def test_pow(self):
x_bounds = [(np.random.uniform(0, 2), np.random.uniform(2, 5)),
(0, np.random.uniform(2, 5)), (0, 0)]
y_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5)),
(0, np.random.uniform(2, 5)),
(np.random.uniform(0, 2), np.random.uniform(2, 5)),
(np.random.uniform(-5, -2), 0),
(np.random.uniform(-5, -2), np.random.uniform(-2, 0))]
for xl, xu in x_bounds:
for yl, yu in y_bounds:
zl, zu = interval.power(xl, xu, yl, yu)
x = np.linspace(xl, xu, 100)
y = np.linspace(yl, yu, 100)
for _x in x:
_z = _x**y
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
x_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5)),
(np.random.uniform(-5, -2), np.random.uniform(-2, 0)),
(np.random.uniform(-5, -2), 0)]
y_bounds = list(range(-4, 4))
for xl, xu in x_bounds:
for yl in y_bounds:
yu = yl
zl, zu = interval.power(xl, xu, yl, yu)
x = np.linspace(xl, xu, 100, endpoint=False)
y = yl
_z = x**y
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
def test_pow(self):
x_bounds = [(np.random.uniform(0, 2), np.random.uniform(2, 5)),
(0, np.random.uniform(2, 5)),
(0, 0)]
y_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5)),
(0, np.random.uniform(2, 5)),
(np.random.uniform(0, 2), np.random.uniform(2, 5)),
(np.random.uniform(-5, -2), 0),
(np.random.uniform(-5, -2), np.random.uniform(-2, 0))]
for xl, xu in x_bounds:
for yl, yu in y_bounds:
zl, zu = interval.power(xl, xu, yl, yu)
x = np.linspace(xl, xu, 100)
y = np.linspace(yl, yu, 100)
for _x in x:
_z = _x ** y
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
x_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5)),
(np.random.uniform(-5, -2), np.random.uniform(-2, 0)),
(np.random.uniform(-5, -2), 0)]
y_bounds = list(range(-4, 4))
for xl, xu in x_bounds:
for yl in y_bounds:
yu = yl
zl, zu = interval.power(xl, xu, yl, yu)
x = np.linspace(xl, xu, 100, endpoint=False)
y = yl
_z = x ** y
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
def test_pow(self):
x_bounds = [(np.random.uniform(0, 2), np.random.uniform(2, 5)),
(0, np.random.uniform(2, 5)), (0, 0)]
y_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5)),
(0, np.random.uniform(2, 5)),
(np.random.uniform(0, 2), np.random.uniform(2, 5)),
(np.random.uniform(-5, -2), 0),
(np.random.uniform(-5, -2), np.random.uniform(-2, 0))]
for xl, xu in x_bounds:
for yl, yu in y_bounds:
zl, zu = interval.power(xl, xu, yl, yu, feasibility_tol=1e-8)
if xl == 0 and xu == 0 and yu < 0:
self.assertEqual(zl, -interval.inf)
self.assertEqual(zu, interval.inf)
x = np.linspace(xl, xu, 100)
y = np.linspace(yl, yu, 100)
for _x in x:
_z = _x**y
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
x_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5)),
(np.random.uniform(-5, -2), np.random.uniform(-2, 0)),
(np.random.uniform(-5, -2), 0)]
y_bounds = list(range(-4, 4))
for xl, xu in x_bounds:
for yl in y_bounds:
yu = yl
zl, zu = interval.power(xl, xu, yl, yu, feasibility_tol=1e-8)
x = np.linspace(xl, xu, 100, endpoint=False)
y = yl
_z = x**y
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
def test_pow2(self):
xl = np.linspace(-2, 2, 9)
xu = np.linspace(-2, 2, 9)
yl = np.linspace(-2, 2, 9)
yu = np.linspace(-2, 2, 9)
for _xl in xl:
for _xu in xu:
if _xl > _xu:
continue
for _yl in yl:
for _yu in yu:
if _yl > _yu:
continue
if _xl == 0 and _xu == 0 and _yu < 0:
lb, ub = interval.power(_xl,
_xu,
_yl,
_yu,
feasibility_tol=1e-8)
self.assertEqual(lb, -interval.inf)
self.assertEqual(ub, interval.inf)
elif _yl == _yu and _yl != round(_yl) and (
_xu < 0 or (_xu < 0 and _yu < 0)):
with self.assertRaises(
(InfeasibleConstraintException,
interval.IntervalException)):
lb, ub = interval.power(_xl,
_xu,
_yl,
_yu,
feasibility_tol=1e-8)
else:
lb, ub = interval.power(_xl,
_xu,
_yl,
_yu,
feasibility_tol=1e-8)
if isfinite(lb) and isfinite(ub):
nan_fill = 0.5 * (lb + ub)
elif isfinite(lb):
nan_fill = lb + 1
elif isfinite(ub):
nan_fill = ub - 1
else:
nan_fill = 0
x = np.linspace(_xl, _xu, 30)
y = np.linspace(_yl, _yu, 30)
z = x**np.split(y, len(y))
z[np.isnan(z)] = nan_fill
all_values = z
estimated_lb = all_values.min()
estimated_ub = all_values.max()
self.assertTrue(lb - 1e-8 <= estimated_lb)
self.assertTrue(ub + 1e-8 >= estimated_ub)
def test_pow2(self):
xl = np.linspace(-2, 2, 17)
xu = np.linspace(-2, 2, 17)
yl = np.linspace(-2, 2, 17)
yu = np.linspace(-2, 2, 17)
for _xl in xl:
for _xu in xu:
if _xl > _xu:
continue
for _yl in yl:
for _yu in yu:
if _yl > _yu:
continue
if _yl == _yu and _yl != round(_yl) and _xu < 0:
with self.assertRaises(
InfeasibleConstraintException):
lb, ub = interval.power(_xl, _xu, _yl, _yu)
else:
lb, ub = interval.power(_xl, _xu, _yl, _yu)
if isfinite(lb) and isfinite(ub):
nan_fill = 0.5 * (lb + ub)
elif isfinite(lb):
nan_fill = lb + 1
elif isfinite(ub):
nan_fill = ub - 1
else:
nan_fill = 0
x = np.linspace(_xl, _xu, 17)
y = np.linspace(_yl, _yu, 17)
all_values = list()
for _x in x:
z = _x**y
#np.nan_to_num(z, copy=False, nan=nan_fill, posinf=np.inf, neginf=-np.inf)
tmp = []
for _z in z:
if math.isnan(_z):
tmp.append(nan_fill)
else:
tmp.append(_z)
all_values.append(np.array(tmp))
all_values = np.array(all_values)
estimated_lb = all_values.min()
estimated_ub = all_values.max()
self.assertTrue(lb - 1e-8 <= estimated_lb)
self.assertTrue(ub + 1e-8 >= estimated_ub)
def _prop_bnds_leaf_to_root_sqrt(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.numeric_expr.UnaryFunctionExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 1
arg = node.args[0]
lb1, ub1 = bnds_dict[arg]
bnds_dict[node] = interval.power(lb1, ub1, 0.5, 0.5)
def _prop_bnds_leaf_to_root_sqrt(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.numeric_expr.UnaryFunctionExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 1
arg = node.args[0]
lb1, ub1 = bnds_dict[arg]
bnds_dict[node] = interval.power(lb1, ub1, 0.5, 0.5)
def _prop_bnds_leaf_to_root_PowExpression(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.expr_pyomo5.PowExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 2
arg1, arg2 = node.args
lb1, ub1 = bnds_dict[arg1]
lb2, ub2 = bnds_dict[arg2]
bnds_dict[node] = interval.power(lb1, ub1, lb2, ub2)
def _prop_bnds_leaf_to_root_PowExpression(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.numeric_expr.PowExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 2
arg1, arg2 = node.args
lb1, ub1 = bnds_dict[arg1]
lb2, ub2 = bnds_dict[arg2]
bnds_dict[node] = interval.power(lb1, ub1, lb2, ub2)
