def test_err1():
"""A case seidel solver fails to solve correctly. I discovered this
while working on toppra. """
v = array([-1.e-09, 1.e+00, 0.e+00])
a = array([-0.02020202, 0.02020202, 1.53515768, 4.3866269, -
3.9954173, -1.53515768, -4.3866269, 3.9954173])
b = array([-1., 1., -185.63664301, 156.27072783, -
209.00954213, 185.63664301, -156.27072783, 209.00954213])
c = array([0., -0.0062788, -1., -2., -4., -1., -1., -1.])
low = array([-100., 0.])
high = array([1.00000000e+02, 6.26434609e-02])
data = seidel.solve_lp2d(v, a, b, c, low, high, np.array(
[0, 5])) # only break at this active constraints
res, optval, optvar, active_c = data
# solve with cvxpy
x = cvx.Variable(2)
constraints = [a * x[0] + b * x[1] + c <= 0,
low <= x, x <= high]
obj = cvx.Maximize(v[0] * x[0] + v[1] * x[1] + v[2])
prob = cvx.Problem(obj, constraints)
prob.solve()
# solve with the method to test and assert correctness
if prob.status == "optimal":
assert res == 1
np.testing.assert_allclose(optval, prob.value)
np.testing.assert_allclose(optvar, np.asarray(x.value).flatten())
elif prob.status == "infeasible":
assert res == 0
else:
assert False, "Solve this LP with cvxpy returns status: {:}".format(
prob.status)
def test_err2():
"""A case that fails. Discovered on 31/10/2018."""
v = array([-1.e-09, 1.e+00, 0.e+00])
a = array([-0.04281662, 0.04281662, 0., 0., 0.,
0., 0., 0., 0., 0.,
0., 0., 0., 0., 0.,
0., -1.27049648, 0.63168407, 0.54493736, -0.17238098,
0.22457236, 0.6543007, 1.24159883, 1.27049648, -0.63168407,
-0.54493736, 0.17238098, -0.22457236, -0.6543007, -1.24159883])
b = array([-1., 1., -70.14534325, 35.42759706,
31.23305996, -9.04430553, 12.51402852, 36.71562421,
68.63795557, 70.14534325, -35.42759706, -31.23305996,
9.04430553, -12.51402852, -36.71562421, -68.63795557,
-9.70931351, 4.71707751, 3.93518034, -1.41196299,
1.69317949, 4.88204872, 9.47085771, 9.70931351,
-4.71707751, -3.93518034, 1.41196299, -1.69317949,
-4.88204872, -9.47085771])
c = array([0., -1.56875277, -50., -50.,
-50., -50., -50., -50.,
-50., -50., -50., -50.,
-50., -50., -50., -50.,
-50., -50., -50., -50.,
-50., -50., -50., -50.,
-50., -50., -50., -50.,
-50., -50.])
low = array([-1.e+08, 0.e+00])
high = array([1.e+08, 1.e+08])
active_c = np.array([0, -4])
data = seidel.solve_lp2d(
v, a, b, c, low, high, np.array([0, -4])) # only break at this active constraints
res, optval, optvar, active_c = data
# solve with cvxpy
x = cvx.Variable(2)
constraints = [a * x[0] + b * x[1] + c <= 0,
low <= x, x <= high]
obj = cvx.Maximize(v[0] * x[0] + v[1] * x[1] + v[2])
prob = cvx.Problem(obj, constraints)
prob.solve(solver='CVXOPT')
# solve with the method to test and assert correctness
if prob.status == "optimal":
assert res == 1
np.testing.assert_allclose(optval, prob.value)
np.testing.assert_allclose(optvar[1], np.asarray(x.value).flatten()[1])
elif prob.status == "infeasible":
assert res == 0
else:
assert False, "Solve this LP with cvxpy returns status: {:}".format(
prob.status)
def test_random_constraints(seed):
"""Generate random problem data, solve with cvxpy and then compare!
Generated problems can be feasible or infeasible. Both cases are
tested in this unit test.
"""
# generate random problem data
d = 50
np.random.seed(seed)
seeds = np.random.randint(1000, size=7)
np.random.seed(seeds[0])
v = np.random.randn(3)
np.random.seed(seeds[1])
a, b = np.random.randn(2, d)
np.random.seed(seeds[2])
if seed % 2 == 0:
c = - np.random.rand(d)
else:
c = np.random.randn(d)
low = np.r_[-0.5, -0.9]
high = np.r_[0.5, 0.9]
np.random.seed(seeds[3])
active_c = np.random.choice(d, size=2)
# solve with cvxpy
x = cvx.Variable(2)
constraints = [a * x[0] + b * x[1] + c <= 0,
low <= x, x <= high]
obj = cvx.Maximize(v[0] * x[0] + v[1] * x[1] + v[2])
prob = cvx.Problem(obj, constraints)
prob.solve()
# solve with the method to test and assert correctness
data = seidel.solve_lp2d(v, a, b, c, low, high, active_c)
res, optval, optvar, active_c = data
if prob.status == "optimal":
assert res == 1
np.testing.assert_allclose(optval, prob.value)
np.testing.assert_allclose(optvar, np.asarray(x.value).flatten())
elif prob.status == "infeasible":
assert res == 0
else:
assert False, "Solve this LP with cvxpy returns status: {:}".format(prob.status)
def test_correct(v, a, b, c, low, high, active_c, res_expected, optval_expected,
optvar_expected, active_c_expected):
if a is None:
a_np = None
b_np = None
c_np = None
else:
a_np = np.array(a, dtype=float)
b_np = np.array(b, dtype=float)
c_np = np.array(c, dtype=float)
data = seidel.solve_lp2d(np.array(v, dtype=float), a_np, b_np, c_np,
np.array(low, dtype=float), np.array(high, dtype=float), np.array(active_c, dtype=int))
res, optval, optvar, active_c = data
if res_expected == 1:
assert res == res_expected
np.testing.assert_allclose(optval, optval_expected)
np.testing.assert_allclose(optvar, optvar_expected)
assert set(active_c) == set(active_c_expected)
else:
assert res == res_expected