def test_softminus_softplus(self): a = pybamm.Scalar(1) b = pybamm.StateVector(slice(0, 1)) minimum = pybamm.softminus(a, b, 50) self.assertAlmostEqual(minimum.evaluate(y=np.array([2]))[0, 0], 1) self.assertAlmostEqual(minimum.evaluate(y=np.array([0]))[0, 0], 0) self.assertEqual( str(minimum), "log(1.9287498479639178e-22 + exp(-50.0 * y[0:1])) / -50.0" ) maximum = pybamm.softplus(a, b, 50) self.assertAlmostEqual(maximum.evaluate(y=np.array([2]))[0, 0], 2) self.assertAlmostEqual(maximum.evaluate(y=np.array([0]))[0, 0], 1) self.assertEqual( str(maximum), "log(5.184705528587072e+21 + exp(50.0 * y[0:1])) / 50.0" ) # Test that smooth min/max are used when the setting is changed pybamm.settings.min_smoothing = 10 pybamm.settings.max_smoothing = 10 self.assertEqual(str(pybamm.minimum(a, b)), str(pybamm.softminus(a, b, 10))) self.assertEqual(str(pybamm.maximum(a, b)), str(pybamm.softplus(a, b, 10))) # But exact min/max should still be used if both variables are constant a = pybamm.Scalar(1) b = pybamm.Scalar(2) self.assertEqual(str(pybamm.minimum(a, b)), str(a)) self.assertEqual(str(pybamm.maximum(a, b)), str(b)) # Change setting back for other tests pybamm.settings.min_smoothing = "exact" pybamm.settings.max_smoothing = "exact"
def test_jac_of_minimum_maximum(self): y = pybamm.StateVector(slice(0, 10)) y_test = np.linspace(0, 2, 10) np.testing.assert_array_equal( np.diag(pybamm.minimum(1, y**2).jac(y).evaluate(y=y_test)), 2 * y_test * (y_test < 1), ) np.testing.assert_array_equal( np.diag(pybamm.maximum(1, y**2).jac(y).evaluate(y=y_test)), 2 * y_test * (y_test > 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_diff_maximum_minimum(self): a = pybamm.Scalar(1) b = pybamm.StateVector(slice(0, 1)) func = pybamm.minimum(a, b ** 3) self.assertEqual(func.diff(b).evaluate(y=np.array([10])), 0) self.assertEqual(func.diff(b).evaluate(y=np.array([2])), 0) self.assertEqual(func.diff(b).evaluate(y=np.array([-2])), 3 * (-2) ** 2) func = pybamm.maximum(a, b ** 3) self.assertEqual(func.diff(b).evaluate(y=np.array([10])), 3 * 10 ** 2) self.assertEqual(func.diff(b).evaluate(y=np.array([2])), 3 * 2 ** 2) self.assertEqual(func.diff(b).evaluate(y=np.array([-2])), 0)
def test_minimum_maximum(self): a = pybamm.Scalar(1) b = pybamm.StateVector(slice(0, 1)) minimum = pybamm.minimum(a, b) self.assertEqual(minimum.evaluate(y=np.array([2])), 1) self.assertEqual(minimum.evaluate(y=np.array([1])), 1) self.assertEqual(minimum.evaluate(y=np.array([0])), 0) self.assertEqual(str(minimum), "minimum(1.0, y[0:1])") maximum = pybamm.maximum(a, b) self.assertEqual(maximum.evaluate(y=np.array([2])), 2) self.assertEqual(maximum.evaluate(y=np.array([1])), 1) self.assertEqual(maximum.evaluate(y=np.array([0])), 1) self.assertEqual(str(maximum), "maximum(1.0, y[0:1])")
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 a heaviside a = pybamm.Vector(np.array([1, 2])) 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)) 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 a minimum or maximum a = pybamm.Vector(np.array([1, 2])) expr = pybamm.minimum(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)) expr = pybamm.maximum(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 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())
def test_evaluator_jax(self): a = pybamm.StateVector(slice(0, 1)) b = pybamm.StateVector(slice(1, 2)) y_tests = [ np.array([[2.0], [3.0]]), np.array([[1.0], [3.0]]), np.array([1.0, 3.0]), ] t_tests = [1.0, 2.0] # test a * b expr = a * b evaluator = pybamm.EvaluatorJax(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.EvaluatorJax(expr) result = evaluator.evaluate(t=None, y=np.array([[2], [3]])) self.assertEqual(result, 12) # test exp expr = pybamm.exp(a * b) evaluator = pybamm.EvaluatorJax(expr) result = evaluator.evaluate(t=None, y=np.array([[2], [3]])) self.assertEqual(result, np.exp(6)) # test a constant expression expr = pybamm.Scalar(2) * pybamm.Scalar(3) evaluator = pybamm.EvaluatorJax(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.EvaluatorJax(expr) for y in y_tests: result = evaluator.evaluate(t=None, y=y) np.testing.assert_allclose(result, expr.evaluate(t=None, y=y)) # test something with time expr = a * pybamm.t evaluator = pybamm.EvaluatorJax(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.EvaluatorJax(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 a heaviside a = pybamm.Vector(np.array([1, 2])) expr = a <= pybamm.StateVector(slice(0, 2)) evaluator = pybamm.EvaluatorJax(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)) expr = a > pybamm.StateVector(slice(0, 2)) evaluator = pybamm.EvaluatorJax(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 a minimum or maximum a = pybamm.Vector(np.array([1, 2])) expr = pybamm.minimum(a, pybamm.StateVector(slice(0, 2))) evaluator = pybamm.EvaluatorJax(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)) expr = pybamm.maximum(a, pybamm.StateVector(slice(0, 2))) evaluator = pybamm.EvaluatorJax(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.EvaluatorJax(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-vector 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.EvaluatorJax(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 the sparse-scalar multiplication A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]]))) for expr in [ A * pybamm.t @ pybamm.StateVector(slice(0, 2)), pybamm.t * A @ pybamm.StateVector(slice(0, 2)), ]: evaluator = pybamm.EvaluatorJax(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 the sparse-scalar division A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]]))) expr = A / (1.0 + pybamm.t) @ pybamm.StateVector(slice(0, 2)) evaluator = pybamm.EvaluatorJax(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]]))) a = pybamm.StateVector(slice(0, 1)) expr = pybamm.SparseStack(A, a * B) with self.assertRaises(NotImplementedError): evaluator = pybamm.EvaluatorJax(expr) # test sparse mat-mat mult 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]]))) a = pybamm.StateVector(slice(0, 1)) expr = A @ (a * B) with self.assertRaises(NotImplementedError): evaluator = pybamm.EvaluatorJax(expr) # test numpy concatenation a = pybamm.Vector(np.array([[1], [2]])) b = pybamm.Vector(np.array([[3]])) expr = pybamm.NumpyConcatenation(a, b) evaluator = pybamm.EvaluatorJax(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 Inner A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1]]))) v = pybamm.StateVector(slice(0, 1)) for expr in [ pybamm.Inner(A, v) @ v, pybamm.Inner(v, A) @ v, pybamm.Inner(v, v) @ v ]: evaluator = pybamm.EvaluatorJax(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))
def _binary_new_copy(self, left, right): "See :meth:`pybamm.BinaryOperator._binary_new_copy()`. " return pybamm.maximum(left, right)
def _get_exchange_current_density(self, variables): """ A private function to obtain the exchange current density Parameters ---------- variables: dict The variables in the full model. Returns ------- j0 : :class: `pybamm.Symbol` The exchange current density. """ c_e = variables[self.domain + " electrolyte concentration"] T = variables[self.domain + " electrode temperature"] if self.reaction == "lithium-ion main": c_s_surf = variables[self.domain + " particle surface concentration"] # If variable was broadcast, take only the orphan if (isinstance(c_s_surf, pybamm.Broadcast) and isinstance(c_e, pybamm.Broadcast) and isinstance(T, pybamm.Broadcast)): c_s_surf = c_s_surf.orphans[0] c_e = c_e.orphans[0] T = T.orphans[0] tol = 1e-8 c_e = pybamm.maximum(tol, c_e) c_s_surf = pybamm.maximum(tol, pybamm.minimum(c_s_surf, 1 - tol)) if self.domain == "Negative": j0 = self.param.j0_n(c_e, c_s_surf, T) / self.param.C_r_n elif self.domain == "Positive": j0 = (self.param.gamma_p * self.param.j0_p(c_e, c_s_surf, T) / self.param.C_r_p) elif self.reaction == "lead-acid main": # If variable was broadcast, take only the orphan if isinstance(c_e, pybamm.Broadcast) and isinstance( T, pybamm.Broadcast): c_e = c_e.orphans[0] T = T.orphans[0] if self.domain == "Negative": j0 = self.param.j0_n(c_e, T) elif self.domain == "Positive": j0 = self.param.j0_p(c_e, T) elif self.reaction == "lead-acid oxygen": # If variable was broadcast, take only the orphan if isinstance(c_e, pybamm.Broadcast) and isinstance( T, pybamm.Broadcast): c_e = c_e.orphans[0] T = T.orphans[0] if self.domain == "Negative": j0 = pybamm.Scalar(0) elif self.domain == "Positive": j0 = self.param.j0_p_Ox(c_e, T) else: j0 = pybamm.Scalar(0) return j0