def test_maximum(self) -> None:
"""Test domain for maximum.
"""
b = Variable()
expr = cp.maximum(self.a, b)
self.a.value = 2
b.value = 4
self.assertAlmostEqual(expr.grad[self.a], 0)
self.assertAlmostEqual(expr.grad[b], 1)
self.a.value = 3
b.value = 0
self.assertAlmostEqual(expr.grad[self.a], 1)
self.assertAlmostEqual(expr.grad[b], 0)
self.a.value = -1
b.value = 2
self.assertAlmostEqual(expr.grad[self.a], 0)
self.assertAlmostEqual(expr.grad[b], 1)
y = Variable(2)
expr = cp.maximum(self.x, y)
self.x.value = [3, 4]
y.value = [5, -5]
val = np.zeros((2, 2)) + np.diag([0, 1])
self.assertItemsAlmostEqual(expr.grad[self.x].toarray(), val)
val = np.zeros((2, 2)) + np.diag([1, 0])
self.assertItemsAlmostEqual(expr.grad[y].toarray(), val)
expr = cp.maximum(self.x, y)
self.x.value = [-1e-9, 4]
y.value = [1, 4]
val = np.zeros((2, 2)) + np.diag([0, 1])
self.assertItemsAlmostEqual(expr.grad[self.x].toarray(), val)
val = np.zeros((2, 2)) + np.diag([1, 0])
self.assertItemsAlmostEqual(expr.grad[y].toarray(), val)
expr = cp.maximum(self.A, self.B)
self.A.value = [[1, 2], [3, 4]]
self.B.value = [[5, 1], [3, 2.3]]
val = np.zeros((4, 4)) + np.diag([0, 1, 1, 1])
self.assertItemsAlmostEqual(expr.grad[self.A].toarray(), val)
val = np.zeros((4, 4)) + np.diag([1, 0, 0, 0])
self.assertItemsAlmostEqual(expr.grad[self.B].toarray(), val)
# cummax
expr = cp.cummax(self.x)
self.x.value = [2, 1]
val = np.zeros((2, 2))
val[0, 0] = 1
self.assertItemsAlmostEqual(expr.grad[self.x].toarray(), val)
expr = cp.cummax(self.x[:, None], axis=1)
self.x.value = [2, 1]
val = np.eye(2)
self.assertItemsAlmostEqual(expr.grad[self.x].toarray(), val)
# Atom, solver pairs known to fail.
KNOWN_SOLVER_ERRORS = [
# See https://github.com/cvxgrp/cvxpy/issues/249
(log_sum_exp_axis_0, CVXOPT),
(log_sum_exp_axis_1, CVXOPT),
(cp.kl_div, CVXOPT),
]
atoms_minimize = [
(cp.abs, (2, 2), [[[-5, 2], [-3, 1]]], Constant([[5, 2], [3, 1]])),
(lambda x: cp.cumsum(x, axis=1), (2, 2), [[[-5, 2], [-3, 1]]],
Constant([[-5, 2], [-8, 3]])),
(lambda x: cp.cumsum(x, axis=0), (2, 2), [[[-5, 2], [-3, 1]]],
Constant([[-5, -3], [-3, -2]])),
(lambda x: cp.cummax(x, axis=1), (2, 2), [[[-5, 2], [-3, 1]]],
Constant([[-5, 2], [-3, 2]])),
(lambda x: cp.cummax(x, axis=0), (2, 2), [[[-5, 2], [-3, 1]]],
Constant([[-5, 2], [-3, 1]])),
(cp.diag, (2, ), [[[-5, 2], [-3, 1]]], Constant([-5, 1])),
(cp.diag, (2, 2), [[-5, 1]], Constant([[-5, 0], [0, 1]])),
(cp.exp, (2, 2), [[[1, 0], [2, -1]]],
Constant([[math.e, 1], [math.e**2, 1.0 / math.e]])),
(cp.huber, (2, 2), [[[0.5, -1.5], [4, 0]]], Constant([[0.25, 2], [7, 0]])),
(lambda x: cp.huber(x, 2.5), (2, 2), [[[0.5, -1.5], [4, 0]]],
Constant([[0.25, 2.25], [13.75, 0]])),
(cp.inv_pos, (2, 2), [[[1, 2], [3, 4]]],
Constant([[1, 1.0 / 2], [1.0 / 3, 1.0 / 4]])),
(lambda x: (x + Constant(0))**-1, (2, 2), [[[1, 2], [3, 4]]],
Constant([[1, 1.0 / 2], [1.0 / 3, 1.0 / 4]])),
(cp.kl_div, tuple(), [math.e, 1], Constant([1])),