def tryvol(A, b, cs):
"""
Try to determine volume of feasible region, otherwise impose box
constraint.
"""
try:
V = con2vert(A, b)[0] # get vertices for constraint set iteration
except NameError: #catch unbound shapes
#create large box around original shape
fixA = r_[eye(cs.nd), -eye(cs.nd)]
fixb = r_[[numpy.max(cs.vert[:, x]) for x in range(cs.vert.shape[1])],
[-numpy.min(cs.vert[:, x]) for x in range(cs.vert.shape[1])]]
fixb = array([fixb]).T
fA = r_[fixA, A]
fb = 2. * r_[fixb, b] # double the box size
V = con2vert(fA, fb)[0]
#return vol (normal or fixed) and vertices (normal or fixed)
return qhull(V, "FS"), V
def objfn2(Ab, *args):
"""Volume objective function for SLSQP."""
initcs = args[0]
A, b = splitAb(Ab, initcs.nd)
cl = con2vert(A, b)[1]
if cl:
closed = 1
else:
closed = -1
vol = tryvol(A, b, initcs)[0]
return closed * -vol
def objfn(Ab, *args):
"""Volume objective function for SLSQP."""
initcs = args[0]
A = r_[eye(initcs.nd), -eye(initcs.nd)]
b = array([Ab]).T
cl = con2vert(A, b)[1]
if cl:
closed = 1
else:
closed = -1
vol = tryvol(A, b, initcs)[0]
return closed * -vol
def intersect(self, conset2):
"""Determine intersection between current constraint set and another"""
def remredcons(A, b, verts):
"""Reduce a constraint set by removing unnecessary constraints."""
eps = 10e-9
#1 Co-planar constraints;
# Remove as not to affect 3rd check
Ab = c_[A, b]
Abnorms = ones((Ab.shape[0], 1))
for i in range(Ab.shape[0]):
Abnorms[i] = linalg.norm(Ab[i, :])
Abn = Ab/Abnorms
Abkeep = ones((0, Ab.shape[1]))
Abtest = ones((0, Ab.shape[1]))
for r1 in range(Abn.shape[0]):
noocc = ones((1, 0))
for r2 in range(Abn.shape[0]):
#print abs(Abn[r1, :] - Abn[r2, :])
if numpy.all(abs(Abn[r1, :] - Abn[r2, :]) < eps):
noocc = c_[noocc, r2]
if noocc.size == 1:
Abtest = vstack([Abtest, Ab[r1, :]])
else:
Abkeep = vstack([Abkeep, Ab[r1, :]])
if Abkeep.shape[0] > 1:
Abkeep = uniqm(Abkeep, eps)
#2 Vert subset satisfying; no action needed (redundancy uncertain)
#3 All vert satisfying constraints;
A, b = splitAb(array(Abtest).ravel(), verts.shape[1])
keepA = ones((0, A.shape[1]))
keepb = ones((0, 1))
bt = tile(b, (1, verts.shape[0]))
k = mat(A)*mat(verts.T) - bt
kk = sum(k > eps, axis=1)
for i in range(len(kk)):
if kk[i] != 0:
keepA = vstack([keepA, A[i, :]])
keepb = vstack([keepb, b[i, :]])
outAb = vstack([c_[keepA, keepb], Abkeep])
return splitAb(outAb.ravel(), verts.shape[1])
#Combine constraints and vertices
combA = vstack((self.A, conset2.A))
combb = vstack((self.b, conset2.b))
combv = vstack((self.vert, conset2.vert))
#Remove redundant constraints
ncombA, ncombb = remredcons(combA, combb, combv)
#Calc and return intersection
intcombvert = con2vert(combA, combb)[0]
return intcombvert
def __init__(self, *inargs):
if len(inargs) == 1:
self.vert = inargs[0]
self.A, self.s, self.b = vert2con(self.vert)
self.closed = True
elif len(inargs) == 3:
if all(sign(inargs[1]) == -1): # ensure an all -1 sign vector
self.A, self.s, self.b = inargs
else:
self.A, self.s, self.b = mat2ab(c_[inargs])
self.vert, self.closed = con2vert(self.A, self.b)
else:
exit(1) # TODO: Raise exception
self.nd = self.A.shape[1]
self.cscent = sum(self.vert, axis=0)/len(self.vert)
def objfn2(Ab, *args):
"""Volume objective function for fmin (Simplex)."""
initcs = args[0]
A = r_[eye(initcs.nd), -eye(initcs.nd)]
b = array([Ab]).T
vol, V = tryvol(A, b, initcs)
Pv = 200.
#Penalties
# points outside of init space
iterset = ConSet(V)
outnorm = linalg.norm(iterset.allinside(initcs)[1])
# open shape
cl = con2vert(A, b)[1]
if cl:
closed = 1
else:
closed = -1
vol = tryvol(A, b, initcs)[0]
return (-vol*closed) + Pv*(outnorm**3)
def objfn(Ab, *args):
"""Volume objective function for fmin (Simplex)."""
initcs = args[0]
A, b = splitAb(Ab, initcs.nd)
vol, V = tryvol(A, b, initcs)
Pv = 200.
Pn = 100.
#Penalties
# large b norm
bnorm = abs(linalg.norm(b) - 1)
# points outside of init space
iterset = ConSet(V)
outnorm = linalg.norm(iterset.allinside(initcs)[1])
#outnorm = iterset.allinside(initcs)[2]
# open shape
cl = con2vert(A, b)[1]
if cl:
closed = 1
else:
closed = -1
vol = tryvol(A, b, initcs)[0]
return (-vol*closed) + Pn*(bnorm**initcs.nd) + Pv*(outnorm**(initcs.nd+3))