def test_sum(self):
""" Test a normal Sum class. """
x = IneqSys.Variable('x', upper=5)
y = IneqSys.Variable('y', upper=7)
sum1 = IneqSys.Sum([x, y])
self.assertEquals(sum1.result(), 12)
self.assertEquals(sum1.tostring(), "x + y")
def test_product(self):
""" Test a normal Product class. """
x = IneqSys.Variable('x', upper=5)
y = IneqSys.Variable('y', upper=7)
prod1 = IneqSys.Product([x, y])
self.assertEquals(prod1.result(), 35)
self.assertEquals(prod1.tostring(), "x * y")
def test_default_inequality(self):
""" Test an inequality with default settings. """
x = IneqSys.Variable('x', upper=100)
y = IneqSys.Variable('y', upper=50)
z = IneqSys.Variable('z', upper=20)
ineq = IneqSys.Inequality(lhs=x, rhs=IneqSys.Sum([y, z]))
self.assertEquals(ineq._coeff, 1)
self.assertEquals(ineq.tostring(), "x <= y + z")
ineq.evaluate()
x.update()
self.assertEquals(x.upper, 70)
self.assertEquals(x._status, _VariableStatus.valid)
def test_simple_sat_system2(self):
""" Test a simple satisfiable system #2. """
sys1 = IneqSys.InequalitySystem()
a = IneqSys.Variable('a')
b = IneqSys.Variable('b')
p = IneqSys.Inequality(lhs=a, rhs=IneqSys.Sum([a, b]))
sys1.add(p)
solution = sys1.solve()
self.assertEquals(solution['a'], sys.maxint)
self.assertEquals(solution['b'], sys.maxint)
def test_inequality(self):
""" Test an inequality with custom coefficient. """
x = IneqSys.Variable('x', upper=100, lower=10)
y = IneqSys.Variable('y', upper=50)
z = IneqSys.Variable('z', upper=20)
ineq = IneqSys.Inequality(coeff=10, lhs=x, rhs=IneqSys.Sum([y, z]))
self.assertEquals(ineq._coeff, 10)
self.assertEquals(ineq.tostring(), "10 * x <= y + z")
ineq.evaluate()
x.update()
self.assertEquals(x.upper, 7)
self.assertTrue(x.is_invalid())
def test_create_default_variable(self):
""" Test creation of a variable with default settings. """
var = IneqSys.Variable('x')
self.assertEquals(var.lower, 1)
self.assertEquals(var.upper, sys.maxint)
self.assertEquals(var.upper, var._candidate)
self.assertEquals(var._status, _VariableStatus.valid)
def test_create_custom_variable(self):
""" Test creation of a variable with custom settings. """
var = IneqSys.Variable('x', lower=5, upper=10)
self.assertEquals(var.lower, 5)
self.assertEquals(var.upper, 10)
self.assertEquals(var.upper, var._candidate)
self.assertEquals(var._status, _VariableStatus.valid)
def test_constant(self):
""" Test creation of a constant. """
cons = IneqSys.Constant(36)
self.assertEquals(cons.name, "36")
self.assertEquals(cons.lower, 36)
self.assertEquals(cons.upper, 36)
self.assertEquals(cons.result(), 36)
self.assertEquals(cons.tostring(), "36")
def test_invalid(self):
""" Test a change to candidate value that invalidates bounds. """
var = IneqSys.Variable('x', lower=5, upper=10)
var.declare_less_than(4)
var.update()
self.assertEquals(var.upper, 4)
self.assertEquals(var._status, _VariableStatus.invalid)
self.assertTrue(var.is_invalid())
def test_add_inequalities_with_dupe_vars(self):
""" Test adding two inequalities to the system with overlapping vars."""
sys = IneqSys.InequalitySystem()
w = IneqSys.Variable('w')
x = IneqSys.Variable('x')
y = IneqSys.Variable('y')
z = IneqSys.Variable('z')
p = IneqSys.Inequality(lhs=w, rhs=IneqSys.Sum([x, z]))
q = IneqSys.Inequality(lhs=x, rhs=IneqSys.Sum([y, z, w]))
sys.add(p)
sys.add(q)
self.assertItemsEqual(sys, [p, q])
self.assertDictEqual(sys._variables, {'w': w, 'x': x, 'y': y, 'z': z})
def test_stable(self):
""" Test a change to candidate value that leaves bounds unchanged. """
var = IneqSys.Variable('x', lower=5, upper=10)
var.declare_less_than(11)
self.assertEquals(var._candidate, 10) # Unchanged
var.update()
self.assertEquals(var.upper, 10)
self.assertEquals(var._status, _VariableStatus.stable)
self.assertTrue(var.is_stable())
def test_change_candidate(self):
""" Test change to candidate value. """
var = IneqSys.Variable('x', lower=5, upper=10)
var.declare_less_than(7)
self.assertEquals(var._candidate, 7)
var.update()
self.assertEquals(var.upper, 7)
self.assertEquals(var._status, _VariableStatus.valid)
self.assertFalse(var.is_stable())
self.assertFalse(var.is_invalid())
def test_simple_unsat_system2(self):
""" Test a simple unsatisfiable system #2 (with product). """
sys1 = IneqSys.InequalitySystem()
a = IneqSys.Variable('a', upper=20)
b = IneqSys.Variable('b', upper=3)
c = IneqSys.Variable('c', upper=5)
d = IneqSys.Variable('d', upper=2)
p = IneqSys.Inequality(lhs=a, rhs=IneqSys.Product([b, c]))
q = IneqSys.Inequality(coeff=10, lhs=c, rhs=IneqSys.Product([d, a]))
sys1.add(p)
sys1.add(q)
solution = sys1.solve()
self.assertEquals(solution, None)
def test_simple_sat_system3(self):
""" Test a simple satisfiable system #3 (with product). """
sys1 = IneqSys.InequalitySystem()
a = IneqSys.Variable('a', upper=20)
b = IneqSys.Variable('b', upper=3)
c = IneqSys.Variable('c', upper=5)
d = IneqSys.Variable('d', upper=2)
p = IneqSys.Inequality(lhs=a, rhs=IneqSys.Product([b, c]))
q = IneqSys.Inequality(coeff=6, lhs=c, rhs=IneqSys.Product([d, a]))
sys1.add(p)
sys1.add(q)
solution = sys1.solve(debug=True)
self.assertEquals(solution['a'], 15)
self.assertEquals(solution['b'], 3)
self.assertEquals(solution['c'], 5)
self.assertEquals(solution['d'], 2)
def test_simple_sat_system(self):
""" Test a simple satisfiable system. """
sys = IneqSys.InequalitySystem()
a = IneqSys.Variable('a', upper=50)
b = IneqSys.Variable('b', lower=20)
c = IneqSys.Variable('c')
p = IneqSys.Inequality(lhs=b, rhs=IneqSys.Sum([a]))
q = IneqSys.Inequality(lhs=c, rhs=IneqSys.Product([a, b]))
sys.add(p)
sys.add(q)
solution = sys.solve(debug=True) # Debug on to achieve coverage
self.assertEquals(solution['a'], 50)
self.assertEquals(solution['b'], 50)
self.assertEquals(solution['c'], 2500)
def test_add_inequality(self):
""" Test adding an inequality to the system. """
sys = IneqSys.InequalitySystem()
x = IneqSys.Variable('x')
y = IneqSys.Variable('y')
z = IneqSys.Variable('z')
q = IneqSys.Inequality(lhs=x, rhs=IneqSys.Sum([y, z]))
sys.add(q)
self.assertItemsEqual(sys, [q])
self.assertDictEqual(sys._variables, {'x': x, 'y': y, 'z': z})
def test_simple_unsat_system(self):
""" Test a simple unsatisfiable system. """
sys = IneqSys.InequalitySystem()
a = IneqSys.Variable('a')
b = IneqSys.Variable('b')
p = IneqSys.Inequality(coeff=2, lhs=a, rhs=IneqSys.Sum([b]))
q = IneqSys.Inequality(lhs=b, rhs=IneqSys.Sum([a]))
sys.add(p)
sys.add(q)
solution = sys.solve(debug=True) # Debug on to achieve coverage
self.assertEquals(solution, None)
self.assertEquals(a.upper, 0)
self.assertEquals(a.lower, 1)
def test_unsat_system_from_paper2(self):
""" Test an unsatisfiable system of inequalities from Smaragdakis
(Fig 9b). """
sys = IneqSys.InequalitySystem()
# Two object types related by a binary fact type
obj1 = IneqSys.Variable("obj1", upper=50)
obj2 = IneqSys.Variable("obj2", upper=2)
rol1 = IneqSys.Variable("rol1", upper=50)
rol2 = IneqSys.Variable("rol2", upper=50)
fact = IneqSys.Variable("fact", upper=50)
# Constant
con3 = IneqSys.Variable("con3", lower=3, upper=3)
# Semantics of roles
sys.add(IneqSys.Inequality(lhs=rol1, rhs=IneqSys.Sum([obj1])))
sys.add(IneqSys.Inequality(lhs=rol1, rhs=IneqSys.Sum([fact])))
sys.add(IneqSys.Inequality(lhs=rol2, rhs=IneqSys.Sum([fact])))
sys.add(IneqSys.Inequality(lhs=rol2, rhs=IneqSys.Sum([obj2])))
# Frequency constraint
sys.add(IneqSys.Inequality(lhs=fact, rhs=IneqSys.Product([con3,
rol1])))
sys.add(IneqSys.Inequality(coeff=3, lhs=rol1, rhs=IneqSys.Sum([fact])))
# Uniqueness
sys.add(IneqSys.Inequality(lhs=fact, rhs=IneqSys.Product([rol1,
rol2])))
# Disjunctive mandatory
sys.add(IneqSys.Inequality(lhs=obj1, rhs=IneqSys.Sum([rol1])))
sys.add(IneqSys.Inequality(lhs=obj2, rhs=IneqSys.Sum([rol2])))
# Solve the system
solution = sys.solve()
self.assertEquals(solution, None)
self.assertEquals(rol1.upper, 0)
def test_product_empty(self):
""" Test an empty Product class. """
prod1 = IneqSys.Product([])
self.assertEquals(prod1.result(), None)
self.assertEquals(prod1.tostring(), "")
def test_sum_empty(self):
""" Test an empty Sum class. """
sum1 = IneqSys.Sum([])
self.assertEquals(sum1.result(), None)
self.assertEquals(sum1.tostring(), "")
def test_unsat_system_from_paper3(self):
""" Test an unsatisfiable system of inequalities from Smaragdakis
(Fig 9c). """
sys = IneqSys.InequalitySystem()
# Two object types related by two binary fact types
obj1 = IneqSys.Variable("obj1", upper=20)
obj2 = IneqSys.Variable("obj2", upper=20)
rol11 = IneqSys.Variable("rol11", upper=20)
rol12 = IneqSys.Variable("rol12", upper=20)
rol21 = IneqSys.Variable("rol21", upper=20)
rol22 = IneqSys.Variable("rol22", upper=20)
fact1 = IneqSys.Variable("fact1", upper=20)
fact2 = IneqSys.Variable("fact2", upper=20)
# Constant
con2 = IneqSys.Variable("con2", lower=2, upper=2)
# Semantics of roles
sys.add(IneqSys.Inequality(lhs=rol11, rhs=IneqSys.Sum([obj1])))
sys.add(IneqSys.Inequality(lhs=rol11, rhs=IneqSys.Sum([fact1])))
sys.add(IneqSys.Inequality(lhs=rol21, rhs=IneqSys.Sum([fact1])))
sys.add(IneqSys.Inequality(lhs=rol21, rhs=IneqSys.Sum([obj2])))
sys.add(IneqSys.Inequality(lhs=rol12, rhs=IneqSys.Sum([obj1])))
sys.add(IneqSys.Inequality(lhs=rol12, rhs=IneqSys.Sum([fact2])))
sys.add(IneqSys.Inequality(lhs=rol22, rhs=IneqSys.Sum([fact2])))
sys.add(IneqSys.Inequality(lhs=rol22, rhs=IneqSys.Sum([obj2])))
# Uniqueness of fact types
sys.add(
IneqSys.Inequality(lhs=fact1, rhs=IneqSys.Product([rol11, rol21])))
sys.add(
IneqSys.Inequality(lhs=fact2, rhs=IneqSys.Product([rol12, rol22])))
# Disjunctive mandatory
sys.add(IneqSys.Inequality(lhs=obj1, rhs=IneqSys.Sum([rol11, rol12])))
sys.add(IneqSys.Inequality(lhs=obj2, rhs=IneqSys.Sum([rol21, rol22])))
# Simple uniqueness
sys.add(IneqSys.Inequality(lhs=fact1, rhs=IneqSys.Sum([rol21])))
sys.add(IneqSys.Inequality(lhs=fact2, rhs=IneqSys.Sum([rol12])))
# Simple mandatory
sys.add(IneqSys.Inequality(lhs=obj1, rhs=IneqSys.Sum([rol11])))
sys.add(IneqSys.Inequality(lhs=obj2, rhs=IneqSys.Sum([rol22])))
# Frequency
sys.add(
IneqSys.Inequality(lhs=fact1, rhs=IneqSys.Product([con2, rol11])))
sys.add(
IneqSys.Inequality(coeff=2, lhs=rol11, rhs=IneqSys.Sum([fact1])))
solution = sys.solve()
self.assertEquals(solution, None)
self.assertEquals(rol11.upper, 0)
def test_unsat_system_from_paper(self):
""" Test an unsatisfiable system of inequalities from Smaragdakis
(Fig 9a). """
sys = IneqSys.InequalitySystem()
# Two object types related by a binary fact type
obj1 = IneqSys.Variable("obj1")
obj2 = IneqSys.Variable("obj2")
rol1 = IneqSys.Variable("rol1")
rol2 = IneqSys.Variable("rol2")
fact = IneqSys.Variable("fact")
# Constants
cons1 = IneqSys.Variable("con1", lower=1000000, upper=1000000)
cons2 = IneqSys.Variable("con2", lower=2, upper=2)
# Inequalities that represent Smaragdakis' rules
# Cardinality: # >= 1000000 for obj1, # <= 2 for obj2
sys.add(IneqSys.Inequality(lhs=cons1, rhs=IneqSys.Sum([obj1])))
sys.add(IneqSys.Inequality(lhs=obj2, rhs=IneqSys.Sum([cons2])))
# Role 1 is mandatory
sys.add(IneqSys.Inequality(lhs=obj1, rhs=IneqSys.Sum([rol1])))
# Simple uniqueness constraints
sys.add(IneqSys.Inequality(lhs=fact, rhs=IneqSys.Sum([rol1])))
sys.add(IneqSys.Inequality(lhs=fact, rhs=IneqSys.Sum([rol2])))
# Semantics of roles
sys.add(IneqSys.Inequality(lhs=rol1, rhs=IneqSys.Sum([obj1])))
sys.add(IneqSys.Inequality(lhs=rol1, rhs=IneqSys.Sum([fact])))
sys.add(IneqSys.Inequality(lhs=rol2, rhs=IneqSys.Sum([fact])))
sys.add(IneqSys.Inequality(lhs=rol2, rhs=IneqSys.Sum([obj2])))
# Solve the system and assert that there is no solution
solution = sys.solve()
self.assertEquals(solution, None)
self.assertEquals(cons1.lower, 1000000)
self.assertEquals(cons1.upper, 2)
