# decompose 4 random 1-cochains
for i in range(4):
omega = sc.get_cochain(1)
omega.v[:] = rand(*omega.v.shape)
(beta, gamma, h) = hodge_decomposition(omega)
h = h.v
for v in H:
h -= inner(v, h) * v
h /= norm(h)
H.append(h)
H = ortho(vstack(H))
# plot the results
from pylab import figure, title, quiver, axis, show
from pydec import triplot, simplex_quivers
for n, h in enumerate(H):
figure()
title('Harmonic 1-cochain #%d' % n)
triplot(vertices, triangles)
bases, dirs = simplex_quivers(sc, h)
quiver(bases[:, 0], bases[:, 1], dirs[:, 0], dirs[:, 1])
axis('equal')
show()
#print 'norm(b2.T * h)', norm(b2.T * h) #should be small
# plot the results
from pylab import figure, title, plot, axis, xlim, ylim, show
from pydec import triplot, lineplot
# Nodes of the Rips complex
figure()
plot(pts[:, 0], pts[:, 1], 'ko')
axis('off')
title('Nodes of the Complex')
# Rips complex (2d triangle mesh)
figure()
title('The Rips Complex')
triplot(pts, simplices[2])
# Harmonic 1-chain
figure()
title('Harmonic 1-chain of the Rips complex')
lineplot(pts, simplices[1], linewidths=(15 * abs(h)).clip(1, 15))
# fiddle with the figures
for i in range(1, 4):
figure(i)
axis('off')
axis('equal')
xlim(-0.1, 1.1)
ylim(-0.1, 1.1)
show()
# plot the results
from pylab import figure, title, plot, axis, xlim, ylim, show
from pydec import triplot, lineplot
# Nodes of the Rips complex
figure()
plot(pts[:,0],pts[:,1],'ko')
axis('off')
title('Nodes of the Complex')
# Rips complex (2d triangle mesh)
figure()
title('The Rips Complex')
triplot(pts,simplices[2])
# Harmonic 1-chain
figure()
title('Harmonic 1-chain of the Rips complex')
lineplot(pts,simplices[1],linewidths=(15*abs(h)).clip(1,15) )
# fiddle with the figures
for i in range(1,4):
figure(i)
axis('off')
axis('equal')
xlim(-0.1,1.1)
ylim(-0.1,1.1)
show()
for i in range(4):
omega = sc.get_cochain(1)
omega.v[:] = rand(*omega.v.shape)
(beta,gamma,h) = hodge_decomposition(omega)
h = h.v
for v in H:
h -= inner(v,h) * v
h /= norm(h)
H.append(h)
H = ortho(vstack(H))
# plot the results
from pylab import figure, title, quiver, axis, show
from pydec import triplot, simplex_quivers
for n,h in enumerate(H):
figure()
title('Harmonic 1-cochain #%d' % n)
triplot(vertices,triangles)
bases,dirs = simplex_quivers(sc,h)
quiver(bases[:,0],bases[:,1],dirs[:,0],dirs[:,1])
axis('equal')
show()