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 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])
