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 main():
# Create the linear solver with the GLOP backend.
solver = Solver('simple_lp_program', Solver.GLOP_LINEAR_PROGRAMMING)
# Create the variables x and y.
x = solver.NumVar(0, 1, 'x')
y = solver.NumVar(0, 2, 'y')
print('Number of variables =', solver.NumVariables())
# Create a linear constraint, 0 <= x + y <= 2.
ct = solver.Constraint(0, 2, 'ct')
ct.SetCoefficient(x, 1)
ct.SetCoefficient(y, 1)
print('Number of constraints =', solver.NumConstraints())
# Create the objective function, 3 * x + y.
objective = solver.Objective()
objective.SetCoefficient(x, 3)
objective.SetCoefficient(y, 1)
objective.SetMaximization()
solver.Solve()
print('Solution:')
print('Objective value =', objective.Value())
print('x =', x.solution_value())
print('y =', y.solution_value())
def _declare_variable(self, solver: pywraplp.Solver, nth_cycle: int,
nth_index: int) -> None:
return solver.NumVar(
MIN_N_PHASES_FOR_SUSTAIN,
MIN_N_PHASES_FOR_SUSTAIN * MAX_N_MIN_PHASES_FOR_SUSTAIN,
self._get_variable_name(nth_cycle, nth_index),
)
def _add_stock_variables(num_types: int, num_time_periods: int, solver: Solver) \
-> Dict[V, Variable]:
"""Create stock variables.
A stock variable $s^t_p$ is a non-negative real variable which represents the number of
items of type $t$ on stock in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each stock variable to its solver variable
"""
stock_vars = dict()
for (item_type, time_period) in product(range(num_types),
range(-1, num_time_periods)):
stock_vars[V(type=item_type, period=time_period)] = \
solver.NumVar(lb=0., ub=solver.infinity(), name=f's_{item_type}_{time_period}')
module_logger.info(f'Created {len(stock_vars)} stock variables.')
return stock_vars
def _set_coefficients(solver: pywraplp.Solver, objective_or_constraint,
coefficient_part: str, line_nr: int, var_names: set):
# Strip the coefficient whitespace
remainder = coefficient_part.strip()
if len(remainder) == 0:
raise ValueError("No variables present in equation on line %d." %
line_nr)
# All variables found
var_names_found = set()
running_constant_sum = 0.0
had_at_least_one_variable = False
while len(remainder) != 0:
# Combination sign
coefficient = 1.0
combination_sign_match = re.search(r"^[-+]", remainder)
if combination_sign_match is not None:
if combination_sign_match.group() == "-":
coefficient = -1.0
remainder = remainder[1:].strip()
# Real sign
sign_match = re.search(r"^[-+]", remainder)
if sign_match is not None:
if sign_match.group() == "-":
coefficient = coefficient * -1.0
remainder = remainder[
1:] # There is no strip() here, as it must be directly in front of the mantissa
# Mantissa and exponent
mantissa_exp_match = re.search(r"^(\d+(\.\d*)?|\.\d+)([eE][-+]?\d+)?",
remainder)
whitespace_after = False
if mantissa_exp_match is not None:
coefficient = coefficient * float(mantissa_exp_match.group())
remainder = remainder[mantissa_exp_match.span()[1]:]
stripped_remainder = remainder.strip()
if len(remainder) != len(stripped_remainder):
whitespace_after = True
remainder = stripped_remainder
# Variable name
var_name_match = re.search(_REGEXP_SINGLE_VAR_NAME_START, remainder)
if var_name_match is not None:
# It must have had at least one variable
had_at_least_one_variable = True
# Retrieve clean variable name
clean_var = var_name_match.group()
var_names.add(clean_var)
if clean_var in var_names_found:
raise ValueError(
"Variable \"%s\" found more than once on line %d." %
(clean_var, line_nr))
var_names_found.add(clean_var)
solver_var = solver.LookupVariable(clean_var)
if solver_var is None:
solver_var = solver.NumVar(-solver.infinity(),
solver.infinity(), clean_var)
# Set coefficient
objective_or_constraint.SetCoefficient(solver_var, coefficient)
# Strip what we matched
remainder = remainder[var_name_match.span()[1]:]
stripped_remainder = remainder.strip()
whitespace_after = False
if len(remainder) != len(stripped_remainder):
whitespace_after = True
remainder = stripped_remainder
elif mantissa_exp_match is None:
raise ValueError(
"Cannot process remainder coefficients of \"%s\" on line %d." %
(remainder, line_nr))
else:
running_constant_sum += coefficient
# At the end of each element there either:
# (a) Must be whitespace (e.g., x1 x2 <= 10)
# (b) The next combination sign (e.g., x1+x2 <= 10)
# (c) Or it was the last one, as such remainder is empty (e.g., x1 <= 10)
if len(remainder) != 0 and not whitespace_after and remainder[
0:1] != "-" and remainder[0:1] != "+":
raise ValueError(
"Unexpected next character \"%s\" on line %d (expected whitespace or "
"combination sign character)." % (remainder[0:1], line_nr))
# There must have been at least one variable
if not had_at_least_one_variable:
raise ValueError(
"Not a single variable present in the coefficients on line %d." %
line_nr)
return running_constant_sum