.T)/2) # may help with round off error??
E = np.real(E) # these come out as complex but imaginary part should b ~eps
V = np.real(V) # same as above
# if len(w)>0:
# W = np.diag(1/np.sqrt(w))
# V = np.dot(W,V)
# sort that mo fo
ind = np.argsort(E)[::-1]
E = E[ind]
V = V[:,ind]
# lets now create our return matrix
if np.sum(E>eps)==0:
Y = 0
else:
Y = V[:,E>eps]*np.sqrt(E[E>eps])
return {"m1":list(Y[:,0]), "m2":list(Y[:,1])}
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)