def __init__(self, *args, **kwds):
super(piecewise_dlog, 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)
assert 2**L == len(breakpoints) - 1
B_LEFT, B_RIGHT = self._branching_scheme(L)
# create indexers
polytopes = range(len(breakpoints) - 1)
vertices = range(len(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 polytope_verts(p))
y = self.v['y'] = variable_tuple(
variable(domain=Binary) for i in range(L))
# create piecewise constraints
self.c = constraint_list()
self.c.append(
linear_constraint(
variables=(self.input, ) + tuple(lmbda[p, v] for p in polytopes
for v in polytope_verts(p)),
coefficients=(-1, ) + tuple(breakpoints[v] for p in polytopes
for v in polytope_verts(p)),
rhs=0))
self.c.append(
linear_constraint(
variables=(self.output, ) + tuple(lmbda[p, v]
for p in polytopes
for v in polytope_verts(p)),
coefficients=(-1, ) + tuple(values[v] for p in polytopes
for v in polytope_verts(p))))
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.values()),
coefficients=(1, ) * len(lmbda),
rhs=1))
clist = []
for i in range(L):
variables = tuple(lmbda[p, v] for p in B_LEFT[i]
for v in polytope_verts(p))
clist.append(
linear_constraint(variables=variables + (y[i], ),
coefficients=(1, ) * len(variables) + (-1, ),
ub=0))
self.c.append(constraint_tuple(clist))
del clist
clist = []
for i in range(L):
variables = tuple(lmbda[p, v] for p in B_RIGHT[i]
for v in polytope_verts(p))
clist.append(
linear_constraint(variables=variables + (y[i], ),
coefficients=(1, ) * len(variables) + (1, ),
ub=1))
self.c.append(constraint_tuple(clist))
def test_log2floor(self):
self.assertEqual(util.log2floor(1), 0)
self.assertEqual(util.log2floor(2), 1)
self.assertEqual(util.log2floor(3), 1)
self.assertEqual(util.log2floor(4), 2)
self.assertEqual(util.log2floor(5), 2)
self.assertEqual(util.log2floor(6), 2)
self.assertEqual(util.log2floor(7), 2)
self.assertEqual(util.log2floor(8), 3)
self.assertEqual(util.log2floor(9), 3)
self.assertEqual(util.log2floor(2**10), 10)
self.assertEqual(util.log2floor(2**10 + 1), 10)
self.assertEqual(util.log2floor(2**20), 20)
self.assertEqual(util.log2floor(2**20 + 1), 20)
self.assertEqual(util.log2floor(2**30), 30)
self.assertEqual(util.log2floor(2**30 + 1), 30)
self.assertEqual(util.log2floor(2**40), 40)
self.assertEqual(util.log2floor(2**40 + 1), 40)
