def get_chiral_diff(self, edges, arc1, arc2, count=[]):
narcs1 = normalized_vectors(arc1)
narcs2 = normalized_vectors(arc2)
### DEBUG
#atoms = ["H", "F", "He", "Cl", "N", "O"]
R = rotation_from_vectors(narcs2, narcs1)
#FIXME(pboyd): ensure that this is the right rotation!!! I think it's supposed to rotate narcs2
narcs1 = (np.dot(R[:3,:3], narcs1.T)).T
#narcs2 = (np.dot(R[:3,:3], narcs2.T)).T
#or1 = np.zeros(3)
#or2 = np.array([3., 3., 0.])
#xyz_str1 = "C %9.5f %9.5f %9.5f\n"%(or1[0], or1[1], or1[2])
#xyz_str2 = "C %9.5f %9.5f %9.5f\n"%(or2[0], or2[1], or2[2])
#for ind, (i, j) in enumerate(zip(narcs1,narcs2)):
# at = atoms[ind]
# pos = i[:3] + or1
# xyz_str1 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
# pos = j + or2
# xyz_str2 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
#xyz_file = open("debugging.xyz", 'a')
#xyz_file.writelines("%i\ndebug\n"%(len(narcs1)*2+2))
#xyz_file.writelines(xyz_str1)
#xyz_file.writelines(xyz_str2)
#xyz_file.close()
### DEBUG
#CI_1 = self.chiral_invariant(edges, narcs1)
#CI_2 = self.chiral_invariant(edges, narcs2)
#count.append(1)
#ff = open("CI1", 'a')
#ff.writelines('%i %e\n'%(len(count), CI_1))
#ff.close()
#ff = open("CI2", 'a')
#ff.writelines('%i %e\n'%(len(count), CI_2))
#ff.close()
#print 'edge assignment ', ','.join([p[2] for p in edges])
#print 'lattice arcs CI ', CI_1
#print 'connect point CI ', CI_2
#if all(item >= 0 for item in (CI_1, CI_2)) or all(item < 0 for item in (CI_1, CI_2)):
# return np.absolute(CI_1 - CI_2)
#else:
# return 150000.
return np.sum(np.absolute((narcs1 - narcs2).flatten()))
def get_chiral_diff(self, edges, arc1, arc2, count=[]):
narcs1 = normalized_vectors(arc1)
narcs2 = normalized_vectors(arc2)
### DEBUG
#atoms = ["H", "F", "He", "Cl", "N", "O"]
R = rotation_from_vectors(narcs2, narcs1)
#FIXME(pboyd): ensure that this is the right rotation!!! I think it's supposed to rotate narcs2
narcs1 = (np.dot(R[:3,:3], narcs1.T)).T
#narcs2 = (np.dot(R[:3,:3], narcs2.T)).T
#or1 = np.zeros(3)
#or2 = np.array([3., 3., 0.])
#xyz_str1 = "C %9.5f %9.5f %9.5f\n"%(or1[0], or1[1], or1[2])
#xyz_str2 = "C %9.5f %9.5f %9.5f\n"%(or2[0], or2[1], or2[2])
#for ind, (i, j) in enumerate(zip(narcs1,narcs2)):
# at = atoms[ind]
# pos = i[:3] + or1
# xyz_str1 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
# pos = j + or2
# xyz_str2 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
#xyz_file = open("debugging.xyz", 'a')
#xyz_file.writelines("%i\ndebug\n"%(len(narcs1)*2+2))
#xyz_file.writelines(xyz_str1)
#xyz_file.writelines(xyz_str2)
#xyz_file.close()
### DEBUG
#CI_1 = self.chiral_invariant(edges, narcs1)
#CI_2 = self.chiral_invariant(edges, narcs2)
#count.append(1)
#ff = open("CI1", 'a')
#ff.writelines('%i %e\n'%(len(count), CI_1))
#ff.close()
#ff = open("CI2", 'a')
#ff.writelines('%i %e\n'%(len(count), CI_2))
#ff.close()
#print 'edge assignment ', ','.join([p[2] for p in edges])
#print 'lattice arcs CI ', CI_1
#print 'connect point CI ', CI_2
#if all(item >= 0 for item in (CI_1, CI_2)) or all(item < 0 for item in (CI_1, CI_2)):
# return np.absolute(CI_1 - CI_2)
#else:
# return 150000.
return np.sum(np.absolute((narcs1 - narcs2).flatten()))
def closest_match_vertices(self, sbu):
g = self._net.graph
if sbu.two_connected and not sbu.linear:
cp_v = normalized_vectors([
self.vector_from_cp_intersecting_pt(cp, sbu) for
cp in sbu.connect_points])
else:
cp_v = normalized_vectors([self.vector_from_cp_SBU(cp, sbu) for
cp in sbu.connect_points])
ipv = self.scaled_ipmatrix(np.inner(cp_v, cp_v))
inds = np.triu_indices(ipv.shape[0], k=1)
max, min = np.absolute(ipv[inds]).max(), np.absolute(ipv[inds]).min()
cmatch = []
for v in self.sbu_vertices:
ee = self._net.neighbours(v)
l_arcs = self._net.lattice_arcs[self._net.return_indices(ee)]
lai = np.dot(np.dot(l_arcs, self._net.metric_tensor), l_arcs.T)
ipc = self.scaled_ipmatrix(lai)
imax, imin = np.absolute(ipc[inds]).max(), np.absolute(ipc[inds]).min()
mm = np.sum(np.absolute([max-imax, min-imin]))
cmatch.append((mm, v))
return sorted(cmatch)
def closest_match_vertices(self, sbu):
g = self._net.graph
if sbu.two_connected and not sbu.linear:
cp_v = normalized_vectors([
self.vector_from_cp_intersecting_pt(cp, sbu) for
cp in sbu.connect_points])
else:
cp_v = normalized_vectors([self.vector_from_cp_SBU(cp, sbu) for
cp in sbu.connect_points])
ipv = self.scaled_ipmatrix(np.inner(cp_v, cp_v))
inds = np.triu_indices(ipv.shape[0], k=1)
max, min = np.absolute(ipv[inds]).max(), np.absolute(ipv[inds]).min()
cmatch = []
for v in self.sbu_vertices:
ee = self._net.neighbours(v)
l_arcs = self._net.lattice_arcs[self._net.return_indices(ee)]
lai = np.dot(np.dot(l_arcs, self._net.metric_tensor), l_arcs.T)
ipc = self.scaled_ipmatrix(lai)
imax, imin = np.absolute(ipc[inds]).max(), np.absolute(ipc[inds]).min()
mm = np.sum(np.absolute([max-imax, min-imin]))
cmatch.append((mm, v))
return sorted(cmatch)
def report_errors(self, sbu_vects, arcs, rot_mat):
rotation = np.dot(rot_mat[:3,:3], sbu_vects.T)
v = normalized_vectors(rotation.T)
angles = np.array([calc_angle(v1, v2) for v1, v2 in zip(v, arcs)])
mean, std = np.mean(angles), np.std(angles)
return mean, std
def sbu_orient(self, v, cell):
"""Least squares optimization of orientation matrix.
Obtained from:
Soderkvist & Wedin
'Determining the movements of the skeleton using well configured markers'
J. Biomech. 26, 12, 1993, 1473-1477.
DOI: 10.1016/0021-9290(93)90098-Y"""
g = self._net.graph
sbu = self._vertex_sbu[v]
edges = self._net.neighbours(v)
debug("Orienting SBU: %i, %s on vertex %s"%(sbu.identifier, sbu.name, v))
# re-index the edges to match the order of the connect points in the sbu list
indexed_edges = sbu.edge_assignments
coefficients = np.array([1. if e in self._net.out_edges(v) else -1. for e in indexed_edges])
if len(indexed_edges) != sbu.degree:
error("There was an error assigning edges "+
"to the sbu %s"%(sbu.name))
Terminate(errcode=1)
inds = self._net.return_indices(indexed_edges)
la = self._net.lattice_arcs[inds]
if self._net.ndim == 2:
la = np.hstack((la, np.zeros((la.shape[0], 1))))
arcs = np.dot(la, cell)
arcs = normalized_vectors(arcs) * coefficients[:, None]
sbu_vects = normalized_vectors(np.array([self.vector_from_cp_SBU(cp, sbu)
for cp in sbu.connect_points]))
#print np.dot(arcs, arcs.T)
#sf = self._net.scale_factor
#la = self._net.lattice_arcs
#mt = self._net.metric_tensor/sf
#obj = la*mt*la.T
#print obj
# issue for ditopic SBUs where the inner product matrices could invert the
# angles (particularly for ZIFs)
if sbu.degree == 2 and not sbu.linear:
sbu_vects = normalized_vectors(np.array([
self.vector_from_cp_intersecting_pt(cp, sbu)
for cp in sbu.connect_points]))
# define the plane generated by the edges
#print "arc angle %9.5f"%(180.*calc_angle(*arcs)/np.pi)
#print "sbu angle %9.5f"%(180.*calc_angle(*sbu_vects)/np.pi)
# For some reason the least squares rotation matrix
# does not work well with just two vectors, so a third
# orthonormal vector is included to create the proper
# rotation matrix
arc3 = np.cross(arcs[0], arcs[1])
arc3 /= np.linalg.norm(arc3)
cp3 = np.cross(sbu_vects[0], sbu_vects[1])
cp3 /= np.linalg.norm(cp3)
sbu_vects = np.vstack((sbu_vects, cp3))
arcs = np.vstack((arcs, arc3))
R = rotation_from_vectors(sbu_vects, arcs)
mean, std = self.report_errors(sbu_vects, arcs, rot_mat=R)
### DEBUGGGGGG
#or1 = np.zeros(3)
#or2 = np.array([3., 3., 0.])
#xyz_str1 = "C %9.5f %9.5f %9.5f\n"%(or1[0], or1[1], or1[2])
#xyz_str2 = "C %9.5f %9.5f %9.5f\n"%(or2[0], or2[1], or2[2])
#atms = ["H", "F", "O", "He", "N", "Cl"]
#sbu_rot_vects = np.dot(R[:3,:3], sbu_vects.T)
#for ind, (i, j) in enumerate(zip(arcs, sbu_rot_vects.T)):
# at = atms[ind]
# pos = i + or1
# xyz_str1 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
# pos = j + or2
# xyz_str2 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
#xyz_file = open("debug_rotation_function.xyz", 'a')
#xyz_file.writelines("%i\ndebug\n"%(len(sbu_rot_vects.T)*2+2))
#xyz_file.writelines(xyz_str1)
#xyz_file.writelines(xyz_str2)
#xyz_file.close()
### DEBUGGGGGG
mean, std = self.report_errors(sbu_vects, arcs, rot_mat=R)
debug("Average orientation error: %12.6f +/- %9.6f degrees"%(mean/DEG2RAD, std/DEG2RAD))
sbu.rotate(R)
def assign_edge_labels(self, vertex):
"""Edge assignment is geometry dependent. This will try to
find the best assignment based on inner product comparison
with the non-placed lattice arcs."""
sbu = self._vertex_sbu[vertex]
local_arcs = sbu.connect_points
edges = self._net.neighbours(vertex)
indices = self._net.return_indices(edges)
lattice_arcs = self._net.lattice_arcs
e_assign = {}
if sbu.two_connected and not sbu.linear:
vects = [self.vector_from_cp_intersecting_pt(cp, sbu) for cp in local_arcs]
else:
vects = [self.vector_from_cp_SBU(cp, sbu) for cp in local_arcs]
norm_cp = normalized_vectors(vects)
li = self.normalized_ipmatrix(vects)
min, chi_diff=15000., 15000.
cc, assign = None, None
# print("hi1")
debug("%s assigned to %s"%(sbu.name, vertex))
# print("hi2")
cell = Cell()
cell.mkcell(self._net.get_3d_params())
if self._net.ndim == 2:
lattice_arcs = np.hstack((lattice_arcs, np.zeros((lattice_arcs.shape[0],1))))
lattice_vects = np.dot(lattice_arcs, cell.lattice)
count = 0
# print("hi1")
print('Number of edges {}'.format(len(edges)))
print(edges)
for i, e in enumerate(itertools.combinations(edges, len(edges))):
print(e)
count += 1
indices = self._net.return_indices(e)
#node_arcs = lattice_arcs[indices]*\
# self._net.metric_tensor*lattice_arcs[indices].T
#max = node_arcs.max()
#la = np.empty((len(indices),len(indices)))
#for (i,j), val in np.ndenumerate(node_arcs):
# if i==j:
# la[i,j] = val/max
# else:
# v = val/np.sqrt(node_arcs[i,i])/np.sqrt(node_arcs[j,j])
# la[i,j] = v
# la[j,i] = v
# using tensor product of the incidences
coeff = np.array([-1. if j in self._net.in_edges(vertex)
else 1. for j in e])
#td = np.tensordot(coeff, coeff, axes=0)
#diff = np.multiply(li, td) - la
#inds = np.triu_indices(diff.shape[0], k=1)
#xmax, xmin = np.absolute(diff[inds]).max(), np.absolute(diff[inds]).min()
#mm = np.sum(diff)
#mm = np.sum(np.absolute(np.multiply(li,td) - la))
# NB Chirality matters!!!
# get the cell
lv_arc = (np.array(lattice_vects[indices])
* coeff[:, None])
# get the lattice arcs
mm = self.get_chiral_diff(e, lv_arc, vects)
print("hi1")
print(i,mm)
#norm_arc = normalized_vectors(lv_arc)
# orient the lattice arcs to the first sbu vector...
#print count , self.chiral_match(e, oriented_arc, norm_cp)
#print count, np.allclose(norm_cp, oriented_arc, atol=0.01)
#or1 = np.zeros(3)
#or2 = np.array([3., 3., 0.])
#xyz_str1 = "C %9.5f %9.5f %9.5f\n"%(or1[0], or1[1], or1[2])
#xyz_str2 = "C %9.5f %9.5f %9.5f\n"%(or2[0], or2[1], or2[2])
#for ind, (i, j) in enumerate(zip(norm_cp,oriented_arc)):
# at = atoms[ind]
# pos = i[:3] + or1
# xyz_str1 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
# pos = j + or2
# xyz_str2 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
#xyz_file = open("debugging.xyz", 'a')
#xyz_file.writelines("%i\ndebug\n"%(len(norm_cp)*2+2))
#xyz_file.writelines(xyz_str1)
#xyz_file.writelines(xyz_str2)
#xyz_file.close()
#print "arc CI", CI_ar, "cp CI", CI_cp
#if (mm < min) and (diff < chi_diff):
#print("hi1")
if (mm <= min):# and self.chiral_match(e, norm_arc, norm_cp):#, tol=xmax):
min = mm
print("mm smaller min")
assign = e
else:
print('mm larger min')
#CI = self.chiral_invariant(assign, norm_arc)
#axis = np.array([1., 3., 1.])
#angle = np.pi/3.
#R = rotation_matrix(axis, angle)
#new_norm = np.dot(R[:3,:3], norm_arc.T)
#nCI = self.chiral_invariant(assign, new_norm.T)
#print "Rotation invariant?", CI, nCI
# NB special MULT function for connect points
#print("hi1")
cp_vert = [i[0] if i[0] != vertex else i[1] for i in assign]
#print 'CI diff', chi_diff
#print 'tensor diff', mm
#print("hi1")
sbu.edge_assignments = assign
for cp, v in zip(local_arcs, cp_vert):
cp.vertex_assign = v
def normalized_ipmatrix(self, vectors):
v = normalized_vectors(vectors)
return np.inner(v,v)
def report_errors(self, sbu_vects, arcs, rot_mat):
rotation = np.dot(rot_mat[:3,:3], sbu_vects.T)
v = normalized_vectors(rotation.T)
angles = np.array([calc_angle(v1, v2) for v1, v2 in zip(v, arcs)])
mean, std = np.mean(angles), np.std(angles)
return mean, std
def sbu_orient(self, v, cell):
"""Least squares optimization of orientation matrix.
Obtained from:
Soderkvist & Wedin
'Determining the movements of the skeleton using well configured markers'
J. Biomech. 26, 12, 1993, 1473-1477.
DOI: 10.1016/0021-9290(93)90098-Y"""
g = self._net.graph
sbu = self._vertex_sbu[v]
edges = self._net.neighbours(v)
debug("Orienting SBU: %i, %s on vertex %s"%(sbu.identifier, sbu.name, v))
# re-index the edges to match the order of the connect points in the sbu list
indexed_edges = sbu.edge_assignments
coefficients = np.array([1. if e in self._net.out_edges(v) else -1. for e in indexed_edges])
if len(indexed_edges) != sbu.degree:
error("There was an error assigning edges "+
"to the sbu %s"%(sbu.name))
Terminate(errcode=1)
inds = self._net.return_indices(indexed_edges)
la = self._net.lattice_arcs[inds]
if self._net.ndim == 2:
la = np.hstack((la, np.zeros((la.shape[0], 1))))
arcs = np.dot(la, cell)
arcs = normalized_vectors(arcs) * coefficients[:, None]
sbu_vects = normalized_vectors(np.array([self.vector_from_cp_SBU(cp, sbu)
for cp in sbu.connect_points]))
#print np.dot(arcs, arcs.T)
#sf = self._net.scale_factor
#la = self._net.lattice_arcs
#mt = self._net.metric_tensor/sf
#obj = la*mt*la.T
#print obj
# issue for ditopic SBUs where the inner product matrices could invert the
# angles (particularly for ZIFs)
if sbu.degree == 2 and not sbu.linear:
sbu_vects = normalized_vectors(np.array([
self.vector_from_cp_intersecting_pt(cp, sbu)
for cp in sbu.connect_points]))
# define the plane generated by the edges
#print "arc angle %9.5f"%(180.*calc_angle(*arcs)/np.pi)
#print "sbu angle %9.5f"%(180.*calc_angle(*sbu_vects)/np.pi)
# For some reason the least squares rotation matrix
# does not work well with just two vectors, so a third
# orthonormal vector is included to create the proper
# rotation matrix
arc3 = np.cross(arcs[0], arcs[1])
arc3 /= np.linalg.norm(arc3)
cp3 = np.cross(sbu_vects[0], sbu_vects[1])
cp3 /= np.linalg.norm(cp3)
sbu_vects = np.vstack((sbu_vects, cp3))
arcs = np.vstack((arcs, arc3))
R = rotation_from_vectors(sbu_vects, arcs)
mean, std = self.report_errors(sbu_vects, arcs, rot_mat=R)
### DEBUGGGGGG
#or1 = np.zeros(3)
#or2 = np.array([3., 3., 0.])
#xyz_str1 = "C %9.5f %9.5f %9.5f\n"%(or1[0], or1[1], or1[2])
#xyz_str2 = "C %9.5f %9.5f %9.5f\n"%(or2[0], or2[1], or2[2])
#atms = ["H", "F", "O", "He", "N", "Cl"]
#sbu_rot_vects = np.dot(R[:3,:3], sbu_vects.T)
#for ind, (i, j) in enumerate(zip(arcs, sbu_rot_vects.T)):
# at = atms[ind]
# pos = i + or1
# xyz_str1 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
# pos = j + or2
# xyz_str2 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
#xyz_file = open("debug_rotation_function.xyz", 'a')
#xyz_file.writelines("%i\ndebug\n"%(len(sbu_rot_vects.T)*2+2))
#xyz_file.writelines(xyz_str1)
#xyz_file.writelines(xyz_str2)
#xyz_file.close()
### DEBUGGGGGG
mean, std = self.report_errors(sbu_vects, arcs, rot_mat=R)
debug("Average orientation error: %12.6f +/- %9.6f degrees"%(mean/DEG2RAD, std/DEG2RAD))
sbu.rotate(R)
def assign_edge_labels(self, vertex):
"""Edge assignment is geometry dependent. This will try to
find the best assignment based on inner product comparison
with the non-placed lattice arcs."""
sbu = self._vertex_sbu[vertex]
local_arcs = sbu.connect_points
edges = self._net.neighbours(vertex)
indices = self._net.return_indices(edges)
lattice_arcs = self._net.lattice_arcs
e_assign = {}
if sbu.two_connected and not sbu.linear:
vects = [self.vector_from_cp_intersecting_pt(cp, sbu) for cp in local_arcs]
else:
vects = [self.vector_from_cp_SBU(cp, sbu) for cp in local_arcs]
norm_cp = normalized_vectors(vects)
li = self.normalized_ipmatrix(vects)
min, chi_diff=15000., 15000.
cc, assign = None, None
debug("%s assigned to %s"%(sbu.name, vertex))
cell = Cell()
cell.mkcell(self._net.get_3d_params())
if self._net.ndim == 2:
lattice_arcs = np.hstack((lattice_arcs, np.zeros((lattice_arcs.shape[0],1))))
lattice_vects = np.dot(lattice_arcs, cell.lattice)
count = 0
for e in itertools.permutations(edges):
count += 1
indices = self._net.return_indices(e)
#node_arcs = lattice_arcs[indices]*\
# self._net.metric_tensor*lattice_arcs[indices].T
#max = node_arcs.max()
#la = np.empty((len(indices),len(indices)))
#for (i,j), val in np.ndenumerate(node_arcs):
# if i==j:
# la[i,j] = val/max
# else:
# v = val/np.sqrt(node_arcs[i,i])/np.sqrt(node_arcs[j,j])
# la[i,j] = v
# la[j,i] = v
# using tensor product of the incidences
coeff = np.array([-1. if j in self._net.in_edges(vertex)
else 1. for j in e])
#td = np.tensordot(coeff, coeff, axes=0)
#diff = np.multiply(li, td) - la
#inds = np.triu_indices(diff.shape[0], k=1)
#xmax, xmin = np.absolute(diff[inds]).max(), np.absolute(diff[inds]).min()
#mm = np.sum(diff)
#mm = np.sum(np.absolute(np.multiply(li,td) - la))
# NB Chirality matters!!!
# get the cell
lv_arc = (np.array(lattice_vects[indices])
* coeff[:, None])
# get the lattice arcs
mm = self.get_chiral_diff(e, lv_arc, vects)
#norm_arc = normalized_vectors(lv_arc)
# orient the lattice arcs to the first sbu vector...
#print count , self.chiral_match(e, oriented_arc, norm_cp)
#print count, np.allclose(norm_cp, oriented_arc, atol=0.01)
#or1 = np.zeros(3)
#or2 = np.array([3., 3., 0.])
#xyz_str1 = "C %9.5f %9.5f %9.5f\n"%(or1[0], or1[1], or1[2])
#xyz_str2 = "C %9.5f %9.5f %9.5f\n"%(or2[0], or2[1], or2[2])
#for ind, (i, j) in enumerate(zip(norm_cp,oriented_arc)):
# at = atoms[ind]
# pos = i[:3] + or1
# xyz_str1 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
# pos = j + or2
# xyz_str2 += "%s %9.5f %9.5f %9.5f\n"%(at, pos[0], pos[1], pos[2])
#xyz_file = open("debugging.xyz", 'a')
#xyz_file.writelines("%i\ndebug\n"%(len(norm_cp)*2+2))
#xyz_file.writelines(xyz_str1)
#xyz_file.writelines(xyz_str2)
#xyz_file.close()
#print "arc CI", CI_ar, "cp CI", CI_cp
#if (mm < min) and (diff < chi_diff):
if (mm <= min):# and self.chiral_match(e, norm_arc, norm_cp):#, tol=xmax):
min = mm
assign = e
#CI = self.chiral_invariant(assign, norm_arc)
#axis = np.array([1., 3., 1.])
#angle = np.pi/3.
#R = rotation_matrix(axis, angle)
#new_norm = np.dot(R[:3,:3], norm_arc.T)
#nCI = self.chiral_invariant(assign, new_norm.T)
#print "Rotation invariant?", CI, nCI
# NB special MULT function for connect points
cp_vert = [i[0] if i[0] != vertex else i[1] for i in assign]
#print 'CI diff', chi_diff
#print 'tensor diff', mm
sbu.edge_assignments = assign
for cp, v in zip(local_arcs, cp_vert):
cp.vertex_assign = v
def normalized_ipmatrix(self, vectors):
v = normalized_vectors(vectors)
return np.inner(v,v)