def test_inequality_binary(self):
"""Test InequalityToEqualityConverter with binary variables"""
op = QuadraticProgram()
for i in range(3):
op.binary_var(name="x{}".format(i))
# Linear constraints
linear_constraint = {"x0": 1, "x1": 1}
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, "x0x1")
linear_constraint = {"x1": 1, "x2": -1}
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, "x1x2")
linear_constraint = {"x0": 1, "x2": 3}
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, "x0x2")
# Quadratic constraints
quadratic = {("x0", "x1"): 1, ("x1", "x2"): 2}
op.quadratic_constraint({}, quadratic, Constraint.Sense.LE, 3,
"x0x1_x1x2LE")
quadratic = {("x0", "x1"): 3, ("x1", "x2"): 4}
op.quadratic_constraint({}, quadratic, Constraint.Sense.GE, 3,
"x0x1_x1x2GE")
# Convert inequality constraints into equality constraints
conv = InequalityToEquality()
op2 = conv.convert(op)
self.assertListEqual(
[v.name for v in op2.variables],
[
"x0",
"x1",
"x2",
"x1x2@int_slack",
"x0x2@int_slack",
"x0x1_x1x2LE@int_slack",
"x0x1_x1x2GE@int_slack",
],
)
# Check names and objective senses
self.assertEqual(op.name, op2.name)
self.assertEqual(op.objective.sense, op2.objective.sense)
# For linear constraints
lst = [
op2.linear_constraints[0].linear.to_dict()[0],
op2.linear_constraints[0].linear.to_dict()[1],
]
self.assertListEqual(lst, [1, 1])
self.assertEqual(op2.linear_constraints[0].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[1].linear.to_dict()[1],
op2.linear_constraints[1].linear.to_dict()[2],
op2.linear_constraints[1].linear.to_dict()[3],
]
self.assertListEqual(lst, [1, -1, 1])
lst = [op2.variables[3].lowerbound, op2.variables[3].upperbound]
self.assertListEqual(lst, [0, 3])
self.assertEqual(op2.linear_constraints[1].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[2].linear.to_dict()[0],
op2.linear_constraints[2].linear.to_dict()[2],
op2.linear_constraints[2].linear.to_dict()[4],
]
self.assertListEqual(lst, [1, 3, -1])
lst = [op2.variables[4].lowerbound, op2.variables[4].upperbound]
self.assertListEqual(lst, [0, 2])
self.assertEqual(op2.linear_constraints[2].sense, Constraint.Sense.EQ)
# For quadratic constraints
lst = [
op2.quadratic_constraints[0].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[0].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[0].linear.to_dict()[5],
]
self.assertListEqual(lst, [1, 2, 1])
lst = [op2.variables[5].lowerbound, op2.variables[5].upperbound]
self.assertListEqual(lst, [0, 3])
lst = [
op2.quadratic_constraints[1].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[1].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[1].linear.to_dict()[6],
]
self.assertListEqual(lst, [3, 4, -1])
lst = [op2.variables[6].lowerbound, op2.variables[6].upperbound]
self.assertListEqual(lst, [0, 4])
new_x = conv.interpret(np.arange(7))
np.testing.assert_array_almost_equal(new_x, np.arange(3))
def test_inequality_integer(self):
""" Test InequalityToEqualityConverter with integer variables """
op = QuadraticProgram()
for i in range(3):
op.integer_var(name='x{}'.format(i), lowerbound=-3, upperbound=3)
# Linear constraints
linear_constraint = {'x0': 1, 'x1': 1}
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {'x1': 1, 'x2': -1}
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {'x0': 1, 'x2': 3}
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, 'x0x2')
# Quadratic constraints
quadratic = {('x0', 'x1'): 1, ('x1', 'x2'): 2}
op.quadratic_constraint({}, quadratic, Constraint.Sense.LE, 3, 'x0x1_x1x2LE')
quadratic = {('x0', 'x1'): 3, ('x1', 'x2'): 4}
op.quadratic_constraint({}, quadratic, Constraint.Sense.GE, 3, 'x0x1_x1x2GE')
conv = InequalityToEquality()
op2 = conv.convert(op)
self.assertListEqual([v.name for v in op2.variables],
['x0', 'x1', 'x2', 'x1x2@int_slack', 'x0x2@int_slack',
'x0x1_x1x2LE@int_slack', 'x0x1_x1x2GE@int_slack'])
# For linear constraints
lst = [
op2.linear_constraints[0].linear.to_dict()[0],
op2.linear_constraints[0].linear.to_dict()[1],
]
self.assertListEqual(lst, [1, 1])
self.assertEqual(op2.linear_constraints[0].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[1].linear.to_dict()[1],
op2.linear_constraints[1].linear.to_dict()[2],
op2.linear_constraints[1].linear.to_dict()[3],
]
self.assertListEqual(lst, [1, -1, 1])
lst = [op2.variables[3].lowerbound, op2.variables[3].upperbound]
self.assertListEqual(lst, [0, 8])
self.assertEqual(op2.linear_constraints[1].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[2].linear.to_dict()[0],
op2.linear_constraints[2].linear.to_dict()[2],
op2.linear_constraints[2].linear.to_dict()[4],
]
self.assertListEqual(lst, [1, 3, -1])
lst = [op2.variables[4].lowerbound, op2.variables[4].upperbound]
self.assertListEqual(lst, [0, 10])
self.assertEqual(op2.linear_constraints[2].sense, Constraint.Sense.EQ)
# For quadratic constraints
lst = [
op2.quadratic_constraints[0].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[0].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[0].linear.to_dict()[5],
]
self.assertListEqual(lst, [1, 2, 1])
lst = [op2.variables[5].lowerbound, op2.variables[5].upperbound]
self.assertListEqual(lst, [0, 30])
lst = [
op2.quadratic_constraints[1].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[1].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[1].linear.to_dict()[6],
]
self.assertListEqual(lst, [3, 4, -1])
lst = [op2.variables[6].lowerbound, op2.variables[6].upperbound]
self.assertListEqual(lst, [0, 60])
new_x = conv.interpret(np.arange(7))
np.testing.assert_array_almost_equal(new_x, np.arange(3))
