def test_sum_smallest(self):
"""Test the sum_smallest atom and related atoms.
"""
with self.assertRaises(Exception) as cm:
cp.sum_smallest(self.x, -1)
self.assertEqual(str(cm.exception),
"Second argument must be a positive integer.")
with self.assertRaises(Exception) as cm:
cp.lambda_sum_smallest(Variable((2, 2)), 2.4)
self.assertEqual(str(cm.exception),
"Second argument must be a positive integer.")
def test_eigval_atoms(self):
"""Test eigenvalue atoms.
"""
P = np.arange(9) - 2j*np.arange(9)
P = np.reshape(P, (3, 3))
P1 = np.conj(P.T).dot(P)/10 + np.eye(3)*.1
P2 = np.array([[10, 1j, 0], [-1j, 10, 0], [0, 0, 1]])
for P in [P1, P2]:
value = cvx.lambda_max(P).value
X = Variable(P.shape, complex=True)
prob = Problem(cvx.Minimize(cvx.lambda_max(X)), [X == P])
result = prob.solve(solver=cvx.SCS, eps=1e-6)
self.assertAlmostEqual(result, value, places=2)
eigs = np.linalg.eigvals(P).real
value = cvx.sum_largest(eigs, 2).value
X = Variable(P.shape, complex=True)
prob = Problem(cvx.Minimize(cvx.lambda_sum_largest(X, 2)), [X == P])
result = prob.solve(solver=cvx.SCS, eps=1e-8)
self.assertAlmostEqual(result, value, places=3)
self.assertItemsAlmostEqual(X.value, P, places=3)
value = cvx.sum_smallest(eigs, 2).value
X = Variable(P.shape, complex=True)
prob = Problem(cvx.Maximize(cvx.lambda_sum_smallest(X, 2)), [X == P])
result = prob.solve(solver=cvx.SCS, eps=1e-6)
self.assertAlmostEqual(result, value, places=3)
def as_objective(self, **kwargs):
"""
main[selected] - branch[0]
selection can be written as Minimize(minimum(main[:] - branch[0]))
"""
Xmain, Ymain = self.inputs.vars
Xb, Yb = self._branch.vars
start_x, start_y = Xb[0], Yb[0]
o = Minimize(
cvx.sum_smallest(
cvx.norm1(Xmain - start_x) + cvx.norm1(Ymain - start_y), 1))
return o
def pmpt(mu, returns, percentile, max_loss):
w = cvx.Variable(returns.shape[1])
nsamples = round(returns.shape[0] * percentile)
portfolio_rets = returns @ w
avg_worst_day = cvx.sum_smallest(portfolio_rets, nsamples) / nsamples
objective = cvx.Maximize(w.T @ mu)
constraints = [avg_worst_day >= max_loss]
problem = cvx.Problem(objective, constraints)
problem.solve()
return w.value.round(4).ravel()
(cp.log1p, (2, 2), [[[0, math.e - 1],
[math.e**2 - 1,
1.0 / math.e - 1]]], Constant([[0, 1], [2, -1]])),
(cp.minimum, (2, ), [[-5, 2], [-3, 1], 0, [1, 2]], Constant([-5, 0])),
(cp.minimum, (2, 2), [[[-5, 2], [-3, -1]], 0,
[[5, 4], [-1, 2]]], Constant([[-5, 0], [-3, -1]])),
(cp.min, tuple(), [[[-5, 2], [-3, 1]]], Constant([-5])),
(cp.min, tuple(), [[-5, -10]], Constant([-10])),
(lambda x: x**0.25, tuple(), [7.45], Constant([7.45**0.25])),
(lambda x: x**0.32, (2, ), [[7.45, 3.9]],
Constant(np.power(np.array([7.45, 3.9]), 0.32))),
(lambda x: x**0.9, (2, 2), [[[7.45, 2.2], [4, 7]]],
Constant(np.power(np.array([[7.45, 2.2], [4, 7]]).T, 0.9))),
(cp.sqrt, (2, 2), [[[2, 4],
[16, 1]]], Constant([[1.414213562373095, 2], [4, 1]])),
(lambda x: cp.sum_smallest(x, 3), tuple(), [[-1, 2, 3, 4,
5]], Constant([-1 + 2 + 3])),
(lambda x: cp.sum_smallest(x, 4), tuple(), [[[-3, -4, 5], [6, 7, 8],
[9, 10, 11]]],
Constant([-3 - 4 + 5 + 6])),
(lambda x: (x + Constant(0))**0.5, (2, 2), [[[2, 4], [16, 1]]],
Constant([[1.414213562373095, 2], [4, 1]])),
]
def check_solver(prob, solver_name) -> bool:
"""Can the solver solve the problem?
"""
try:
if solver_name == ROBUST_CVXOPT:
solver_name = CVXOPT
(cp.log, (2, 2), [[[1, math.e], [math.e**2, 1.0 / math.e]]], Constant([[0, 1], [2, -1]])),
(cp.log1p, (2, 2), [[[0, math.e - 1],
[math.e**2 - 1, 1.0 / math.e - 1]]], Constant([[0, 1], [2, -1]])),
(cp.minimum, (2,), [[-5, 2], [-3, 1], 0, [1, 2]], Constant([-5, 0])),
(cp.minimum, (2, 2), [[[-5, 2], [-3, -1]],
0,
[[5, 4], [-1, 2]]], Constant([[-5, 0], [-3, -1]])),
(cp.min, tuple(), [[[-5, 2], [-3, 1]]], Constant([-5])),
(cp.min, tuple(), [[-5, -10]], Constant([-10])),
(lambda x: x**0.25, tuple(), [7.45], Constant([7.45**0.25])),
(lambda x: x**0.32, (2,), [[7.45, 3.9]], Constant(np.power(np.array([7.45, 3.9]), 0.32))),
(lambda x: x**0.9, (2, 2), [[[7.45, 2.2],
[4, 7]]], Constant(np.power(np.array([[7.45, 2.2],
[4, 7]]).T, 0.9))),
(cp.sqrt, (2, 2), [[[2, 4], [16, 1]]], Constant([[1.414213562373095, 2], [4, 1]])),
(lambda x: cp.sum_smallest(x, 3), tuple(), [[-1, 2, 3, 4, 5]], Constant([-1 + 2 + 3])),
(lambda x: cp.sum_smallest(x, 4), tuple(),
[[[-3, -4, 5], [6, 7, 8], [9, 10, 11]]], Constant([-3 - 4 + 5 + 6])),
(lambda x: (x + Constant(0))**0.5, (2, 2),
[[[2, 4], [16, 1]]], Constant([[1.414213562373095, 2], [4, 1]])),
]
def check_solver(prob, solver_name) -> bool:
"""Can the solver solve the problem?
"""
try:
if solver_name == ROBUST_CVXOPT:
solver_name = CVXOPT
prob._construct_chain(solver=solver_name)
