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 _parse_declaration(solver: pywraplp.Solver, core_line: str, line_nr: int,
var_names: set):
spl_whitespace = core_line.split(maxsplit=1)
if spl_whitespace[0] != "int":
raise ValueError("Declaration on line %d should start with \"int \"." %
line_nr)
if len(spl_whitespace) != 2:
raise ValueError("Declaration on line %d has no variables." % line_nr)
spl_variables = spl_whitespace[1].split(",")
for raw_var in spl_variables:
clean_var = raw_var.strip()
if not re.match(_REGEXP_SINGLE_VAR_NAME_ALL, clean_var):
raise ValueError(
"Non-permitted variable name (\"%s\") on line %d." %
(clean_var, line_nr))
if clean_var in var_names:
raise ValueError("Variable \"%s\" declared again on line %d." %
(clean_var, line_nr))
var_names.add(clean_var)
solver.IntVar(-solver.infinity(), solver.infinity(), clean_var)
