def compute_data(self):
"""Compute the convex hull and associated data"""
self.edges = set()
self.point_edges = [[] for i in range(len(self.points))]
self.edge_normals = {}
ps = self.points
self.planar = len(ps) <= 2
if len(ps) == 1:
self.edges.add((0, 0)) #phantom edge
self.point_edges[0].append((0, 0)) #only one edge
self.edge_normals = {(0, 0): [np.zeros(3), np.zeros(3)]}
elif len(ps) == 2:
self.edges.add((0, 1)) #unique edge
self.point_edges[0].append((0, 1)) #only one edge
self.point_edges[1].append((0, 1)) #only one edge
#compute the normal of the arc
n1 = np.cross(ps[0], ps[1])
if nla.norm(n1) > 1e-7:
n1 /= nla.norm(n1)
self.edge_normals = {(0, 1): [n1, -n1]}
#compute second normal of the arc
n2 = ps[0] + ps[1]
if nla.norm(n2) > 1e-7:
n2 /= nla.norm(n2)
self.edge_arc = {(0, 1): (n1, n2, 2 * np.pi)}
else:
data = ['']
try:
data = pyhull.qconvex('i FN Fn n -A%1.5f' % self.cos_merge, ps)
except:
data = ['']
if not data[0]:
#try the planar convex hull projecting in XY
self.planar = True
try:
data = pyhull.qconvex(
'i FN Fn n Qb0:0B0:0 -A%1.5f' % self.cos_merge, ps)
except:
data = ['']
if not data[0]:
#try the planar convex hull projecting in XZ
try:
data = pyhull.qconvex(
'i FN Fn n Qb1:0B1:0 -A%1.5f' % self.cos_merge, ps)
except:
data = ['']
if not data[0]:
#it should never get to this point!!!
#try the planar convex hull projecting in YZ
data = pyhull.qconvex(
'i FN Fn n Qb2:0B2:0 -A%1.5f' % self.cos_merge, ps)
self.parse_data(data)
def test_qconvex(self):
data = [[-0.5, -0.5], [-0.5, 0.5], [0.5, -0.5], [0.5, 0.5]]
self.assertEqual(['4', '0 2', '1 0', '2 3', '3 1'], qconvex("i", data))
self.assertEqual(['4', '0 2', '1 0', '2 3', '3 1'],
qconvex("i Qt", data))
self.assertEqual(qconvex("n", data), [
'3', '4', '-0 -1 -0.5', '-1 0 -0.5',
'1 -0 -0.5', '0 1 -0.5'
])
self.assertIsNotNone(qconvex('QR0 FA Pp', data))
def test_qconvex(self):
data = [[-0.5, -0.5], [-0.5, 0.5], [0.5, -0.5], [0.5, 0.5]]
self.assertEqual(['4', '0 2', '1 0', '2 3', '3 1'],
qconvex("i", data))
self.assertEqual(['4', '0 2', '1 0', '2 3', '3 1'],
qconvex("i Qt", data))
self.assertEqual(qconvex("n", data), ['3', '4',
'-0 -1 -0.5',
'-1 0 -0.5',
'1 -0 -0.5',
'0 1 -0.5'])
self.assertIsNotNone(qconvex('QR0 FA Pp', data))
def zonotope_add(V, Sign, normals):
# N: normals of the hyperplanes
num_normals = normals.shape[0]
dim = normals.shape[1]
for i in range(num_normals):
normal = normals[i]
V_ = np.empty((0, dim))
Sign_ = np.empty((0, i + Sign.shape[1]))
for k in range(V.shape[0]):
v = V[k]
v_pm = np.vstack((v + normal, v - normal))
v_sign = np.hstack((np.array([Sign[k], Sign[k]]), [[1], [-1]]))
ind_v = [True, True]
Sign_ = np.vstack((Sign_, v_sign[ind_v]))
V_ = np.vstack((V_, v_pm[ind_v]))
# take the convex hull of V_
orth = sp.linalg.orth((V_ - V_[1, :]).T)
if orth.shape[1] != V.shape[1]:
Vr = np.dot((V_ - V_[1, :]), orth)
else:
Vr = V_ - V_[1, :]
vertices = [list(Vr[i]) for i in range(Vr.shape[0])]
ret = pyhull.qconvex('Fx', vertices)
ind_vertices = [int(ret[j]) for j in range(1, len(ret))]
V = V_[ind_vertices]
Sign = Sign_[ind_vertices]
return V, Sign
def compute_hiperspaces(self):
if not len(self.points) > 0:
logger.error('No points to compute hull!')
raise Exception('No points to compute hull!')
# The heuristic caracteristic when searching to connect
# different clusters does that it might fail
# so we redirect the stdout to avoid such error
# being visible to user
stderr_fd = sys.stderr.fileno()
with open('/tmp/qhull-output.log', 'w') as f, stderr_redirected(f):
points = list(self.points)
logger.info('Searching for hull in dimension %s based on %s points',
len(points[0]),len(points))
output = qconvex('n',points)
if len(output) == 1:
logger.debug('Could not get Hull. Joggle input?')
try:
dim, facets_nbr, facets = self.__parse_hs_output(output)
except IncorrectOutput:
logger.error('Could not get hull')
raise CannotGetHull()
logger.info('Found hull in dimension %s of %s facets',
dim,facets_nbr)
self.dim = dim
self.facets = facets
return self.dim
def get_lines_voronoi(data):
from pyhull import qconvex
output = qconvex("o", data)
nb_points = int(output[1].split(" ")[0])
list_lines = []
list_points = []
for i in range(2, 2 + nb_points):
list_points.append([float(c) for c in output[i].strip().split()])
facets = []
for i in range(2 + nb_points, len(output)):
if output[i] != "":
tmp = output[i].strip().split(" ")
facets.append([int(tmp[j]) for j in range(1, len(tmp))])
for i in range(len(facets)):
for line in itertools.combinations(facets[i], 2):
for j in range(len(facets)):
if i != j and line[0] in facets[j] and line[1] in facets[j]:
# check if the two facets i and j are not coplanar
vector1 = np.array(list_points[facets[j][0]]) - np.array(list_points[facets[j][1]])
vector2 = np.array(list_points[facets[j][0]]) - np.array(list_points[facets[j][2]])
n1 = np.cross(vector1, vector2)
vector1 = np.array(list_points[facets[i][0]]) - np.array(list_points[facets[i][1]])
vector2 = np.array(list_points[facets[i][0]]) - np.array(list_points[facets[i][2]])
n2 = np.cross(vector1, vector2)
dot = math.fabs(np.dot(n1, n2) / (np.linalg.norm(n1) * np.linalg.norm(n2)))
if 1.05 > dot > 0.95:
continue
list_lines.append({"start": list_points[line[0]], "end": list_points[line[1]]})
break
return list_lines
def convex_hull_volume_pyhull(pts):
# call pyhull library
output = pyhull.qconvex("Qt FA", pts)
# parse output
volume = -999.0
facetArea = -999.0
cnt1 = 0
cnt2 = 0
for line in output:
if "facet area" in line:
array = line.split(":")
facetArea = float(array[1])
cnt1 += 1
if "volume" in line:
array = line.split(":")
volume = float(array[1])
cnt2 += 1
assert cnt1 == 1, "ERROR: 'facet area' found %d times in pyhull output" % cnt1
assert cnt2 == 1, "ERROR: 'volume' found %d times in pyhull output" % cnt2
return volume, facetArea
def compute_hiperspaces(self):
# La característica heurística al buscar conexiones entre
# diferentes clusters hace que pueda fallar
# por lo que redirigimos la salida para ser silenciosos
# en esos casos
if not len(self.points) > 0:
logger.error('No points to compute hull!')
raise Exception('No points to compute hull!')
stderr_fd = sys.stderr.fileno()
with open('/tmp/qhull-output.log', 'w') as f, stderr_redirected(f):
points = list(self.points)
logger.info('Searching for hull in dimension %s based on %s points',
len(points[0]),len(points))
output = qconvex('n',points)
if len(output) == 1:
logger.debug('Could not get Hull. Joggle input?')
try:
dim, facets_nbr, facets = self.__parse_hs_output(output)
except IncorrectOutput:
logger.warning('Could not get hull')
raise CannotGetHull()
logger.info('Found hull in dimension %s of %s facets',
dim,len(facets))
self.dim = dim
self.facets = facets
if self.verbose:
print "Computed MCH with ",facets_nbr," halfspaces"
print 'This are them:\n'
for facet in self.facets:print facet
return self.dim
def zonotope_incidence_graph_opposite(A):
V, S = zonotope_vertices(A)
V_aff = project_affine_subspace(V.T).T
if DEBUG:
print('V_aff')
print(V_aff)
verts = [list(V_aff[i]) for i in range(V_aff.shape[0])]
ret = pyhull.qconvex('Fv', verts)
M = build_vertex_facet_matrix(ret, verts).T
n = A.shape[0]
d = V_aff.shape[1]
I = build_incidence_graph(M, d)
# Assign sign vectors for topes.
for i in range(M.shape[1]):
vf_key = tuple(np.where(M[:, i])[0].astype(int))
f = I.rank(d - 1)[vf_key]
f.pos = S[i]
# Assign sign vectors for k faces.
for k in range(d - 2, -1, -1):
for u in I.rank(k).values():
# print(u._sv_key, k)
pos = np.zeros((n, ), int)
for v in u.superfaces:
# print('v', v.pos)
pos += v.pos
pos = (pos / len(u.superfaces)).astype(int)
u.pos = pos
# print('u', u.pos)
return I
def convex_hull_volume_pyhull(pts):
# call pyhull library
output = pyhull.qconvex("Qt FA", pts)
# parse output
volume = -999.0
facetArea = -999.0
cnt1 = 0
cnt2 = 0
for line in output:
if "facet area" in line:
array = line.split(":")
facetArea = float(array[1])
cnt1 += 1
if "volume" in line:
array = line.split(":")
volume = float(array[1])
cnt2 += 1
assert cnt1 == 1, "ERROR: 'facet area' found %d times in pyhull output" % cnt1
assert cnt2 == 1, "ERROR: 'volume' found %d times in pyhull output" % cnt2
return volume, facetArea
def zonotope_projected_vertex(normals):
# N: normals of the hyperplanes
num_normals = normals.shape[0]
dim = normals.shape[1]
V = np.vstack((normals[0], -normals[0]))
Sign = np.array([[1], [-1]])
for i in range(1, num_normals):
normal = normals[i]
V_ = np.vstack((V + normal, V - normal))
Sign_ = np.ones((2 * Sign.shape[0], Sign.shape[1] + 1), dtype=int)
Sign_[:, 0:Sign.shape[1]] = np.vstack((Sign, Sign))
Sign_[Sign.shape[0]:, -1] = -1
# take the convex hull of V_
orth = sp.linalg.orth((V_ - np.mean(V_, axis=0)).T)
if orth.shape[1] != V.shape[1]:
Vr = np.dot((V_ - np.mean(V_, axis=0)), orth)
else:
Vr = V_ - V_[1, :]
vertices = [list(Vr[i]) for i in range(Vr.shape[0])]
info['n'].append(len(vertices))
info['d'].append(len(vertices[0]))
t_start = time()
ret = pyhull.qconvex('Fv', vertices)
info['time conv'].append(time() - t_start)
#ind_vertices = [int(ret[j]) for j in range(1, len(ret))]
ind_vertices = []
for i in range(1, len(ret)):
ind_vertices = ind_vertices + [int(x)
for x in ret[i].split(' ')][1:]
ind_vertices = np.unique(ind_vertices)
info['# d-1 faces'].append(len(ret) - 1)
info['# 0 faces'].append(len(ind_vertices))
V = V_[ind_vertices]
Sign = Sign_[ind_vertices]
#
# facets = np.zeros((int(ret[0]),len([int(x) for x in ret[1].split(' ')][1:])),dtype=int)
# for i in range(1, len(ret)):
# facets[i-1] = [int(x) for x in ret[i].split(' ')][1:]
# ret_facets = np.array(facets)
#
# for i in range(len(ind_vertices)):
# ret_facets[ret_facets == ind_vertices[i]] = i
return V, Sign, info #, ret_facets
def main():
with open('res.txt', 'r') as rfile:
lines = rfile.readlines()
labels = np.array([x.split()[-1] for x in lines[1:]])
data = np.array([[float(x) for x in y.split()[:-1]] for y in lines[1:]])
data2 = data[:, :2]
idx = [[int(x) for x in y.split()] for y in pyhull.qconvex('s i', data2)[1:]]
coords = [[float(x) for x in y.split()]
for y in pyhull.qconvex('s p', data2)[2:]]
np_idx = np.array(idx)
np_coords = np.array(coords)
# print(idx)
# print(coords)
zero = np_coords[np_coords[:, 0] == 0][0][1]
one = np_coords[np_coords[:, 0] == 1][0][1]
zero_zero = np.copy(np_coords)
zero_zero[:, 1] = np_coords[:, 1] - zero * (1 - np_coords[:, 0]) - one * np_coords[:, 0]
bottom = np_coords[zero_zero[:, 1] <= 0]
zero_zero = zero_zero[zero_zero[:, 1] <= 0]
s_bottom = np.array(sorted(bottom, key=lambda x:x[0]))
f = interpolate.interp1d(s_bottom[:, 0], s_bottom[:, 1])
# test plot
# x = np.linspace(0, 1, 100)
# pylab.plot(x, f(x))
# pylab.show()
from_cvxhll = np.copy(data2)
from_cvxhll[:, 1] = data2[:, 1] - f(data2[:, 0])
print(sum(from_cvxhll[:, 1] < 0.001))
low_e = data[from_cvxhll[:, 1] < 0.001]
pylab.plot(low_e[:, 0], low_e[:, 1], 'o')
pylab.plot(data[:, 0], data[:, 1], '*')
# pylab.show()
dir_list = labels[from_cvxhll[:, 1] < 0.001]
for dirc in dir_list:
print(dirc)
def construct_convex_hull_from_coords(coords: np.ndarray) -> Polyhedron:
"""Construct a polyhedron as a convex hull from a coordinate matrix.
:param coords: An array of coordinates.
:returns: A polyhedron whose facets are the non-simplicial facets of the
convex hull of the vertices defined by `coords`.
"""
dim = coords.shape[1]
assert dim <= 3, 'We cannot visualise anything with more than three\
dimensions.'
vertices = []
for i in range(coords.shape[0]):
if dim == 2:
vertices.append(Point(np.array([coords[i, 0], coords[i, 1], 0])))
else:
vertices.append(Point(coords[i, :]))
if dim == 3:
hull = qconvex("i", coords)
n_facets = int(hull[0])
facets = []
for facet_vertices_str in hull[1:]:
facet_vertices_idx = [
int(x) for x in facet_vertices_str.split(' ')
]
facet_vertices = [vertices[i] for i in facet_vertices_idx]
facet = Facet([Contour.from_vertices(facet_vertices)])
facets.append(facet)
polyhedron = Polyhedron(facets)
elif dim == 2:
hull = qconvex("Fx", coords)
n_hull_vertices = int(hull[0])
hull_vertices = []
for vertex_str in hull[1:]:
vertex_idx = int(vertex_str)
hull_vertices.append(vertices[vertex_idx])
contour = Contour.from_vertices(hull_vertices)
polyhedron = Polyhedron([Facet([contour])])
return polyhedron
def zonotope_minkowski_sum(a, V, S):
"""Compute the Minkowski sum V ⊕ [a,-a].
Arguments:
a {1xd vector} -- End-point of line segment [a,-a]
V {nxd matrix} -- Zonotope vertices
S {nxn matrix} -- Zonotope sign vectors
Returns:
[matrix, matrix] -- Updated zonotope vertices and sign vectors.
"""
a = np.reshape(a, (1, -1))
V_sum = np.vstack((V + a, V - a))
if DEBUG:
print('V_sum')
print(V_sum)
S_sum = np.ones((2 * S.shape[0], S.shape[1] + 1), dtype=int)
S_sum[:, 0:S.shape[1]] = np.vstack((S, S))
S_sum[S.shape[0]:, -1] = -1
if DEBUG:
print('S_sum')
print(S_sum)
V_aff = project_affine_subspace(V_sum.T).T
if DEBUG:
print('V_aff')
print(V_aff)
vertices = [list(V_aff[i]) for i in range(V_aff.shape[0])]
ret = pyhull.qconvex('Fv', vertices)
idx = []
for i in range(1, len(ret)):
idx = idx + [int(x) for x in ret[i].split(' ')][1:]
idx = np.unique(idx)
if DEBUG:
print('idx')
print(idx)
V = V_sum[idx]
S = S_sum[idx]
return V, S
def get_lines_voronoi(data):
from pyhull import qconvex
output = qconvex("o", data)
nb_points = int(output[1].split(" ")[0])
list_lines = []
list_points = []
for i in range(2, 2 + nb_points):
list_points.append([float(c) for c in output[i].strip().split()])
facets = []
for i in range(2 + nb_points, len(output)):
if output[i] != '':
tmp = output[i].strip().split(" ")
facets.append([int(tmp[j]) for j in range(1, len(tmp))])
for i in range(len(facets)):
for line in itertools.combinations(facets[i], 2):
for j in range(len(facets)):
if i != j and line[0] in facets[j] and line[1] in facets[j]:
#check if the two facets i and j are not coplanar
vector1 = np.array(list_points[facets[j][0]])\
- np.array(list_points[facets[j][1]])
vector2 = np.array(list_points[facets[j][0]])\
- np.array(list_points[facets[j][2]])
n1 = np.cross(vector1, vector2)
vector1 = np.array(list_points[facets[i][0]])\
- np.array(list_points[facets[i][1]])
vector2 = np.array(list_points[facets[i][0]])\
- np.array(list_points[facets[i][2]])
n2 = np.cross(vector1, vector2)
dot = math.fabs(
np.dot(n1, n2) /
(np.linalg.norm(n1) * np.linalg.norm(n2)))
if 1.05 > dot > 0.95:
continue
list_lines.append({
'start': list_points[line[0]],
'end': list_points[line[1]]
})
break
return list_lines
def construct_convex_hull(vertices: Sequence[Point]) -> Polyhedron:
"""Construct a polyhedron as a convex hull from a list of vertices.
:param vertices: A list of all vertices to be analysed.
:returns: A polyhedron whose facets are the non-simplicial facets of the
convex hull of `vertices`.
"""
coords = np.zeros((len(vertices), 3))
for i, vertex in enumerate(vertices):
coords[i, :] = vertex.coordinates
hull = qconvex("i", coords)
n_facets = int(hull[0])
facets = []
for facet_vertices_str in hull[1:]:
facet_vertices_idx = [int(x) for x in facet_vertices_str.split(' ')]
facet_vertices = [vertices[i] for i in facet_vertices_idx]
facet = Facet([Contour.from_vertices(facet_vertices)])
facets.append(facet)
polyhedron = Polyhedron(facets)
return polyhedron
def __init__(self, points, joggle=False):
"""
Args:
points:
All the points as a sequence of sequences. e.g., [[-0.5, -0.5],
[-0.5, 0.5], [0.5, -0.5], [0.5, 0.5]]
joggle:
Use qhull option to joggle inputs until simplical result is
obtained instead of merging facets.
"""
self.points = points
dim = map(len, self.points)
if max(dim) != min(dim):
raise ValueError("Input points must all have the same dimension!")
self.dim = dim[0]
if joggle:
options = "i QJ"
else:
options = "i Qt"
output = qconvex(options, points)
output.pop(0)
self.vertices = [map(int, row.strip().split()) for row in output]
def __init__(self, points, joggle=False):
"""
Initializes a ConvexHull from points.
Args:
points ([[float]]): All the points as a sequence of sequences.
e.g., [[-0.5, -0.5], [-0.5, 0.5], [0.5, -0.5], [0.5, 0.5]]
joggle (bool): Use qhull option to joggle inputs until simplical
result is obtained instead of merging facets.
"""
self.points = points
dim = [len(i) for i in self.points]
if max(dim) != min(dim):
raise ValueError("Input points must all have the same dimension!")
self.dim = dim[0]
if joggle:
options = "i QJ"
else:
options = "i Qt"
output = qconvex(options, points)
output.pop(0)
self.vertices = [[int(i) for i in row.strip().split()]
for row in output]
def __init__(self, points, joggle=False):
"""
Initializes a ConvexHull from points.
Args:
points ([[float]]): All the points as a sequence of sequences.
e.g., [[-0.5, -0.5], [-0.5, 0.5], [0.5, -0.5], [0.5, 0.5]]
joggle (bool): Use qhull option to joggle inputs until simplical
result is obtained instead of merging facets.
"""
self.points = points
dim = [len(i) for i in self.points]
if max(dim) != min(dim):
raise ValueError("Input points must all have the same dimension!")
self.dim = dim[0]
if joggle:
options = "i QJ"
else:
options = "i Qt"
output = qconvex(options, points)
output.pop(0)
self.vertices = [[int(i) for i in row.strip().split()]
for row in output]
def vertex2lattice(V):
# orth = sp.linalg.orth((V - np.mean(V, 0)).T)
# dim_V = orth.shape[1]
#print(V)
V_aff = proj_affine(V.T).T
#print(V_aff)
dim_V = V_aff.shape[1]
n_vert = V.shape[0]
if n_vert == 2 or n_vert == 1 or dim_V == 1:
M = np.ones((n_vert, 1), int)
L = FaceLattice(M, dim_V)
return L
# project V into affine space
# if dim_V != V.shape[1]:
# V = np.dot((V - np.mean(V,0)), orth)
# vertices = [list(V[i]) for i in range(n_vert)]
vertices = [list(V_aff[i]) for i in range(n_vert)]
ret = pyhull.qconvex('Fv', vertices)
# get the convex hull of V
# select faces with desired modes
# Build facet-vertex incidence matrix.
n_facets = int(ret[0])
M = np.zeros((n_vert, n_facets), int)
for i in range(1, len(ret)):
vert_set = [int(x) for x in ret[i].split(' ')][1:]
for v in vert_set:
M[v, i - 1] = 1
# Build face lattice.
L = FaceLattice(M, dim_V)
return L
def count_surface(sites):
""" 多面体を構成する面の数を return する """
out = pyhull.qconvex('s i', sites)
# voro = pyhull.qvoronoi('s o', sites)
return len(out) - 1
def computeConvexHullVolume(points):
outputStr = qconvex("FA", points)
volumeSize = outputStr[-2].split()[3]
print "ConvexHullSize:",volumeSize
return volumeSize
def zonotope_vertex(normals):
# solve info
info = dict()
info['iter'] = []
info['n'] = []
info['d'] = []
info['time conv'] = []
info['# 0 faces'] = []
info['# d-1 faces'] = []
# normals_proj = proj_affine(normals.T).T
# normals_u, idu = unique_row(normals_proj)
# normals = normals_u
# N: normals of the hyperplanes
num_normals = normals.shape[0]
dim = normals.shape[1]
V = np.vstack((normals[0], -normals[0]))
Sign = np.array([[1], [-1]])
for i in range(1, num_normals):
info['iter'].append(i)
normal = normals[i]
V_ = np.vstack((V + normal, V - normal))
Sign_ = np.ones((2 * Sign.shape[0], Sign.shape[1] + 1), dtype=int)
Sign_[:, 0:Sign.shape[1]] = np.vstack((Sign, Sign))
Sign_[Sign.shape[0]:, -1] = -1
# take the convex hull of V_
# orth = sp.linalg.orth((V_ - np.mean(V_,axis=0)).T)
Vr = proj_affine(V_.T).T
#print(Vr)
# if orth.shape[1] != V.shape[1]:
# Vr = np.dot((V_ - np.mean(V_,axis=0)), orth)
# else:
# Vr = V_ - np.mean(V_,axis=0)
if Vr.shape[1] <= 1:
V = V_[[np.argmax(Vr), np.argmin(Vr)]]
Sign = Sign_[[np.argmax(Vr), np.argmin(Vr)]]
continue
vertices = [list(Vr[i]) for i in range(Vr.shape[0])]
ret = pyhull.qconvex('Fv', vertices)
if len(ret) - 1 == 0:
return [], []
#ind_vertices = [int(ret[j]) for j in range(1, len(ret))]
ind_vertices = []
for i in range(1, len(ret)):
ind_vertices = ind_vertices + [int(x)
for x in ret[i].split(' ')][1:]
ind_vertices = np.unique(ind_vertices)
#print(ret)
V = V_[ind_vertices]
Sign = Sign_[ind_vertices]
#
# facets = np.zeros((int(ret[0]),len([int(x) for x in ret[1].split(' ')][1:])),dtype=int)
# for i in range(1, len(ret)):
# facets[i-1] = [int(x) for x in ret[i].split(' ')][1:]
# ret_facets = np.array(facets)
#
# for i in range(len(ind_vertices)):
# ret_facets[ret_facets == ind_vertices[i]] = i
#Sign = Sign[:,idu]
return V, Sign #, ret_facets
def prob_qhull(samples, data, rho_D_M, d_distr_samples,
lam_domain, d_Tree=None):
r"""
Calculates :math:`P_{\Lambda}(\mathcal{V}_{\lambda_{emulate}})`, the
probability assoicated with a set of voronoi cells defined by
``num_l_emulate`` iid samples :math:`(\lambda_{emulate})`.
This method is only intended when ``lam_domain`` is a generalized rectangle.
:param samples: The samples in parameter space for which the model was run.
:type samples: :class:`~numpy.ndarray` of shape (num_samples, ndim)
:param data: The data from running the model given the samples.
:type data: :class:`~numpy.ndarray` of size (num_samples, mdim)
:param rho_D_M: The simple function approximation of rho_D
:type rho_D_M: :class:`~numpy.ndarray` of shape (M,mdim)
:param d_distr_samples: The samples in the data space that define a
parition of D to for the simple function approximation
:type d_distr_samples: :class:`~numpy.ndarray` of shape (M,mdim)
:param d_Tree: :class:`~scipy.spatial.KDTree` for d_distr_samples
:param lam_domain: The domain for each parameter for the model.
:type lam_domain: :class:`~numpy.ndarray` of shape (ndim, 2)
:returns: (P, io_ptr, lam_vol)
"""
import pyhull
if len(d_distr_samples.shape) == 1:
d_distr_samples = np.expand_dims(d_distr_samples, axis=1)
if d_Tree == None:
d_Tree = spatial.KDTree(d_distr_samples)
# Determine which inputs go to which M bins using the QoI
#io_ptr = dsearchn(d_distr_samples, data);
io_ptr = d_Tree.query(data)
# Calcuate the bounding region for the parameters
lam_bound = np.copy(samples)
lam_width = lam_domain[:, 1] - lam_domain[:, 0]
nbins = d_distr_samples.shape[1]
# Add fake samples outside of lam_domain to close Voronoi tesselations.
pts_per_edge = nbins
sides = np.zeros((2, pts_per_edge))
for i in range(lam_domain.shape[0]):
sides[i, :] = np.linspace(lam_domain[i, 0], lam_domain[i, 1],
pts_per_edge)
# add midpoints
for i in range(lam_domain.shape[0]):
new_pt = sides
new_pt[i, :] = np.repeat(lam_domain[i, 0] - lam_width[i]/pts_per_edge,
pts_per_edge, 0).transpose()
lam_bound = np.vstack((lam_bound, new_pt))
new_pt = sides
new_pt[i, :] = np.repeat(lam_domain[i, 1] - lam_width[i]/pts_per_edge,
pts_per_edge, 0).transpose()
lam_bound = np.vstack((lam_bound, new_pt))
# add corners
corners = np.zeros((2**lam_domain.shape[0], lam_domain.shape[0]))
for i in range(lam_domain.shape[0]):
corners[i, :] = lam_domain[i, np.repeat(np.hstack((np.ones((1,
2**(i-1))), 2*np.ones((1, 2**(i - 1))))),
2**(lam_domain.shape[0]-i), 0).transpose()]
corners[i, :] += lam_width[i]*np.repeat(np.hstack((np.ones((1,
2**(i-1))), -np.ones((1, 2**(i - 1))))),
2**(lam_domain.shape[0]-i)/pts_per_edge, 0).transpose()
lam_bound = np.vstack((lam_bound, corners))
# Calculate the Voronoi diagram for samples. Calculate the volumes of
# the convex hulls of the corresponding Voronoi regions.
lam_vol = np.zeros((samples.shape[-1],))
for i in range((samples.shape[0])):
vornoi = spatial.Voronoi(lam_bound)
lam_vol[i] = float(pyhull.qconvex('Qt FA', vornoi.vertices).split()[-1])
# Calculate probabilities.
P = np.zeros((samples.shape[0],))
for i in range(rho_D_M.shape[0]):
Itemp = np.equal(io_ptr, i)
P[Itemp] = rho_D_M[i]*lam_vol[Itemp]/np.sum(lam_vol[Itemp])
P = P/np.sum[P]
return (P, lam_vol, io_ptr)
def enumerate_contact_separating_3d(A, b):
# Create solve info.
info = dict()
# Create halfspace inequalities, Ax - b <= 0.
# A, b = build_normal_velocity_constraints(system.collider.manifolds)
# b = np.zeros(b.shape)
if DEBUG:
print('A')
print(A)
print('b')
print(b)
n_pts = A.shape[0]
info['n'] = n_pts
# Get interior point using linear programming.
t_lp = time()
int_pt = int_pt_cone(A)
info['time lp'] = time() - t_lp
if DEBUG:
print('int_pt2')
print(int_pt, '\n', A @ int_pt)
# Filter contact points which are always in contact.
mask = np.zeros(n_pts, dtype=bool)
c = np.where(np.abs(A @ int_pt) < 1e-6)[0] # always contacting.
mask[c] = 1
A_c = A[mask, :]
b_c = b[mask, :]
A = A[~mask, :]
b = b[~mask, :]
if DEBUG:
print(c)
print(mask)
# Project into null space of contacting points.
# [A'; A_c]x ≤ 0, A_c⋅x = 0 ⇒ x ∈ NULL(A_c)
# let NULL(A_c) = [x0, ... , xc]
# A'⋅NULL(A_c)x' ≤ 0
if np.sum(mask) > 0:
N = null(A_c, np.finfo(np.float32).eps)
A = A @ N
int_pt = np.linalg.lstsq(N, int_pt, None)[0]
if DEBUG:
print('Null A_c')
print(N)
print('new int pt')
print(int_pt)
print(A @ int_pt)
# Compute dual points.
b_off = b - np.dot(A, int_pt)
dual = A / b_off
if DEBUG:
print('b off')
print(b_off)
print('dual')
print(dual)
# Handle degenerate cases when d = 0 or 1.
if np.sum(mask) == n_pts:
cs_modes = [np.array(['c'] * n_pts)]
lattice = FaceLattice()
lattice.L = [[Face(range(n_pts), 0)]]
lattice.L[0][0].m = cs_modes[0]
return cs_modes, lattice, info
if dual.shape[1] == 1:
lattice = FaceLattice(M=np.ones((1, 1), int), d=1)
dual_map = [list(np.where(~mask)[0])]
cs_modes = lattice.csmodes(mask, dual_map)
lattice.L = lattice.L[1:3]
return cs_modes[1:3], lattice, info
# Project dual points into affine space.
dual = proj_affine(dual.T).T
if DEBUG:
print('proj dual')
print(dual)
info['d'] = dual.shape[1]
# Filter duplicate points.
idx = np.lexsort(np.rot90(dual))
dual_map = []
dual_unique = []
i = 0
while i < len(idx):
if i == 0:
dual_unique.append(dual[idx[i], :])
dual_map.append([idx[i]])
else:
curr = dual[idx[i], :]
last = dual_unique[-1]
if np.linalg.norm(last - curr) < 1e-6:
dual_map[-1].append(idx[i])
else:
dual_unique.append(dual[idx[i], :])
dual_map.append([idx[i]])
i += 1
if DEBUG:
print('dual map')
print(dual_map)
print('dual unique')
print(dual_unique)
# Handle various cases.
dual = [list(dual_unique[i]) for i in range(len(dual_unique))]
if len(dual_unique) == 1:
d = 0
M = np.array([[]])
elif len(dual_unique[0]) == 1:
d = 1
M = np.zeros((len(dual), 2), int)
i_min = np.argmin(np.array(dual).flatten())
i_max = np.argmax(np.array(dual).flatten())
M[i_min, 0] = 1
M[i_max, 1] = 1
else:
d = len(dual[0])
# Compute dual convex hull.
t_start = time()
ret = pyhull.qconvex('Fv', dual)
info['time conv'] = time() - t_start
if DEBUG:
print(np.array(ret))
# Build facet-vertex incidence matrix.
n_facets = int(ret[0])
M = np.zeros((len(dual), n_facets), int)
for i in range(1, len(ret)):
vert_set = [int(x) for x in ret[i].split(' ')][1:]
for v in vert_set:
M[v, i - 1] = 1
if DEBUG:
print('dual')
print(np.array(dual))
if DEBUG:
print('M')
print(M)
# Build face lattice.
t_start = time()
lattice = FaceLattice(M, d)
info['time lattice'] = time() - t_start
# Build mode strings.
cs_modes = lattice.csmodes(mask, dual_map)
if DEBUG:
print(cs_modes)
info['# 0 faces'] = lattice.num_k_faces(0)
info['# d-1 faces'] = lattice.num_k_faces(info['d'] - 1)
info['# faces'] = lattice.num_faces()
# Return mode strings.
return cs_modes, lattice, info