def get_implementations_f_r(self, f, r):
f1, f2 = f
r1, r2 = r
_, pack, _ = self._get_product()
m1s = self.dp1.get_implementations_f_r(f1, r1)
m2s = self.dp2.get_implementations_f_r(f2, r2)
options = set()
if do_extra_checks():
for m1 in m1s:
self.M1.belongs(m1)
try:
for m2 in m2s:
self.M2.belongs(m2)
except NotBelongs as e:
msg = ' Invalid result from dp2'
raise_wrapped(NotBelongs, e, msg, dp2=self.dp2.repr_long())
for m1 in m1s:
for m2 in m2s:
m = pack(m1, m2)
options.add(m)
if do_extra_checks():
for _ in options:
self.I.belongs(_)
return options
def get_implementations_f_r(self, f, r):
""" Returns a nonempty set of elements of self.M.
Might raise NotFeasible() """
res = set()
es = []
ms = None
for j, dp in enumerate(self.dps):
try:
ms = dp.get_implementations_f_r(f, r)
# print('%s: dp.get_implementations_f_r(f, r) = %s ' % (j, ms))
for m in ms:
if do_extra_checks():
Mj = dp.get_imp_space()
try:
Mj.belongs(m)
except NotBelongs:
raise ValueError(dp)
res.add(self.M.pack(j, m))
except NotFeasible as e:
es.append(e)
if not ms:
# no one was feasible
msg = 'None was feasible'
msg += '\n\n' + '\n\n'.join(str(e) for e in es)
raise_desc(NotFeasible, msg, f=f, r=r, self=self)
if do_extra_checks():
for _ in res:
self.M.belongs(_)
return res
def __init__(self, R, value):
if do_extra_checks():
R.belongs(value)
Map.__init__(self, R, R)
self.value = value
self.R = R
def __init__(self, F, value):
if do_extra_checks():
F.belongs(value)
Map.__init__(self, F, F)
self.value = value
self.F = F
def solve_f_iterate(dp0, f1, R, S, trace):
"""
Returns the next iteration si \in UR
Min ( h(f1, r20) \cup !r20 )
"""
UR = UpperSets(R)
if do_extra_checks():
UR.belongs(S)
R2 = R[1]
converged = set() # subset of solutions for which they converged
nextit = set()
# find the set of all r2s
for ra in S.minimals:
hr = dp0.solve_trace((f1, ra[1]), trace)
for rb in hr.minimals:
valid = R.leq(ra, rb)
if valid:
nextit.add(rb)
feasible = R2.leq(rb[1], ra[1])
if feasible:
converged.add(rb)
nextit = R.Us(poset_minima(nextit, R.leq))
converged = R.Us(poset_minima(converged, R.leq))
return nextit, converged
def solve_r_iterate(dp0, r1, F, S, trace):
LF = LowerSets(F)
if do_extra_checks():
LF.belongs(S)
F2 = F[1]
converged = set() # subset of solutions for which they converged
nextit = set()
# find the set of all r2s
for fa in S.maximals:
hr = dp0.solve_r_trace((r1, fa[1]), trace)
for fb in hr.maximals:
# valid = R.leq(ra, rb) # ra <= rb
valid = F.leq(fb, fa) # fb <= fa
if valid:
nextit.add(fb)
feasible = F2.leq(fa[1], fb[1])
if feasible:
converged.add(fb)
nextit = F.Ls(poset_maxima(nextit, F.leq))
converged = F.Ls(poset_maxima(converged, F.leq))
return nextit, converged
def evaluate(self, i):
if do_extra_checks():
self.I.belongs(i)
f = i
rs = self.solve(f)
fs = LowerSet(set([f]), self.F)
return fs, rs
def _unpack_m(self, m):
if do_extra_checks():
self.M.belongs(m)
from mcdp_dp.dp_series import get_product_compact
_, _, unpack = get_product_compact(self.M0, self.F2, self.R2)
m0, f2, r2 = unpack(m)
return m0, f2, r2
def solve_trace(self, func, trace):
if func in self._solve_cache:
# trace.log('using cache for %s' % str(func))
return trace.result(self._solve_cache[func])
trace.values(type='series')
with trace.child('dp1') as t:
u1 = self.dp1.solve_trace(func, t)
if do_extra_checks():
R1 = self.dp1.get_res_space()
tr1 = UpperSets(R1)
tr1.belongs(u1)
mcdp_dev_warning('rewrite this keeping structure')
mins = set([])
for u in u1.minimals:
with trace.child('dp2') as t:
v = self.dp2.solve_trace(u, t)
mins.update(v.minimals)
R = self.get_res_space()
minimals = poset_minima(mins, R.leq)
us = UpperSet(minimals, R)
self._solve_cache[func] = us
return trace.result(us)
def check_leq(self, a, b):
if do_extra_checks():
self.belongs(a)
self.belongs(b)
if not self._leq(a, b):
msg = '%s ≰ %s' % (a, b)
raise NotLeq(msg)
def format(self, x):
if do_extra_checks():
self.belongs(x)
if x == self.top:
return self.top.__repr__()
else:
# TODO: add parameter
if x == int(x):
return '%d' % int(x)
else:
if x == finfo.tiny:
return 'tiny'
if x == finfo.eps:
return 'eps'
if x == finfo.max:
return 'max'
# s = '%.5f' % x
# s = '%.10f' % x
s = '%f' % x
# remove trailing 0s
s = s.rstrip('0')
return s
def __init__(self, P):
self.P = P
if do_extra_checks():
top = self.get_top()
bot = self.get_bottom()
self.belongs(top)
self.belongs(bot)
assert self.leq(bot, top)
assert not self.leq(top, bot) # unless empty
def Us(self, elements):
elements = list(elements)
if do_extra_checks():
for e in elements:
self.belongs(e)
# XXX n^2
from mcdp_posets import check_minimal
check_minimal(elements, poset=self)
from mcdp_posets import UpperSet
return UpperSet(elements, self)
def __init__(self, elements, S):
N = Nat()
if do_extra_checks():
for e, howmany in elements.items():
S.belongs(e)
N.belongs(howmany)
self._elements = frozendict2(elements)
self._S = S
def get_implementations_f_r(self, f, r):
# print('%s get_implementaion(%s, %s)' % (id(self), f, r))
f1 = f
_, pack, _ = self._get_product()
R2 = self.dp2.get_res_space()
res = set()
# First let's solve again for r1
r1s = self.dp1.solve(f)
for r1 in r1s.minimals:
m1s = self.dp1.get_implementations_f_r(f1, r1)
if do_extra_checks():
try:
for m1 in m1s:
self.M1.belongs(m1)
except NotBelongs as e:
msg = 'Invalid result from dp1 (%s)' % type(self.dp1)
raise_wrapped(DPInternalError, e, msg, M1=self.M1, m1=m1,
dp1=self.dp1.repr_long())
assert m1s, (self.dp1, f1, r1)
f2 = r1
r2s = self.dp2.solve(f2)
for r2 in r2s.minimals:
if not R2.leq(r2, r):
continue
m2s = self.dp2.get_implementations_f_r(f2, r2)
for m1 in m1s:
for m2 in m2s:
m = pack(m1, m2)
res.add(m)
if not res:
msg = 'The (f,r) pair was not feasible.'
raise_desc(NotFeasible, msg, f=f, r=r, self=self)
if do_extra_checks():
M = self.get_imp_space()
for _ in res:
M.belongs(_)
assert res
return res
def is_feasible(self, f, i, r):
if do_extra_checks():
self.F.belongs(f)
self.I.belongs(i)
self.R.belongs(r)
try:
self.check_feasible(f, i, r)
except NotFeasible:
return False
else:
return True
def __call__(self, x):
if do_extra_checks():
D = self.get_domain()
try:
D.belongs(x)
except NotBelongs as e:
msg = 'Point does not belong to domain.'
raise_wrapped(NotBelongs, e, msg, map=self, x=x, domain=D)
y = self._call(x)
if do_extra_checks():
C = self.get_codomain()
try:
C.belongs(y)
except NotBelongs as e:
msg = 'Point does not belong to codomain.'
raise_wrapped(NotBelongs, e, msg, map=self, y=y, codomain=C)
return y
def eval_constant_lowersetfromcollection(op, context):
x = eval_constant(op.value, context)
v = x.value
u = x.unit
S = u.S
maximals = poset_minima(v.elements, S.leq)
value = LowerSet(maximals, S)
unit = LowerSets(S)
if do_extra_checks():
unit.belongs(value)
vu = ValueWithUnits(value, unit)
return vu
def check_feasible(self, f, m, r):
if do_extra_checks():
self.F.belongs(f)
self.M.belongs(m)
self.R.belongs(r)
lf, ur = self.evaluate(m)
try:
lf.belongs(f)
ur.belongs(r)
except NotBelongs:
msg = 'check_feasible failed.'
raise_desc(NotFeasible, msg, f=f, m=m, r=r, lf=lf, ur=ur)
def get_top(self):
if isinstance(self.S, FiniteCollectionAsSpace):
res = FiniteCollection(elements=self.S.elements,
S=self.S)
if do_extra_checks():
self.belongs(res)
return res
mcdp_dev_warning('Maybe should use a TooMuchComputation error.')
msg = 'Cannot enumerate the elements of this space.'
raise_desc(NotBounded, msg, space=self.S)
def solveU(self, ufunc):
if do_extra_checks():
UF = UpperSets(self.get_fun_space())
UF.belongs(ufunc)
res = set([])
for m in ufunc.minimals:
u = self.solve(m)
res.update(u.minimals)
ressp = self.get_res_space()
minima = poset_minima(res, ressp.leq)
return ressp.Us(minima)
def solve_all(self, f1, trace):
""" Returns an upperset in UR. You want to project
it to R1 to use as the output. """
dp0 = self.dp1
R = dp0.get_res_space()
R1 = R[0]
UR = UpperSets(R)
# we consider a set of iterates
# we start from the bottom
trace.log('Iterating in UR = %s' % UR.__str__())
s0 = R.Us(R.get_minimal_elements())
S = [KleeneIteration(s=s0, s_converged=R.Us(set()),
r=upperset_project(s0, 0),
r_converged=R1.Us(set()))]
for i in range(1, 1000000): # XXX
with trace.iteration(i) as t:
si_prev = S[-1].s
si_next, converged = solve_f_iterate(dp0, f1, R, si_prev, t)
iteration = KleeneIteration(s=si_next,
s_converged=converged,
r=upperset_project(si_next, 0),
r_converged=upperset_project(converged, 0))
S.append(iteration)
t.log('R = %s' % UR.format(si_next))
if do_extra_checks():
try:
UR.check_leq(si_prev, si_next)
except NotLeq as e:
msg = 'Loop iteration invariant not satisfied.'
raise_wrapped(Exception, e, msg, si_prev=si_prev,
si_next=si_next, dp=self.dp1)
t.values(state=S[-1])
if UR.leq(si_next, si_prev):
t.log('Breaking because converged (iteration %s) ' % i)
#t.log(' solution is %s' % (UR.format(sip)))
# todo: add reason why interrupted
break
trace.values(type='loop2', UR=UR, R=R, dp=self, iterations=S)
res_all = S[-1].s
res_r1 = upperset_project(res_all, 0)
result = dict(res_all=res_all, res_r1=res_r1)
return result
def solve_r_all(self, r1, trace):
""" Returns an upperset in UR. You want to project
it to R1 to use as the output. """
dp0 = self.dp1
F = dp0.get_fun_space()
F1 = F[0]
LF = LowerSets(F)
# we consider a set of iterates
# we start from the bottom
trace.log('Iterating in LF = %s' % LF.__str__())
s0 = F.Ls(F.get_maximal_elements())
S = [KleeneIteration(s=s0, s_converged=F.Ls(set()),
r=lowerset_project(s0, 0),
r_converged=F1.Ls(set()))]
for i in range(1, 1000000): # XXX
with trace.iteration(i) as t:
si_prev = S[-1].s
si_next, converged = solve_r_iterate(dp0, r1, F, si_prev, t)
iteration = KleeneIteration(s=si_next,
s_converged=converged,
r=lowerset_project(si_next, 0),
r_converged=lowerset_project(converged, 0))
S.append(iteration)
t.log('si_next = %s' % LF.format(si_next))
if do_extra_checks():
try:
LF.check_leq(si_prev, si_next)
except NotLeq as e:
msg = 'Loop iteration invariant not satisfied.'
raise_wrapped(Exception, e, msg, si_prev=si_prev,
si_next=si_next, dp=self.dp1)
t.values(state=S[-1])
if LF.leq(si_next, si_prev):
t.log('Breaking because converged (iteration %s) ' % i)
break
trace.values(type='loop2r', LF=LF, F=F, dp=self, iterations=S)
res_all = S[-1].s
res_f1 = lowerset_project(res_all, 0)
result = dict(res_all=res_all, res_f1=res_f1)
return result
def __init__(self, universe, relations):
check_isinstance(universe, set)
FiniteCollectionAsSpace.__init__(self, universe)
closure = transitive_closure(relations)
# relations contains all closures, but not the cycles
self.relations = frozenset(closure)
self._find_top()
self._find_bottom()
if do_extra_checks():
for a, b in self.relations:
assert a in universe
assert b in universe
def leq(self, a, b):
assert isinstance(a, tuple), (self, a)
assert isinstance(b, tuple), (self, b)
assert len(a) == len(self.subs), (self, a)
assert len(b) == len(self.subs), (self, b)
if do_extra_checks():
self.belongs(a)
self.belongs(b)
for sub, x, y in zip(self.subs, a, b):
if not sub.leq(x, y):
return False
return True
def check_unfeasible(self, f, i, r):
if do_extra_checks():
self.F.belongs(f)
self.I.belongs(i)
self.R.belongs(r)
lf, ur = self.evaluate(i)
try:
lf.belongs(f)
ur.belongs(r)
except NotBelongs:
pass
else:
msg = 'check_feasible failed.'
raise_desc(NotFeasible, msg, f=f, i=i, r=r, lf=lf, ur=ur)
def __init__(self, elements, S):
self.elements = frozenset(elements)
self.S = S
if do_extra_checks():
# XXX
problems = []
for m in elements:
try:
self.S.belongs(m)
except NotBelongs as e:
problems.append(e)
if problems:
msg = "Cannot create finite collection:\n"
msg += "\n".join(str(p) for p in problems)
raise NotBelongs(msg)
def upperset_project_map(ur, f):
""" Projects the upper set through the given map. """
check_isinstance(ur, UpperSet)
check_isinstance(f, Map)
from .types_universe import get_types_universe
tu = get_types_universe()
if do_extra_checks():
tu.check_equal(ur.P, f.get_domain())
Q = f.get_codomain()
assert isinstance(Q, Poset)
minimals = set()
for m in ur.minimals:
mi = f(m)
minimals.add(mi)
minimals = poset_minima(minimals, leq=Q.leq)
return UpperSet(minimals, P=Q)
def check_leq(self, a, b):
if do_extra_checks():
self.belongs(a)
self.belongs(b)
if a == b:
return True
if False:
if a == self.bot:
return True
if b == self.top:
return True
if b == self.bot:
raise NotLeq('b = my ⊥')
if a == self.top:
raise NotLeq('a = my ⊤')
self.my_leq_(a, b)
def solve(self, f):
if do_extra_checks():
F = self.get_fun_space()
F.belongs(f)
f1, f2 = f
r1 = self.dp1.solve(f1)
r2 = self.dp2.solve(f2)
R = self.get_res_space()
s = []
for m1, m2 in itertools.product(r1.minimals, r2.minimals):
s.append((m1, m2))
res = R.Us(set(s))
return res