def test_linearize(self) -> None:
"""Test linearize method.
"""
# Affine.
expr = (2 * self.x - 5)[0]
self.x.value = [1, 2]
lin_expr = linearize(expr)
self.x.value = [55, 22]
self.assertAlmostEqual(lin_expr.value, expr.value)
self.x.value = [-1, -5]
self.assertAlmostEqual(lin_expr.value, expr.value)
# Convex.
expr = self.A**2 + 5
with self.assertRaises(Exception) as cm:
linearize(expr)
self.assertEqual(
str(cm.exception),
"Cannot linearize non-affine expression with missing variable values."
)
self.A.value = [[1, 2], [3, 4]]
lin_expr = linearize(expr)
manual = expr.value + 2 * cp.reshape(
cp.diag(cp.vec(self.A)).value @ cp.vec(self.A - self.A.value),
(2, 2))
self.assertItemsAlmostEqual(lin_expr.value, expr.value)
self.A.value = [[-5, -5], [8.2, 4.4]]
assert (lin_expr.value <= expr.value).all()
self.assertItemsAlmostEqual(lin_expr.value, manual.value)
# Concave.
expr = cp.log(self.x) / 2
self.x.value = [1, 2]
lin_expr = linearize(expr)
manual = expr.value + cp.diag(
0.5 * self.x**-1).value @ (self.x - self.x.value)
self.assertItemsAlmostEqual(lin_expr.value, expr.value)
self.x.value = [3, 4.4]
assert (lin_expr.value >= expr.value).all()
self.assertItemsAlmostEqual(lin_expr.value, manual.value)
def test_linearize(self):
"""Test linearize method.
"""
# Affine.
expr = (2*self.x - 5)[0]
self.x.value = [1, 2]
lin_expr = linearize(expr)
self.x.value = [55, 22]
self.assertAlmostEqual(lin_expr.value, expr.value)
self.x.value = [-1, -5]
self.assertAlmostEqual(lin_expr.value, expr.value)
# Convex.
expr = (self.A)**2 + 5
with self.assertRaises(Exception) as cm:
linearize(expr)
self.assertEqual(str(cm.exception),
"Cannot linearize non-affine expression with missing variable values.")
self.A.value = [[1, 2], [3, 4]]
lin_expr = linearize(expr)
manual = expr.value + 2*reshape(diag(vec(self.A)).value*vec(self.A - self.A.value), 2, 2)
self.assertItemsAlmostEqual(lin_expr.value, expr.value)
self.A.value = [[-5, -5], [8.2, 4.4]]
assert (lin_expr.value <= expr.value).all()
self.assertItemsAlmostEqual(lin_expr.value, manual.value)
# Concave.
expr = log(self.x)/2
self.x.value = [1, 2]
lin_expr = linearize(expr)
manual = expr.value + diag(0.5*self.x**-1).value*(self.x - self.x.value)
self.assertItemsAlmostEqual(lin_expr.value, expr.value)
self.x.value = [3, 4.4]
assert (lin_expr.value >= expr.value).all()
self.assertItemsAlmostEqual(lin_expr.value, manual.value)