def test_margins_2d(self):
cc = ChanceConstraint([self.U <= 0, min(self.V) >= 5])
self.U.value = np.array([[1, 2], [3, 4]])
self.V.value = np.array([[-2, 3], [-1, 2], [0, 1]])
margins = cc.margins()
self.assertEqual(len(margins), 2)
self.assertItemsAlmostEqual(margins[0], self.U.value, places=8)
self.assertItemsAlmostEqual(margins[1],
5 - np.min(self.V.value),
places=8)
def test_dcp(self):
# Prob(g(x) >= 0) <= p is DCP iff g is convex.
constr = [ChanceConstraint(log(self.x) >= 0, 0.5)]
p = ccprob.Problem(Minimize(norm(self.x)), constr)
with self.assertRaises(DCPError) as cm:
p.solve()
# Prob(h(x) <= 0) <= p is DCP iff h is concave.
constr = [ChanceConstraint(exp(self.x) <= 5, 0.8)]
p = ccprob.Problem(Minimize(norm(self.x)), constr)
with self.assertRaises(DCPError) as cm:
p.solve()
def test_restriction_2d(self):
cc = ChanceConstraint([self.U <= 0], 0.8)
self.U.value = np.array([[-1, -2], [3, 4]])
cc.slope.value = 0.5
val = np.sum(np.maximum(0.5 - self.U.value,
0)) / self.U.size - 0.5 * 0.8
self.assertItemsAlmostEqual(cc.restriction.expr.value, val)
def test_slack(self):
b = np.abs(np.random.randn(*self.x.shape))
obj = sum_squares(self.x - b)
constr = [ChanceConstraint(self.x >= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve(slack=False)
val_noslack = p.value
slacks = [cc.slack_value for cc in p.chance_constraints]
self.assertItemsAlmostEqual(slacks, len(p.chance_constraints) * [0])
p.solve(slack=True)
self.assertTrue(p.value <= val_noslack)
slacks = [cc.slack_value for cc in p.chance_constraints]
for slack in slacks:
self.assertAlmostGeq(slack, 0)
# Conflicting constraints: Prob(x <= 0) >= 0.2 and x >= 1.
constr += [self.x >= 1]
p = ccprob.Problem(Minimize(obj), constr)
with self.assertRaises(SolverError) as cm:
p.solve(slack=False)
# Solvable with slackened chance constraint.
p.solve(slack=True)
slacks = [cc.slack_value for cc in p.chance_constraints]
for slack in slacks:
self.assertAlmostGeq(slack, 0)
def test_solve(self):
b = np.abs(np.random.randn(*self.x.shape))
obj = sum_squares(self.x - b)
constr = [ChanceConstraint(self.x <= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve()
self.assertTrue(
np.sum(self.x.value <= self.tolerance) <= 0.8 * self.x.size)
b = np.random.randn(self.A.shape[0])
obj = sum_squares(self.A * self.x - b)
constr = [ChanceConstraint(self.x >= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve()
self.assertTrue(
np.sum(self.x.value >= -self.tolerance) <= 0.8 * self.x.size)
def test_2step(self):
b = np.abs(np.random.randn(*self.x.shape))
obj = sum_squares(self.x - b)
constr = [ChanceConstraint(self.x <= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve(two_step=False)
val_1step = p.value
p.solve(two_step=True)
self.assertTrue(p.value <= val_1step)
def test_probability(self):
b = np.random.randn(self.A.shape[0])
obj = sum_squares(self.A * self.x - b)
cc = ChanceConstraint([self.x <= 0], 0.8)
pc = prob(self.x <= 0) <= 0.8
self.assertEqual(cc.size, pc.size)
self.assertEqual(cc.fraction, pc.fraction)
self.assertEqual(cc.max_violations, pc.max_violations)
self.assertAlmostEqual(
ccprob.Problem(Minimize(obj), [cc]).solve(),
ccprob.Problem(Minimize(obj), [pc]).solve())
cc = ChanceConstraint([self.x >= 0], 0.8)
pc = prob(self.x <= 0) >= 0.2
self.assertEqual(cc.size, pc.size)
self.assertEqual(cc.fraction, pc.fraction)
self.assertEqual(cc.max_violations, pc.max_violations)
self.assertAlmostEqual(
ccprob.Problem(Minimize(obj), [cc]).solve(),
ccprob.Problem(Minimize(obj), [pc]).solve())
def test_restriction(self):
cc = ChanceConstraint([self.x <= 0], 0.8)
self.assertEqual(cc.restriction.shape, ())
self.assertEqual(cc.restriction.size, 1)
self.assertEqual(cc.restriction.expr.value, None)
self.x.value = [-1, 1]
cc.slope.value = 0.5
val = np.sum(np.maximum(0.5 - self.x.value, 0)) / 2 - 0.5 * 0.8
self.assertItemsAlmostEqual(cc.restriction.expr.value, val)
cc.constraints = [self.x >= 0]
val = np.sum(np.maximum(0.5 - self.x.value, 0)) / 2 - 0.5 * 0.8
self.assertItemsAlmostEqual(cc.restriction.expr.value, val)
cc.fraction = 0.4
cc.slope.value = 1.5
val = np.sum(np.maximum(1.5 - self.x.value, 0)) / 2 - 1.5 * 0.4
self.assertItemsAlmostEqual(cc.restriction.expr.value, val)
b = np.random.randn(self.A.shape[0])
cc = ChanceConstraint([self.A * self.x == b], 0.8)
self.x.value = [-1, 1]
cc.slope.value = 0.5
expr = np.abs(self.A.dot(self.x.value) - b)
val = np.sum(np.maximum(0.5 - expr, 0)) / expr.size - 0.5 * 0.8
self.assertItemsAlmostEqual(cc.restriction.expr.value, val)
def test_properties(self):
self.assertEqual(ChanceConstraint([self.x >= 0]).size, 2)
self.assertEqual(
ChanceConstraint([self.x >= 0, self.y >= 0]).size, 2 + 3)
self.assertEqual(
ChanceConstraint([self.U >= 0, self.V >= 0]).size, 2 * 2 + 3 * 2)
self.assertEqual(ChanceConstraint([self.x >= 0]).max_violations, 2)
self.assertEqual(
ChanceConstraint([self.x >= 0], 0.8).max_violations, 0.8 * 2)
self.assertEqual(
ChanceConstraint([self.x >= 0, self.y >= 0], 0.8).max_violations,
0.8 * (2 + 3))
self.assertEqual(
ChanceConstraint([self.U >= 0, self.V >= 0], 0.8).max_violations,
0.8 * (2 * 2 + 3 * 2))
def test_margins(self):
cc = ChanceConstraint([self.x <= 0])
self.assertItemsAlmostEqual(cc.margins(), [None])
self.x.value = [-1, 1]
margins = cc.margins()
self.assertEqual(len(margins), 1)
self.assertItemsAlmostEqual(margins[0], self.x.value, places=8)
cc.constraints = [self.x >= 0]
self.assertItemsAlmostEqual(cc.margins()[0], -self.x.value, places=8)
cc.constraints = [self.x >= 0, self.y <= 0]
margins = cc.margins()
self.assertEqual(len(margins), 2)
self.assertItemsAlmostEqual(margins[0], -self.x.value, places=8)
self.assertEqual(margins[1], None)
self.y.value = [-5, 0, 10]
self.assertItemsAlmostEqual(cc.margins()[1], self.y.value)
b = np.random.randn(self.A.shape[0])
cc = ChanceConstraint([self.A * self.x == b])
self.x.value = [-1, 1]
margins = cc.margins()
self.assertItemsAlmostEqual(margins[0],
np.abs(self.A.dot(self.x.value) - b))
def test_weights(self):
cc = ChanceConstraint([self.x >= 0], 0.8)
self.assertEqual(len(cc.weights), 1)
self.assertItemsAlmostEqual(cc.weights[0], np.array([0.5, 0.5]))
cc = ChanceConstraint([self.x >= 0], 0.8, [np.array([0, 1])])
self.assertEqual(len(cc.weights), 1)
self.assertItemsAlmostEqual(cc.weights[0], np.array([0, 1]))
cc = ChanceConstraint(
[self.x >= 0, self.y <= 0], 0.8,
[np.array([0, 0.5]),
np.array([0.05, 0.1, 0.35])])
self.assertEqual(len(cc.weights), 2)
self.assertItemsAlmostEqual(cc.weights[0], np.array([0, 0.5]))
self.assertItemsAlmostEqual(cc.weights[1], np.array([0.05, 0.1, 0.35]))
cc = ChanceConstraint([self.U >= 0], 0.8)
self.assertEqual(len(cc.weights), 1)
self.assertItemsAlmostEqual(cc.weights[0],
np.full(self.U.shape, 1.0 / self.U.size))
with self.assertRaises(ValueError) as cm:
ChanceConstraint(
[self.x >= 0], 0.8,
[np.array([0, 1]), np.array([1, 0])])
with self.assertRaises(ValueError) as cm:
ChanceConstraint([self.x >= 0, self.y <= 0], 0.8,
[np.array([0, 1])])
with self.assertRaises(ValueError) as cm:
ChanceConstraint([self.x >= 0], 0.8, [np.array([0.1, 0.2, 0.7])])
with self.assertRaises(ValueError) as cm:
ChanceConstraint([self.x >= 0], 0.8, [np.array([0.5])])
with self.assertRaises(ValueError) as cm:
ChanceConstraint([self.y >= 0], 0.8, [np.array([-0.5, 0.5, 1.0])])
with self.assertRaises(ValueError) as cm:
ChanceConstraint([self.y >= 0], 0.8, [np.array([0.25, 0.5, 0.75])])
with self.assertRaises(ValueError) as cm:
ChanceConstraint(
[self.U >= 0], 0.8,
[np.array([[0.125, 0.125], [0.125, 0.125], [0.25, 0.25]])])