def con2vert(A, b):
"""
Convert sets of constraints to a list of vertices (of the feasible region).
If the shape is open, con2vert returns False for the closed property.
"""
# Python implementation of con2vert.m by Michael Kleder (July 2005),
# available: http://www.mathworks.com/matlabcentral/fileexchange/7894
# -con2vert-constraints-to-vertices
# Author: Michael Kelder (Original)
# Andre Campher (Python implementation)
c = linalg.lstsq(mat(A), mat(b))[0]
btmp = mat(b)-mat(A)*c
D = mat(A)/matlib.repmat(btmp, 1, A.shape[1])
fmatv = qhull(D, "Ft") #vertices on facets
G = zeros((fmatv.shape[0], D.shape[1]))
for ix in range(0, fmatv.shape[0]):
F = D[fmatv[ix, :], :].squeeze()
G[ix, :] = linalg.lstsq(F, ones((F.shape[0], 1)))[0].transpose()
V = G + matlib.repmat(c.transpose(), G.shape[0], 1)
ux = uniqm(V)
eps = 1e-13
Av = dot(A, ux.T)
bv = tile(b, (1, ux.shape[0]))
closed = sciall(Av - bv <= eps)
return ux, closed
def allinside(self, conset2):
"""
Determine if all vertices of self is within conset2. allvinside merely
returns True/False whereas insidenorm returns a measure of 'inside-ness'
better suited for optimisers.
"""
# Inside check
Av = dot(conset2.A, self.vert.T)
bv = tile(conset2.b, (1, self.vert.shape[0]))
eps = 1e-13
intmpvals = Av - bv
intmp = intmpvals <= eps
allvinside = sciall(intmp)
# Inside norm
insidenorm = zeros((Av.shape[0], 1))
for cons in range(Av.shape[0]):
for verts in range(Av.shape[1]):
dist = abs(intmpvals[cons, verts])/sqrt(sum(conset2.A[cons, :]**2))
if not intmp[cons, verts]: # outside
insidenorm[cons] = insidenorm[cons] - dist
# Outside volume
return allvinside, insidenorm#, outsidevol
