def setup_aut(xmax=15, ymax=15):
fol = _fol.Context()
fol.bdd.configure(reordering=True)
# CAUTION: remember that type hints (safety)
# needs to be added as care set
fol.declare(x=(0, xmax), y=(0, ymax))
x_vars = ['x', 'y']
p_table = lat._parameter_table(
x_vars, fol.vars, a_name='a', b_name='b')
q_table = lat._parameter_table(
x_vars, fol.vars, a_name='u', b_name='v')
fol.declare(**p_table)
fol.declare(**q_table)
px = lat._map_vars_to_parameters(
x_vars, a_name='a', b_name='b')
qx = lat._map_vars_to_parameters(
x_vars, a_name='u', b_name='v')
varmap = lat.parameter_varmap(px, qx)
p_to_q = lat._renaming_between_parameters(px, qx)
prm = lat.Parameters()
prm.x_vars = x_vars
prm.p_vars = set(p_table)
prm.q_vars = set(q_table)
prm.p_to_q = p_to_q
prm._px = px
prm._qx = qx
prm._varmap = varmap
return fol, prm
def test_transpose():
fol = _fol.Context()
dvars = {'p': (0, 4), 'q': (0, 4), "p_cp": (0, 4)}
fol.declare(**dvars)
s = '(p = 1) \/ (p = 2) \/ (p = 4)'
p_is_prime = fol.add_expr(s)
s = '(p = 1) \/ (p = 3)'
p_is_signature = fol.add_expr(s)
p_to_q = {'p': 'q'}
p_leq_q = fol.add_expr("p <= q")
u_leq_p = fol.add_expr("p_cp <= p")
p_leq_u = fol.add_expr("p <= p_cp")
prm = lat.Parameters()
prm.u_leq_p = u_leq_p
prm.p_leq_u = p_leq_u
prm.p_leq_q = p_leq_q
prm.p_to_q = p_to_q
prm.p_vars = {'p'}
prm.q_vars = {'q'}
prm.u_vars = {'p_cp'}
prm.p_to_u = {'p': 'p_cp'}
bab = cov._BranchAndBound(prm, fol)
tau = cov._floor(
p_is_signature, p_is_prime, bab, fol)
s = 'p = 1 \/ p = 3'
tau_ = fol.add_expr(s)
assert tau == tau_
def test_max_transpose():
fol = _fol.Context()
# `p'` serves as `u`
dvars = {'p': (0, 4), 'q': (0, 4), "p_cp": (0, 4)}
fol.declare(**dvars)
s = '(p = 2) \/ (p = 4)'
p_is_prime = fol.add_expr(s)
s = '(p = 1) \/ (p = 3)'
p_is_signature = fol.add_expr(s)
p_to_q = {'p': 'q'}
# we use intervals `0..p` as literals
px = dict(p=dict(a='0', b='p'))
qx = dict(p=dict(a='0', b='q'))
u_leq_p = fol.add_expr("p_cp <= p")
p_leq_u = fol.add_expr("p <= p_cp")
p_leq_q = fol.add_expr("p <= q")
p_eq_q = fol.add_expr("p = q") # /\ (0 = 0)
prm = lat.Parameters()
prm._px = px
prm._qx = qx
prm.u_leq_p = u_leq_p
prm.p_leq_u = p_leq_u
prm.p_leq_q = p_leq_q
prm.p_eq_q = p_eq_q
prm.p_to_q = p_to_q
prm.p_vars = {'p'}
prm.q_vars = {'q'}
prm.u_vars = {'p_cp'}
prm.p_to_u = {'p': 'p_cp'}
bab = cov._BranchAndBound(prm, fol)
max_tau_x = cov._max_transpose(
p_is_signature, p_is_prime, bab, fol)
s = 'p = 3'
max_tau_x_ = fol.add_expr(s)
assert max_tau_x == max_tau_x_
def setup_orthotope_vars():
fol = _fol.Context()
fol.declare(
x=(0, 5),
y=(2, 14),
px=(0, 5),
qx=(0, 5),
py=(2, 14),
qy=(2, 14),
ax=(0, 5),
bx=(0, 5),
ay=(2, 14),
by=(2, 14),
)
xvars = ['x', 'y']
px = dict(x=dict(a='px', b='qx'), y=dict(a='py', b='qy'))
qx = dict(x=dict(a='ax', b='bx'), y=dict(a='ay', b='by'))
prm = lat.Parameters()
prm.x_vars = xvars
prm._px = px
prm._qx = qx
prm.p_to_q = dict(px='ax', py='ay', qx='bx', qy='by')
prm.p_vars = set(prm.p_to_q)
prm.q_vars = set(prm.p_to_q.values())
varmap = lat.parameter_varmap(px, qx)
prm.p_leq_q = lat.subseteq(varmap, fol)
prm.p_eq_q = lat.eq(varmap, fol)
return fol, prm
def test_list_orthotope_expr():
fol = _fol.Context()
fol.declare(
x=(-4, 5), a_x=(-4, 5), b_x=(-4, 5),
y=(-7, 15), a_y=(-7, 15), b_y=(-7, 15))
px, _ = dummy_parameters()
prm = lat.Parameters()
prm._px = px
f = fol.add_expr('x = 1')
care = fol.true
s = (
'(a_x = 2) /\ (2 <= b_x) /\ (b_x <= 3) '
'/\ (a_y = 1 ) /\ (b_y = 5)')
cover = fol.add_expr(s)
r = lat.list_expr(cover, prm, fol)
r = set(r)
r_ = {'(x = 2) /\ (y \in 1 .. 5)',
'(x \in 2 .. 3) /\ (y \in 1 .. 5)'}
assert r == r_, (r, r_)
# simple syntax, for parsing back
# (needed until able to parse `x \in a .. b` expressions)
r = lat.list_expr(cover, prm, fol, simple=True)
r = set(r)
r_ = {'(x = 2) /\ (1 <= y) /\ (y <= 5)',
'(2 <= x) /\ (x <= 3) /\ (1 <= y) /\ (y <= 5)'}
assert r == r_, (r, r_)
# clipping on, but nothing to clip
r = lat.list_expr(cover, prm, fol, use_dom=True)
r = set(r)
r_ = {'(x = 2) /\ (y \in 1 .. 5)',
'(x \in 2 .. 3) /\ (y \in 1 .. 5)'}
assert r == r_, (r, r_)
# clip using type hints
s = (
'(a_x = -4) /\ (5 <= b_x)'
'/\ (a_y = 1 ) /\ (b_y = 5)')
cover = fol.add_expr(s)
r = lat.list_expr(cover, prm, fol, use_dom=True)
r = set(r)
r_ = {'(y \in 1 .. 5)'}
assert r == r_, (r, r_)
# empty orthotopes
s = (
'(a_x = -4) /\ (5 <= b_x)'
'/\ (a_y = 3 ) /\ (b_y = 1)')
cover = fol.add_expr(s)
with assert_raises(AssertionError):
lat.list_expr(cover, prm, fol, use_dom=True)
with assert_raises(AssertionError):
lat.list_expr(cover, prm, fol)
def test_branch_and_bound_class():
fol = _fol.Context()
prm = lat.Parameters()
bab = cov._BranchAndBound(prm, fol)
bab.lower_bound = 15
with assert_raises(AssertionError):
bab.upper_bound = 10
bab.upper_bound = 20
# only init for lower bound
with assert_raises(AssertionError):
bab.lower_bound = 17
with assert_raises(AssertionError):
bab.upper_bound = 10
bab.upper_bound = 18
def test_contains_covered():
fol = _fol.Context()
fol.declare(p_cp=(0, 4), p=(0, 4), q=(0, 4))
s = 'p_cp = 1 \/ p_cp = 2 \/ p_cp = 5'
u_is_signature = fol.add_expr(s)
prm = lat.Parameters()
prm.p_vars = {'p'}
prm.q_vars = {'q'}
prm.u_vars = {'p_cp'}
prm.p_to_q = {'p': 'q'}
prm.u_leq_p = fol.add_expr('p_cp <= p')
prm.p_leq_q = fol.add_expr('p <= q')
# prm.p_to_u = {'p': 'u'}
p_like_q = cov._contains_covered(u_is_signature, prm.u_leq_p, prm, fol)
supp = fol.support(p_like_q)
# pprint.pprint(list(fol.pick_iter(p_like_q, care_vars=supp)))
s = ('((q >= 1) => (p >= 1)) /\ '
'((q >= 2) => (p >= 2)) /\ '
'((q >= 5) => (p >= 5))')
p_like_q_ = fol.add_expr(s)
assert p_like_q == p_like_q_
def test_scaling_equality():
aut = _fol.Context()
x_vars = dict(x=(0, 10), y=(0, 15), z=(0, 15))
aut.declare(**x_vars)
params = dict(pa='a', pb='b', qa='u', qb='v')
p_dom = lat._parameter_table(x_vars,
aut.vars,
a_name=params['pa'],
b_name=params['pb'])
q_dom = lat._parameter_table(x_vars,
aut.vars,
a_name=params['qa'],
b_name=params['qb'])
aut.declare(**p_dom)
aut.declare(**q_dom)
px = lat._map_vars_to_parameters(x_vars,
a_name=params['pa'],
b_name=params['pb'])
qx = lat._map_vars_to_parameters(x_vars,
a_name=params['qa'],
b_name=params['qb'])
p_to_q = lat._renaming_between_parameters(px, qx)
x_as_x = {xj: dict(a=xj, b=xj) for xj in px}
varmap = lat.parameter_varmap(px, x_as_x)
log.info('Number of variables: {n}'.format(n=len(varmap)))
u = lat.subseteq(varmap, aut)
#
s = ('( '
'(z = 1 /\ y <= 0) \/ '
'(x = 0 /\ z = 1) \/ '
'(y >= 1 /\ x <= 0) \/ '
'(y >= 1 /\ z <= 0) \/ '
'(x >= 1 /\ z <= 0) \/ '
'(x >= 1 /\ y <= 0) '
') ')
f = aut.add_expr(s)
prm = lat.Parameters()
prm._px = px
lat.embed_as_implicants(f, prm, aut)
def test_maxima():
prm = lat.Parameters()
fol, _ = setup_aut(5, 5)
s = 'x = 1 \/ x = 3 \/ x = 4'
u = fol.add_expr(s)
# x <= y
s = '(x = 1 /\ y = 1) \/ (x = 1 /\ y = 3)'
prm.p_leq_q = fol.add_expr(s)
prm.p_vars = {'x'}
prm.q_vars = {'y'}
prm.p_to_q = {'x': 'y'}
r = stx.conj('{pj} = {qj}'.format(pj=pj, qj=qj)
for pj, qj in prm.p_to_q.items())
prm.p_eq_q = fol.add_expr(r)
t0 = time.time()
m = cov._maxima(u, prm, fol)
t1 = time.time()
dt = t1 - t0
log.info('`maxima` time (sec): {dt:1.2f}'.format(dt=dt))
# print result
gen = fol.pick_iter(m, care_vars=['x'])
c = list(gen)
log.info(c)