def spectral_partition(W,q,method = 'complete', metric = 'cosine'):
n,m = W.shape
K = Kmatrix(W)
if n == m:
try:
e,v = linalg.eigen(K, q)
except TypeError:
e,v = linalg.eigs(K, q)
else:
try:
u,e,v = linalg.svds(K, q)
except AttributeError:
u,e,v = linalg.svd(K, q)
v = np.concatenate((u, v.T), 0)
max_index = e.argmax()
v = np.delete(v,max_index,1)
Obs = np.real(v)
D = distance.pdist(Obs,metric = metric)
D = np.multiply(D >= 0, D)
Z = linkage(D, method = method, metric = metric)
cluster = fcluster(Z, q, criterion = 'maxclust')
cluster += - 1
cluster = {'spectral' : cluster}
return cluster
def laplaceeigs(k,N,n):
import scipy.linalg as sl
tag = "B1"
elements = H1Elements(k)
quadrule = pyramidquadrature(k+1)
system = SymmetricSystem(elements, quadrule, lambda m: buildcubemesh(N, m, tag), [tag])
SM = system.systemMatrix(True)
S, SIBs, Gs = system.processBoundary(SM, {tag:lambda p: numpy.zeros((len(p),1))})
print S.shape
MM = system.systemMatrix(False)
M, _, _ = system.processBoundary(MM, {tag:lambda p: numpy.zeros((len(p),1))})
MLU = ssl.splu(M)
L = A = ssl.LinearOperator( M.shape, matvec=lambda x: MLU.solve(S* x), dtype=float)
return ssl.eigen(L, k=n, which='SM', return_eigenvectors=False)
vw=np.max(abs(W))
vl=np.max(abs(L))
figure(2, figsize=(6,3))
suptitle('Weight and Laplacian matrices')
subplot(1,2,1)
imshow(W, interpolation='nearest', cmap='RdBu', vmin=-vw, vmax=vw)
subplot(1,2,2)
imshow(L, interpolation='nearest', cmap='RdBu', vmin=-vl/20, vmax=vl/20)
savefig('spec2.png', dpi=100)
figure(3, figsize=(6,3))
lam,u = eigen(L , k=4, which='SR')
lamall,ulixo = eigen(L , k=10, which='SR')
lamall=real(lamall)
lam =real(lam)
u =real(u)
print lam
subplot(1,2,1)
title('First eigenvalues')
plot(sort(lamall), '-+')
subplot(1,2,2)
title('First eigenvectors')
plot(u[:,:4])
savefig('spec3.png', dpi=100)
