def __init__(self, *args, **kwds):
super(piecewise_dcc, self).__init__(*args, **kwds)
# create index sets
polytopes = range(len(self.breakpoints) - 1)
vertices = range(len(self.breakpoints))
def polytope_verts(p):
return xrange(p, p + 2)
# create vars
self.v = variable_dict()
lmbda = self.v['lambda'] = variable_dict(
((p, v), variable(lb=0)) for p in polytopes for v in vertices)
y = self.v['y'] = variable_tuple(
variable(domain=Binary) for p in polytopes)
# create piecewise constraints
self.c = constraint_list()
self.c.append(linear_constraint(
variables=tuple(lmbda[p,v]
for p in polytopes
for v in polytope_verts(p)) + \
(self.input,),
coefficients=tuple(self.breakpoints[v]
for p in polytopes
for v in polytope_verts(p)) + \
(-1,),
rhs=0))
self.c.append(linear_constraint(
variables=tuple(lmbda[p,v]
for p in polytopes
for v in polytope_verts(p)) + \
(self.output,),
coefficients=tuple(self.values[v]
for p in polytopes
for v in polytope_verts(p)) + (-1,)))
if self.bound == 'ub':
self.c[-1].lb = 0
elif self.bound == 'lb':
self.c[-1].ub = 0
else:
assert self.bound == 'eq'
self.c[-1].rhs = 0
clist = []
for p in polytopes:
variables = tuple(lmbda[p, v] for v in polytope_verts(p))
clist.append(
linear_constraint(variables=variables + (y[p], ),
coefficients=(1, ) * len(variables) + (-1, ),
rhs=0))
self.c.append(constraint_tuple(clist))
self.c.append(
linear_constraint(variables=tuple(y),
coefficients=(1, ) * len(y),
rhs=1))
def __init__(self, *args, **kwds):
super(piecewise_inc, self).__init__(*args, **kwds)
# create indexers
polytopes = range(len(self.breakpoints)-1)
# create vars
self.v = variable_dict()
delta = self.v['delta'] = variable_tuple(
variable() for p in polytopes)
delta[0].ub = 1
delta[-1].lb = 0
delta_tuple = tuple(delta)
y = self.v['y'] = variable_tuple(
variable(domain=Binary) for p in polytopes[:-1])
# create piecewise constraints
self.c = constraint_list()
self.c.append(linear_constraint(
variables=(self.input,) + delta_tuple,
coefficients=(-1,) + tuple(self.breakpoints[p+1] - \
self.breakpoints[p]
for p in polytopes),
rhs=-self.breakpoints[0]))
self.c.append(linear_constraint(
variables=(self.output,) + delta_tuple,
coefficients=(-1,) + tuple(self.values[p+1] - \
self.values[p]
for p in polytopes)))
if self.bound == 'ub':
self.c[-1].lb = -self.values[0]
elif self.bound == 'lb':
self.c[-1].ub = -self.values[0]
else:
assert self.bound == 'eq'
self.c[-1].rhs = -self.values[0]
clist1 = []
clist2 = []
for p in polytopes[:-1]:
clist1.append(linear_constraint(
variables=(delta[p+1], y[p]),
coefficients=(1, -1),
ub=0))
clist2.append(linear_constraint(
variables=(y[p], delta[p]),
coefficients=(1, -1),
ub=0))
self.c.append(constraint_tuple(clist1))
self.c.append(constraint_tuple(clist2))
def __init__(self, *args, **kwds):
super(piecewise_mc, self).__init__(*args, **kwds)
# create indexers
polytopes = range(len(self.breakpoints)-1)
# create constants (using future division)
# these might also be expressions if the breakpoints
# or values lists contain mutable objects
slopes = tuple((self.values[p+1] - self.values[p]) / \
(self.breakpoints[p+1] - self.breakpoints[p])
for p in polytopes)
intercepts = tuple(self.values[p] - \
(slopes[p] * self.breakpoints[p])
for p in polytopes)
# create vars
self.v = variable_dict()
lmbda = self.v['lambda'] = variable_tuple(
variable() for p in polytopes)
lmbda_tuple = tuple(lmbda)
y = self.v['y'] = variable_tuple(
variable(domain=Binary) for p in polytopes)
y_tuple = tuple(y)
# create piecewise constraints
self.c = constraint_list()
self.c.append(linear_constraint(
variables=lmbda_tuple + (self.input,),
coefficients=(1,)*len(lmbda) + (-1,),
rhs=0))
self.c.append(linear_constraint(
variables=lmbda_tuple + y_tuple + (self.output,),
coefficients=slopes + intercepts + (-1,)))
if self.bound == 'ub':
self.c[-1].lb = 0
elif self.bound == 'lb':
self.c[-1].ub = 0
else:
assert self.bound == 'eq'
self.c[-1].rhs = 0
clist1 = []
clist2 = []
for p in polytopes:
clist1.append(linear_constraint(
variables=(y[p], lmbda[p]),
coefficients=(self.breakpoints[p], -1),
ub=0))
clist2.append(linear_constraint(
variables=(lmbda[p], y[p]),
coefficients=(1, -self.breakpoints[p+1]),
ub=0))
self.c.append(constraint_tuple(clist1))
self.c.append(constraint_tuple(clist2))
self.c.append(linear_constraint(
variables=y_tuple,
coefficients=(1,)*len(y),
rhs=1))
def __init__(self, *args, **kwds):
super(piecewise_cc, self).__init__(*args, **kwds)
# create index sets
polytopes = range(len(self.breakpoints)-1)
vertices = range(len(self.breakpoints))
def vertex_polys(v):
if v == 0:
return [v]
if v == len(self.breakpoints)-1:
return [v-1]
else:
return [v-1,v]
# create vars
self.v = variable_dict()
lmbda = self.v['lambda'] = variable_tuple(
variable(lb=0) for v in vertices)
y = self.v['y'] = variable_tuple(
variable(domain=Binary)
for p in polytopes)
lmbda_tuple = tuple(lmbda)
# create piecewise constraints
self.c = constraint_list()
self.c.append(linear_constraint(
variables=lmbda_tuple + (self.input,),
coefficients=self.breakpoints + (-1,),
rhs=0))
self.c.append(linear_constraint(
variables=lmbda_tuple + (self.output,),
coefficients=self.values + (-1,)))
if self.bound == 'ub':
self.c[-1].lb = 0
elif self.bound == 'lb':
self.c[-1].ub = 0
else:
assert self.bound == 'eq'
self.c[-1].rhs = 0
self.c.append(linear_constraint(
variables=lmbda_tuple,
coefficients=(1,)*len(lmbda),
rhs=1))
clist = []
for v in vertices:
variables = tuple(y[p] for p in vertex_polys(v))
clist.append(linear_constraint(
variables=variables + (lmbda[v],),
coefficients=(1,)*len(variables) + (-1,),
lb=0))
self.c.append(constraint_tuple(clist))
self.c.append(linear_constraint(
variables=tuple(y),
coefficients=(1,)*len(y),
rhs=1))
def __init__(self, *args, **kwds):
super(piecewise_log, self).__init__(*args, **kwds)
breakpoints = self.breakpoints
values = self.values
if not is_positive_power_of_two(len(breakpoints)-1):
raise ValueError("The list of breakpoints must be "
"of length (2^n)+1 for some positive "
"integer n. Invalid length: %s"
% (len(breakpoints)))
# create branching schemes
L = log2floor(len(breakpoints)-1)
S,B_LEFT,B_RIGHT = self._branching_scheme(L)
# create indexers
polytopes = range(len(breakpoints) - 1)
vertices = range(len(breakpoints))
# create vars
self.v = variable_dict()
lmbda = self.v['lambda'] = variable_tuple(
variable(lb=0) for v in vertices)
y = self.v['y'] = variable_list(
variable(domain=Binary) for s in S)
# create piecewise constraints
self.c = constraint_list()
self.c.append(linear_constraint(
variables=(self.input,) + tuple(lmbda),
coefficients=(-1,) + breakpoints,
rhs=0))
self.c.append(linear_constraint(
variables=(self.output,) + tuple(lmbda),
coefficients=(-1,) + values))
if self.bound == 'ub':
self.c[-1].lb = 0
elif self.bound == 'lb':
self.c[-1].ub = 0
else:
assert self.bound == 'eq'
self.c[-1].rhs = 0
self.c.append(linear_constraint(
variables=tuple(lmbda),
coefficients=(1,)*len(lmbda),
rhs=1))
clist = []
for s in S:
variables=tuple(lmbda[v] for v in B_LEFT[s])
clist.append(linear_constraint(
variables=variables + (y[s],),
coefficients=(1,)*len(variables) + (-1,),
ub=0))
self.c.append(constraint_tuple(clist))
del clist
clist = []
for s in S:
variables=tuple(lmbda[v] for v in B_RIGHT[s])
clist.append(linear_constraint(
variables=variables + (y[s],),
coefficients=(1,)*len(variables) + (1,),
ub=1))
self.c.append(constraint_tuple(clist))
class TestComponentSet(unittest.TestCase):
_components = [
variable(),
variable_dict(),
variable_list(),
constraint(),
constraint_dict(),
constraint_list(),
objective(),
objective_dict(),
objective_list(),
expression(),
expression_dict(),
expression_list(),
block(),
block_dict(),
block_list(),
suffix()
]
def test_pickle(self):
c = ComponentSet()
self.assertEqual(len(c), 0)
cup = pickle.loads(pickle.dumps(c))
self.assertIsNot(cup, c)
self.assertEqual(len(cup), 0)
v = variable()
c.add(v)
self.assertEqual(len(c), 1)
self.assertTrue(v in c)
cup = pickle.loads(pickle.dumps(c))
vup = cup.pop()
cup.add(vup)
self.assertIsNot(cup, c)
self.assertIsNot(vup, v)
self.assertEqual(len(cup), 1)
self.assertTrue(vup in cup)
self.assertEqual(vup.parent, None)
b = block()
V = b.V = variable_list()
b.V.append(v)
b.c = c
self.assertEqual(len(c), 1)
self.assertTrue(v in c)
self.assertIs(v.parent, b.V)
self.assertIs(V.parent, b)
self.assertIs(b.parent, None)
bup = pickle.loads(pickle.dumps(b))
Vup = bup.V
vup = Vup[0]
cup = bup.c
self.assertIsNot(cup, c)
self.assertIsNot(vup, v)
self.assertIsNot(Vup, V)
self.assertIsNot(bup, b)
self.assertEqual(len(cup), 1)
self.assertTrue(vup in cup)
self.assertIs(vup.parent, Vup)
self.assertIs(Vup.parent, bup)
self.assertIs(bup.parent, None)
self.assertEqual(len(c), 1)
self.assertTrue(v in c)
def test_init(self):
cset = ComponentSet()
cset = ComponentSet(self._components)
with self.assertRaises(TypeError):
cset = ComponentSet(*self._components)
def test_type(self):
cset = ComponentSet()
self.assertTrue(isinstance(cset, collections.Set))
self.assertTrue(isinstance(cset, collections.MutableSet))
self.assertTrue(issubclass(type(cset), collections.Set))
self.assertTrue(issubclass(type(cset), collections.MutableSet))
def test_str(self):
cset = ComponentSet()
self.assertEqual(str(cset), "ComponentSet([])")
cset.update(self._components)
str(cset)
def test_len(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
cset.update(self._components)
self.assertEqual(len(cset), len(self._components))
cset = ComponentSet(self._components)
self.assertEqual(len(cset), len(self._components))
self.assertTrue(len(self._components) > 0)
def test_iter(self):
cset = ComponentSet()
self.assertEqual(list(iter(cset)), [])
cset.update(self._components)
ids_seen = set()
for c in cset:
ids_seen.add(id(c))
self.assertEqual(ids_seen, set(id(c) for c in self._components))
def set_add(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
for i, c in enumerate(self._components):
self.assertTrue(c not in cset)
cset.add(c)
self.assertTrue(c in cset)
self.assertEqual(len(cset), i + 1)
self.assertEqual(len(cset), len(self._components))
for c in self._components:
self.assertTrue(c in cset)
cset.add(c)
self.assertTrue(c in cset)
self.assertEqual(len(cset), len(self._components))
def test_pop(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
with self.assertRaises(KeyError):
cset.pop()
v = variable()
cset.add(v)
self.assertTrue(v in cset)
self.assertEqual(len(cset), 1)
v_ = cset.pop()
self.assertIs(v, v_)
self.assertTrue(v not in cset)
self.assertEqual(len(cset), 0)
def test_update(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
cset.update(self._components)
self.assertEqual(len(cset), len(self._components))
for c in self._components:
self.assertTrue(c in cset)
def test_clear(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
cset.update(self._components)
self.assertEqual(len(cset), len(self._components))
cset.clear()
self.assertEqual(len(cset), 0)
def test_remove(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
cset.update(self._components)
self.assertEqual(len(cset), len(self._components))
for i, c in enumerate(self._components):
cset.remove(c)
self.assertEqual(len(cset), len(self._components) - (i + 1))
for c in self._components:
self.assertTrue(c not in cset)
with self.assertRaises(KeyError):
cset.remove(c)
def test_discard(self):
cset = ComponentSet()
self.assertEqual(len(cset), 0)
cset.update(self._components)
self.assertEqual(len(cset), len(self._components))
for i, c in enumerate(self._components):
cset.discard(c)
self.assertEqual(len(cset), len(self._components) - (i + 1))
for c in self._components:
self.assertTrue(c not in cset)
cset.discard(c)
def test_isdisjoint(self):
cset1 = ComponentSet()
cset2 = ComponentSet()
self.assertTrue(cset1.isdisjoint(cset2))
self.assertTrue(cset2.isdisjoint(cset1))
v = variable()
cset1.add(v)
self.assertTrue(cset1.isdisjoint(cset2))
self.assertTrue(cset2.isdisjoint(cset1))
cset2.add(v)
self.assertFalse(cset1.isdisjoint(cset2))
self.assertFalse(cset2.isdisjoint(cset1))
def test_misc_set_ops(self):
v1 = variable()
cset1 = ComponentSet([v1])
v2 = variable()
cset2 = ComponentSet([v2])
cset3 = ComponentSet([v1, v2])
empty = ComponentSet([])
self.assertEqual(cset1 | cset2, cset3)
self.assertEqual((cset1 | cset2) - cset3, empty)
self.assertEqual(cset1 ^ cset2, cset3)
self.assertEqual(cset1 ^ cset3, cset2)
self.assertEqual(cset2 ^ cset3, cset1)
self.assertEqual(cset1 & cset2, empty)
self.assertEqual(cset1 & cset3, cset1)
self.assertEqual(cset2 & cset3, cset2)
def test_eq(self):
cset1 = ComponentSet()
self.assertEqual(cset1, set())
self.assertTrue(cset1 == set())
self.assertNotEqual(cset1, list())
self.assertFalse(cset1 == list())
self.assertNotEqual(cset1, tuple())
self.assertFalse(cset1 == tuple())
self.assertNotEqual(cset1, dict())
self.assertFalse(cset1 == dict())
cset1.update(self._components)
self.assertNotEqual(cset1, set())
self.assertFalse(cset1 == set())
self.assertNotEqual(cset1, list())
self.assertFalse(cset1 == list())
self.assertNotEqual(cset1, tuple())
self.assertFalse(cset1 == tuple())
self.assertNotEqual(cset1, dict())
self.assertFalse(cset1 == dict())
self.assertTrue(cset1 == cset1)
self.assertEqual(cset1, cset1)
cset2 = ComponentSet(self._components)
self.assertTrue(cset2 == cset1)
self.assertFalse(cset2 != cset1)
self.assertEqual(cset2, cset1)
self.assertTrue(cset1 == cset2)
self.assertFalse(cset1 != cset2)
self.assertEqual(cset1, cset2)
cset2.remove(self._components[0])
self.assertFalse(cset2 == cset1)
self.assertTrue(cset2 != cset1)
self.assertNotEqual(cset2, cset1)
self.assertFalse(cset1 == cset2)
self.assertTrue(cset1 != cset2)
self.assertNotEqual(cset1, cset2)
class TestComponentMap(unittest.TestCase):
_components = [(variable(), "v"), (variable_dict(), "vdict"),
(variable_list(), "vlist"), (constraint(), "c"),
(constraint_dict(), "cdict"), (constraint_list(), "clist"),
(objective(), "o"), (objective_dict(), "odict"),
(objective_list(), "olist"), (expression(), "e"),
(expression_dict(), "edict"), (expression_list(), "elist"),
(block(), "b"), (block_dict(), "bdict"),
(block_list(), "blist"), (suffix(), "s")]
def test_pickle(self):
c = ComponentMap()
self.assertEqual(len(c), 0)
cup = pickle.loads(pickle.dumps(c))
self.assertIsNot(cup, c)
self.assertEqual(len(cup), 0)
v = variable()
c[v] = 1.0
self.assertEqual(len(c), 1)
self.assertEqual(c[v], 1.0)
cup = pickle.loads(pickle.dumps(c))
vup = list(cup.keys())[0]
self.assertIsNot(cup, c)
self.assertIsNot(vup, v)
self.assertEqual(len(cup), 1)
self.assertEqual(cup[vup], 1)
self.assertEqual(vup.parent, None)
b = block()
V = b.V = variable_list()
b.V.append(v)
b.c = c
self.assertEqual(len(c), 1)
self.assertEqual(c[v], 1.0)
self.assertIs(v.parent, b.V)
self.assertIs(V.parent, b)
self.assertIs(b.parent, None)
bup = pickle.loads(pickle.dumps(b))
Vup = bup.V
vup = Vup[0]
cup = bup.c
self.assertIsNot(cup, c)
self.assertIsNot(vup, v)
self.assertIsNot(Vup, V)
self.assertIsNot(bup, b)
self.assertEqual(len(cup), 1)
self.assertEqual(cup[vup], 1)
self.assertIs(vup.parent, Vup)
self.assertIs(Vup.parent, bup)
self.assertIs(bup.parent, None)
self.assertEqual(len(c), 1)
self.assertEqual(c[v], 1)
def test_init(self):
cmap = ComponentMap()
cmap = ComponentMap(self._components)
with self.assertRaises(TypeError):
cmap = ComponentMap(*self._components)
def test_type(self):
cmap = ComponentMap()
self.assertTrue(isinstance(cmap, collections.Mapping))
self.assertTrue(isinstance(cmap, collections.MutableMapping))
self.assertTrue(issubclass(type(cmap), collections.Mapping))
self.assertTrue(issubclass(type(cmap), collections.MutableMapping))
def test_str(self):
cmap = ComponentMap()
self.assertEqual(str(cmap), "ComponentMap({})")
cmap.update(self._components)
str(cmap)
def test_len(self):
cmap = ComponentMap()
self.assertEqual(len(cmap), 0)
cmap.update(self._components)
self.assertEqual(len(cmap), len(self._components))
cmap = ComponentMap(self._components)
self.assertEqual(len(cmap), len(self._components))
self.assertTrue(len(self._components) > 0)
def test_getsetdelitem(self):
cmap = ComponentMap()
for c, val in self._components:
self.assertTrue(c not in cmap)
for c, val in self._components:
cmap[c] = val
self.assertEqual(cmap[c], val)
self.assertEqual(cmap.get(c), val)
del cmap[c]
with self.assertRaises(KeyError):
cmap[c]
with self.assertRaises(KeyError):
del cmap[c]
self.assertEqual(cmap.get(c), None)
def test_iter(self):
cmap = ComponentMap()
self.assertEqual(list(iter(cmap)), [])
cmap.update(self._components)
ids_seen = set()
for c in cmap:
ids_seen.add(id(c))
self.assertEqual(ids_seen, set(id(c) for c, val in self._components))
def test_keys(self):
cmap = ComponentMap(self._components)
self.assertEqual(
sorted(cmap.keys(), key=id),
sorted(list(c for c, val in self._components), key=id))
def test_values(self):
cmap = ComponentMap(self._components)
self.assertEqual(sorted(cmap.values()),
sorted(list(val for c, val in self._components)))
def test_items(self):
cmap = ComponentMap(self._components)
for x in cmap.items():
self.assertEqual(type(x), tuple)
self.assertEqual(len(x), 2)
self.assertEqual(
sorted(cmap.items(), key=lambda _x: (id(_x[0]), _x[1])),
sorted(self._components, key=lambda _x: (id(_x[0]), _x[1])))
def test_update(self):
cmap = ComponentMap()
self.assertEqual(len(cmap), 0)
cmap.update(self._components)
self.assertEqual(len(cmap), len(self._components))
for c, val in self._components:
self.assertEqual(cmap[c], val)
def test_clear(self):
cmap = ComponentMap()
self.assertEqual(len(cmap), 0)
cmap.update(self._components)
self.assertEqual(len(cmap), len(self._components))
cmap.clear()
self.assertEqual(len(cmap), 0)
def test_setdefault(self):
cmap = ComponentMap()
for c, _ in self._components:
with self.assertRaises(KeyError):
cmap[c]
self.assertTrue(c not in cmap)
cmap.setdefault(c, []).append(1)
self.assertEqual(cmap[c], [1])
del cmap[c]
with self.assertRaises(KeyError):
cmap[c]
self.assertTrue(c not in cmap)
cmap[c] = []
cmap.setdefault(c, []).append(1)
self.assertEqual(cmap[c], [1])
def test_eq(self):
cmap1 = ComponentMap()
self.assertNotEqual(cmap1, set())
self.assertFalse(cmap1 == set())
self.assertNotEqual(cmap1, list())
self.assertFalse(cmap1 == list())
self.assertNotEqual(cmap1, tuple())
self.assertFalse(cmap1 == tuple())
self.assertEqual(cmap1, dict())
self.assertTrue(cmap1 == dict())
cmap1.update(self._components)
self.assertNotEqual(cmap1, set())
self.assertFalse(cmap1 == set())
self.assertNotEqual(cmap1, list())
self.assertFalse(cmap1 == list())
self.assertNotEqual(cmap1, tuple())
self.assertFalse(cmap1 == tuple())
self.assertNotEqual(cmap1, dict())
self.assertFalse(cmap1 == dict())
self.assertTrue(cmap1 == cmap1)
self.assertEqual(cmap1, cmap1)
cmap2 = ComponentMap(self._components)
self.assertTrue(cmap2 == cmap1)
self.assertFalse(cmap2 != cmap1)
self.assertEqual(cmap2, cmap1)
self.assertTrue(cmap1 == cmap2)
self.assertFalse(cmap1 != cmap2)
self.assertEqual(cmap1, cmap2)
del cmap2[self._components[0][0]]
self.assertFalse(cmap2 == cmap1)
self.assertTrue(cmap2 != cmap1)
self.assertNotEqual(cmap2, cmap1)
self.assertFalse(cmap1 == cmap2)
self.assertTrue(cmap1 != cmap2)
self.assertNotEqual(cmap1, cmap2)
def __init__(self, *args, **kwds):
super(piecewise_nd_cc, self).__init__(*args, **kwds)
ndim = len(self.input)
nsimplices = len(self.triangulation.simplices)
npoints = len(self.triangulation.points)
pointsT = list(zip(*self.triangulation.points))
# create index objects
dimensions = range(ndim)
simplices = range(nsimplices)
vertices = range(npoints)
# create vars
self.v = variable_dict()
lmbda = self.v['lambda'] = variable_tuple(
variable(lb=0) for v in vertices)
y = self.v['y'] = variable_tuple(
variable(domain=Binary) for s in simplices)
lmbda_tuple = tuple(lmbda)
# create constraints
self.c = constraint_list()
clist = []
for d in dimensions:
clist.append(
linear_constraint(variables=lmbda_tuple + (self.input[d], ),
coefficients=tuple(pointsT[d]) + (-1, ),
rhs=0))
self.c.append(constraint_tuple(clist))
del clist
self.c.append(
linear_constraint(variables=lmbda_tuple + (self.output, ),
coefficients=tuple(self.values) + (-1, )))
if self.bound == 'ub':
self.c[-1].lb = 0
elif self.bound == 'lb':
self.c[-1].ub = 0
else:
assert self.bound == 'eq'
self.c[-1].rhs = 0
self.c.append(
linear_constraint(variables=lmbda_tuple,
coefficients=(1, ) * len(lmbda_tuple),
rhs=1))
# generate a map from vertex index to simplex index,
# which avoids an n^2 lookup when generating the
# constraint
vertex_to_simplex = [[] for v in vertices]
for s, simplex in enumerate(self.triangulation.simplices):
for v in simplex:
vertex_to_simplex[v].append(s)
clist = []
for v in vertices:
variables = tuple(y[s] for s in vertex_to_simplex[v])
clist.append(
linear_constraint(variables=variables + (lmbda[v], ),
coefficients=(1, ) * len(variables) + (-1, ),
lb=0))
self.c.append(constraint_tuple(clist))
del clist
self.c.append(
linear_constraint(variables=y, coefficients=(1, ) * len(y), rhs=1))