def inner(left, right):
"""Return inner product of two symbols."""
left, right = preprocess_binary(left, right)
# simplify multiply by scalar zero, being careful about shape
if pybamm.is_scalar_zero(left):
return pybamm.zeros_like(right)
if pybamm.is_scalar_zero(right):
return pybamm.zeros_like(left)
# if one of the children is a zero matrix, we have to be careful about shapes
if pybamm.is_matrix_zero(left) or pybamm.is_matrix_zero(right):
return pybamm.zeros_like(pybamm.Inner(left, right))
# anything multiplied by a scalar one returns itself
if pybamm.is_scalar_one(left):
return right
if pybamm.is_scalar_one(right):
return left
return pybamm.simplify_if_constant(pybamm.Inner(left, right))
def simplified_matrix_multiplication(left, right):
left, right = preprocess_binary(left, right)
if pybamm.is_matrix_zero(left) or pybamm.is_matrix_zero(right):
return pybamm.zeros_like(pybamm.MatrixMultiplication(left, right))
if isinstance(right, Multiplication) and left.is_constant():
# Simplify A @ (b * c) to (A * b) @ c if (A * b) is constant
if right.left.evaluates_to_constant_number():
r_left, r_right = right.orphans
new_left = left * r_left
return new_left @ r_right
# Simplify A @ (b * c) to (A * c) @ b if (A * c) is constant
elif right.right.evaluates_to_constant_number():
r_left, r_right = right.orphans
new_left = left * r_right
return new_left @ r_left
elif isinstance(right, Division) and left.is_constant():
# Simplify A @ (b / c) to (A / c) @ b if (A / c) is constant
if right.right.evaluates_to_constant_number():
r_left, r_right = right.orphans
new_left = left / r_right
new_mul = new_left @ r_left
# Keep the domain of the old left
new_mul.copy_domains(left)
return new_mul
# Simplify A @ (B @ c) to (A @ B) @ c if (A @ B) is constant
# This is a common construction that appears from discretisation of spatial
# operators
if (isinstance(right, MatrixMultiplication) and right.left.is_constant()
and left.is_constant()):
r_left, r_right = right.orphans
new_left = left @ r_left
# be careful about domains to avoid weird errors
new_left.clear_domains()
new_mul = new_left @ r_right
# Keep the domain of the old right
new_mul.copy_domains(right)
return new_mul
# Simplify A @ (b + c) to (A @ b) + (A @ c) if (A @ b) or (A @ c) is constant
# This is a common construction that appears from discretisation of spatial
# operators
# Don't do this if either b or c is a number as this will lead to matmul errors
elif isinstance(right, Addition):
if (right.left.is_constant() or right.right.is_constant()
) and not (right.left.size_for_testing == 1
or right.right.size_for_testing == 1):
r_left, r_right = right.orphans
return (left @ r_left) + (left @ r_right)
return pybamm.simplify_if_constant(pybamm.MatrixMultiplication(
left, right))
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 simplified_multiplication(left, right):
left, right = simplify_elementwise_binary_broadcasts(left, right)
# Check for Concatenations and Broadcasts
out = simplified_binary_broadcast_concatenation(left, right,
simplified_multiplication)
if out is not None:
return out
# simplify multiply by scalar zero, being careful about shape
if pybamm.is_scalar_zero(left):
return pybamm.zeros_like(right)
if pybamm.is_scalar_zero(right):
return pybamm.zeros_like(left)
# if one of the children is a zero matrix, we have to be careful about shapes
if pybamm.is_matrix_zero(left) or pybamm.is_matrix_zero(right):
return pybamm.zeros_like(pybamm.Multiplication(left, right))
# anything multiplied by a scalar one returns itself
if pybamm.is_scalar_one(left):
return right
if pybamm.is_scalar_one(right):
return left
# anything multiplied by a scalar negative one returns negative itself
if pybamm.is_scalar_minus_one(left):
return -right
if pybamm.is_scalar_minus_one(right):
return -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(left):
return right
elif pybamm.is_matrix_one(right):
return left
# also check for negative one
if pybamm.is_matrix_minus_one(left):
return -right
elif 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.Multiplication(left, right))
# Simplify (B @ c) * a to (a * B) @ c if (a * B) is constant
# This is a common construction that appears from discretisation of spatial
# operators
if (isinstance(left, MatrixMultiplication) and left.left.is_constant()
and right.is_constant()
and not (right.ndim_for_testing == 2
and right.shape_for_testing[1] > 1)):
l_left, l_right = left.orphans
new_left = right * l_left
# Special hack for the case where l_left is a matrix one
# because of weird domain errors otherwise
if new_left == right and isinstance(right, pybamm.Array):
new_left = right.new_copy()
# be careful about domains to avoid weird errors
new_left.clear_domains()
new_mul = new_left @ l_right
# Keep the domain of the old left
new_mul.copy_domains(left)
return new_mul
elif isinstance(left, Multiplication) and right.is_constant():
# 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
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
return l_left * new_right
elif isinstance(left, Division) and right.is_constant():
# Simplify (a / b) * c to a * (c / b) if (c / b) is constant
if left.right.is_constant():
l_left, l_right = left.orphans
new_right = right / l_right
return l_left * new_right
# Simplify a * (B @ c) to (a * B) @ c if (a * B) is constant
if (isinstance(right, MatrixMultiplication) and right.left.is_constant()
and left.is_constant()
and not (left.ndim_for_testing == 2
and left.shape_for_testing[1] > 1)):
r_left, r_right = right.orphans
new_left = left * r_left
# Special hack for the case where r_left is a matrix one
# because of weird domain errors otherwise
if new_left == left and isinstance(left, pybamm.Array):
new_left = left.new_copy()
# be careful about domains to avoid weird errors
new_left.clear_domains()
new_mul = new_left @ r_right
# Keep the domain of the old right
new_mul.copy_domains(right)
return new_mul
elif isinstance(right, Multiplication) 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
new_left = left * r_left
return new_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
new_left = left * r_right
return new_left * r_left
elif isinstance(right, Division) and left.is_constant():
# Simplify a * (b / c) to (a / c) * b if (a / c) is constant
if right.right.is_constant():
r_left, r_right = right.orphans
new_left = left / r_right
return new_left * r_left
# Simplify a * (b + c) to (a * b) + (a * c) if (a * b) or (a * c) is constant
# This is a common construction that appears from discretisation of spatial
# operators
# Also do this for cases like a * (b @ c + d) where (a * b) is constant
elif isinstance(right, Addition):
mul_classes = (
pybamm.Multiplication,
pybamm.MatrixMultiplication,
pybamm.Division,
)
if (right.left.is_constant() or right.right.is_constant()
or (isinstance(right.left, mul_classes)
and right.left.left.is_constant())
or (isinstance(right.right, mul_classes)
and right.right.left.is_constant())):
r_left, r_right = right.orphans
if (r_left.domain == right.domain
or r_left.domain == []) and (r_right.domain == right.domain
or r_right.domain == []):
return (left * r_left) + (left * r_right)
# Negation simplifications
if 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.Multiplication(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))