def test_xexp(self) -> None:
x = cvxpy.Variable(2, pos=True)
b = np.array([1, 0.5])
expr = cvxpy.xexp(x)
x.value = b
self.assertItemsAlmostEqual(expr.value, [np.e, 0.5 * np.e**.5])
prob = cvxpy.Problem(cvxpy.Minimize(cvxpy.prod(expr)), [x >= b])
prob.solve(solver=SOLVER, gp=True)
self.assertItemsAlmostEqual(expr.value, [np.e, 0.5 * np.e**.5])
def test_prod(self):
X = np.arange(12).reshape((4, 3))
np.testing.assert_almost_equal(np.prod(X), cvxpy.prod(X).value)
np.testing.assert_almost_equal(np.prod(X, axis=0),
cvxpy.prod(X, axis=0).value)
np.testing.assert_almost_equal(np.prod(X, axis=1),
cvxpy.prod(X, axis=1).value)
np.testing.assert_almost_equal(
np.prod(X, axis=0, keepdims=True),
cvxpy.prod(X, axis=0, keepdims=True).value)
np.testing.assert_almost_equal(
np.prod(X, axis=1, keepdims=True),
cvxpy.prod(X, axis=1, keepdims=True).value)
prod = cvxpy.prod(X)
X_canon, _ = dgp_atom_canon.prod_canon(prod, prod.args)
np.testing.assert_almost_equal(np.sum(X), X_canon.value)
prod = cvxpy.prod(X, axis=0)
X_canon, _ = dgp_atom_canon.prod_canon(prod, prod.args)
np.testing.assert_almost_equal(np.sum(X, axis=0), X_canon.value)
prod = cvxpy.prod(X, axis=1)
X_canon, _ = dgp_atom_canon.prod_canon(prod, prod.args)
np.testing.assert_almost_equal(np.sum(X, axis=1), X_canon.value)
prod = cvxpy.prod(X, axis=0, keepdims=True)
X_canon, _ = dgp_atom_canon.prod_canon(prod, prod.args)
np.testing.assert_almost_equal(np.sum(X, axis=0, keepdims=True),
X_canon.value)
prod = cvxpy.prod(X, axis=1, keepdims=True)
X_canon, _ = dgp_atom_canon.prod_canon(prod, prod.args)
np.testing.assert_almost_equal(np.sum(X, axis=1, keepdims=True),
X_canon.value)
X = np.arange(12)
np.testing.assert_almost_equal(np.prod(X), cvxpy.prod(X).value)
np.testing.assert_almost_equal(np.prod(X, keepdims=True),
cvxpy.prod(X, keepdims=True).value)
prod = cvxpy.prod(X)
X_canon, _ = dgp_atom_canon.prod_canon(prod, prod.args)
np.testing.assert_almost_equal(np.sum(X), X_canon.value)
x = cvxpy.Variable(pos=True)
y = cvxpy.Variable(pos=True)
posy1 = x * y**0.5 + 3.0 * x * y**0.5
posy2 = x * y**0.5 + 3.0 * x**2 * y**0.5
self.assertTrue(cvxpy.prod([posy1, posy2]).is_log_log_convex())
self.assertFalse(cvxpy.prod([posy1, posy2]).is_log_log_concave())
self.assertFalse(cvxpy.prod([posy1, 1 / posy1]).is_dgp())
m = x * y**0.5
self.assertTrue(cvxpy.prod([m, m]).is_log_log_affine())
self.assertTrue(cvxpy.prod([m, 1 / posy1]).is_log_log_concave())
self.assertFalse(cvxpy.prod([m, 1 / posy1]).is_log_log_convex())
import numpy as np
import cvxpy as cp
from scipy.stats import bernoulli
from progressbar import progressbar
# Retrieve data
path = "../storage/max-volume-rectangle.csv"
A = np.genfromtxt(path, skip_footer=1, delimiter=" ")
b = np.genfromtxt(path, skip_header=len(A), delimiter=" ")
# Problem definition
n = A.shape[1]
lower = cp.Variable(n)
upper = cp.Variable(n)
sides = upper - lower
volume = cp.prod(sides)
objective = cp.Maximize(cp.geo_mean(sides))
A_u = np.maximum(A, 0)
A_l = np.maximum(-A, 0)
constraints = [
sides >= 0,
A_u @ upper - A_l @ lower <= b,
]
problem = cp.Problem(objective, constraints)
problem.solve()
volume.value
# constraints checker
checks = 1000000
print(f"Starting {checks} random corner checks...")
for _ in progressbar(range(checks)):
#!/usr/bin/env python3 import cvxpy as cp import numpy as np # Problem data. # Glove eqn 18/8 m = 30 n = 20 np.random.seed(1) X = np.random.randn(n, n) fX = np.random.randn(n, n) B = np.random.randn(n, n) # Construct the problem. W = cp.Variable((n, n)) objective = cp.Maximize(cp.prod(fX, cp.sum(W @ W.T + B - np.log(X)))) #objective = cp.Minimize(cp.sum_squares(A@x - b)) # constraints = [0 <= x, x <= 1] contraints = [W >= 0] prob = cp.Problem(objective, constraints) # The optimal objective value is returned by `prob.solve()`. result = prob.solve() # The optimal value for x is stored in `x.value`. print(x.value) # The optimal Lagrange multiplier for a constraint is stored in # `constraint.dual_value`. print(constraints[0].dual_value)