def test_rel_entr(self) -> None:
"""Test domain for rel_entr.
"""
b = Variable()
dom = cp.rel_entr(self.a, b).domain
Problem(Minimize(self.a + b), dom).solve()
self.assertAlmostEqual(self.a.value, 0)
self.assertAlmostEqual(b.value, 0)
def test_rel_entr(self) -> None:
"""Test domain for rel_entr.
"""
b = Variable()
expr = cp.rel_entr(self.a, b)
self.a.value = 2
b.value = 4
self.assertAlmostEqual(expr.grad[self.a], np.log(2 / 4) + 1)
self.assertAlmostEqual(expr.grad[b], -(2 / 4))
self.a.value = 3
b.value = 0
self.assertAlmostEqual(expr.grad[self.a], None)
self.assertAlmostEqual(expr.grad[b], None)
self.a.value = -1
b.value = 2
self.assertAlmostEqual(expr.grad[self.a], None)
self.assertAlmostEqual(expr.grad[b], None)
y = Variable(2)
expr = cp.rel_entr(self.x, y)
self.x.value = [3, 4]
y.value = [5, 8]
val = np.zeros((2, 2)) + np.diag(np.log([3, 4]) - np.log([5, 8]) + 1)
self.assertItemsAlmostEqual(expr.grad[self.x].toarray(), val)
val = np.zeros((2, 2)) + np.diag([-3 / 5, -4 / 8])
self.assertItemsAlmostEqual(expr.grad[y].toarray(), val)
expr = cp.rel_entr(self.x, y)
self.x.value = [-1e-9, 4]
y.value = [1, 2]
self.assertAlmostEqual(expr.grad[self.x], None)
self.assertAlmostEqual(expr.grad[y], None)
expr = cp.rel_entr(self.A, self.B)
self.A.value = [[1, 2], [3, 4]]
self.B.value = [[5, 1], [3.5, 2.3]]
div = (self.A.value / self.B.value).ravel(order='F')
val = np.zeros((4, 4)) + np.diag(np.log(div) + 1)
self.assertItemsAlmostEqual(expr.grad[self.A].toarray(), val)
val = np.zeros((4, 4)) + np.diag(-div)
self.assertItemsAlmostEqual(expr.grad[self.B].toarray(), val)
def test_difference_kl_div_rel_entr(self) -> None:
"""A test showing the difference between kl_div and rel_entr
"""
x = cvx.Variable()
y = cvx.Variable()
kl_div_prob = cvx.Problem(cvx.Minimize(cvx.kl_div(x, y)),
constraints=[x + y <= 1])
kl_div_prob.solve(solver=cvx.ECOS)
self.assertItemsAlmostEqual(x.value, y.value)
self.assertItemsAlmostEqual(kl_div_prob.value, 0)
rel_entr_prob = cvx.Problem(cvx.Minimize(cvx.rel_entr(x, y)),
constraints=[x + y <= 1])
rel_entr_prob.solve(solver=cvx.ECOS)
"""
Reference solution computed by passing the following command to Wolfram Alpha:
minimize x*log(x/y) subject to {x + y <= 1, 0 <= x, 0 <= y}
"""
self.assertItemsAlmostEqual(x.value, 0.2178117, places=4)
self.assertItemsAlmostEqual(y.value, 0.7821882, places=4)
self.assertItemsAlmostEqual(rel_entr_prob.value, -0.278464)
def test_rel_entr(self) -> None:
"""Test a problem with rel_entr.
"""
kK = 50
kSeed = 10
prng = np.random.RandomState(kSeed)
# Generate a random reference distribution
npSPriors = prng.uniform(0.0, 1.0, kK)
npSPriors = npSPriors / sum(npSPriors)
# Reference distribution
p_refProb = cvx.Parameter(kK, nonneg=True)
# Distribution to be estimated
v_prob = cvx.Variable(kK)
obj_rel_entr = cvx.sum(cvx.rel_entr(v_prob, p_refProb))
constrs = [cvx.sum(v_prob) == 1]
rel_entr_prob = cvx.Problem(cvx.Minimize(obj_rel_entr), constrs)
p_refProb.value = npSPriors
rel_entr_prob.solve(solver=cvx.SCS, verbose=True)
self.assertItemsAlmostEqual(v_prob.value, npSPriors, places=3)
rel_entr_prob.solve(solver=cvx.ECOS, verbose=True)
self.assertItemsAlmostEqual(v_prob.value, npSPriors)
