def test_minimize():
# minimize x1 + 2 x2 + 3 x3 + ... + 10 x10
# subject to x1 + x2 + x3 + x4 + x5 == 1
# x6 + x7 + x8 + x9 + x10 == 1
C = Clauses(10)
C.Require(C.ExactlyOne, range(1,6))
C.Require(C.ExactlyOne, range(6,11))
objective = [(k,k) for k in range(1,11)]
sol = C.sat()
C.unsat = True
assert C.minimize(objective, sol)[1] == 56
C.unsat = False
sol2, sval = C.minimize(objective, sol)
assert C.minimize(objective, sol)[1] == 7, (objective, sol2, sval)
def test_sat():
C = Clauses()
C.new_var('x1')
C.new_var('x2')
assert C.sat([(+1,),(+2,)], names=True) == {'x1','x2'}
assert C.sat([(-1,),(+2,)], names=True) == {'x2'}
assert C.sat([(-1,),(-2,)], names=True) == set()
assert C.sat([(+1,),(-1,)], names=True) is None
C.unsat = True
assert C.sat() is None
assert len(Clauses(10).sat([[1]])) == 10
def test_AMONE():
my_TEST(my_AMONE, Clauses.AtMostOne_NSQ, 0,3, True)
my_TEST(my_AMONE, Clauses.AtMostOne_BDD, 0,3, True)
my_TEST(my_AMONE, Clauses.AtMostOne, 0,3, True)
C1 = Clauses(10)
x1 = C1.AtMostOne_BDD((1,2,3,4,5,6,7,8,9,10))
C2 = Clauses(10)
x2 = C2.AtMostOne((1,2,3,4,5,6,7,8,9,10))
assert x1 == x2 and C1.clauses == C2.clauses
def gen_clauses(self, groups, trackers, specs):
C = Clauses()
# Creates a variable that represents the proposition:
# Does the package set include a package that matches MatchSpec "ms"?
def push_MatchSpec(ms):
name = self.ms_to_v(ms)
m = C.from_name(name)
if m is None:
libs = [fn for fn in self.find_matches_group(ms, groups, trackers)]
# If the MatchSpec is optional, then there may be cases where we want
# to assert that it is *not* True. This requires polarity=None.
m = C.Any(libs, polarity=None if ms.optional else True, name=name)
return m
# Creates a variable that represents the proposition:
# Does the package set include package "fn"?
for group in itervalues(groups):
for fn in group:
C.new_var(fn)
# Install no more than one version of each package
C.Require(C.AtMostOne, group)
# Create a variable that represents the proposition:
# Is the feature "name" active in this package set?
# We mark this as "optional" below because sometimes we need to be able to
# assert the proposition is False during the feature minimization pass.
for name in iterkeys(trackers):
ms = MatchSpec('@' + name)
ms.optional = True
push_MatchSpec(ms)
# Create a variable that represents the proposition:
# Is the MatchSpec "ms" satisfied by the current package set?
for ms in specs:
push_MatchSpec(ms)
# Create propositions that assert:
# If package "fn" is installed, its dependencie must be satisfied
for group in itervalues(groups):
for fn in group:
for ms in self.ms_depends(fn):
if not ms.optional:
C.Require(C.Or, C.Not(fn), push_MatchSpec(ms))
return C
def my_TEST(Mfunc, Cfunc, mmin, mmax, is_iter):
for m in range(mmin,mmax+1):
if m == 0:
ijprod = [()]
else:
ijprod = (True,False)+sum(((k,my_NOT(k)) for k in range(1,m+1)),())
ijprod = product(ijprod, repeat=m)
for ij in ijprod:
C = Clauses()
Cpos = Clauses()
Cneg = Clauses()
for k in range(1,m+1):
nm = 'x%d' % k
C.new_var(nm)
Cpos.new_var(nm)
Cneg.new_var(nm)
ij2 = tuple(C.from_index(k) if type(k) is int else k for k in ij)
if is_iter:
x = Cfunc.__get__(C,Clauses)(ij2)
Cpos.Require(Cfunc.__get__(Cpos,Clauses), ij)
Cneg.Prevent(Cfunc.__get__(Cneg,Clauses), ij)
else:
x = Cfunc.__get__(C,Clauses)(*ij2)
Cpos.Require(Cfunc.__get__(Cpos,Clauses), *ij)
Cneg.Prevent(Cfunc.__get__(Cneg,Clauses), *ij)
tsol = Mfunc(*ij)
if type(tsol) is bool:
assert x is tsol, (ij2, Cfunc.__name__, C.clauses)
assert Cpos.unsat == (not tsol) and not Cpos.clauses, (ij, 'Require(%s)')
assert Cneg.unsat == tsol and not Cneg.clauses, (ij, 'Prevent(%s)')
continue
for sol in C.itersolve([(x,)]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is True, (ij2, sol, Cfunc.__name__, C.clauses)
for sol in Cpos.itersolve([]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is True, (ij, sol,'Require(%s)' % Cfunc.__name__, Cpos.clauses)
for sol in C.itersolve([(C.Not(x),)]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is False, (ij2, sol, Cfunc.__name__, C.clauses)
for sol in Cneg.itersolve([]):
qsol = Mfunc(*my_SOL(ij,sol))
assert qsol is False, (ij, sol,'Prevent(%s)' % Cfunc.__name__, Cneg.clauses)
def sat(val):
return Clauses(max(abs(v) for v in chain(*val))).sat(val)
def test_LinearBound():
L = [
([], [0, 1], 10),
([], [1, 2], 10),
({'x1':2, 'x2':2}, [3, 3], 10),
({'x1':2, 'x2':2}, [0, 1], 1000),
({'x1':1, 'x2':2}, [0, 2], 1000),
({'x1':2, '!x2':2}, [0, 2], 1000),
([(1, 1), (2, 2), (3, 3)], [3, 3], 1000),
([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7)], [0, 2], 1000),
([(0, 1), (1, 2), (2, 3), (0, 4), (1, 5), (0, 6), (1, 7),
(3, False), (2, True)], [2, 4], 1000),
([(1, 15), (2, 16), (3, 17), (4, 18), (5, 6), (5, 19), (6, 7),
(6, 20), (7, 8), (7, 21), (7, 28), (8, 9), (8, 22), (8, 29), (8, 41), (9,
10), (9, 23), (9, 30), (9, 42), (10, 1), (10, 11), (10, 24), (10, 31),
(10, 34), (10, 37), (10, 43), (10, 46), (10, 50), (11, 2), (11, 12), (11,
25), (11, 32), (11, 35), (11, 38), (11, 44), (11, 47), (11, 51), (12, 3),
(12, 4), (12, 5), (12, 13), (12, 14), (12, 26), (12, 27), (12, 33), (12,
36), (12, 39), (12, 40), (12, 45), (12, 48), (12, 49), (12, 52), (12, 53),
(12, 54)], [192, 204], 100),
]
for eq, rhs, max_iter in L:
if isinstance(eq, dict):
N = len(eq)
else:
N = max([0]+[a for c,a in eq if a is not True and a is not False])
C = Clauses(N)
Cpos = Clauses(N)
Cneg = Clauses(N)
if isinstance(eq, dict):
for k in range(1,N+1):
nm = 'x%d'%k
C.name_var(k, nm)
Cpos.name_var(k, nm)
Cneg.name_var(k, nm)
eq2 = [(v,C.from_name(c)) for c,v in iteritems(eq)]
else:
eq2 = eq
x = C.LinearBound(eq, rhs[0], rhs[1])
Cpos.Require(Cpos.LinearBound, eq, rhs[0], rhs[1])
Cneg.Prevent(Cneg.LinearBound, eq, rhs[0], rhs[1])
if x is not False:
for _, sol in zip(range(max_iter), C.itersolve([] if x is True else [(x,)],N)):
assert rhs[0] <= my_EVAL(eq2,sol) <= rhs[1], C.clauses
if x is not True:
for _, sol in zip(range(max_iter), C.itersolve([] if x is True else [(C.Not(x),)],N)):
assert not(rhs[0] <= my_EVAL(eq2,sol) <= rhs[1]), C.clauses
for _, sol in zip(range(max_iter), Cpos.itersolve([],N)):
assert rhs[0] <= my_EVAL(eq2,sol) <= rhs[1], ('Cpos',Cpos.clauses)
for _, sol in zip(range(max_iter), Cneg.itersolve([],N)):
assert not(rhs[0] <= my_EVAL(eq2,sol) <= rhs[1]), ('Cneg',Cneg.clauses)