def test_yz_average(self):
a = pybamm.Scalar(1)
z_average_a = pybamm.z_average(a)
yz_average_a = pybamm.yz_average(a)
self.assertEqual(z_average_a.id, a.id)
self.assertEqual(yz_average_a.id, a.id)
z_average_broad_a = pybamm.z_average(
pybamm.PrimaryBroadcast(a, ["current collector"]))
yz_average_broad_a = pybamm.yz_average(
pybamm.PrimaryBroadcast(a, ["current collector"]))
self.assertEqual(z_average_broad_a.evaluate(), np.array([1]))
self.assertEqual(yz_average_broad_a.evaluate(), np.array([1]))
a = pybamm.Variable("a", domain=["current collector"])
y = pybamm.SpatialVariable("y", ["current collector"])
z = pybamm.SpatialVariable("z", ["current collector"])
z_av_a = pybamm.z_average(a)
yz_av_a = pybamm.yz_average(a)
self.assertIsInstance(yz_av_a, pybamm.Division)
self.assertIsInstance(z_av_a, pybamm.Division)
self.assertIsInstance(z_av_a.children[0], pybamm.Integral)
self.assertIsInstance(yz_av_a.children[0], pybamm.Integral)
self.assertEqual(z_av_a.children[0].integration_variable[0].domain,
z.domain)
self.assertEqual(yz_av_a.children[0].integration_variable[0].domain,
y.domain)
self.assertEqual(yz_av_a.children[0].integration_variable[1].domain,
z.domain)
self.assertIsInstance(z_av_a.children[1], pybamm.Integral)
self.assertIsInstance(yz_av_a.children[1], pybamm.Integral)
self.assertEqual(z_av_a.children[1].integration_variable[0].domain,
a.domain)
self.assertEqual(z_av_a.children[1].children[0].id,
pybamm.ones_like(a).id)
self.assertEqual(yz_av_a.children[1].integration_variable[0].domain,
y.domain)
self.assertEqual(yz_av_a.children[1].integration_variable[0].domain,
z.domain)
self.assertEqual(yz_av_a.children[1].children[0].id,
pybamm.ones_like(a).id)
self.assertEqual(z_av_a.domain, [])
self.assertEqual(yz_av_a.domain, [])
a = pybamm.Symbol("a", domain="bad domain")
with self.assertRaises(pybamm.DomainError):
pybamm.z_average(a)
with self.assertRaises(pybamm.DomainError):
pybamm.yz_average(a)
# average of symbol that evaluates on edges raises error
symbol_on_edges = pybamm.PrimaryBroadcastToEdges(1, "domain")
with self.assertRaisesRegex(
ValueError,
"Can't take the z-average of a symbol that evaluates on edges"
):
pybamm.z_average(symbol_on_edges)
def simplified_subtraction(left, right):
"""
Note
----
We check for scalars first, then matrices. This is because
(Zero Matrix) - (Zero Scalar)
should return (Zero Matrix), not -(Zero Scalar).
"""
left, right = simplify_elementwise_binary_broadcasts(left, right)
# Check for Concatenations and Broadcasts
out = simplified_binary_broadcast_concatenation(left, right,
simplified_subtraction)
if out is not None:
return out
# anything added by a scalar zero returns the other child
if pybamm.is_scalar_zero(left):
return -right
if pybamm.is_scalar_zero(right):
return left
# Check matrices after checking scalars
if pybamm.is_matrix_zero(left):
if right.evaluates_to_number():
return -right * pybamm.ones_like(left)
# See comments in simplified_addition
elif all(left_dim_size <= right_dim_size
for left_dim_size, right_dim_size in zip(
left.shape_for_testing, right.shape_for_testing)) and all(
left.evaluates_on_edges(dim) ==
right.evaluates_on_edges(dim)
for dim in ["primary", "secondary", "tertiary"]):
return -right
if pybamm.is_matrix_zero(right):
if left.evaluates_to_number():
return left * pybamm.ones_like(right)
# See comments in simplified_addition
elif all(left_dim_size >= right_dim_size
for left_dim_size, right_dim_size in zip(
left.shape_for_testing, right.shape_for_testing)) and all(
left.evaluates_on_edges(dim) ==
right.evaluates_on_edges(dim)
for dim in ["primary", "secondary", "tertiary"]):
return left
# a symbol minus itself is 0s of the same shape
if left.id == right.id:
return pybamm.zeros_like(left)
return pybamm.simplify_if_constant(pybamm.Subtraction(left, right))
def test_x_average(self):
a = pybamm.Scalar(1)
average_a = pybamm.x_average(a)
self.assertEqual(average_a.id, a.id)
average_broad_a = pybamm.x_average(
pybamm.PrimaryBroadcast(a, ["negative electrode"]))
self.assertEqual(average_broad_a.evaluate(), np.array([1]))
conc_broad = pybamm.Concatenation(
pybamm.PrimaryBroadcast(1, ["negative electrode"]),
pybamm.PrimaryBroadcast(2, ["separator"]),
pybamm.PrimaryBroadcast(3, ["positive electrode"]),
)
average_conc_broad = pybamm.x_average(conc_broad)
self.assertIsInstance(average_conc_broad, pybamm.Division)
for domain in [
["negative electrode"],
["separator"],
["positive electrode"],
["negative electrode", "separator", "positive electrode"],
]:
a = pybamm.Symbol("a", domain=domain)
x = pybamm.SpatialVariable("x", domain)
av_a = pybamm.x_average(a)
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[0].integration_variable[0].domain,
x.domain)
self.assertEqual(av_a.domain, [])
a = pybamm.Symbol("a", domain="new domain")
av_a = pybamm.x_average(a)
self.assertEqual(av_a.domain, [])
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[0].integration_variable[0].domain,
a.domain)
self.assertIsInstance(av_a.children[1], pybamm.Integral)
self.assertEqual(av_a.children[1].integration_variable[0].domain,
a.domain)
self.assertEqual(av_a.children[1].children[0].id,
pybamm.ones_like(a).id)
# x-average of symbol that evaluates on edges raises error
symbol_on_edges = pybamm.PrimaryBroadcastToEdges(1, "domain")
with self.assertRaisesRegex(
ValueError,
"Can't take the x-average of a symbol that evaluates on edges"
):
pybamm.x_average(symbol_on_edges)
def test_ones_like(self):
a = pybamm.Variable("a")
ones_like_a = pybamm.ones_like(a)
self.assertEqual(ones_like_a.id, pybamm.Scalar(1).id)
a = pybamm.Variable(
"a",
domain="negative electrode",
auxiliary_domains={"secondary": "current collector"},
)
ones_like_a = pybamm.ones_like(a)
self.assertIsInstance(ones_like_a, pybamm.FullBroadcast)
self.assertEqual(ones_like_a.name, "broadcast")
self.assertEqual(ones_like_a.domain, a.domain)
self.assertEqual(ones_like_a.auxiliary_domains, a.auxiliary_domains)
b = pybamm.Variable("b", domain="current collector")
ones_like_ab = pybamm.ones_like(b, a)
self.assertIsInstance(ones_like_ab, pybamm.FullBroadcast)
self.assertEqual(ones_like_ab.name, "broadcast")
self.assertEqual(ones_like_ab.domain, a.domain)
self.assertEqual(ones_like_ab.auxiliary_domains, a.auxiliary_domains)
def z_average(symbol):
"""
convenience function for creating an average in the z-direction.
Parameters
----------
symbol : :class:`pybamm.Symbol`
The function to be averaged
Returns
-------
:class:`Symbol`
the new averaged symbol
"""
# Can't take average if the symbol evaluates on edges
if symbol.evaluates_on_edges("primary"):
raise ValueError("Can't take the z-average of a symbol that evaluates on edges")
# Symbol must have domain [] or ["current collector"]
if symbol.domain not in [[], ["current collector"]]:
raise pybamm.DomainError(
"""z-average only implemented in the 'current collector' domain,
but symbol has domains {}""".format(
symbol.domain
)
)
# If symbol doesn't have a domain, its average value is itself
if symbol.domain == []:
new_symbol = symbol.new_copy()
new_symbol.parent = None
return new_symbol
# If symbol is a Broadcast, its average value is its child
elif isinstance(symbol, pybamm.Broadcast):
return symbol.orphans[0]
# Otherwise, use Integral to calculate average value
else:
# We compute the length as Integral(1, z) as this will be easier to identify
# for simplifications later on and it gives the correct behaviour when using
# ZeroDimensionalSpatialMethod
z = pybamm.standard_spatial_vars.z
v = pybamm.ones_like(symbol)
l = pybamm.Integral(v, z)
return Integral(symbol, z) / l
def simplified_power(left, right):
left, right = simplify_elementwise_binary_broadcasts(left, right)
# Check for Concatenations and Broadcasts
out = simplified_binary_broadcast_concatenation(left, right,
simplified_power)
if out is not None:
return out
# anything to the power of zero is one
if pybamm.is_scalar_zero(right):
return pybamm.ones_like(left)
# zero to the power of anything is zero
if pybamm.is_scalar_zero(left):
return pybamm.Scalar(0)
# anything to the power of one is itself
if pybamm.is_scalar_one(right):
return left
if isinstance(left, Multiplication):
# Simplify (a * b) ** c to (a ** c) * (b ** c)
# if (a ** c) is constant or (b ** c) is constant
if left.left.is_constant() or left.right.is_constant():
l_left, l_right = left.orphans
new_left = l_left**right
new_right = l_right**right
if new_left.is_constant() or new_right.is_constant():
return new_left * new_right
elif isinstance(left, Division):
# Simplify (a / b) ** c to (a ** c) / (b ** c)
# if (a ** c) is constant or (b ** c) is constant
if left.left.is_constant() or left.right.is_constant():
l_left, l_right = left.orphans
new_left = l_left**right
new_right = l_right**right
if new_left.is_constant() or new_right.is_constant():
return new_left / new_right
return pybamm.simplify_if_constant(pybamm.Power(left, right))
def _process_symbol(self, symbol):
""" See :meth:`ParameterValues.process_symbol()`. """
if isinstance(symbol, pybamm.Parameter):
value = self[symbol.name]
if isinstance(value, numbers.Number):
# Scalar inherits name (for updating parameters) and domain (for
# Broadcast)
return pybamm.Scalar(value,
name=symbol.name,
domain=symbol.domain)
elif isinstance(value, pybamm.Symbol):
new_value = self.process_symbol(value)
new_value.domain = symbol.domain
return new_value
else:
raise TypeError("Cannot process parameter '{}'".format(value))
elif isinstance(symbol, pybamm.FunctionParameter):
new_children = []
for child in symbol.children:
if symbol.diff_variable is not None and any(
x.id == symbol.diff_variable.id
for x in child.pre_order()):
# Wrap with NotConstant to avoid simplification,
# which would stop symbolic diff from working properly
new_child = pybamm.NotConstant(child.new_copy())
new_children.append(self.process_symbol(new_child))
else:
new_children.append(self.process_symbol(child))
function_name = self[symbol.name]
# Create Function or Interpolant or Scalar object
if isinstance(function_name, tuple):
# If function_name is a tuple then it should be (name, data) and we need
# to create an Interpolant
name, data = function_name
function = pybamm.Interpolant(data[:, 0],
data[:, 1],
*new_children,
name=name)
# Define event to catch extrapolation. In these events the sign is
# important: it should be positive inside of the range and negative
# outside of it
self.parameter_events.append(
pybamm.Event(
"Interpolant {} lower bound".format(name),
pybamm.min(new_children[0] - min(data[:, 0])),
pybamm.EventType.INTERPOLANT_EXTRAPOLATION,
))
self.parameter_events.append(
pybamm.Event(
"Interpolant {} upper bound".format(name),
pybamm.min(max(data[:, 0]) - new_children[0]),
pybamm.EventType.INTERPOLANT_EXTRAPOLATION,
))
elif isinstance(function_name, numbers.Number):
# If the "function" is provided is actually a scalar, return a Scalar
# object instead of throwing an error.
# Also use ones_like so that we get the right shapes
function = pybamm.Scalar(
function_name,
name=symbol.name) * pybamm.ones_like(*new_children)
elif (isinstance(function_name, pybamm.Symbol)
and function_name.evaluates_to_number()):
# If the "function" provided is a pybamm scalar-like, use ones_like to
# get the right shape
# This also catches input parameters
function = function_name * pybamm.ones_like(*new_children)
elif callable(function_name):
# otherwise evaluate the function to create a new PyBaMM object
function = function_name(*new_children)
elif isinstance(function_name, pybamm.Interpolant):
function = function_name
else:
raise TypeError(
"Parameter provided for '{}' ".format(symbol.name) +
"is of the wrong type (should either be scalar-like or callable)"
)
# Differentiate if necessary
if symbol.diff_variable is None:
function_out = function
else:
# return differentiated function
new_diff_variable = self.process_symbol(symbol.diff_variable)
function_out = function.diff(new_diff_variable)
# Convert possible float output to a pybamm scalar
if isinstance(function_out, numbers.Number):
return pybamm.Scalar(function_out)
# Process again just to be sure
return self.process_symbol(function_out)
elif isinstance(symbol, pybamm.BinaryOperator):
# process children
new_left = self.process_symbol(symbol.left)
new_right = self.process_symbol(symbol.right)
# Special case for averages, which can appear as "integral of a broadcast"
# divided by "integral of a broadcast"
# this construction seems very specific but can appear often when averaging
if (isinstance(symbol, pybamm.Division)
# right is integral(Broadcast(1))
and (isinstance(new_right, pybamm.Integral)
and isinstance(new_right.child, pybamm.Broadcast)
and new_right.child.child.id == pybamm.Scalar(1).id)
# left is integral
and isinstance(new_left, pybamm.Integral)):
# left is integral(Broadcast)
if (isinstance(new_left.child, pybamm.Broadcast)
and new_left.child.child.domain == []):
integrand = new_left.child
if integrand.auxiliary_domains == {}:
return integrand.orphans[0]
else:
domain = integrand.auxiliary_domains["secondary"]
if "tertiary" not in integrand.auxiliary_domains:
return pybamm.PrimaryBroadcast(
integrand.orphans[0], domain)
else:
auxiliary_domains = {
"secondary":
integrand.auxiliary_domains["tertiary"]
}
return pybamm.FullBroadcast(
integrand.orphans[0], domain,
auxiliary_domains)
# left is "integral of concatenation of broadcasts"
elif isinstance(new_left.child, pybamm.Concatenation) and all(
isinstance(child, pybamm.Broadcast)
for child in new_left.child.children):
return self.process_symbol(pybamm.x_average(
new_left.child))
# make new symbol, ensure domain remains the same
new_symbol = symbol._binary_new_copy(new_left, new_right)
new_symbol.domain = symbol.domain
return new_symbol
# Unary operators
elif isinstance(symbol, pybamm.UnaryOperator):
new_child = self.process_symbol(symbol.child)
new_symbol = symbol._unary_new_copy(new_child)
# ensure domain remains the same
new_symbol.domain = symbol.domain
return new_symbol
# Functions
elif isinstance(symbol, pybamm.Function):
new_children = [
self.process_symbol(child) for child in symbol.children
]
return symbol._function_new_copy(new_children)
# Concatenations
elif isinstance(symbol, pybamm.Concatenation):
new_children = [
self.process_symbol(child) for child in symbol.children
]
return symbol._concatenation_new_copy(new_children)
else:
# Backup option: return new copy of the object
try:
return symbol.new_copy()
except NotImplementedError:
raise NotImplementedError(
"Cannot process parameters for symbol of type '{}'".format(
type(symbol)))
def x_average(symbol):
"""convenience function for creating an average in the x-direction
Parameters
----------
symbol : :class:`pybamm.Symbol`
The function to be averaged
Returns
-------
:class:`Symbol`
the new averaged symbol
"""
# Can't take average if the symbol evaluates on edges
if symbol.evaluates_on_edges("primary"):
raise ValueError(
"Can't take the x-average of a symbol that evaluates on edges")
# If symbol doesn't have a domain, its average value is itself
if symbol.domain in [[], ["current collector"]]:
new_symbol = symbol.new_copy()
new_symbol.parent = None
return new_symbol
# If symbol is a Broadcast, its average value is its child
elif isinstance(symbol, pybamm.Broadcast):
return symbol.orphans[0]
# If symbol is a concatenation of Broadcasts, its average value is its child
elif (isinstance(symbol, pybamm.Concatenation) and all(
isinstance(child, pybamm.Broadcast) for child in symbol.children)
and symbol.domain
== ["negative electrode", "separator", "positive electrode"]):
a, b, c = [orp.orphans[0] for orp in symbol.orphans]
if a.id == b.id == c.id:
return a
else:
geo = pybamm.geometric_parameters
l_n = geo.l_n
l_s = geo.l_s
l_p = geo.l_p
return (l_n * a + l_s * b + l_p * c) / (l_n + l_s + l_p)
# Otherwise, use Integral to calculate average value
else:
geo = pybamm.geometric_parameters
if symbol.domain == ["negative electrode"]:
x = pybamm.standard_spatial_vars.x_n
l = geo.l_n
elif symbol.domain == ["separator"]:
x = pybamm.standard_spatial_vars.x_s
l = geo.l_s
elif symbol.domain == ["positive electrode"]:
x = pybamm.standard_spatial_vars.x_p
l = geo.l_p
elif symbol.domain == [
"negative electrode", "separator", "positive electrode"
]:
x = pybamm.standard_spatial_vars.x
l = pybamm.Scalar(1)
elif symbol.domain == ["negative particle"]:
x = pybamm.standard_spatial_vars.x_n
l = geo.l_n
elif symbol.domain == ["positive particle"]:
x = pybamm.standard_spatial_vars.x_p
l = geo.l_p
else:
x = pybamm.SpatialVariable("x", domain=symbol.domain)
v = pybamm.ones_like(symbol)
l = pybamm.Integral(v, x)
return Integral(symbol, x) / l
def _process_symbol(self, symbol):
""" See :meth:`ParameterValues.process_symbol()`. """
if isinstance(symbol, pybamm.Parameter):
value = self[symbol.name]
if isinstance(value, numbers.Number):
# Scalar inherits name (for updating parameters) and domain (for
# Broadcast)
return pybamm.Scalar(value,
name=symbol.name,
domain=symbol.domain)
elif isinstance(value, pybamm.InputParameter):
value.domain = symbol.domain
return value
elif isinstance(symbol, pybamm.FunctionParameter):
new_children = [
self.process_symbol(child) for child in symbol.children
]
function_name = self[symbol.name]
# Create Function or Interpolant or Scalar object
if isinstance(function_name, tuple):
# If function_name is a tuple then it should be (name, data) and we need
# to create an Interpolant
name, data = function_name
function = pybamm.Interpolant(data, *new_children, name=name)
elif isinstance(function_name, numbers.Number):
# If the "function" is provided is actually a scalar, return a Scalar
# object instead of throwing an error.
# Also use ones_like so that we get the right shapes
function = pybamm.Scalar(
function_name,
name=symbol.name) * pybamm.ones_like(*new_children)
elif isinstance(function_name, pybamm.InputParameter):
# Replace the function with an input parameter
function = function_name
elif (isinstance(function_name, pybamm.Symbol)
and function_name.evaluates_to_number()):
# If the "function" provided is a pybamm scalar-like, use ones_like to
# get the right shape
function = function_name * pybamm.ones_like(*new_children)
elif callable(function_name):
# otherwise evaluate the function to create a new PyBaMM object
function = function_name(*new_children)
else:
raise TypeError(
"Parameter provided for '{}' ".format(symbol.name) +
"is of the wrong type (should either be scalar-like or callable)"
)
# Differentiate if necessary
if symbol.diff_variable is None:
function_out = function
else:
# return differentiated function
new_diff_variable = self.process_symbol(symbol.diff_variable)
function_out = function.diff(new_diff_variable)
# Convert possible float output to a pybamm scalar
if isinstance(function_out, numbers.Number):
return pybamm.Scalar(function_out)
# Process again just to be sure
return self.process_symbol(function_out)
elif isinstance(symbol, pybamm.BinaryOperator):
# process children
new_left = self.process_symbol(symbol.left)
new_right = self.process_symbol(symbol.right)
# make new symbol, ensure domain remains the same
new_symbol = symbol._binary_new_copy(new_left, new_right)
new_symbol.domain = symbol.domain
return new_symbol
# Unary operators
elif isinstance(symbol, pybamm.UnaryOperator):
new_child = self.process_symbol(symbol.child)
new_symbol = symbol._unary_new_copy(new_child)
# ensure domain remains the same
new_symbol.domain = symbol.domain
return new_symbol
# Functions
elif isinstance(symbol, pybamm.Function):
new_children = [
self.process_symbol(child) for child in symbol.children
]
return symbol._function_new_copy(new_children)
# Concatenations
elif isinstance(symbol, pybamm.Concatenation):
new_children = [
self.process_symbol(child) for child in symbol.children
]
return symbol._concatenation_new_copy(new_children)
else:
# Backup option: return new copy of the object
try:
return symbol.new_copy()
except NotImplementedError:
raise NotImplementedError(
"Cannot process parameters for symbol of type '{}'".format(
type(symbol)))
def x_average(symbol):
"""
convenience function for creating an average in the x-direction
Parameters
----------
symbol : :class:`pybamm.Symbol`
The function to be averaged
Returns
-------
:class:`Symbol`
the new averaged symbol
"""
# Can't take average if the symbol evaluates on edges
if symbol.evaluates_on_edges("primary"):
raise ValueError(
"Can't take the x-average of a symbol that evaluates on edges")
# If symbol doesn't have a domain, its average value is itself
if symbol.domain in [[], ["current collector"]]:
new_symbol = symbol.new_copy()
new_symbol.parent = None
return new_symbol
# If symbol is a primary or full broadcast, reduce by one dimension
if isinstance(symbol, (pybamm.PrimaryBroadcast, pybamm.FullBroadcast)):
return symbol.reduce_one_dimension()
# If symbol is a concatenation of Broadcasts, its average value is its child
elif (isinstance(symbol, pybamm.Concatenation) and all(
isinstance(child, pybamm.Broadcast) for child in symbol.children)
and symbol.domain
== ["negative electrode", "separator", "positive electrode"]):
a, b, c = [orp.orphans[0] for orp in symbol.orphans]
geo = pybamm.geometric_parameters
l_n = geo.l_n
l_s = geo.l_s
l_p = geo.l_p
out = (l_n * a + l_s * b + l_p * c) / (l_n + l_s + l_p)
# To respect domains we may need to broadcast the child back out
child = symbol.children[0]
# If symbol being returned doesn't have empty domain, return it
if out.domain != []:
return out
# Otherwise we may need to broadcast it
elif child.auxiliary_domains == {}:
return out
else:
domain = child.auxiliary_domains["secondary"]
if "tertiary" not in child.auxiliary_domains:
return pybamm.PrimaryBroadcast(out, domain)
else:
auxiliary_domains = {
"secondary": child.auxiliary_domains["tertiary"]
}
return pybamm.FullBroadcast(out, domain, auxiliary_domains)
# Otherwise, use Integral to calculate average value
else:
geo = pybamm.geometric_parameters
# Even if domain is "negative electrode", "separator", or
# "positive electrode", and we know l, we still compute it as Integral(1, x)
# as this will be easier to identify for simplifications later on
if symbol.domain == ["negative particle"]:
x = pybamm.standard_spatial_vars.x_n
l = geo.l_n
elif symbol.domain == ["positive particle"]:
x = pybamm.standard_spatial_vars.x_p
l = geo.l_p
else:
x = pybamm.SpatialVariable("x", domain=symbol.domain)
v = pybamm.ones_like(symbol)
l = pybamm.Integral(v, x)
return Integral(symbol, x) / l
def simplified_addition(left, right):
"""
Note
----
We check for scalars first, then matrices. This is because
(Zero Matrix) + (Zero Scalar)
should return (Zero Matrix), not (Zero Scalar).
"""
left, right = simplify_elementwise_binary_broadcasts(left, right)
# Check for Concatenations and Broadcasts
out = simplified_binary_broadcast_concatenation(left, right,
simplified_addition)
if out is not None:
return out
# anything added by a scalar zero returns the other child
elif pybamm.is_scalar_zero(left):
return right
elif pybamm.is_scalar_zero(right):
return left
# Check matrices after checking scalars
elif pybamm.is_matrix_zero(left):
if right.evaluates_to_number():
return right * pybamm.ones_like(left)
# If left object is zero and has size smaller than or equal to right object in
# all dimensions, we can safely return the right object. For example, adding a
# zero vector a matrix, we can just return the matrix
elif all(left_dim_size <= right_dim_size
for left_dim_size, right_dim_size in zip(
left.shape_for_testing, right.shape_for_testing)) and all(
left.evaluates_on_edges(dim) ==
right.evaluates_on_edges(dim)
for dim in ["primary", "secondary", "tertiary"]):
return right
elif pybamm.is_matrix_zero(right):
if left.evaluates_to_number():
return left * pybamm.ones_like(right)
# See comment above
elif all(left_dim_size >= right_dim_size
for left_dim_size, right_dim_size in zip(
left.shape_for_testing, right.shape_for_testing)) and all(
left.evaluates_on_edges(dim) ==
right.evaluates_on_edges(dim)
for dim in ["primary", "secondary", "tertiary"]):
return left
# Return constant if both sides are constant
if left.is_constant() and right.is_constant():
return pybamm.simplify_if_constant(pybamm.Addition(left, right))
# Simplify A @ c + B @ c to (A + B) @ c if (A + B) is constant
# This is a common construction that appears from discretisation of spatial
# operators
elif (isinstance(left, MatrixMultiplication)
and isinstance(right, MatrixMultiplication)
and left.right.id == right.right.id):
l_left, l_right = left.orphans
r_left = right.orphans[0]
new_left = l_left + r_left
if new_left.is_constant():
new_sum = new_left @ l_right
new_sum.copy_domains(pybamm.Addition(left, right))
return new_sum
if isinstance(right, pybamm.Addition) and left.is_constant():
# Simplify a + (b + c) to (a + b) + c if (a + b) is constant
if right.left.is_constant():
r_left, r_right = right.orphans
return (left + r_left) + r_right
# Simplify a + (b + c) to (a + c) + b if (a + c) is constant
elif right.right.is_constant():
r_left, r_right = right.orphans
return (left + r_right) + r_left
if isinstance(left, pybamm.Addition) and right.is_constant():
# Simplify (a + b) + c to a + (b + c) if (b + c) is constant
if left.right.is_constant():
l_left, l_right = left.orphans
return l_left + (l_right + right)
# Simplify (a + b) + c to (a + c) + b if (a + c) is constant
elif left.left.is_constant():
l_left, l_right = left.orphans
return (l_left + right) + l_right
return pybamm.simplify_if_constant(pybamm.Addition(left, right))
def simplified_division(left, right):
left, right = simplify_elementwise_binary_broadcasts(left, right)
# Check for Concatenations and Broadcasts
out = simplified_binary_broadcast_concatenation(left, right,
simplified_division)
if out is not None:
return out
# zero divided by anything returns zero (being careful about shape)
if pybamm.is_scalar_zero(left):
return pybamm.zeros_like(right)
# matrix zero divided by anything returns matrix zero (i.e. itself)
if pybamm.is_matrix_zero(left):
return pybamm.zeros_like(pybamm.Division(left, right))
# anything divided by zero raises error
if pybamm.is_scalar_zero(right):
raise ZeroDivisionError
# anything divided by one is itself
if pybamm.is_scalar_one(right):
return left
# a symbol divided by itself is 1s of the same shape
if left.id == right.id:
return pybamm.ones_like(left)
# anything multiplied by a matrix one returns itself if
# - the shapes are the same
# - both left and right evaluate on edges, or both evaluate on nodes, in all
# dimensions
# (and possibly more generally, but not implemented here)
try:
if left.shape_for_testing == right.shape_for_testing and all(
left.evaluates_on_edges(dim) == right.evaluates_on_edges(dim)
for dim in ["primary", "secondary", "tertiary"]):
if pybamm.is_matrix_one(right):
return left
# also check for negative one
if pybamm.is_matrix_minus_one(right):
return -left
except NotImplementedError:
pass
# Return constant if both sides are constant
if left.is_constant() and right.is_constant():
return pybamm.simplify_if_constant(pybamm.Division(left, right))
# Simplify (B @ c) / a to (B / a) @ c if (B / a) is constant
# This is a common construction that appears from discretisation of averages
elif isinstance(left, MatrixMultiplication) and right.is_constant():
l_left, l_right = left.orphans
new_left = l_left / right
if new_left.is_constant():
# be careful about domains to avoid weird errors
new_left.clear_domains()
new_division = new_left @ l_right
# Keep the domain of the old left
new_division.copy_domains(left)
return new_division
if isinstance(left, Multiplication):
# Simplify (a * b) / c to (a / c) * b if (a / c) is constant
if left.left.is_constant():
l_left, l_right = left.orphans
new_left = l_left / right
if new_left.is_constant():
return new_left * l_right
# Simplify (a * b) / c to a * (b / c) if (b / c) is constant
elif left.right.is_constant():
l_left, l_right = left.orphans
new_right = l_right / right
if new_right.is_constant():
return l_left * new_right
# Negation simplifications
elif isinstance(left, pybamm.Negate) and right.is_constant():
# Simplify (-a) / b to a / (-b) if (-b) is constant
return left.orphans[0] / (-right)
elif isinstance(right, pybamm.Negate) and left.is_constant():
# Simplify a / (-b) to (-a) / b if (-a) is constant
return (-left) / right.orphans[0]
return pybamm.simplify_if_constant(pybamm.Division(left, right))
def test_x_average(self):
a = pybamm.Scalar(4)
average_a = pybamm.x_average(a)
self.assertEqual(average_a.id, a.id)
# average of a broadcast is the child
average_broad_a = pybamm.x_average(
pybamm.PrimaryBroadcast(a, ["negative electrode"]))
self.assertEqual(average_broad_a.id, pybamm.Scalar(4).id)
# average of a number times a broadcast is the number times the child
average_two_broad_a = pybamm.x_average(
2 * pybamm.PrimaryBroadcast(a, ["negative electrode"]))
self.assertEqual(average_two_broad_a.id, pybamm.Scalar(8).id)
average_t_broad_a = pybamm.x_average(
pybamm.t * pybamm.PrimaryBroadcast(a, ["negative electrode"]))
self.assertEqual(average_t_broad_a.id,
(pybamm.t * pybamm.Scalar(4)).id)
# x-average of concatenation of broadcasts
conc_broad = pybamm.concatenation(
pybamm.PrimaryBroadcast(1, ["negative electrode"]),
pybamm.PrimaryBroadcast(2, ["separator"]),
pybamm.PrimaryBroadcast(3, ["positive electrode"]),
)
average_conc_broad = pybamm.x_average(conc_broad)
self.assertIsInstance(average_conc_broad, pybamm.Division)
self.assertEqual(average_conc_broad.domain, [])
# with auxiliary domains
conc_broad = pybamm.concatenation(
pybamm.FullBroadcast(
1,
["negative electrode"],
auxiliary_domains={"secondary": "current collector"},
),
pybamm.FullBroadcast(
2, ["separator"],
auxiliary_domains={"secondary": "current collector"}),
pybamm.FullBroadcast(
3,
["positive electrode"],
auxiliary_domains={"secondary": "current collector"},
),
)
average_conc_broad = pybamm.x_average(conc_broad)
self.assertIsInstance(average_conc_broad, pybamm.PrimaryBroadcast)
self.assertEqual(average_conc_broad.domain, ["current collector"])
conc_broad = pybamm.concatenation(
pybamm.FullBroadcast(
1,
["negative electrode"],
auxiliary_domains={
"secondary": "current collector",
"tertiary": "test",
},
),
pybamm.FullBroadcast(
2,
["separator"],
auxiliary_domains={
"secondary": "current collector",
"tertiary": "test",
},
),
pybamm.FullBroadcast(
3,
["positive electrode"],
auxiliary_domains={
"secondary": "current collector",
"tertiary": "test",
},
),
)
average_conc_broad = pybamm.x_average(conc_broad)
self.assertIsInstance(average_conc_broad, pybamm.FullBroadcast)
self.assertEqual(average_conc_broad.domain, ["current collector"])
self.assertEqual(average_conc_broad.auxiliary_domains,
{"secondary": ["test"]})
# x-average of broadcast
for domain in [
["negative electrode"],
["separator"],
["positive electrode"],
]:
a = pybamm.Variable("a", domain=domain)
x = pybamm.SpatialVariable("x", domain)
av_a = pybamm.x_average(a)
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[0].integration_variable[0].domain,
x.domain)
self.assertEqual(av_a.domain, [])
# whole electrode domain is different as the division by 1 gets simplified out
domain = ["negative electrode", "separator", "positive electrode"]
a = pybamm.Variable("a", domain=domain)
x = pybamm.SpatialVariable("x", domain)
av_a = pybamm.x_average(a)
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[0].integration_variable[0].domain,
x.domain)
self.assertEqual(av_a.domain, [])
a = pybamm.Variable("a", domain="new domain")
av_a = pybamm.x_average(a)
self.assertEqual(av_a.domain, [])
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[0].integration_variable[0].domain,
a.domain)
self.assertIsInstance(av_a.children[1], pybamm.Integral)
self.assertEqual(av_a.children[1].integration_variable[0].domain,
a.domain)
self.assertEqual(av_a.children[1].children[0].id,
pybamm.ones_like(a).id)
# x-average of symbol that evaluates on edges raises error
symbol_on_edges = pybamm.PrimaryBroadcastToEdges(1, "domain")
with self.assertRaisesRegex(
ValueError,
"Can't take the x-average of a symbol that evaluates on edges"
):
pybamm.x_average(symbol_on_edges)
# Particle domains
geo = pybamm.geometric_parameters
l_n = geo.l_n
l_p = geo.l_p
a = pybamm.Symbol(
"a",
domain="negative particle",
auxiliary_domains={"secondary": "negative electrode"},
)
av_a = pybamm.x_average(a)
self.assertEqual(a.domain, ["negative particle"])
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[1].id, l_n.id)
a = pybamm.Symbol(
"a",
domain="positive particle",
auxiliary_domains={"secondary": "positive electrode"},
)
av_a = pybamm.x_average(a)
self.assertEqual(a.domain, ["positive particle"])
self.assertIsInstance(av_a, pybamm.Division)
self.assertIsInstance(av_a.children[0], pybamm.Integral)
self.assertEqual(av_a.children[1].id, l_p.id)
