def _prop_bnds_root_to_leaf_PowExpression(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.expr_pyomo5.ProductExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 2
arg1, arg2 = node.args
lb0, ub0 = bnds_dict[node]
lb1, ub1 = bnds_dict[arg1]
lb2, ub2 = bnds_dict[arg2]
_lb1a, _ub1a = interval.log(lb0, ub0)
_lb1a, _ub1a = interval.div(_lb1a, _ub1a, lb2, ub2)
_lb1a, _ub1a = interval.exp(_lb1a, _ub1a)
_lb1b, _ub1b = interval.sub(0, 0, _lb1a, _ub1a)
_lb1 = min(_lb1a, _lb1b)
_ub1 = max(_ub1a, _ub1b)
_lb2a, _ub2a = interval.log(lb0, ub0)
_lb2b, _ub2b = interval.log(lb1, ub1)
_lb2, _ub2 = interval.div(_lb2a, _ub2a, _lb2b, _ub2b)
if _lb1 > lb1:
lb1 = _lb1
if _ub1 < ub1:
ub1 = _ub1
if _lb2 > lb2:
lb2 = _lb2
if _ub2 < ub2:
ub2 = _ub2
bnds_dict[arg1] = (lb1, ub1)
bnds_dict[arg2] = (lb2, ub2)
def _prop_bnds_root_to_leaf_ProductExpression(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.expr_pyomo5.ProductExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 2
arg1, arg2 = node.args
lb0, ub0 = bnds_dict[node]
lb1, ub1 = bnds_dict[arg1]
lb2, ub2 = bnds_dict[arg2]
_lb1, _ub1 = interval.div(lb0, ub0, lb2, ub2)
_lb2, _ub2 = interval.div(lb0, ub0, lb1, ub1)
if _lb1 > lb1:
lb1 = _lb1
if _ub1 < ub1:
ub1 = _ub1
if _lb2 > lb2:
lb2 = _lb2
if _ub2 < ub2:
ub2 = _ub2
bnds_dict[arg1] = (lb1, ub1)
bnds_dict[arg2] = (lb2, ub2)
def _prop_bnds_root_to_leaf_ProductExpression(node, bnds_dict):
"""
Parameters
----------
node: pyomo.core.expr.numeric_expr.ProductExpression
bnds_dict: ComponentMap
"""
assert len(node.args) == 2
arg1, arg2 = node.args
lb0, ub0 = bnds_dict[node]
lb1, ub1 = bnds_dict[arg1]
lb2, ub2 = bnds_dict[arg2]
_lb1, _ub1 = interval.div(lb0, ub0, lb2, ub2)
_lb2, _ub2 = interval.div(lb0, ub0, lb1, ub1)
if _lb1 > lb1:
lb1 = _lb1
if _ub1 < ub1:
ub1 = _ub1
if _lb2 > lb2:
lb2 = _lb2
if _ub2 < ub2:
ub2 = _ub2
bnds_dict[arg1] = (lb1, ub1)
bnds_dict[arg2] = (lb2, ub2)
def test_div_edge_cases(self):
lb, ub = interval.div(0, -1e-16, 0, 0, 1e-8)
self.assertEqual(lb, -interval.inf)
self.assertEqual(ub, interval.inf)
lb, ub = interval.div(0, 1e-16, 0, 0, 1e-8)
self.assertEqual(lb, -interval.inf)
self.assertEqual(ub, interval.inf)
lb, ub = interval.div(-1e-16, 0, 0, 0, 1e-8)
self.assertEqual(lb, -interval.inf)
self.assertEqual(ub, interval.inf)
lb, ub = interval.div(1e-16, 0, 0, 0, 1e-8)
self.assertEqual(lb, -interval.inf)
self.assertEqual(ub, interval.inf)
def test_div(self):
x_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5))]
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.div(xl, xu, yl, yu, feasibility_tol=1e-8)
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))
def test_div(self):
x_bounds = [(np.random.uniform(-5, -2), np.random.uniform(2, 5))]
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.div(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))