def inject(self, weights):
"""map weights on curve to d2 form on sphere"""
brush = np.zeros(self.complex.shape, np.float) #brush is d2; it s a conserved quantity
util.scatter(
self.raveled_indices,
self.baries*weights[:,None],
brush)
return self.complex.boundify(brush)
def metric(self):
"""
calc metric properties and hodges; nicely vectorized
"""
topology = self.topology
#metrics
MP0 = np.ones (topology.P0)
MP1 = np.zeros(topology.P1)
MP2 = np.zeros(topology.P2)
MD0 = np.ones (topology.D0)
MD1 = np.zeros(topology.D1)
MD2 = np.zeros(topology.D2)
#precomputations
EVP = util.gather(topology.EVi, self.primal)
FEVP = util.gather(topology.FEi, EVP) #[faces, e3, v2, c3]
FEM = util.normalize(FEVP.sum(axis=2))
FEV = util.gather(topology.FEi, topology.EVi)
#calculate areas; devectorization over e makes things a little more elegant, by avoiding superfluous stacking
for e in xrange(3):
areas = triangle_area_from_corners(FEVP[:,e,0,:], FEVP[:,e,1,:], self.dual)
MP2 += areas #add contribution to primal face
util.scatter( #add contributions divided over left and right dual face
FEV[:,e,:], #get both verts of each edge
np.repeat(areas/2, 2), #half of domain area for both verts
MD2)
#calc edge lengths
MP1 += edge_length(EVP[:,0,:], EVP[:,1,:])
for e in xrange(3):
util.scatter(
topology.FEi[:,e],
edge_length(FEM[:,e,:], self.dual),
MD1)
#hodge operators
self.D2P0 = MD2 / MP0
self.P0D2 = MP0 / MD2
self.D1P1 = MD1 / MP1
self.P1D1 = MP1 / MD1
self.D0P2 = MD0 / MP2
self.P2D0 = MP2 / MD0
