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)
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))