def find_transform(x, y, limit, threshold=1e-7):
"""
find a integer solution to ax + b - cxy - dy = 0
this will give us the mobius transform: T(x) = y
:param x: numeric constant to check
:param y: numeric manipulation of constant
:param limit: range to look at
:param threshold: optimal solution threshold.
:return MobiusTransform in case of success or None.
"""
x1 = x
x2 = dec(1.0)
x3 = -x * y
x4 = -y
solver = Solver('mobius', Solver.CBC_MIXED_INTEGER_PROGRAMMING)
a = solver.IntVar(-limit, limit, 'a')
b = solver.IntVar(-limit, limit, 'b')
c = solver.IntVar(-limit, limit, 'c')
d = solver.IntVar(-limit, limit, 'd')
f = solver.NumVar(0, 1, 'f')
solver.Add(f == (a * x1 + b * x2 + c * x3 + d * x4))
solver.Add(a * x1 + b >=
1) # don't except trivial solutions and remove some redundancy
solver.Minimize(f)
status = solver.Solve()
if status == Solver.OPTIMAL:
if abs(solver.Objective().Value()) <= threshold:
res_a, res_b, res_c, res_d = int(a.solution_value()), int(b.solution_value()),\
int(c.solution_value()), int(d.solution_value())
ret = MobiusTransform(
np.array([[res_a, res_b], [res_c, res_d]], dtype=object))
ret.normalize()
return ret
else:
return None
def _declare_constraint(
solver: pywraplp.Solver,
group: "Group",
variables: typing.Tuple[typing.Tuple[pywraplp.Variable]],
) -> None:
higher_groups = group.get_simultaneous_groups_of_higher_cycle()
if higher_groups:
# fixed duration of group
summed_active_transitions_of_group = Group._sum_active_transitions_of_group(
group, higher_groups)
# fixed duration of higher groups
summed_transitions_of_higher_groups = sum(
Group._calculate_duration_of_n_phases(higher_group,
higher_group.attack)
for higher_group in higher_groups)
summed_transitions_of_higher_groups += Group._calculate_duration_of_n_phases(
higher_groups[-1], higher_groups[-1].release)
difference_of_duration = (summed_active_transitions_of_group -
summed_transitions_of_higher_groups)
constraint = sum(
Group._calculate_duration_of_n_phases(higher_group, var)
for var, higher_group in zip(variables[1], higher_groups))
constraint = constraint - (Group._calculate_duration_of_n_phases(
group, variables[0][0]))
solver.Add(constraint == difference_of_duration)