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 _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,
}
except ImportError: #pragma:nocover
_sympy_available = False
# A "public" attribute indicating that differentiate() can be called
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,
}
except ImportError: #pragma:nocover
_sympy_available = False
