def test_random_3d(self):
N = 200
R = 0.25
pts = rand(N, 3)
rc = rips_complex(pts, R)
edges = set([tuple(e) for e in rc.simplices[1]])
for i in range(N):
for j in range(i + 1, N):
if norm(pts[i] - pts[j]) < R:
assert ((i, j) in edges)
else:
assert ((i, j) not in edges)
for t in rc.simplices[2]:
for i, j in [(0, 1), (0, 2), (1, 2)]:
assert ((t[i], t[j]) in edges)
for t in rc.simplices[3]:
for i, j in [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]:
assert ((t[i], t[j]) in edges)
ensure_complex_exactness(rc)
def test_random_3d(self):
N = 200
R = 0.25
pts = rand(N,3)
rc = rips_complex( pts, R )
edges = set( [tuple(e) for e in rc.simplices[1]] )
for i in range(N):
for j in range(i+1,N):
if norm(pts[i] - pts[j]) < R:
assert( (i,j) in edges )
else:
assert( (i,j) not in edges )
for t in rc.simplices[2]:
for i,j in [(0,1),(0,2),(1,2)]:
assert( (t[i],t[j]) in edges )
for t in rc.simplices[3]:
for i,j in [(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)]:
assert( (t[i],t[j]) in edges )
ensure_complex_exactness(rc)
"""
Detection of holes in coverage in an idealized abstraction of a sensor
network. Hodge decomposition of a random cochain is used to compute a
harmonic cochain.
"""
from scipy import rand
from scipy.linalg import norm
from scipy.sparse.linalg import cg
from pydec import kd_tree, flatten, triplot, read_array
from pydec.dec.rips_complex import rips_complex
pts = read_array('300pts.mtx') # 300 random points in 2D
rc = rips_complex( pts, 0.15 )
simplices = rc.simplices
cmplx = rc.chain_complex() # boundary operators [ b0, b1, b2 ]
b1 = cmplx[1].astype(float) # edge boundary operator
b2 = cmplx[2].astype(float) # face boundary operator
x = rand(b1.shape[1]) # random 1-chain
# Decompose x using discrete Hodge decomposition
alpha = cg( b1 * b1.T, b1 * x, tol=1e-8)[0]
beta = cg( b2.T * b2, b2.T * x, tol=1e-8)[0]
h = x - (b1.T * alpha) - (b2 * beta) # harmonic component of x
h /= abs(h).max() # normalize h
"""
Detection of holes in coverage in an idealized abstraction of a sensor
network. Hodge decomposition of a random cochain is used to compute a
harmonic cochain.
"""
from scipy import rand
from scipy.linalg import norm
from scipy.sparse.linalg import cg
from pydec import kd_tree, flatten, triplot, read_array
from pydec.dec.rips_complex import rips_complex
pts = read_array('300pts.mtx') # 300 random points in 2D
rc = rips_complex(pts, 0.15)
simplices = rc.simplices
cmplx = rc.chain_complex() # boundary operators [ b0, b1, b2 ]
b1 = cmplx[1].astype(float) # edge boundary operator
b2 = cmplx[2].astype(float) # face boundary operator
x = rand(b1.shape[1]) # random 1-chain
# Decompose x using discrete Hodge decomposition
alpha = cg(b1 * b1.T, b1 * x, tol=1e-8)[0]
beta = cg(b2.T * b2, b2.T * x, tol=1e-8)[0]
h = x - (b1.T * alpha) - (b2 * beta) # harmonic component of x
h /= abs(h).max() # normalize h
#print 'norm( h )',norm(h)
#print 'norm(b1 * h)', norm(b1 * h) #should be small