def test_mc_2d(self):
m = ConcreteModel()
m.x = Var(bounds=(pi / 6, pi / 3), initialize=pi / 4)
m.e = Expression(expr=cos(pow(m.x, 2)) * sin(pow(m.x, -3)))
mc_ccVals, mc_cvVals, aff_cc, aff_cv = make2dPlot(m.e.expr, 50)
self.assertAlmostEqual(mc_ccVals[1], 0.6443888590411435)
self.assertAlmostEqual(mc_cvVals[1], 0.2328315489072924)
self.assertAlmostEqual(aff_cc[1], 0.9674274332870583)
self.assertAlmostEqual(aff_cv[1], -1.578938503009686)
def test_mc_2d(self):
m = ConcreteModel()
m.x = Var(bounds=(pi / 6, pi / 3), initialize=pi / 4)
m.e = Expression(expr=cos(pow(m.x, 2)) * sin(pow(m.x, -3)))
mc_ccVals, mc_cvVals, aff_cc, aff_cv = make2dPlot(m.e.expr, 50)
self.assertAlmostEqual(mc_ccVals[1], 0.6443888590411435)
self.assertAlmostEqual(mc_cvVals[1], 0.2328315489072924)
self.assertAlmostEqual(aff_cc[1], 0.9674274332870583)
self.assertAlmostEqual(aff_cv[1], -1.578938503009686)
def test_trig(self):
m = ConcreteModel()
m.x = Var(bounds=(pi / 4, pi / 2), initialize=pi / 4)
mc_expr = mc(tan(atan((m.x))))
self.assertAlmostEqual(mc_expr.lower(), pi / 4)
self.assertAlmostEqual(mc_expr.upper(), pi / 2)
m.y = Var(bounds=(0, sin(pi / 4)), initialize=0)
mc_expr = mc(asin((m.y)))
self.assertEqual(mc_expr.lower(), 0)
self.assertAlmostEqual(mc_expr.upper(), pi / 4)
m.z = Var(bounds=(0, cos(pi / 4)), initialize=0)
mc_expr = mc(acos((m.z)))
self.assertAlmostEqual(mc_expr.lower(), pi / 4)
self.assertAlmostEqual(mc_expr.upper(), pi / 2)
def test_trig(self):
m = ConcreteModel()
m.x = Var(bounds=(pi / 4, pi / 2), initialize=pi / 4)
mc_expr = mc(tan(atan((m.x))))
self.assertAlmostEqual(mc_expr.lower(), pi / 4)
self.assertAlmostEqual(mc_expr.upper(), pi / 2)
m.y = Var(bounds=(0, sin(pi / 4)), initialize=0)
mc_expr = mc(asin((m.y)))
self.assertEqual(mc_expr.lower(), 0)
self.assertAlmostEqual(mc_expr.upper(), pi / 4)
m.z = Var(bounds=(0, cos(pi / 4)), initialize=0)
mc_expr = mc(acos((m.z)))
self.assertAlmostEqual(mc_expr.lower(), pi / 4)
self.assertAlmostEqual(mc_expr.upper(), pi / 2)
def test_collect_mutable_parameters(self):
model = pc.ConcreteModel()
model.p = pc.Param(mutable=True)
model.q = pc.Param([1], mutable=True, initialize=1.0)
model.r = pc.Param(initialize=1.1, mutable=False)
model.x = pc.Var()
for obj in [model.p, model.q[1]]:
result = EmbeddedSP._collect_mutable_parameters(
obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
obj + 1)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * (obj + 1))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * obj + 1)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * obj + 1 + model.x)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
obj * model.x)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x / obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x / (2 * obj))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
obj * pc.log(2 * model.x))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
obj * pc.sin(model.r) ** model.x)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x**(obj * pc.sin(model.r)))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
1.0)
self.assertEqual(len(result), 0)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.p + model.q[1] + model.r)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.p + 1 + model.r + model.q[1])
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
result = EmbeddedSP._collect_mutable_parameters(
model.q[1] * 2 * (model.p + model.r) + model.r)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * model.x * model.p * model.q[1] * model.r)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * obj * model.q[1] * model.r + 1)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
2 * model.q[1] + 1 + model.x - model.p)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.r * model.x)
self.assertEqual(len(result), 0)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x / obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x / (2 * model.q[1] / model.p))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
(model.p / model.q[1]) * pc.log(2 * model.x))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.q[1] * pc.sin(model.p) ** (model.x + model.r))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
(model.p + model.x) ** (model.q[1] * pc.sin(model.r)))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
def _sum(*x):
return sum(i for i in x)
def _nondifferentiable(*x):
raise NondifferentiableError(
"The sub-expression '%s' is not differentiable with respect to %s"
% (x[0], x[1]))
_operatorMap = {
sympy.Add: _sum,
sympy.Mul: _prod,
sympy.Pow: lambda x, y: x**y,
sympy.exp: lambda x: core.exp(x),
sympy.log: lambda x: core.log(x),
sympy.sin: lambda x: core.sin(x),
sympy.asin: lambda x: core.asin(x),
sympy.sinh: lambda x: core.sinh(x),
sympy.asinh: lambda x: core.asinh(x),
sympy.cos: lambda x: core.cos(x),
sympy.acos: lambda x: core.acos(x),
sympy.cosh: lambda x: core.cosh(x),
sympy.acosh: lambda x: core.acosh(x),
sympy.tan: lambda x: core.tan(x),
sympy.atan: lambda x: core.atan(x),
sympy.tanh: lambda x: core.tanh(x),
sympy.atanh: lambda x: core.atanh(x),
sympy.ceiling: lambda x: core.ceil(x),
sympy.floor: lambda x: core.floor(x),
sympy.Derivative: _nondifferentiable,
}
return ans
def _sum(*x):
return sum(i for i in x)
def _nondifferentiable(*x):
raise NondifferentiableError(
"The sub-expression '%s' is not differentiable with respect to %s"
% (x[0],x[1]) )
_operatorMap = {
sympy.Add: _sum,
sympy.Mul: _prod,
sympy.Pow: lambda x,y: x**y,
sympy.log: lambda x: core.log(x),
sympy.sin: lambda x: core.sin(x),
sympy.asin: lambda x: core.asin(x),
sympy.sinh: lambda x: core.sinh(x),
sympy.asinh: lambda x: core.asinh(x),
sympy.cos: lambda x: core.cos(x),
sympy.acos: lambda x: core.acos(x),
sympy.cosh: lambda x: core.cosh(x),
sympy.acosh: lambda x: core.acosh(x),
sympy.tan: lambda x: core.tan(x),
sympy.atan: lambda x: core.atan(x),
sympy.tanh: lambda x: core.tanh(x),
sympy.atanh: lambda x: core.atanh(x),
sympy.ceiling: lambda x: core.ceil(x),
sympy.floor: lambda x: core.floor(x),
sympy.Derivative: _nondifferentiable,
}
def test_collect_mutable_parameters(self):
model = pc.ConcreteModel()
model.p = pc.Param(mutable=True)
model.q = pc.Param([1], mutable=True, initialize=1.0)
model.r = pc.Param(initialize=1.1, mutable=False)
model.x = pc.Var()
for obj in [model.p, model.q[1]]:
result = EmbeddedSP._collect_mutable_parameters(obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(obj + 1)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * (obj + 1))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * obj + 1)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * obj + 1 +
model.x)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(obj * model.x)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(model.x / obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(model.x /
(2 * obj))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
obj * pc.log(2 * model.x))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
obj * pc.sin(model.r)**model.x)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x**(obj * pc.sin(model.r)))
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(1.0)
self.assertEqual(len(result), 0)
del result
result = EmbeddedSP._collect_mutable_parameters(model.p + model.q[1] +
model.r)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(model.p + 1 + model.r +
model.q[1])
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
result = EmbeddedSP._collect_mutable_parameters(model.q[1] * 2 *
(model.p + model.r) +
model.r)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * model.x * model.p *
model.q[1] * model.r)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * obj * model.q[1] *
model.r + 1)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(2 * model.q[1] + 1 +
model.x - model.p)
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(model.r * model.x)
self.assertEqual(len(result), 0)
del result
result = EmbeddedSP._collect_mutable_parameters(model.x / obj)
self.assertTrue(id(obj) in result)
self.assertEqual(len(result), 1)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.x / (2 * model.q[1] / model.p))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
(model.p / model.q[1]) * pc.log(2 * model.x))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
model.q[1] * pc.sin(model.p)**(model.x + model.r))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result
result = EmbeddedSP._collect_mutable_parameters(
(model.p + model.x)**(model.q[1] * pc.sin(model.r)))
self.assertTrue(id(model.p) in result)
self.assertTrue(id(model.q[1]) in result)
self.assertEqual(len(result), 2)
del result