def test_faces():
"""check whether faces are correct"""
for mesh in meshes.itervalues():
sc = simplicial_complex(mesh)
for face_data, cell_data in zip(sc[:-1], sc[1:]):
#compute all faces and store in a set
boundary_set = set()
for row in cell_data.simplices:
boundary_set.update(simplex(row).boundary())
face_set = set([simplex(row) for row in face_data.simplices])
assert_equal(boundary_set, face_set)
def test_faces():
"""check whether faces are correct"""
for mesh in meshes.itervalues():
sc = simplicial_complex(mesh)
for face_data,cell_data in zip(sc[:-1],sc[1:]):
#compute all faces and store in a set
boundary_set = set()
for row in cell_data.simplices:
boundary_set.update(simplex(row).boundary())
face_set = set([simplex(row) for row in face_data.simplices])
assert_equal(boundary_set, face_set)
def test_simple(self):
V = array([[0,0],[1,0],[0,1]])
S = array([[0,1,2]])
sc = simplicial_complex((V,S))
rows,cols = massmatrix_rowcols(sc,0)
assert_equal(rows,array([0,0,0,1,1,1,2,2,2]))
assert_equal(cols,array([0,1,2,0,1,2,0,1,2]))
rows,cols = massmatrix_rowcols(sc,1)
edges = [simplex(x) for x in combinations(range(3),2)]
edge0 = sc[1].simplex_to_index[edges[0]]
edge1 = sc[1].simplex_to_index[edges[1]]
edge2 = sc[1].simplex_to_index[edges[2]]
assert_equal(rows,array([edge0,edge0,edge0,edge1,edge1,edge1,edge2,edge2,edge2]))
assert_equal(cols,array([edge0,edge1,edge2,edge0,edge1,edge2,edge0,edge1,edge2]))
rows,cols = massmatrix_rowcols(sc,2)
assert_equal(rows,array([0]))
assert_equal(cols,array([0]))
def test_simple(self):
V = array([[0, 0], [1, 0], [0, 1]])
S = array([[0, 1, 2]])
sc = simplicial_complex((V, S))
rows, cols = massmatrix_rowcols(sc, 0)
assert_equal(rows, array([0, 0, 0, 1, 1, 1, 2, 2, 2]))
assert_equal(cols, array([0, 1, 2, 0, 1, 2, 0, 1, 2]))
rows, cols = massmatrix_rowcols(sc, 1)
edges = [simplex(x) for x in combinations(range(3), 2)]
edge0 = sc[1].simplex_to_index[edges[0]]
edge1 = sc[1].simplex_to_index[edges[1]]
edge2 = sc[1].simplex_to_index[edges[2]]
assert_equal(
rows,
array([
edge0, edge0, edge0, edge1, edge1, edge1, edge2, edge2, edge2
]))
assert_equal(
cols,
array([
edge0, edge1, edge2, edge0, edge1, edge2, edge0, edge1, edge2
]))
rows, cols = massmatrix_rowcols(sc, 2)
assert_equal(rows, array([0]))
assert_equal(cols, array([0]))
def test_boundary():
"""check boundary operators (assumes correct faces)"""
for mesh in meshes.itervalues():
sc = simplicial_complex(mesh)
assert_equal(sc[0].boundary.shape, (1, sc[0].simplices.shape[0]))
assert_equal(sc[0].boundary.nnz, 0)
for face_data, cell_data in zip(sc[:-1], sc[1:]):
B = cell_data.boundary
assert_equal(B.shape,
(face_data.num_simplices, cell_data.num_simplices))
assert_equal(B.nnz, cell_data.num_simplices * (cell_data.dim + 1))
for row, parity in zip(cell_data.simplices,
cell_data.simplex_parity):
s = simplex(row)
s_index = cell_data.simplex_to_index[s]
for f in s.boundary():
f_index = face_data.simplex_to_index[f]
assert_equal(B[f_index, s_index],
(-1)**(f.parity ^ int(parity)))
def test_all(self):
for k,v,s,o,expected in self.cases:
sc = simplicial_complex((v,s))
M = whitney_innerproduct(sc,k)
M = M.todense()
#Permute the matrix to coincide with the ordering of the known matrix
permute = [sc[k].simplex_to_index[simplex(x)] for x in o]
M = M[permute,:][:,permute]
assert_almost_equal(M,expected)
#check whether matrix is S.P.D.
self.assert_(alltrue(isreal(eigvals(M))))
self.assert_(min(real(eigvals(M))) >= 0)
assert_almost_equal(M,M.T)
def test_all(self):
for k, v, s, o, expected in self.cases:
sc = simplicial_complex((v, s))
M = whitney_innerproduct(sc, k)
M = M.todense()
#Permute the matrix to coincide with the ordering of the known matrix
permute = [sc[k].simplex_to_index[simplex(x)] for x in o]
M = M[permute, :][:, permute]
assert_almost_equal(M, expected)
#check whether matrix is S.P.D.
self.assert_(alltrue(isreal(eigvals(M))))
self.assert_(min(real(eigvals(M))) >= 0)
assert_almost_equal(M, M.T)
def test_boundary():
"""check boundary operators (assumes correct faces)"""
for mesh in meshes.itervalues():
sc = simplicial_complex(mesh)
assert_equal(sc[0].boundary.shape,(1,sc[0].simplices.shape[0]))
assert_equal(sc[0].boundary.nnz,0)
for face_data,cell_data in zip(sc[:-1],sc[1:]):
B = cell_data.boundary
assert_equal(B.shape,(face_data.num_simplices,cell_data.num_simplices))
assert_equal(B.nnz,cell_data.num_simplices*(cell_data.dim+1))
for row,parity in zip(cell_data.simplices,cell_data.simplex_parity):
s = simplex(row)
s_index = cell_data.simplex_to_index[s]
for f in s.boundary():
f_index = face_data.simplex_to_index[f]
assert_equal(B[f_index,s_index],(-1)**(f.parity ^ int(parity)))
