def test_outer(self):
# Outer class
v = pybamm.Vector(np.ones(5), domain="current collector")
w = pybamm.Vector(2 * np.ones(3), domain="test")
outer = pybamm.Outer(v, w)
np.testing.assert_array_equal(outer.evaluate(), 2 * np.ones((15, 1)))
self.assertEqual(outer.domain, w.domain)
self.assertEqual(
str(outer),
"outer(Column vector of length 5, Column vector of length 3)")
# outer function
# if there is no domain clash, normal multiplication is retured
u = pybamm.Vector(np.linspace(0, 1, 5))
outer = pybamm.outer(u, v)
self.assertIsInstance(outer, pybamm.Multiplication)
np.testing.assert_array_equal(outer.evaluate(), u.evaluate())
# otherwise, Outer class is returned
outer_fun = pybamm.outer(v, w)
outer_class = pybamm.Outer(v, w)
self.assertEqual(outer_fun.id, outer_class.id)
# failures
y = pybamm.StateVector(slice(10))
with self.assertRaisesRegex(
TypeError,
"right child must only contain SpatialVariable and scalars"):
pybamm.Outer(v, y)
with self.assertRaises(NotImplementedError):
outer_fun.diff(None)
def test_simplify_outer(self):
v = pybamm.Vector(np.ones(5), domain="current collector")
w = pybamm.Vector(2 * np.ones(3), domain="test")
outer_simp = pybamm.Outer(v, w).simplify()
self.assertIsInstance(outer_simp, pybamm.Vector)
np.testing.assert_array_equal(outer_simp.evaluate(), 2 * np.ones(
(15, 1)))
def outer(left, right):
"""
Return outer product of two symbols. If the symbols have the same domain, the outer
product is just a multiplication. If they have different domains, make a copy of the
left child with same domain as right child, and then take outer product.
"""
try:
return left * right
except pybamm.DomainError:
return pybamm.Outer(left, right)
def test_jac_of_domain_concatenation(self):
# create mesh
disc = get_1p1d_discretisation_for_testing()
mesh = disc.mesh
y = pybamm.StateVector(slice(0, 1500))
# Jacobian of a DomainConcatenation of constants is a zero matrix of the
# appropriate size
a_dom = ["negative electrode"]
b_dom = ["separator"]
c_dom = ["positive electrode"]
a_npts = mesh[a_dom[0]][0].npts
b_npts = mesh[b_dom[0]][0].npts
c_npts = mesh[c_dom[0]][0].npts
cc_npts = mesh["current collector"][0].npts
curr_coll_vector = pybamm.Vector(np.ones(cc_npts),
domain="current collector")
a = 2 * pybamm.Outer(curr_coll_vector,
pybamm.Vector(np.ones(a_npts), domain=a_dom))
b = pybamm.Outer(curr_coll_vector,
pybamm.Vector(np.ones(b_npts), domain=b_dom))
c = 3 * pybamm.Outer(curr_coll_vector,
pybamm.Vector(np.ones(c_npts), domain=c_dom))
conc = pybamm.DomainConcatenation([a, b, c], mesh)
jac = conc.jac(y).evaluate().toarray()
np.testing.assert_array_equal(jac, np.zeros((1500, 1500)))
# Jacobian of a DomainConcatenation of StateVectors
a = pybamm.Variable("a", domain=a_dom)
b = pybamm.Variable("b", domain=b_dom)
c = pybamm.Variable("c", domain=c_dom)
conc = pybamm.Concatenation(a, b, c)
disc.set_variable_slices([conc])
conc_disc = disc.process_symbol(conc)
y0 = np.ones(1500)
jac = conc_disc.jac(y).evaluate(y=y0).toarray()
np.testing.assert_array_equal(jac, np.eye(1500))
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_array_symbols(self):
# Arrays
a = np.array([1, 2, 3, 4, 5])
pybamm_a = pybamm.Array(a)
self.assertTrue(casadi.is_equal(pybamm_a.to_casadi(), casadi.SX(a)))
casadi_t = casadi.SX.sym("t")
casadi_y = casadi.SX.sym("y", 10)
pybamm_t = pybamm.Time()
pybamm_y = pybamm.StateVector(slice(0, 10))
# Time
self.assertEqual(pybamm_t.to_casadi(casadi_t, casadi_y), casadi_t)
# State Vector
self.assertTrue(
casadi.is_equal(pybamm_y.to_casadi(casadi_t, casadi_y), casadi_y))
# outer product
outer = pybamm.Outer(pybamm_a, pybamm_a)
self.assertTrue(
casadi.is_equal(outer.to_casadi(), casadi.SX(outer.evaluate())))
def broadcast(self, symbol, domain, auxiliary_domains, broadcast_type):
"""
Broadcast symbol to a specified domain.
Parameters
----------
symbol : :class:`pybamm.Symbol`
The symbol to be broadcasted
domain : iterable of strings
The domain to broadcast to
broadcast_type : str
The type of broadcast, either: 'primary' or 'full'
Returns
-------
broadcasted_symbol: class: `pybamm.Symbol`
The discretised symbol of the correct size for the spatial method
"""
primary_pts_for_broadcast = sum(
self.mesh[dom][0].npts_for_broadcast for dom in domain
)
full_pts_for_broadcast = sum(
subdom.npts_for_broadcast for dom in domain for subdom in self.mesh[dom]
)
if broadcast_type == "primary":
out = pybamm.Outer(
symbol, pybamm.Vector(np.ones(primary_pts_for_broadcast), domain=domain)
)
elif broadcast_type == "full":
out = symbol * pybamm.Vector(np.ones(full_pts_for_broadcast), domain=domain)
out.auxiliary_domains = auxiliary_domains
return out
def test_process_symbol(self):
parameter_values = pybamm.ParameterValues({"a": 1, "b": 2, "c": 3})
# process parameter
a = pybamm.Parameter("a")
processed_a = parameter_values.process_symbol(a)
self.assertIsInstance(processed_a, pybamm.Scalar)
self.assertEqual(processed_a.value, 1)
# process binary operation
b = pybamm.Parameter("b")
add = a + b
processed_add = parameter_values.process_symbol(add)
self.assertIsInstance(processed_add, pybamm.Addition)
self.assertIsInstance(processed_add.children[0], pybamm.Scalar)
self.assertIsInstance(processed_add.children[1], pybamm.Scalar)
self.assertEqual(processed_add.children[0].value, 1)
self.assertEqual(processed_add.children[1].value, 2)
scal = pybamm.Scalar(34)
mul = a * scal
processed_mul = parameter_values.process_symbol(mul)
self.assertIsInstance(processed_mul, pybamm.Multiplication)
self.assertIsInstance(processed_mul.children[0], pybamm.Scalar)
self.assertIsInstance(processed_mul.children[1], pybamm.Scalar)
self.assertEqual(processed_mul.children[0].value, 1)
self.assertEqual(processed_mul.children[1].value, 34)
# process integral
aa = pybamm.Parameter("a", domain=["negative electrode"])
x = pybamm.SpatialVariable("x", domain=["negative electrode"])
integ = pybamm.Integral(aa, x)
processed_integ = parameter_values.process_symbol(integ)
self.assertIsInstance(processed_integ, pybamm.Integral)
self.assertIsInstance(processed_integ.children[0], pybamm.Scalar)
self.assertEqual(processed_integ.children[0].value, 1)
self.assertEqual(processed_integ.integration_variable[0].id, x.id)
# process unary operation
grad = pybamm.Gradient(a)
processed_grad = parameter_values.process_symbol(grad)
self.assertIsInstance(processed_grad, pybamm.Gradient)
self.assertIsInstance(processed_grad.children[0], pybamm.Scalar)
self.assertEqual(processed_grad.children[0].value, 1)
# process delta function
aa = pybamm.Parameter("a")
delta_aa = pybamm.DeltaFunction(aa, "left", "some domain")
processed_delta_aa = parameter_values.process_symbol(delta_aa)
self.assertIsInstance(processed_delta_aa, pybamm.DeltaFunction)
self.assertEqual(processed_delta_aa.side, "left")
processed_a = processed_delta_aa.children[0]
self.assertIsInstance(processed_a, pybamm.Scalar)
self.assertEqual(processed_a.value, 1)
# process boundary operator (test for BoundaryValue)
aa = pybamm.Parameter("a", domain=["negative electrode"])
x = pybamm.SpatialVariable("x", domain=["negative electrode"])
boundary_op = pybamm.BoundaryValue(aa * x, "left")
processed_boundary_op = parameter_values.process_symbol(boundary_op)
self.assertIsInstance(processed_boundary_op, pybamm.BoundaryOperator)
processed_a = processed_boundary_op.children[0].children[0]
processed_x = processed_boundary_op.children[0].children[1]
self.assertIsInstance(processed_a, pybamm.Scalar)
self.assertEqual(processed_a.value, 1)
self.assertEqual(processed_x.id, x.id)
# process broadcast
whole_cell = ["negative electrode", "separator", "positive electrode"]
broad = pybamm.Broadcast(a, whole_cell)
processed_broad = parameter_values.process_symbol(broad)
self.assertIsInstance(processed_broad, pybamm.Broadcast)
self.assertEqual(processed_broad.domain, whole_cell)
self.assertIsInstance(processed_broad.children[0], pybamm.Scalar)
self.assertEqual(processed_broad.children[0].evaluate(), np.array([1]))
# process concatenation
conc = pybamm.Concatenation(pybamm.Vector(np.ones(10)),
pybamm.Vector(2 * np.ones(15)))
processed_conc = parameter_values.process_symbol(conc)
self.assertIsInstance(processed_conc.children[0], pybamm.Vector)
self.assertIsInstance(processed_conc.children[1], pybamm.Vector)
np.testing.assert_array_equal(processed_conc.children[0].entries, 1)
np.testing.assert_array_equal(processed_conc.children[1].entries, 2)
# process domain concatenation
c_e_n = pybamm.Variable("c_e_n", ["negative electrode"])
c_e_s = pybamm.Variable("c_e_p", ["separator"])
test_mesh = shared.get_mesh_for_testing()
dom_con = pybamm.DomainConcatenation([a * c_e_n, b * c_e_s], test_mesh)
processed_dom_con = parameter_values.process_symbol(dom_con)
a_proc = processed_dom_con.children[0].children[0]
b_proc = processed_dom_con.children[1].children[0]
self.assertIsInstance(a_proc, pybamm.Scalar)
self.assertIsInstance(b_proc, pybamm.Scalar)
self.assertEqual(a_proc.value, 1)
self.assertEqual(b_proc.value, 2)
# process variable
c = pybamm.Variable("c")
processed_c = parameter_values.process_symbol(c)
self.assertIsInstance(processed_c, pybamm.Variable)
self.assertEqual(processed_c.name, "c")
# process scalar
d = pybamm.Scalar(14)
processed_d = parameter_values.process_symbol(d)
self.assertIsInstance(processed_d, pybamm.Scalar)
self.assertEqual(processed_d.value, 14)
# process array types
e = pybamm.Vector(np.ones(4))
processed_e = parameter_values.process_symbol(e)
self.assertIsInstance(processed_e, pybamm.Vector)
np.testing.assert_array_equal(processed_e.evaluate(), np.ones((4, 1)))
f = pybamm.Matrix(np.ones((5, 6)))
processed_f = parameter_values.process_symbol(f)
self.assertIsInstance(processed_f, pybamm.Matrix)
np.testing.assert_array_equal(processed_f.evaluate(), np.ones((5, 6)))
# process statevector
g = pybamm.StateVector(slice(0, 10))
processed_g = parameter_values.process_symbol(g)
self.assertIsInstance(processed_g, pybamm.StateVector)
np.testing.assert_array_equal(processed_g.evaluate(y=np.ones(10)),
np.ones((10, 1)))
# process outer
c = pybamm.Parameter("c", domain="current collector")
outer = pybamm.Outer(c, b)
processed_outer = parameter_values.process_symbol(outer)
self.assertIsInstance(processed_outer, pybamm.Outer)
# not implemented
sym = pybamm.Symbol("sym")
with self.assertRaises(NotImplementedError):
parameter_values.process_symbol(sym)
def _binary_simplify(self, left, right):
""" See :meth:`pybamm.BinaryOperator.simplify()`. """
# Make sure left child keeps same domain
left.domain = self.left.domain
return pybamm.Outer(left, right)
def test_linear(self):
y = pybamm.StateVector(slice(0, 4))
u = pybamm.StateVector(slice(0, 2))
v = pybamm.StateVector(slice(2, 4))
y0 = np.ones(4)
func = u
jacobian = np.array([[1, 0, 0, 0], [0, 1, 0, 0]])
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = -v
jacobian = np.array([[0, 0, -1, 0], [0, 0, 0, -1]])
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = 3 * u + 4 * v
jacobian = np.array([[3, 0, 4, 0], [0, 3, 0, 4]])
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = 7 * u - v * 9
jacobian = np.array([[7, 0, -9, 0], [0, 7, 0, -9]])
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
A = pybamm.Matrix(2 * eye(2))
func = A @ u
jacobian = np.array([[2, 0, 0, 0], [0, 2, 0, 0]])
dfunc_dy = func.jac(y).simplify().evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = u @ pybamm.StateVector(slice(0, 1))
with self.assertRaises(NotImplementedError):
func.jac(y)
# when differentiating by independent part of the state vector
jacobian = np.array([[0, 0], [0, 0]])
du_dv = u.jac(v).evaluate().toarray()
np.testing.assert_array_equal(du_dv, jacobian)
# test Jacobian of Outer (must set domain to be 'current collector')
u.domain = ["current collector"]
func = pybamm.Outer(u, pybamm.Scalar(4))
jacobian = np.array([[4, 0, 0, 0], [0, 4, 0, 0]])
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
func = pybamm.Outer(u, pybamm.Vector(np.array([1, 2, 3])))
jacobian = np.array([
[1, 0, 0, 0],
[2, 0, 0, 0],
[3, 0, 0, 0],
[0, 1, 0, 0],
[0, 2, 0, 0],
[0, 3, 0, 0],
])
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(jacobian, dfunc_dy.toarray())
# test jac of outer if left evaluates to number
func = pybamm.Outer(pybamm.Scalar(1), pybamm.Scalar(4))
dfunc_dy = func.jac(y).evaluate(y=y0)
np.testing.assert_array_equal(0, dfunc_dy.toarray())
def _binary_simplify(self, left, right):
""" See :meth:`pybamm.BinaryOperator._binary_simplify()`. """
return pybamm.Outer(left, right)
def test_evaluator_python(self):
a = pybamm.StateVector(slice(0, 1))
b = pybamm.StateVector(slice(1, 2))
y_tests = [np.array([[2], [3]]), np.array([[1], [3]])]
t_tests = [1, 2]
# test a * b
expr = a * b
evaluator = pybamm.EvaluatorPython(expr)
result = evaluator.evaluate(t=None, y=np.array([[2], [3]]))
self.assertEqual(result, 6)
result = evaluator.evaluate(t=None, y=np.array([[1], [3]]))
self.assertEqual(result, 3)
# test function(a*b)
expr = pybamm.Function(test_function, a * b)
evaluator = pybamm.EvaluatorPython(expr)
result = evaluator.evaluate(t=None, y=np.array([[2], [3]]))
self.assertEqual(result, 12)
# test a constant expression
expr = pybamm.Scalar(2) * pybamm.Scalar(3)
evaluator = pybamm.EvaluatorPython(expr)
result = evaluator.evaluate()
self.assertEqual(result, 6)
# test a larger expression
expr = a * b + b + a**2 / b + 2 * a + b / 2 + 4
evaluator = pybamm.EvaluatorPython(expr)
for y in y_tests:
result = evaluator.evaluate(t=None, y=y)
self.assertEqual(result, expr.evaluate(t=None, y=y))
# test something with time
expr = a * pybamm.t
evaluator = pybamm.EvaluatorPython(expr)
for t, y in zip(t_tests, y_tests):
result = evaluator.evaluate(t=t, y=y)
self.assertEqual(result, expr.evaluate(t=t, y=y))
# test something with a matrix multiplication
A = pybamm.Matrix(np.array([[1, 2], [3, 4]]))
expr = A @ pybamm.StateVector(slice(0, 2))
evaluator = pybamm.EvaluatorPython(expr)
for t, y in zip(t_tests, y_tests):
result = evaluator.evaluate(t=t, y=y)
np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
# test something with an index
expr = pybamm.Index(A @ pybamm.StateVector(slice(0, 2)), 0)
evaluator = pybamm.EvaluatorPython(expr)
for t, y in zip(t_tests, y_tests):
result = evaluator.evaluate(t=t, y=y)
self.assertEqual(result, expr.evaluate(t=t, y=y))
# test something with a sparse matrix multiplication
A = pybamm.Matrix(np.array([[1, 2], [3, 4]]))
B = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
C = pybamm.Matrix(scipy.sparse.coo_matrix(np.array([[1, 0], [0, 4]])))
expr = A @ B @ C @ pybamm.StateVector(slice(0, 2))
evaluator = pybamm.EvaluatorPython(expr)
for t, y in zip(t_tests, y_tests):
result = evaluator.evaluate(t=t, y=y)
np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
# test numpy concatenation
a = pybamm.Vector(np.array([[1], [2]]))
b = pybamm.Vector(np.array([[3]]))
expr = pybamm.NumpyConcatenation(a, b)
evaluator = pybamm.EvaluatorPython(expr)
for t, y in zip(t_tests, y_tests):
result = evaluator.evaluate(t=t, y=y)
np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
# test sparse stack
A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
B = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[2, 0], [5, 0]])))
expr = pybamm.SparseStack(A, B)
evaluator = pybamm.EvaluatorPython(expr)
for t, y in zip(t_tests, y_tests):
result = evaluator.evaluate(t=t, y=y).toarray()
np.testing.assert_allclose(result,
expr.evaluate(t=t, y=y).toarray())
# test Outer
v = pybamm.Vector(np.ones(5), domain="current collector")
w = pybamm.Vector(2 * np.ones(3), domain="test")
expr = pybamm.Outer(v, w)
evaluator = pybamm.EvaluatorPython(expr)
result = evaluator.evaluate()
np.testing.assert_allclose(result, expr.evaluate())
# test Inner
v = pybamm.Vector(np.ones(5), domain="test")
w = pybamm.Vector(2 * np.ones(5), domain="test")
expr = pybamm.Inner(v, w)
evaluator = pybamm.EvaluatorPython(expr)
result = evaluator.evaluate()
np.testing.assert_allclose(result, expr.evaluate())