def test_external_variable_diff(self):
a = pybamm.ExternalVariable("a", 10)
b = pybamm.Variable("b")
self.assertIsInstance(a.diff(a), pybamm.Scalar)
self.assertEqual(a.diff(a).evaluate(), 1)
self.assertIsInstance(a.diff(b), pybamm.Scalar)
self.assertEqual(a.diff(b).evaluate(), 0)
def test_external_variable_scalar(self):
a = pybamm.ExternalVariable("a", 1)
self.assertEqual(a.size, 1)
self.assertEqual(a.evaluate(u={"a": 3}), 3)
with self.assertRaisesRegex(KeyError, "External variable"):
a.evaluate()
with self.assertRaisesRegex(TypeError, "inputs u"):
a.evaluate(u="not a dictionary")
def test_external_variable_vector(self):
a = pybamm.ExternalVariable("a", 10)
self.assertEqual(a.size, 10)
a_test = 2 * np.ones((10, 1))
np.testing.assert_array_equal(a.evaluate(inputs={"a": a_test}), a_test)
np.testing.assert_array_equal(a.evaluate(inputs={"a": 2}), a_test)
with self.assertRaisesRegex(ValueError, "External variable"):
a.evaluate(inputs={"a": np.ones((5, 1))})
def test_symbol_new_copy(self):
a = pybamm.Parameter("a")
b = pybamm.Parameter("b")
v_n = pybamm.Variable("v", "negative electrode")
x_n = pybamm.standard_spatial_vars.x_n
v_s = pybamm.Variable("v", "separator")
vec = pybamm.Vector([1, 2, 3, 4, 5])
mat = pybamm.Matrix([[1, 2], [3, 4]])
mesh = get_mesh_for_testing()
for symbol in [
a + b,
a - b,
a * b,
a / b,
a**b,
-a,
abs(a),
pybamm.Function(np.sin, a),
pybamm.FunctionParameter("function", {"a": a}),
pybamm.grad(v_n),
pybamm.div(pybamm.grad(v_n)),
pybamm.upwind(v_n),
pybamm.IndefiniteIntegral(v_n, x_n),
pybamm.BackwardIndefiniteIntegral(v_n, x_n),
pybamm.BoundaryValue(v_n, "right"),
pybamm.BoundaryGradient(v_n, "right"),
pybamm.PrimaryBroadcast(a, "domain"),
pybamm.SecondaryBroadcast(v_n, "current collector"),
pybamm.FullBroadcast(a, "domain",
{"secondary": "other domain"}),
pybamm.concatenation(v_n, v_s),
pybamm.NumpyConcatenation(a, b, v_s),
pybamm.DomainConcatenation([v_n, v_s], mesh),
pybamm.Parameter("param"),
pybamm.InputParameter("param"),
pybamm.StateVector(slice(0, 56)),
pybamm.Matrix(np.ones((50, 40))),
pybamm.SpatialVariable("x", ["negative electrode"]),
pybamm.t,
pybamm.Index(vec, 1),
pybamm.NotConstant(a),
pybamm.ExternalVariable(
"external variable",
20,
domain="test",
auxiliary_domains={"secondary": "test2"},
),
pybamm.minimum(a, b),
pybamm.maximum(a, b),
pybamm.SparseStack(mat, mat),
]:
self.assertEqual(symbol.id, symbol.new_copy().id)
def test_convert_external_variable(self):
casadi_t = casadi.MX.sym("t")
casadi_y = casadi.MX.sym("y", 10)
casadi_us = {
"External 1": casadi.MX.sym("External 1", 3),
"External 2": casadi.MX.sym("External 2", 10),
}
pybamm_y = pybamm.StateVector(slice(0, 10))
pybamm_u1 = pybamm.ExternalVariable("External 1", 3)
pybamm_u2 = pybamm.ExternalVariable("External 2", 10)
# External only
self.assert_casadi_equal(
pybamm_u1.to_casadi(casadi_t, casadi_y, casadi_us),
casadi_us["External 1"])
# More complex
expr = pybamm_u2 + pybamm_y
self.assert_casadi_equal(
expr.to_casadi(casadi_t, casadi_y, casadi_us),
casadi_us["External 2"] + casadi_y,
)
def test_time_derivative_of_variable(self):
a = (pybamm.Variable("a")).diff(pybamm.t)
self.assertIsInstance(a, pybamm.VariableDot)
self.assertEqual(a.name, "a'")
p = pybamm.Parameter("p")
a = (1 + p * pybamm.Variable("a")).diff(pybamm.t).simplify()
self.assertIsInstance(a, pybamm.Multiplication)
self.assertEqual(a.children[0].name, "p")
self.assertEqual(a.children[1].name, "a'")
with self.assertRaises(pybamm.ModelError):
a = (pybamm.Variable("a")).diff(pybamm.t).diff(pybamm.t)
with self.assertRaises(pybamm.ModelError):
a = pybamm.ExternalVariable("a", 1).diff(pybamm.t)
def _process_symbol(self, symbol):
""" See :meth:`Discretisation.process_symbol()`. """
if symbol.domain != []:
spatial_method = self.spatial_methods[symbol.domain[0]]
# If boundary conditions are provided, need to check for BCs on tabs
if self.bcs:
key_id = list(self.bcs.keys())[0]
if any("tab" in side
for side in list(self.bcs[key_id].keys())):
self.bcs[key_id] = self.check_tab_conditions(
symbol, self.bcs[key_id])
if isinstance(symbol, pybamm.BinaryOperator):
# Pre-process children
left, right = symbol.children
disc_left = self.process_symbol(left)
disc_right = self.process_symbol(right)
if symbol.domain == []:
return symbol._binary_new_copy(disc_left, disc_right)
else:
return spatial_method.process_binary_operators(
symbol, left, right, disc_left, disc_right)
elif isinstance(symbol, pybamm.UnaryOperator):
child = symbol.child
disc_child = self.process_symbol(child)
if child.domain != []:
child_spatial_method = self.spatial_methods[child.domain[0]]
if isinstance(symbol, pybamm.Gradient):
return child_spatial_method.gradient(child, disc_child,
self.bcs)
elif isinstance(symbol, pybamm.Divergence):
return child_spatial_method.divergence(child, disc_child,
self.bcs)
elif isinstance(symbol, pybamm.Laplacian):
return child_spatial_method.laplacian(child, disc_child,
self.bcs)
elif isinstance(symbol, pybamm.Gradient_Squared):
return child_spatial_method.gradient_squared(
child, disc_child, self.bcs)
elif isinstance(symbol, pybamm.Mass):
return child_spatial_method.mass_matrix(child, self.bcs)
elif isinstance(symbol, pybamm.BoundaryMass):
return child_spatial_method.boundary_mass_matrix(
child, self.bcs)
elif isinstance(symbol, pybamm.IndefiniteIntegral):
return child_spatial_method.indefinite_integral(
child, disc_child)
elif isinstance(symbol, pybamm.Integral):
out = child_spatial_method.integral(child, disc_child)
out.copy_domains(symbol)
return out
elif isinstance(symbol, pybamm.DefiniteIntegralVector):
return child_spatial_method.definite_integral_matrix(
child.domain, vector_type=symbol.vector_type)
elif isinstance(symbol, pybamm.BoundaryIntegral):
return child_spatial_method.boundary_integral(
child, disc_child, symbol.region)
elif isinstance(symbol, pybamm.Broadcast):
# Broadcast new_child to the domain specified by symbol.domain
# Different discretisations may broadcast differently
if symbol.domain == []:
symbol = disc_child * pybamm.Vector(np.array([1]))
else:
symbol = spatial_method.broadcast(
disc_child,
symbol.domain,
symbol.auxiliary_domains,
symbol.broadcast_type,
)
return symbol
elif isinstance(symbol, pybamm.DeltaFunction):
return spatial_method.delta_function(symbol, disc_child)
elif isinstance(symbol, pybamm.BoundaryOperator):
# if boundary operator applied on "negative tab" or
# "positive tab" *and* the mesh is 1D then change side to
# "left" or "right" as appropriate
if symbol.side in ["negative tab", "positive tab"]:
mesh = self.mesh[symbol.children[0].domain[0]][0]
if isinstance(mesh, pybamm.SubMesh1D):
symbol.side = mesh.tabs[symbol.side]
return child_spatial_method.boundary_value_or_flux(
symbol, disc_child, self.bcs)
else:
return symbol._unary_new_copy(disc_child)
elif isinstance(symbol, pybamm.Function):
disc_children = [
self.process_symbol(child) for child in symbol.children
]
return symbol._function_new_copy(disc_children)
elif isinstance(symbol, pybamm.Variable):
# Check if variable is a standard variable or an external variable
if any(symbol.id == var.id
for var in self.external_variables.values()):
# Look up dictionary key based on value
idx = [x.id for x in self.external_variables.values()
].index(symbol.id)
name, parent_and_slice = list(
self.external_variables.keys())[idx]
if parent_and_slice is None:
# Variable didn't come from a concatenation so we can just create a
# normal external variable using the symbol's name
return pybamm.ExternalVariable(
symbol.name,
size=self._get_variable_size(symbol),
domain=symbol.domain,
auxiliary_domains=symbol.auxiliary_domains,
)
else:
# We have to use a special name since the concatenation doesn't have
# a very informative name. Needs improving
parent, start, end = parent_and_slice
ext = pybamm.ExternalVariable(
name,
size=self._get_variable_size(parent),
domain=parent.domain,
auxiliary_domains=parent.auxiliary_domains,
)
out = ext[slice(start, end)]
out.domain = symbol.domain
return out
else:
return pybamm.StateVector(
*self.y_slices[symbol.id],
domain=symbol.domain,
auxiliary_domains=symbol.auxiliary_domains)
elif isinstance(symbol, pybamm.SpatialVariable):
return spatial_method.spatial_variable(symbol)
elif isinstance(symbol, pybamm.Concatenation):
new_children = [
self.process_symbol(child) for child in symbol.children
]
new_symbol = spatial_method.concatenation(new_children)
return new_symbol
else:
# Backup option: return new copy of the object
try:
return symbol.new_copy()
except NotImplementedError:
raise NotImplementedError(
"Cannot discretise symbol of type '{}'".format(
type(symbol)))
def _process_symbol(self, symbol):
""" See :meth:`Discretisation.process_symbol()`. """
if symbol.domain != []:
spatial_method = self.spatial_methods[symbol.domain[0]]
# If boundary conditions are provided, need to check for BCs on tabs
if self.bcs:
key_id = list(self.bcs.keys())[0]
if any("tab" in side
for side in list(self.bcs[key_id].keys())):
self.bcs[key_id] = self.check_tab_conditions(
symbol, self.bcs[key_id])
if isinstance(symbol, pybamm.BinaryOperator):
# Pre-process children
left, right = symbol.children
disc_left = self.process_symbol(left)
disc_right = self.process_symbol(right)
if symbol.domain == []:
return symbol._binary_new_copy(disc_left, disc_right)
else:
return spatial_method.process_binary_operators(
symbol, left, right, disc_left, disc_right)
elif isinstance(symbol, pybamm.UnaryOperator):
child = symbol.child
disc_child = self.process_symbol(child)
if child.domain != []:
child_spatial_method = self.spatial_methods[child.domain[0]]
if isinstance(symbol, pybamm.Gradient):
return child_spatial_method.gradient(child, disc_child,
self.bcs)
elif isinstance(symbol, pybamm.Divergence):
return child_spatial_method.divergence(child, disc_child,
self.bcs)
elif isinstance(symbol, pybamm.Laplacian):
return child_spatial_method.laplacian(child, disc_child,
self.bcs)
elif isinstance(symbol, pybamm.Gradient_Squared):
return child_spatial_method.gradient_squared(
child, disc_child, self.bcs)
elif isinstance(symbol, pybamm.Mass):
return child_spatial_method.mass_matrix(child, self.bcs)
elif isinstance(symbol, pybamm.BoundaryMass):
return child_spatial_method.boundary_mass_matrix(
child, self.bcs)
elif isinstance(symbol, pybamm.IndefiniteIntegral):
return child_spatial_method.indefinite_integral(
child, disc_child, "forward")
elif isinstance(symbol, pybamm.BackwardIndefiniteIntegral):
return child_spatial_method.indefinite_integral(
child, disc_child, "backward")
elif isinstance(symbol, pybamm.Integral):
integral_spatial_method = self.spatial_methods[
symbol.integration_variable[0].domain[0]]
out = integral_spatial_method.integral(
child, disc_child, symbol._integration_dimension)
out.copy_domains(symbol)
return out
elif isinstance(symbol, pybamm.DefiniteIntegralVector):
return child_spatial_method.definite_integral_matrix(
child, vector_type=symbol.vector_type)
elif isinstance(symbol, pybamm.BoundaryIntegral):
return child_spatial_method.boundary_integral(
child, disc_child, symbol.region)
elif isinstance(symbol, pybamm.Broadcast):
# Broadcast new_child to the domain specified by symbol.domain
# Different discretisations may broadcast differently
if symbol.domain == []:
symbol = disc_child * pybamm.Vector([1])
else:
symbol = spatial_method.broadcast(
disc_child,
symbol.domain,
symbol.auxiliary_domains,
symbol.broadcast_type,
)
return symbol
elif isinstance(symbol, pybamm.DeltaFunction):
return spatial_method.delta_function(symbol, disc_child)
elif isinstance(symbol, pybamm.BoundaryOperator):
# if boundary operator applied on "negative tab" or
# "positive tab" *and* the mesh is 1D then change side to
# "left" or "right" as appropriate
if symbol.side in ["negative tab", "positive tab"]:
mesh = self.mesh[symbol.children[0].domain[0]]
if isinstance(mesh, pybamm.SubMesh1D):
symbol.side = mesh.tabs[symbol.side]
return child_spatial_method.boundary_value_or_flux(
symbol, disc_child, self.bcs)
elif isinstance(symbol, pybamm.UpwindDownwind):
direction = symbol.name # upwind or downwind
return spatial_method.upwind_or_downwind(
child, disc_child, self.bcs, direction)
else:
return symbol._unary_new_copy(disc_child)
elif isinstance(symbol, pybamm.Function):
disc_children = [
self.process_symbol(child) for child in symbol.children
]
return symbol._function_new_copy(disc_children)
elif isinstance(symbol, pybamm.VariableDot):
return pybamm.StateVectorDot(
*self.y_slices[symbol.get_variable().id],
domain=symbol.domain,
auxiliary_domains=symbol.auxiliary_domains,
)
elif isinstance(symbol, pybamm.Variable):
# Check if variable is a standard variable or an external variable
if any(symbol.id == var.id
for var in self.external_variables.values()):
# Look up dictionary key based on value
idx = [x.id for x in self.external_variables.values()
].index(symbol.id)
name, parent_and_slice = list(
self.external_variables.keys())[idx]
if parent_and_slice is None:
# Variable didn't come from a concatenation so we can just create a
# normal external variable using the symbol's name
return pybamm.ExternalVariable(
symbol.name,
size=self._get_variable_size(symbol),
domain=symbol.domain,
auxiliary_domains=symbol.auxiliary_domains,
)
else:
# We have to use a special name since the concatenation doesn't have
# a very informative name. Needs improving
parent, start, end = parent_and_slice
ext = pybamm.ExternalVariable(
name,
size=self._get_variable_size(parent),
domain=parent.domain,
auxiliary_domains=parent.auxiliary_domains,
)
out = pybamm.Index(ext, slice(start, end))
out.domain = symbol.domain
return out
else:
# add a try except block for a more informative error if a variable
# can't be found. This should usually be caught earlier by
# model.check_well_posedness, but won't be if debug_mode is False
try:
y_slices = self.y_slices[symbol.id]
except KeyError:
raise pybamm.ModelError("""
No key set for variable '{}'. Make sure it is included in either
model.rhs, model.algebraic, or model.external_variables in an
unmodified form (e.g. not Broadcasted)
""".format(symbol.name))
return pybamm.StateVector(
*y_slices,
domain=symbol.domain,
auxiliary_domains=symbol.auxiliary_domains,
)
elif isinstance(symbol, pybamm.SpatialVariable):
return spatial_method.spatial_variable(symbol)
elif isinstance(symbol, pybamm.Concatenation):
new_children = [
self.process_symbol(child) for child in symbol.children
]
new_symbol = spatial_method.concatenation(new_children)
return new_symbol
elif isinstance(symbol, pybamm.InputParameter):
# Return a new copy of the input parameter, but set the expected size
# according to the domain of the input parameter
expected_size = self._get_variable_size(symbol)
new_input_parameter = symbol.new_copy()
new_input_parameter.set_expected_size(expected_size)
return new_input_parameter
else:
# Backup option: return new copy of the object
try:
return symbol.new_copy()
except NotImplementedError:
raise NotImplementedError(
"Cannot discretise symbol of type '{}'".format(
type(symbol)))
