def test_convert_scalar_symbols(self):
a = pybamm.Scalar(0)
b = pybamm.Scalar(1)
c = pybamm.Scalar(-1)
d = pybamm.Scalar(2)
e = pybamm.Scalar(3)
g = pybamm.Scalar(3.3)
self.assertEqual(a.to_casadi(), casadi.MX(0))
self.assertEqual(d.to_casadi(), casadi.MX(2))
# negate
self.assertEqual((-b).to_casadi(), casadi.MX(-1))
# absolute value
self.assertEqual(abs(c).to_casadi(), casadi.MX(1))
# floor
self.assertEqual(pybamm.Floor(g).to_casadi(), casadi.MX(3))
# ceiling
self.assertEqual(pybamm.Ceiling(g).to_casadi(), casadi.MX(4))
# function
def square_plus_one(x):
return x**2 + 1
f = pybamm.Function(square_plus_one, b)
self.assertEqual(f.to_casadi(), 2)
def myfunction(x, y):
return x + y
f = pybamm.Function(myfunction, b, d)
self.assertEqual(f.to_casadi(), casadi.MX(3))
# use classes to avoid simplification
# addition
self.assertEqual((pybamm.Addition(a, b)).to_casadi(), casadi.MX(1))
# subtraction
self.assertEqual(pybamm.Subtraction(c, d).to_casadi(), casadi.MX(-3))
# multiplication
self.assertEqual(
pybamm.Multiplication(c, d).to_casadi(), casadi.MX(-2))
# power
self.assertEqual(pybamm.Power(c, d).to_casadi(), casadi.MX(1))
# division
self.assertEqual(pybamm.Division(b, d).to_casadi(), casadi.MX(1 / 2))
# modulo
self.assertEqual(pybamm.Modulo(e, d).to_casadi(), casadi.MX(1))
# minimum and maximum
self.assertEqual(pybamm.Minimum(a, b).to_casadi(), casadi.MX(0))
self.assertEqual(pybamm.Maximum(a, b).to_casadi(), casadi.MX(1))
def test_simplify_divide_outer(self):
u = pybamm.Scalar(1)
v = pybamm.StateVector(slice(0, 5), domain="current collector")
outer = pybamm.Outer(v, u)
exp1 = pybamm.Division(pybamm.Division(outer, u), u)
self.assertIsInstance(exp1.simplify(), pybamm.Outer)
exp2 = pybamm.Division(pybamm.Division(outer, 2 * u), u)
self.assertIsInstance(exp2.simplify(), pybamm.Multiplication)
exp3 = pybamm.Division(pybamm.Division(outer, u), 2 * u)
self.assertIsInstance(exp3.simplify(), pybamm.Multiplication)
exp4 = pybamm.Division(pybamm.Division(outer, 2 * u), 2 * u)
self.assertIsInstance(exp4.simplify(), pybamm.Multiplication)
def test_convert_scalar_symbols(self):
a = pybamm.Scalar(0)
b = pybamm.Scalar(1)
c = pybamm.Scalar(-1)
d = pybamm.Scalar(2)
self.assertEqual(a.to_casadi(), casadi.MX(0))
self.assertEqual(d.to_casadi(), casadi.MX(2))
# negate
self.assertEqual((-b).to_casadi(), casadi.MX(-1))
# absolute value
self.assertEqual(abs(c).to_casadi(), casadi.MX(1))
# function
def sin(x):
return np.sin(x)
f = pybamm.Function(sin, b)
self.assertEqual(f.to_casadi(), casadi.MX(np.sin(1)))
def myfunction(x, y):
return x + y
f = pybamm.Function(myfunction, b, d)
self.assertEqual(f.to_casadi(), casadi.MX(3))
# use classes to avoid simplification
# addition
self.assertEqual((pybamm.Addition(a, b)).to_casadi(), casadi.MX(1))
# subtraction
self.assertEqual(pybamm.Subtraction(c, d).to_casadi(), casadi.MX(-3))
# multiplication
self.assertEqual(
pybamm.Multiplication(c, d).to_casadi(), casadi.MX(-2))
# power
self.assertEqual(pybamm.Power(c, d).to_casadi(), casadi.MX(1))
# division
self.assertEqual(pybamm.Division(b, d).to_casadi(), casadi.MX(1 / 2))
# minimum and maximum
self.assertEqual(pybamm.Minimum(a, b).to_casadi(), casadi.MX(0))
self.assertEqual(pybamm.Maximum(a, b).to_casadi(), casadi.MX(1))
def test_to_equation(self):
# Test print_name
pybamm.Addition.print_name = "test"
self.assertEqual(pybamm.Addition(1, 2).to_equation(), sympy.symbols("test"))
# Test Power
self.assertEqual(pybamm.Power(7, 2).to_equation(), 49)
# Test Division
self.assertEqual(pybamm.Division(10, 2).to_equation(), 5)
# Test Matrix Multiplication
arr1 = pybamm.Array([[1, 0], [0, 1]])
arr2 = pybamm.Array([[4, 1], [2, 2]])
self.assertEqual(
pybamm.MatrixMultiplication(arr1, arr2).to_equation(),
sympy.Matrix([[4.0, 1.0], [2.0, 2.0]]),
)
# Test EqualHeaviside
self.assertEqual(pybamm.EqualHeaviside(1, 0).to_equation(), False)
# Test NotEqualHeaviside
self.assertEqual(pybamm.NotEqualHeaviside(2, 4).to_equation(), True)
def __rtruediv__(self, other):
"""return a :class:`Division` object"""
return pybamm.simplify_if_constant(pybamm.Division(other, self),
keep_domains=True)
def __rtruediv__(self, other):
"""return a :class:`Division` object"""
if isinstance(other, (Symbol, numbers.Number)):
return pybamm.Division(other, self)
else:
raise NotImplementedError
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))
