def test_pownd_constraint(self) -> None:
n = 4
W, z = Variable(n), Variable()
np.random.seed(0)
alpha = 0.5 + np.random.rand(n)
alpha /= np.sum(alpha)
with self.assertRaises(ValueError):
# entries don't sum to one
con = PowConeND(W, z, alpha + 0.01)
with self.assertRaises(ValueError):
# shapes don't match exactly
con = PowConeND(W, z, alpha.reshape((n, 1)))
with self.assertRaises(ValueError):
# wrong axis
con = PowConeND(reshape_atom(W, (n, 1)),
z,
alpha.reshape((n, 1)),
axis=1)
# Compute a violation
con = PowConeND(W, z, alpha)
W0 = 0.1 + np.random.rand(n)
z0 = np.prod(np.power(W0, alpha)) + 0.05
W.value, z.value = W0, z0
viol = con.violation()
self.assertGreaterEqual(viol, 0.01)
self.assertLessEqual(viol, 0.06)
def pcp_4(ceei: bool = True):
"""
A power cone formulation of a Fisher market equilibrium pricing model.
ceei = Competitive Equilibrium from Equal Incomes
"""
# Generate test data
np.random.seed(0)
n_buyer = 4
n_items = 6
V = np.random.rand(n_buyer, n_items)
X = cp.Variable(shape=(n_buyer, n_items), nonneg=True)
u = cp.sum(cp.multiply(V, X), axis=1)
if ceei:
b = np.ones(n_buyer) / n_buyer
else:
b = np.array([0.3, 0.15, 0.2, 0.35])
log_objective = cp.Maximize(cp.sum(cp.multiply(b, cp.log(u))))
log_cons = [cp.sum(X, axis=0) <= 1]
log_prob = cp.Problem(log_objective, log_cons)
log_prob.solve(solver='SCS', eps=1e-8)
expect_X = X.value
z = cp.Variable()
pow_objective = (cp.Maximize(z), np.exp(log_prob.value))
pow_cons = [(cp.sum(X, axis=0) <= 1, None),
(PowConeND(W=u, z=z, alpha=b), None)]
pow_vars = [(X, expect_X)]
sth = STH.SolverTestHelper(pow_objective, pow_vars, pow_cons)
return sth