def initial_lattice(self):
lattice = []
vertex_ref = cln.OrderedDict()
ref_vertex = cln.OrderedDict()
n = self.dim
for m in range(self.dim):
num = 2**(n - m) * self.ncr(n, m)
d = cln.OrderedDict()
for i in range(num):
id = rf.Refer(i)
d.update({id: [set(), set()]})
if m == 0:
vertex_ref.update({self.vertex[i]: id})
ref_vertex.update({id: self.vertex[i]})
lattice.append(d)
return lattice, vertex_ref, ref_vertex
def intersect_hss(self, m, n, aset):
set0 = set()
set1 = cp.copy(aset)
set2 = set()
hss = []
m_face = cln.OrderedDict()
for i in range(m, n + 1):
for ref in set1:
val_temp = cp.copy(self.lattice[i][ref])
set2.update(val_temp[1])
m_face.update({
ref: [
cp.copy(self.lattice[i][ref][0]),
cp.copy(self.lattice[i][ref][1])
]
})
val_temp2 = cp.copy(val_temp[0])
for r in val_temp2:
if r not in set0:
m_face[ref][0].remove(r)
hss.append(m_face)
m_face = cln.OrderedDict()
set0 = cp.copy(set1)
set1 = cp.copy(set2)
set2 = set()
# m == 1 when to find the intersected hss
if m == 1 and n >= 1:
new_ref = rf.Refer(-1)
new_facet = cln.OrderedDict({new_ref: [set(), set()]})
for ref in hss[n - 1].keys():
hss[n - 1][ref][1] = set([new_ref])
new_facet[new_ref][0].add(ref)
hss.append(new_facet)
return hss
def intersectPlane(self, idx):
# map the plane into lower dimension
a = self.M[idx, :]
d = self.b[idx, :]
new_pl = np.concatenate((a, d))
# insert ones to vertices matrix
start_time = time.time()
Varray = self.vertex
Varray1 = np.insert(Varray, Varray.shape[1], 1, axis=1)
Vsign = np.dot(Varray1, new_pl)
end_time = time.time() - start_time
# x1 = np.dot(self.M, Varray.transpose()) + self.b
# x255 = x1[255,:]
# x255p = len(x255[x255>=0])
# ********* no intersection *******************#
if np.all(Vsign <= 0):
return [], self, end_time
elif np.all(Vsign >= 0):
return self, [], end_time
# ********************************************#
ref_keys = list(self.ref_vertex.keys())
pVlist = [
ref_keys[idx] for idx in range(Vsign.shape[0]) if Vsign[idx] >= 0
]
sign_dict = cln.OrderedDict((el, 1) for el in pVlist)
nVlist = [
ref_keys[idx] for idx in range(Vsign.shape[0]) if Vsign[idx] <= 0
]
sign_dict.update(cln.OrderedDict((el, -1) for el in nVlist))
# ********** self.actual_dim==1 ***************#
if self.actual_dim == 1:
p0 = self.ref_vertex[pVlist[0]]
p1 = self.ref_vertex[nVlist[0]]
vvector = p1 - p0
interp = p0 - vvector * ((d + np.dot(p0, a.transpose())) /
(np.dot(vvector, a.transpose())))
self.vertex = np.concatenate((self.vertex, interp))
ref0 = rf.Refer(-1)
p_ref_vertex = cln.OrderedDict({pVlist[0]: p0, ref0: interp})
p_hss = [
cln.OrderedDict({
pVlist[0]: [set(), set()],
ref0: [set(), set()]
})
]
p_lattice = PolyLattice(p_hss, p_ref_vertex, 1, cp.copy(self.M),
cp.copy(self.b))
n_ref_vertex = cln.OrderedDict({nVlist[0]: p1, ref0: interp})
n_hss = [
cln.OrderedDict({
nVlist[0]: [set(), set()],
ref0: [set(), set()]
})
]
n_lattice = PolyLattice(n_hss, n_ref_vertex, 1, cp.copy(self.M),
cp.copy(self.b))
# ************* self.actual_dim>2 ***************#
# consider the smaller set
if len(pVlist) >= len(nVlist):
lessVlist = nVlist
sign_flag = 1
else:
lessVlist = pVlist
sign_flag = -1
f1_set = set() # store all the 1_face that intersects with plane
ref_interp = cln.OrderedDict()
for lessV in lessVlist:
for f1 in self.lattice[0][lessV][1]:
for f0 in self.lattice[1][f1][0]:
lessVn = f0
if sign_dict[lessVn] == sign_flag:
p0 = self.ref_vertex[lessV]
p1 = self.ref_vertex[lessVn]
vvector = p1 - p0
point = p0 - vvector * ((d + np.dot(p0, a)) /
(np.dot(vvector, a)))
pointxx = np.dot(self.M,
np.array([point
]).transpose()) + self.b
f1_set.add(f1)
# input new vertex
ref_interp.update({f1: point})
point = np.array([point])
self.vertex = np.append(self.vertex, point, axis=0)
# extract the intersected hss
orig_hss = self.intersect_hss(1, self.actual_dim - 1, f1_set)
# assign different memory address to the hss
new_hss = cp.deepcopy(orig_hss)
# insert the new hss to the orginal lattice
point_refs = self.insert_hss(orig_hss, new_hss, ref_interp)
pVlist.extend(point_refs)
nVlist.extend(point_refs)
n_lattice = self.extract_polylattice(nVlist, f1_set)
p_lattice = self.extract_polylattice(pVlist, f1_set)
return p_lattice, n_lattice, end_time
def intersectHalfspace(self, pl_a, pl_d):
# map the plane into lower dimension
a = np.dot(pl_a, self.M)
d = np.dot(pl_a, self.b) + pl_d
new_pl = np.concatenate((a, d))
# insert ones to vertices matrix
# Varray = np.array(self.vertex)
Varray = self.vertex
Varray1 = np.insert(Varray, Varray.shape[1], 1, axis=1)
# signs indicate vertex's side of plane
Vsign = np.dot(Varray1, new_pl)
ref_keys = list(self.ref_vertex.keys())
pVlist = [
ref_keys[idx] for idx in range(Vsign.shape[0]) if Vsign[idx] >= 0
]
sign_dict = cln.OrderedDict((el, 1) for el in pVlist)
nVlist = [
ref_keys[idx] for idx in range(Vsign.shape[0]) if Vsign[idx] <= 0
]
sign_dict.update(cln.OrderedDict((el, -1) for el in nVlist))
# ********* no intersection *******************#
if not pVlist:
return self
elif not nVlist:
return None
# ********** self.actual_dim==1 ***************#
if self.actual_dim == 1:
p0 = self.ref_vertex[pVlist[0]]
p1 = self.ref_vertex[nVlist[0]]
vvector = p1 - p0
interp = p0 - vvector * ((d + np.dot(p0, a.transpose())) /
(np.dot(vvector, a.transpose())))
interp = np.array([interp])
self.vertex = np.append(self.vertex, interp, axis=0)
ref0 = rf.Refer(-1)
n_ref_vertex = cln.OrderedDict({nVlist[0]: p1, ref0: interp})
n_hss = [
cln.OrderedDict({
nVlist[0]: [set(), set()],
ref0: [set(), set()]
})
]
n_vertex = np.concatenate((p1, interp), axis=0)
n_lattice = PolyLattice(n_hss, n_ref_vertex, n_vertex, 1,
cp.copy(self.M), cp.copy(self.b))
return n_lattice
# ************* self.actual_dim>2 ***************#
# consider the smaller set
if len(pVlist) >= len(nVlist):
lessVlist = nVlist
sign_flag = 1
else:
lessVlist = pVlist
sign_flag = -1
f1_set = set() # store all the 1_face that intersects with plane
ref_interp = cln.OrderedDict()
for lessV in lessVlist:
for f1 in self.lattice[0][lessV][1]:
for f0 in self.lattice[1][f1][0]:
lessVn = f0
if sign_dict[lessVn] == sign_flag:
p0 = self.ref_vertex[lessV]
p1 = self.ref_vertex[lessVn]
vvector = p1 - p0
point = p0 - vvector * ((d + np.dot(p0, a)) /
(np.dot(vvector, a)))
f1_set.add(f1)
# input new vertex
ref_interp.update({f1: point})
point = np.array([point])
self.vertex = np.append(self.vertex, point, axis=0)
# extract the intersected hss
orig_hss = self.intersect_hss(1, self.actual_dim - 1, f1_set)
# self.test_face_num(self.lattice)
# self.test_face_num(orig_hss)
# assign different memory address to the hss
new_hss = cp.deepcopy(orig_hss)
# insert the new hss to the orginal lattice
point_refs = self.insert_hss(orig_hss, new_hss, ref_interp)
# pVlist.extend(point_refs)
nVlist.extend(point_refs)
n_lattice = self.extract_polylattice(nVlist, f1_set)
return n_lattice
def intersectPlane_mnist(self, idx):
a = np.zeros(self.vertex.shape[1])
a[idx] = 1
d = np.array([0])
vertex = self.vertex
if np.all(vertex[:, idx] >= 0):
return self, []
elif np.all(vertex[:, idx] <= 0):
return [], self
ref_keys = list(self.ref_vertex.keys())
pVlist = [
ref_keys[i] for i in range(vertex.shape[0]) if vertex[i, idx] >= 0
]
sign_dict = cln.OrderedDict((el, 1) for el in pVlist)
nVlist = [
ref_keys[i] for i in range(vertex.shape[0]) if vertex[i, idx] <= 0
]
sign_dict.update(cln.OrderedDict((el, -1) for el in nVlist))
# ********** self.actual_dim==1 ***************#
if self.actual_dim == 1:
p0 = self.ref_vertex[pVlist[0]]
p1 = self.ref_vertex[nVlist[0]]
vvector = p1 - p0
interp = p0 + vvector * np.abs((p0[idx]) / vvector[idx])
self.vertex = np.concatenate((self.vertex, interp))
ref0 = rf.Refer(-1)
p_ref_vertex = cln.OrderedDict({pVlist[0]: p0, ref0: interp})
p_hss = [
cln.OrderedDict({
pVlist[0]: [set(), set()],
ref0: [set(), set()]
})
]
p_lattice = PolyLattice(p_hss, p_ref_vertex, 1, cp.copy(self.M),
cp.copy(self.b))
n_ref_vertex = cln.OrderedDict({nVlist[0]: p1, ref0: interp})
n_hss = [
cln.OrderedDict({
nVlist[0]: [set(), set()],
ref0: [set(), set()]
})
]
n_lattice = PolyLattice(n_hss, n_ref_vertex, 1, cp.copy(self.M),
cp.copy(self.b))
return p_lattice, n_lattice
# ************* self.actual_dim>2 ***************#
# consider the smaller set
if len(pVlist) >= len(nVlist):
lessVlist = nVlist
sign_flag = 1
else:
lessVlist = pVlist
sign_flag = -1
f1_set = set() # store all the 1_face that intersects with plane
ref_interp = cln.OrderedDict()
for lessV in lessVlist:
for f1 in self.lattice[0][lessV][1]:
for f0 in self.lattice[1][f1][0]:
lessVn = f0
if sign_dict[lessVn] == sign_flag:
p0 = self.ref_vertex[lessV]
p1 = self.ref_vertex[lessVn]
vvector = p1 - p0
point = p0 + vvector * np.abs((p0[idx]) / vvector[idx])
# point = p0 - vvector * ((d + np.dot(p0, a)) / (np.dot(vvector, a)))
f1_set.add(f1)
# input new vertex
ref_interp.update({f1: point})
point = np.array([point])
self.vertex = np.append(self.vertex, point, axis=0)
# extract the intersected hss
orig_hss = self.intersect_hss(1, self.actual_dim - 1, f1_set)
# assign different memory address to the hss
new_hss = cp.deepcopy(orig_hss)
# insert the new hss to the orginal lattice
point_refs = self.insert_hss(orig_hss, new_hss, ref_interp)
pVlist.extend(point_refs)
nVlist.extend(point_refs)
n_lattice = self.extract_polylattice(nVlist, f1_set)
p_lattice = self.extract_polylattice(pVlist, f1_set)
return p_lattice, n_lattice