def test_power(self):
m = aml.Model()
x = 2.5
y = -3.7
m.x = aml.Var(x)
m.y = aml.Var(y)
expr = m.x ** (m.y)
self.assertAlmostEqual(expr.evaluate(), x ** y, 10)
ders = expr.reverse_ad()
self.assertAlmostEqual(ders[m.x], y * x ** (y - 1), 10)
self.assertAlmostEqual(ders[m.y], x ** y * np.log(x), 10)
def test_multiply(self):
m = aml.Model()
x = 2.5
y = -3.7
m.x = aml.Var(x)
m.y = aml.Var(y)
expr = m.x * m.y
self.assertAlmostEqual(expr.evaluate(), x * y, 10)
ders = expr.reverse_ad()
self.assertEqual(ders[m.x], y)
self.assertEqual(ders[m.y], x)
def test_divide(self):
m = aml.Model()
x = 2.5
y = -3.7
m.x = aml.Var(x)
m.y = aml.Var(y)
expr = m.x / m.y
self.assertAlmostEqual(expr.evaluate(), x / y, 10)
ders = expr.reverse_ad()
self.assertAlmostEqual(ders[m.x], 1 / y, 10)
self.assertAlmostEqual(ders[m.y], -x / y ** 2, 10)
def test_subtract(self):
m = aml.Model()
x = 2.5
y = -3.7
m.x = aml.Var(x)
m.y = aml.Var(y)
expr = m.x - m.y
self.assertAlmostEqual(expr.evaluate(), x - y, 10)
ders = expr.reverse_ad()
self.assertEqual(ders[m.x], 1)
self.assertEqual(ders[m.y], -1)
def test_structure_exception(self):
m = aml.Model()
m.x = aml.Var()
m.c = aml.Constraint(m.x - 1)
with self.assertRaises(RuntimeError):
m.get_x()
m.set_structure()
m.get_x()
m.y = aml.Var()
m.c2 = aml.Constraint(m.x + m.y)
with self.assertRaises(RuntimeError):
m.get_x()
m.set_structure()
x = m.get_x()
self.assertEqual(len(x), 2)
def test_log(self):
m = aml.Model()
x = 2.5
m.x = aml.Var(x)
expr = aml.log(m.x)
self.assertAlmostEqual(aml.value(expr), np.log(x), 10)
self.assertAlmostEqual(expr.reverse_ad()[m.x], 1 / x, 10)
def test_add(self):
m = aml.Model()
x = 2.5
y = -3.7
z = 10.0
c1 = 8.6
c2 = 3.3
m.x = aml.Var(x)
m.y = aml.Var(y)
m.c1 = aml.Param(c1)
expr = m.x + m.y + m.c1 + c2
self.assertAlmostEqual(expr.evaluate(), x + y + c1 + c2, 10)
ders = expr.reverse_ad()
self.assertEqual(ders[m.x], 1)
self.assertEqual(ders[m.y], 1)
def test_chain_rule(self):
m = aml.Model()
x = 1.1
m.x = aml.Var(x)
expr = aml.exp((m.x + m.x**0.5)**2) - m.x
actual_deriv = np.exp((x + x**0.5)**2)*2*(x + x**0.5)*(1 + 0.5*x**(-0.5)) - 1
self.assertAlmostEqual(aml.value(expr), np.exp((x + x**0.5)**2) - x, 10)
self.assertAlmostEqual(expr.reverse_ad()[m.x], actual_deriv, 10)
def test_basic_constraints(self):
m = aml.Model()
x = 2.5
y = -3.7
c = 1.5
m.x = aml.Var(x)
m.y = aml.Var(y)
m.c = aml.Param(c)
m.con1 = aml.Constraint(m.x + 2.0 * m.y + m.c)
m.con2 = aml.Constraint(m.x ** 2 - m.y ** 2 + 10)
true_con_values = OrderedDict()
true_con_values[m.con1] = x + 2 * y + c
true_con_values[m.con2] = x ** 2 - y ** 2 + 10
true_jac = OrderedDict()
true_jac[m.con1] = OrderedDict()
true_jac[m.con2] = OrderedDict()
true_jac[m.con1][m.x] = 1
true_jac[m.con1][m.y] = 2
true_jac[m.con2][m.x] = 2 * x
true_jac[m.con2][m.y] = -2 * y
compare_evaluation(self, m, true_con_values, true_jac)
del true_con_values[m.con2]
del true_jac[m.con2]
del m.con2
m.con3 = aml.Constraint(m.x * m.y)
true_con_values[m.con3] = x * y
true_jac[m.con3] = OrderedDict()
true_jac[m.con3][m.x] = y
true_jac[m.con3][m.y] = x
compare_evaluation(self, m, true_con_values, true_jac)
def leak_rate_var(m, wn, index_over=None):
"""
Add a variable to the model for leak flow rate
Parameters
----------
m: wntr.aml.aml.aml.Model
wn: wntr.network.model.WaterNetworkModel
index_over: list of str
list of junction/tank names
"""
if not hasattr(m, 'leak_rate'):
m.leak_rate = aml.VarDict()
if index_over is None:
index_over = wn.junction_name_list + wn.tank_name_list
for node_name in index_over:
m.leak_rate[node_name] = aml.Var(0)
def head_var(m, wn, index_over=None):
"""
Add a head variable to the model
Parameters
----------
m: wntr.aml.aml.aml.Model
wn: wntr.network.model.WaterNetworkModel
index_over: list of str
list of junction names
"""
if not hasattr(m, 'head'):
m.head = aml.VarDict()
if index_over is None:
index_over = wn.junction_name_list
for node_name in index_over:
node = wn.get_node(node_name)
m.head[node_name] = aml.Var(node.elevation)
def flow_var(m, wn, index_over=None):
"""
Add a flow variable to the model
Parameters
----------
m: wntr.aml.aml.aml.Model
wn: wntr.network.model.WaterNetworkModel
index_over: list of str
list of link names
"""
if not hasattr(m, 'flow'):
m.flow = aml.VarDict()
if index_over is None:
index_over = wn.link_name_list
for link_name in index_over:
link = wn.get_link(link_name)
m.flow[link_name] = aml.Var(0.001)
def demand_var(m, wn, index_over=None):
"""
Add a demand variable to the model
Parameters
----------
m: wntr.aml.aml.aml.Model
wn: wntr.network.model.WaterNetworkModel
index_over: list of str
list of junction names
"""
if not hasattr(m, 'demand'):
m.demand = aml.VarDict()
if index_over is None:
index_over = wn.junction_name_list
demand_multiplier = wn.options.hydraulic.demand_multiplier
pattern_start = wn.options.time.pattern_start
for node_name in index_over:
node = wn.get_node(node_name)
m.demand[node_name] = aml.Var(node.demand_timeseries_list.at(wn.sim_time+pattern_start, multiplier=demand_multiplier))
def test_register_and_remove_constraint(self):
m = aml.Model()
m.x = aml.Var(2.0)
m.y = aml.Var(3.0)
m.z = aml.Var(4.0)
m.v = aml.Var(10.0)
m.c1 = aml.Constraint(m.x + m.y)
m.c2 = aml.Constraint(m.x * m.y * m.v)
m.c3 = aml.Constraint(m.z ** 3.0)
m.c4 = aml.Constraint(m.x + 1.0 / m.v)
m.set_structure()
con_values = m.evaluate_residuals()
A = m.evaluate_jacobian()
true_con_values = OrderedDict()
true_con_values[m.c1] = 5.0
true_con_values[m.c2] = 60.0
true_con_values[m.c3] = 64.0
true_con_values[m.c4] = 2.1
for c in m.cons():
self.assertTrue(true_con_values[c] == con_values[c.index])
true_jac = OrderedDict()
true_jac[m.c1] = OrderedDict()
true_jac[m.c2] = OrderedDict()
true_jac[m.c3] = OrderedDict()
true_jac[m.c4] = OrderedDict()
true_jac[m.c1][m.x] = 1.0
true_jac[m.c1][m.y] = 1.0
true_jac[m.c1][m.z] = 0.0
true_jac[m.c1][m.v] = 0.0
true_jac[m.c2][m.x] = 30.0
true_jac[m.c2][m.y] = 20.0
true_jac[m.c2][m.z] = 0.0
true_jac[m.c2][m.v] = 6.0
true_jac[m.c3][m.x] = 0.0
true_jac[m.c3][m.y] = 0.0
true_jac[m.c3][m.z] = 48.0
true_jac[m.c3][m.v] = 0.0
true_jac[m.c4][m.x] = 1.0
true_jac[m.c4][m.y] = 0.0
true_jac[m.c4][m.z] = 0.0
true_jac[m.c4][m.v] = -0.01
for c in m.cons():
for v in m.vars():
self.assertTrue(true_jac[c][v] == A[c.index, v.index])
del m.c3
m.c3 = aml.Constraint(m.z)
m.set_structure()
con_values = m.evaluate_residuals()
A = m.evaluate_jacobian()
true_con_values[m.c1] = 5.0
true_con_values[m.c2] = 60.0
true_con_values[m.c3] = 4.0
true_con_values[m.c4] = 2.1
for c in m.cons():
self.assertTrue(true_con_values[c] == con_values[c.index])
true_jac[m.c3] = OrderedDict()
true_jac[m.c3][m.x] = 0.0
true_jac[m.c3][m.y] = 0.0
true_jac[m.c3][m.z] = 1.0
true_jac[m.c3][m.v] = 0.0
for c in m.cons():
for v in m.vars():
self.assertTrue(true_jac[c][v] == A[c.index, v.index])
def test_if_then_constraints(self):
m = aml.Model()
x = -4.5
y = -3.7
m.x = aml.Var(x)
m.y = aml.Var(y)
e = aml.ConditionalExpression()
e.add_condition(
aml.inequality(body=m.x, ub=-1), -((-m.x) ** 1.852) - (-m.x) ** 2 - m.y
)
e.add_condition(aml.inequality(body=m.x, ub=1), m.x)
e.add_final_expr(m.x ** 1.852 + m.x ** 2 - m.y)
m.con1 = aml.Constraint(e)
e = aml.ConditionalExpression()
e.add_condition(
aml.inequality(body=m.y, ub=-1), -((-m.y) ** (1.852)) - (-m.y) ** (2) - m.x
)
e.add_condition(aml.inequality(body=m.y, ub=1), m.y)
e.add_final_expr(m.y ** (1.852) + m.y ** (2) - m.x)
m.con2 = aml.Constraint(e)
true_con_values = OrderedDict()
true_jac = OrderedDict()
true_con_values[m.con1] = -(abs(x) ** 1.852 + abs(x) ** 2) - y
true_con_values[m.con2] = -(abs(y) ** 1.852 + abs(y) ** 2) - x
true_jac[m.con1] = OrderedDict()
true_jac[m.con2] = OrderedDict()
true_jac[m.con1][m.x] = 1.852 * abs(x) ** 0.852 + 2 * abs(x)
true_jac[m.con1][m.y] = -1
true_jac[m.con2][m.x] = -1
true_jac[m.con2][m.y] = 1.852 * abs(y) ** 0.852 + 2 * abs(y)
compare_evaluation(self, m, true_con_values, true_jac)
x = 0.5
y = 0.3
m.x.value = x
m.y.value = y
true_con_values[m.con1] = x
true_con_values[m.con2] = y
true_jac[m.con1][m.x] = 1
true_jac[m.con1][m.y] = 0
true_jac[m.con2][m.x] = 0
true_jac[m.con2][m.y] = 1
compare_evaluation(self, m, true_con_values, true_jac)
x = 4.5
y = 3.7
m.x.value = x
m.y.value = y
true_con_values[m.con1] = x ** 1.852 + x ** 2 - y
true_con_values[m.con2] = y ** 1.852 + y ** 2 - x
true_jac[m.con1][m.x] = 1.852 * x ** 0.852 + 2 * x
true_jac[m.con1][m.y] = -1
true_jac[m.con2][m.x] = -1
true_jac[m.con2][m.y] = 1.852 * y ** 0.852 + 2 * y
compare_evaluation(self, m, true_con_values, true_jac)
del true_con_values[m.con2]
del true_jac[m.con2]
del m.con2
e = aml.ConditionalExpression()
e.add_condition(
aml.inequality(body=m.y, ub=-1), -((-m.y) ** 2.852) - (-m.y) ** 3 - m.x
)
e.add_condition(aml.inequality(body=m.y, ub=1), m.y ** 2)
e.add_final_expr(m.y ** 2.852 + m.y ** 3 - m.x)
m.con2 = aml.Constraint(e)
true_jac[m.con2] = OrderedDict()
x = -4.5
y = -3.7
m.x.value = x
m.y.value = y
true_con_values[m.con1] = -(abs(x) ** 1.852 + abs(x) ** 2) - y
true_con_values[m.con2] = -(abs(y) ** 2.852 + abs(y) ** 3) - x
true_jac[m.con1][m.x] = 1.852 * abs(x) ** 0.852 + 2 * abs(x)
true_jac[m.con1][m.y] = -1
true_jac[m.con2][m.x] = -1
true_jac[m.con2][m.y] = 2.852 * abs(y) ** 1.852 + 3 * abs(y) ** 2
compare_evaluation(self, m, true_con_values, true_jac)
x = 0.5
y = 0.3
m.x.value = x
m.y.value = y
true_con_values[m.con1] = x
true_con_values[m.con2] = y ** 2
true_jac[m.con1][m.x] = 1
true_jac[m.con1][m.y] = 0
true_jac[m.con2][m.x] = 0
true_jac[m.con2][m.y] = 2 * y
compare_evaluation(self, m, true_con_values, true_jac)
x = 4.5
y = 3.7
m.x.value = x
m.y.value = y
true_con_values[m.con1] = x ** 1.852 + x ** 2 - y
true_con_values[m.con2] = y ** 2.852 + y ** 3 - x
true_jac[m.con1][m.x] = 1.852 * x ** 0.852 + 2 * x
true_jac[m.con1][m.y] = -1
true_jac[m.con2][m.x] = -1
true_jac[m.con2][m.y] = 2.852 * y ** 1.852 + 3 * y ** 2
compare_evaluation(self, m, true_con_values, true_jac)
