def test_linprog_feasible(self):
# Sample problem instance
A_ub = io.tensor([[-2.0, -5.0], [-2.0, 3.0], [-2.0, -1.0], [2.0, 1.0]])
b_ub = io.tensor([[-10.0], [6.0], [-4.0], [10.0]])
A_eq = io.tensor([[-0.05, 1.0]])
b_eq = io.tensor([[1.0]])
# Compute a feasible point
x = io.linprog_feasible(A_ub, b_ub, A_eq, b_eq)
self.assertStrictlyFeasible(x, A_ub, b_ub, A_eq, b_eq)
# Check that infeasibility is detected due to EQUALITIES
A_eq2 = io.tensor([[0.0, 1.0], [1.0, 0.0]])
b_eq2 = io.tensor([[5.0], [5.0]])
with self.assertRaises(RuntimeError):
x = io.linprog_feasible(A_ub, b_ub, A_eq2, b_eq2)
# Check that infeasibility is detected due to INEQUALITIES
A_ub2 = io.tensor([[-1.0, -1.0], [1.0, 1.0]])
b_ub2 = io.tensor([[-1.0], [1.0]])
with self.assertRaises(RuntimeError):
x = io.linprog_feasible(A_ub2, b_ub2, A_eq, b_eq)
# Check that a feasible point is detected under multiple EQUALITIES
A_ub3 = io.tensor([
[-1.0, 0.0], # x1 >= 0
[0.0, -1.0]
]) # x2 >= 0
b_ub3 = io.tensor([[0.0], [0.0]])
x = io.linprog_feasible(A_ub3, b_ub3, A_eq2, b_eq2)
self.assertVectorEqual(x, [5, 5])
def test_inverse_linprog(self):
# Sample problem instance
c = io.tensor([[1.0], [1.0]])
A_ub = io.tensor([[-2.0, -5.0], [-2.0, 3.0], [2.0, 1.0]])
b_ub = io.tensor([[-10.0], [6.0], [10.0]])
A_eq = io.tensor([[0.0, 1.0]])
b_eq = io.tensor([[1.0]])
x_target = io.tensor([[5.0], [0.0]])
# Check that solution before training is (0.0, 2.0)
x = io.linprog(c, A_ub, b_ub)
self.assertVectorEqual(x, [0.0, 2.0])
# Check INEQUALITIES only
params = io.inverse_linprog(x_target, c, A_ub, b_ub)
x = io.linprog(*params)
self.assertVectorEqual(x, [5.0, 0.0])
# Check INEQUALITIES and EQUALITIES
params = io.inverse_linprog(
x_target, c, A_ub, b_ub, A_eq, b_eq,
eps_decay=True) # This one needs eps_decay to work
x = io.linprog(*params)
self.assertVectorEqual(x, [4.5, 1.0])
# Check ABS DUALITY GAP with INEQUALITIES and EQUALITIES
params = io.inverse_linprog(x_target,
c,
A_ub,
b_ub,
A_eq,
b_eq,
loss=io.abs_duality_gap)
x = io.linprog(*params)
self.assertVectorEqual(
x, [4.5, 1.0
]) # Currently linprog doesn't get 3 decimals correct, but ok
c_inv, *constraints = io.inverse_linprog(x_target,
c,
A_ub,
b_ub,
A_eq,
b_eq,
loss=io.abs_duality_gap)
x = io.linprog(c_inv, *constraints)
self.assertAlmostEqual((c_inv.t() @ (x - x_target)).item(), 0)
# Check MULTIPOINT finds solution with minimal average error,
# regardless if initial c has support of one target point
# (Note this doesn't work for abs_duality_gap yet; reasons unknown)
x_target = io.tensor([[0.0, 5.0, 4.9, 4.8], [2.0, 0.0, 0.1, 0.2]])
params = io.inverse_linprog(x_target, c, A_ub, b_ub)
x = io.linprog(*params)
self.assertVectorEqual(
x, [4.85, 0.06], places=2
) # linprog's line-search manages to get IPM to generate a non-vertex
def test_linprog(self):
# Sample problem instance
c = io.tensor([[-1.0], [0.0]])
A_ub = io.tensor([[-2.0, -5.0], [-2.0, 3.0], [2.0, 1.0]])
b_ub = io.tensor([[-10.0], [6.0], [10.0]])
A_eq = io.tensor([[0.0, 1.0]])
b_eq = io.tensor([[1.0]])
# Check INEQUALITIES only
x = io.linprog(c, A_ub, b_ub)
self.assertVectorEqual(x, [5.0, 0.0])
# Check INEQUALITIES and EQUALITIES
x = io.linprog(c, A_ub, b_ub, A_eq, b_eq)
self.assertVectorEqual(x, [4.5, 1.0])
# Check that linprog doesn't blow up when c is normal to constraints
for ai in A_ub:
x = io.linprog(-ai.view(-1, 1), A_ub, b_ub)
def test_linprog_feasible_unbounded(self):
# Basic instance: x1 >= 1 and x2 >= 3
A_ub = io.tensor([[-1.0, 0.0], [0.0, -1.0]])
b_ub = io.tensor([[-1.0], [-3.0]])
A_eq = io.tensor([[-1.0, 1.0]])
b_eq = io.tensor([[0.5]])
# (0, 0) is infeasible
x = io.linprog_feasible(A_ub, b_ub)
self.assertStrictlyFeasible(x, A_ub, b_ub)
# (0, 0) is feasible
x = io.linprog_feasible(A_ub, -b_ub)
self.assertStrictlyFeasible(x, A_ub, -b_ub)
# Large coefficients
x = io.linprog_feasible(10000 * A_ub, 10000 * b_ub)
self.assertStrictlyFeasible(x, 10000 * A_ub, 10000 * b_ub)
# Equality constraints
x = io.linprog_feasible(A_ub, b_ub, A_eq, b_eq)
self.assertStrictlyFeasible(x, A_ub, b_ub, A_eq, b_eq)
b_ub = [[0.0], [0.0], [2.0], [2.0], [4.0]]
# [0.0]] ## uncomment this only if you need to contraint only w positive values
A_eq = [[1.0 + (u * (w**2)), 0.0]]
b_eq = [[1.0]]
return c, A_ub, b_ub, A_eq, b_eq
# Evaluate the parametric LP at specific values of u
plp_true = ExamplePLP(weights=[float(sys.argv[4])])
x_train = io.tensor(
np.array(sys.argv[1].split(',')).astype(np.float).reshape(
(-1, 1))) # targets given as empirical rates from participants
u_train = io.tensor(
np.array(sys.argv[2].split(',')).astype(np.float).reshape(
(-1, 1))) # the Pb/Pf value declared as u on this model
u_train_sal_model = torch.cat(
[io.linprog(*plp_true(ui)).detach().t() for ui in u_train])
# Plot it
xylim = ((0, 2), (0, 2))
cxy = (5, 5)
plt.figure(figsize=(16, 4))
for i, w in enumerate([7, 6, 5, 1]):