def generate_expression(self, variable_list):
"""
The ``generate_expression`` method returns the Pyomo expression for the Kriging model trained.
The expression is constructed based on the supplied list of variables **variable_list** and the results of the previous Kriging training process.
Args:
variable_list(list) : List of input variables to be used in generating expression. This can be the a list generated from the output of ``get_feature_vector``. The user can also choose to supply a new list of the appropriate length.
Returns:
Pyomo Expression : Pyomo expression of the Kriging model based on the variables provided in **variable_list**
"""
t1 = np.array([variable_list])
phi_var = []
for i in range(0, self.x_data.shape[0]):
curr_term = sum(self.optimal_weights[j] * ( ((t1[0, j] - self.x_data_min[0, j])/(self.x_data_max[0, j] - self.x_data_min[0, j])) - self.x_data_scaled[i, j]) ** self.optimal_p for j in range(0, self.x_data.shape[1]))
curr_term = exp(-curr_term)
phi_var.append(curr_term)
phi_var_array = np.asarray(phi_var)
phi_inv_times_y_mu = np.matmul(self.covariance_matrix_inverse, self.optimal_y_mu)
phi_inv_times_y_mu = phi_inv_times_y_mu.reshape(phi_inv_times_y_mu.shape[0], )
kriging_expr = self.optimal_mean[0,0]
kriging_expr += sum(w * t for w, t in zip(np.nditer(phi_inv_times_y_mu), np.nditer(phi_var_array, flags=['refs_ok']) ))
return kriging_expr
def rule_odes(m,t):
Ra = m.P['k']*pyomo.exp(-m.P['ER']/m.X[t,'T'])*m.Z[t,'A']
exprs = dict()
exprs['A'] = C['F']/C['V']*(m.P['Cfa']-m.Z[t,'A']) - Ra
exprs['T'] = C['F']/C['V']*(m.P['Tf']-m.X[t,'T']) + m.P['delH']/(m.P['rho'])/C['Cp']*Ra - m.P['h']*C['A']/(m.P['rho'])/C['Cp']/C['V']*(m.X[t,'T'] - m.X[t,'Tc'])
exprs['Tc'] = C['Fc']/C['Vc']*(m.P['Tfc']-m.X[t,'Tc']) + m.P['h']*C['A']/(m.P['rhoc'])/C['Cpc']/C['Vc']*(m.X[t,'T'] - m.X[t,'Tc'])
return exprs
def test_mc_3d(self):
m = ConcreteModel()
m.x = Var(bounds=(-2, 1), initialize=-1)
m.y = Var(bounds=(-1, 2), initialize=0)
m.e = Expression(expr=m.x * pow(exp(m.x) - m.y, 2))
ccSurf, cvSurf, ccAffine, cvAffine = make3dPlot(m.e.expr, 30)
self.assertAlmostEqual(ccSurf[48], 11.5655473482574)
self.assertAlmostEqual(cvSurf[48], -15.28102124928224)
self.assertAlmostEqual(ccAffine[48], 11.565547348257398)
self.assertAlmostEqual(cvAffine[48], -23.131094696514797)
def test_mc_3d(self):
m = ConcreteModel()
m.x = Var(bounds=(-2, 1), initialize=-1)
m.y = Var(bounds=(-1, 2), initialize=0)
m.e = Expression(expr=m.x * pow(exp(m.x) - m.y, 2))
ccSurf, cvSurf, ccAffine, cvAffine = make3dPlot(m.e.expr, 30)
self.assertAlmostEqual(ccSurf[48], 11.5655473482574)
self.assertAlmostEqual(cvSurf[48], -15.28102124928224)
self.assertAlmostEqual(ccAffine[48], 11.565547348257398)
self.assertAlmostEqual(cvAffine[48], -23.131094696514797)
def test_divide_by_mutable(self):
#
# Test from https://github.com/Pyomo/pyomo/issues/153
#
m = ConcreteModel()
m.x = Var(bounds=(1,5))
m.p = Param(initialize=100, mutable=True)
m.con = Constraint(expr=exp(5*(1/m.x - 1/m.p))<=10)
m.obj = Objective(expr=m.x**2)
test = gar(m.con.body)
self.assertEqual(test.constant, 0)
self.assertEqual(test.linear_vars, tuple())
self.assertEqual(test.linear_coefs, tuple())
self.assertEqual(set(id(v) for v in test.nonlinear_vars), set([id(m.x)]))
self.assertIs(test.nonlinear_expr, m.con.body)
ans *= i
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.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),
# Model constants
cA0 = r1.constant('ca0', value=4.0)
v0 = r1.constant('v0', value=240)
cpA = r1.constant('cpA', value=30)
cpB = r1.constant('cpB', value=60)
cpC = r1.constant('cpC', value=20)
TA0 = r1.constant('TA0', value=305)
hrxnA = r1.constant('hrxnA', value=6500)
hrxnB = r1.constant('hrxnB', value=8000)
Tc = r1.constant('Tc', value=298)
Uc = r1.constant('Uc', value=35000)
# Define the expressions
k1 = r1.add_expression('k1', 1.25 * exp(
(9500 / 1.987) * (1 / 320.0 - 1 / T)))
k2 = r1.add_expression('k2', 0.08 * exp(
(7000 / 1.987) * (1 / 290.0 - 1 / T)))
rA = r1.add_reaction('rA', k1 * A)
rB = r1.add_reaction('rB', k2 * B)
SM = {'A': [-1, 0], 'B': [0.5, -1], 'C': [0, 3]}
RE = r1.reactions_from_stoich(SM, add_odes=False)
RE['A'] += cA0 * v0 / V
r1.add_odes(RE)
# Energy balances
T1 = Uc * (Tc - T) # heat transfer
T2 = cA0 * v0 * cpA * (T - TA0) # enthalpy from adding A
filename = 'data/init_X.csv'
rm.add_data('init_X', category='trajectory', file=filename)
filename = 'data/init_Y.csv'
rm.add_data('init_Y', category='trajectory', file=filename)
# Reactions
r0 = rm.add_reaction('r0', k0 * SA * AA, description='Reaction 0')
r1 = rm.add_reaction('r1', k1 * ASA * AA, description='Reaction 1')
r2 = rm.add_reaction('r2', k2 * ASAA * H2O, description='Reaction 2')
r3 = rm.add_reaction('r3', k3 * AA * H2O, description='Reaction 3')
#step = r1.step('step', time=210, fixed=False, switch='off')
step = 1 / (1 + exp(-Msa / 1e-4))
r4 = rm.add_reaction('r4',
kd * (Csa - SA + 1e-6)**1.90 * step,
description='Reaction 4')
diff = ASA - Csat
r5 = rm.add_reaction('r5',
0.3950206559 * kc * (diff +
((diff)**2 + 1e-6)**0.5)**1.34,
description='Reaction 5')
# Generate the ODEs for the reactions based on the stoichiometric matrix
# Since we need to modfiy the ODEs, add_odes should be False
odes = rm.reactions_from_stoich(gammas, add_odes=False)
# Build expression for the volume
