def _rule_result(self, terms):
coefficients = [c for c, _ in terms]
children = [PE() for _ in terms]
cvxs = [c for _, c in terms]
ctx = ConvexityContext()
for child, cvx in zip(children, cvxs):
ctx.set_convexity(child, cvx)
rule = LinearRule()
return rule.checked_apply(PE(ET.Linear, children=children, coefficients=coefficients), ctx)
def test_linear_over_variable(coef):
rule = FractionalRule()
x = PE(ET.Variable)
num = PE(ET.Linear, [x], coefficients=[coef], constant_term=0.0)
ctx = FractionalContext({
x: I(0, None),
})
result = rule.apply(PE(ET.Division, [num, x]), ctx)
assert result == Convexity.Linear
def _rule_result(self, A):
n = A.shape[0]
var = [PE(ET.Variable) for _ in range(n)]
terms = []
for i in range(n):
for j in range(i + 1):
terms.append(BilinearTerm(var[i], var[j], A[i, j]))
expr = PE(ET.Quadratic, terms=terms, children=var)
rule = QuadraticRule()
return rule.apply(expr, None)
def _rule_result(self, cvx_f, cvx_g, mono_f, mono_g, bounds_f, bounds_g):
rule = DivisionRule()
f = PE()
g = PE()
convexity = ComponentMap()
convexity[f] = cvx_f
convexity[g] = cvx_g
mono = ComponentMap()
mono[f] = mono_f
mono[g] = mono_g
bounds = ComponentMap()
bounds[f] = bounds_f
bounds[g] = bounds_g
return rule.apply(PE(ET.Division, [f, g]), convexity, mono, bounds)
def _result_with_terms(self, terms):
rule = LinearRule()
monotonicity = {}
coefficients = [c for c, _ in terms]
children = [PE(ET.Variable) for _ in terms]
monos = [m for _, m in terms]
for child, mono in zip(children, monos):
monotonicity[child] = mono
ctx = MonotonicityContext(monotonicity, {})
result = rule.checked_apply(
PE(ET.Linear, children=children, coefficients=coefficients),
ctx,
)
return result
def test_linear_with_constant_over_variable(coef, const):
assume(coef != 0.0)
assume(coef < MAX_NUM and const < MAX_NUM)
rule = FractionalRule()
x = PE(ET.Variable)
num = PE(ET.Linear, [x], coefficients=[coef], constant_term=const)
ctx = FractionalContext({
x: I(0, None),
})
result = rule.apply(PE(ET.Division, [num, x]), ctx)
if almosteq(const, 0):
expected = Convexity.Linear
elif const > 0:
expected = Convexity.Convex
elif const < 0:
expected = Convexity.Concave
def test_constant_is_constant():
rule = ConstantRule()
result = rule.apply(PE(ET.Constant), None, None)
assert result.is_constant()
def test_variable_is_nondecreasing():
rule = VariableRule()
result = rule.apply(PE(ET.Variable), None, None)
assert result.is_nondecreasing() and (not result.is_constant())
def test_l2_norm(children):
rule = L2NormRule()
sum_ = PE(ET.Sum, children)
result = rule.checked_apply(PE(ET.UnaryFunction, [sum_], func_type=UFT.Sqrt), None)
assert result.is_convex()
def products(draw):
x = PE(ET.Variable)
return PE(ET.Product, [x, x])
def powers(draw):
base = PE(ET.Variable)
expo = PE(ET.Constant, value=2.0)
return PE(ET.Power, [base, expo])
def constants(draw):
return PE(ET.Constant)