From 783d230efb483f8a926cddfa7fbfda34612f5be7 Mon Sep 17 00:00:00 2001
From: Robert Timms <timms@maths.ox.ac.uk>
Date: Thu, 3 Oct 2019 13:10:27 +0100
Subject: [PATCH 1/5] #644 set atol and rtol

---
 .../full_battery_models/base_battery_model.py |  6 +-
 pybamm/solvers/base_solver.py                 | 31 ++++++---
 pybamm/solvers/dae_solver.py                  | 18 +++--
 pybamm/solvers/ode_solver.py                  | 10 +--
 pybamm/solvers/scikits_dae_solver.py          | 25 ++++---
 pybamm/solvers/scikits_ode_solver.py          | 17 ++---
 pybamm/solvers/scipy_solver.py                | 21 +++---
 .../change_solver_tolerances.py               | 52 ++++++++++++++
 results/change_settings/compare_var_pts.py    | 68 +++++++++++++++++++
 tests/unit/test_processed_variable.py         | 10 ++-
 tests/unit/test_solvers/test_base_solver.py   | 13 ++--
 .../unit/test_solvers/test_scikits_solvers.py | 56 +++++++--------
 tests/unit/test_solvers/test_scipy_solver.py  | 22 +++---
 13 files changed, 251 insertions(+), 98 deletions(-)
 create mode 100644 results/change_settings/change_solver_tolerances.py
 create mode 100644 results/change_settings/compare_var_pts.py

diff --git a/pybamm/models/full_battery_models/base_battery_model.py b/pybamm/models/full_battery_models/base_battery_model.py
index 1db1276c54..c301255a70 100644
--- a/pybamm/models/full_battery_models/base_battery_model.py
+++ b/pybamm/models/full_battery_models/base_battery_model.py
@@ -128,9 +128,9 @@ def default_geometry(self):
     def default_var_pts(self):
         var = pybamm.standard_spatial_vars
         return {
-            var.x_n: 40,
-            var.x_s: 25,
-            var.x_p: 35,
+            var.x_n: 20,
+            var.x_s: 20,
+            var.x_p: 20,
             var.r_n: 10,
             var.r_p: 10,
             var.y: 10,
diff --git a/pybamm/solvers/base_solver.py b/pybamm/solvers/base_solver.py
index 63dd82ad6d..c98fa63e47 100644
--- a/pybamm/solvers/base_solver.py
+++ b/pybamm/solvers/base_solver.py
@@ -10,13 +10,16 @@ class BaseSolver(object):
 
     Parameters
     ----------
-    tolerance : float, optional
-        The tolerance for the solver (default is 1e-8).
+    rtol : float, optional
+        The relative tolerance for the solver (default is 1e-3).
+    atol : float, optional
+        The relative tolerance for the solver (default is 1e-6).
     """
 
-    def __init__(self, method=None, tol=1e-8):
+    def __init__(self, method=None, rtol=1e-3, atol=1e-6):
         self._method = method
-        self._tol = tol
+        self._rtol = rtol
+        self._atol = atol
 
     @property
     def method(self):
@@ -27,12 +30,20 @@ def method(self, value):
         self._method = value
 
     @property
-    def tol(self):
-        return self._tol
+    def rtol(self):
+        return self._rtol
 
-    @tol.setter
-    def tol(self, value):
-        self._tol = value
+    @rtol.setter
+    def rtol(self, value):
+        self._rtol = value
+
+    @property
+    def atol(self):
+        return self._atol
+
+    @atol.setter
+    def atol(self, value):
+        self._atol = value
 
     def solve(self, model, t_eval):
         """
@@ -73,7 +84,7 @@ def solve(self, model, t_eval):
         solution.total_time = timer.time() - start_time
         solution.set_up_time = set_up_time
 
-        pybamm.logger.warning("Finish solving {} ({})".format(model.name, termination))
+        pybamm.logger.info("Finish solving {} ({})".format(model.name, termination))
         pybamm.logger.info(
             "Set-up time: {}, Solve time: {}, Total time: {}".format(
                 timer.format(solution.set_up_time),
diff --git a/pybamm/solvers/dae_solver.py b/pybamm/solvers/dae_solver.py
index 035a31f050..0828a819ea 100644
--- a/pybamm/solvers/dae_solver.py
+++ b/pybamm/solvers/dae_solver.py
@@ -12,11 +12,13 @@ class DaeSolver(pybamm.BaseSolver):
 
     Parameters
     ----------
-    tolerance : float, optional
-        The tolerance for the solver (default is 1e-8).
+    rtol : float, optional
+        The relative tolerance for the solver (default is 1e-3).
+    atol : float, optional
+        The relative tolerance for the solver (default is 1e-6)
     root_method : str, optional
         The method to use to find initial conditions (default is "lm")
-    tolerance : float, optional
+    root_tol : float, optional
         The tolerance for the initial-condition solver (default is 1e-8).
     max_steps: int, optional
         The maximum number of steps the solver will take before terminating
@@ -24,9 +26,15 @@ class DaeSolver(pybamm.BaseSolver):
     """
 
     def __init__(
-        self, method=None, tol=1e-8, root_method="lm", root_tol=1e-6, max_steps=1000
+        self,
+        method=None,
+        rtol=1e-3,
+        atol=1e-6,
+        root_method="lm",
+        root_tol=1e-6,
+        max_steps=1000,
     ):
-        super().__init__(method, tol)
+        super().__init__(method, rtol, atol)
         self.root_method = root_method
         self.root_tol = root_tol
         self.max_steps = max_steps
diff --git a/pybamm/solvers/ode_solver.py b/pybamm/solvers/ode_solver.py
index 7d16dcb998..54d4c5e946 100644
--- a/pybamm/solvers/ode_solver.py
+++ b/pybamm/solvers/ode_solver.py
@@ -10,12 +10,14 @@ class OdeSolver(pybamm.BaseSolver):
 
     Parameters
     ----------
-    tolerance : float, optional
-        The tolerance for the solver (default is 1e-8).
+    rtol : float, optional
+        The relative tolerance for the solver (default is 1e-3).
+    atol : float, optional
+        The relative tolerance for the solver (default is 1e-6).
     """
 
-    def __init__(self, method=None, tol=1e-8):
-        super().__init__(method, tol)
+    def __init__(self, method=None, rtol=1e-3, atol=1e-6):
+        super().__init__(method, rtol, atol)
 
     def compute_solution(self, model, t_eval):
         """Calculate the solution of the model at specified times.
diff --git a/pybamm/solvers/scikits_dae_solver.py b/pybamm/solvers/scikits_dae_solver.py
index 0ed22a1030..d59e33f69c 100644
--- a/pybamm/solvers/scikits_dae_solver.py
+++ b/pybamm/solvers/scikits_dae_solver.py
@@ -22,12 +22,13 @@ class ScikitsDaeSolver(pybamm.DaeSolver):
     ----------
     method : str, optional
         The method to use in solve_ivp (default is "BDF")
-    tolerance : float, optional
-        The tolerance for the solver (default is 1e-8). Set as the both reltol and
-        abstol in solve_ivp.
+    rtol : float, optional
+        The relative tolerance for the solver (default is 1e-3).
+    atol : float, optional
+        The relative tolerance for the solver (default is 1e-6).
     root_method : str, optional
         The method to use to find initial conditions (default is "lm")
-    tolerance : float, optional
+    root_tol : float, optional
         The tolerance for the initial-condition solver (default is 1e-8).
     max_steps: int, optional
         The maximum number of steps the solver will take before terminating
@@ -35,12 +36,18 @@ class ScikitsDaeSolver(pybamm.DaeSolver):
     """
 
     def __init__(
-        self, method="ida", tol=1e-8, root_method="lm", root_tol=1e-6, max_steps=1000
+        self,
+        method="ida",
+        rtol=1e-3,
+        atol=1e-6,
+        root_method="lm",
+        root_tol=1e-6,
+        max_steps=1000,
     ):
         if scikits_odes_spec is None:
             raise ImportError("scikits.odes is not installed")
 
-        super().__init__(method, tol, root_method, root_tol, max_steps)
+        super().__init__(method, rtol, atol, root_method, root_tol, max_steps)
 
     def integrate(
         self, residuals, y0, t_eval, events=None, mass_matrix=None, jacobian=None
@@ -76,8 +83,8 @@ def rootfn(t, y, ydot, return_root):
 
         extra_options = {
             "old_api": False,
-            "rtol": self.tol,
-            "atol": self.tol,
+            "rtol": self.rtol,
+            "atol": self.atol,
             "max_steps": self.max_steps,
         }
 
@@ -120,7 +127,7 @@ def jacfn(t, y, ydot, residuals, cj, J):
                 np.transpose(sol.values.y),
                 sol.roots.t,
                 np.transpose(sol.roots.y),
-                termination
+                termination,
             )
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/pybamm/solvers/scikits_ode_solver.py b/pybamm/solvers/scikits_ode_solver.py
index 17cfff62a0..b0329d59ba 100644
--- a/pybamm/solvers/scikits_ode_solver.py
+++ b/pybamm/solvers/scikits_ode_solver.py
@@ -26,18 +26,19 @@ class ScikitsOdeSolver(pybamm.OdeSolver):
     ----------
     method : str, optional
         The method to use in solve_ivp (default is "BDF")
-    tolerance : float, optional
-        The tolerance for the solver (default is 1e-8). Set as the both reltol and
-        abstol in solve_ivp.
+    rtol : float, optional
+        The relative tolerance for the solver (default is 1e-3).
+    atol : float, optional
+        The relative tolerance for the solver (default is 1e-6).
     linsolver : str, optional
             Can be 'dense' (= default), 'lapackdense', 'spgmr', 'spbcgs', 'sptfqmr'
     """
 
-    def __init__(self, method="cvode", tol=1e-8, linsolver="dense"):
+    def __init__(self, method="cvode", rtol=1e-3, atol=1e-6, linsolver="dense"):
         if scikits_odes_spec is None:
             raise ImportError("scikits.odes is not installed")
 
-        super().__init__(method, tol)
+        super().__init__(method, rtol, atol)
         self.linsolver = linsolver
 
     def integrate(
@@ -98,8 +99,8 @@ def jac_times_setupfn(t, y, fy, userdata):
 
         extra_options = {
             "old_api": False,
-            "rtol": self.tol,
-            "atol": self.tol,
+            "rtol": self.rtol,
+            "atol": self.atol,
             "linsolver": self.linsolver,
         }
 
@@ -134,7 +135,7 @@ def jac_times_setupfn(t, y, fy, userdata):
                 np.transpose(sol.values.y),
                 sol.roots.t,
                 np.transpose(sol.roots.y),
-                termination
+                termination,
             )
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/pybamm/solvers/scipy_solver.py b/pybamm/solvers/scipy_solver.py
index 60e3db9ac5..c1c97882be 100644
--- a/pybamm/solvers/scipy_solver.py
+++ b/pybamm/solvers/scipy_solver.py
@@ -14,13 +14,14 @@ class ScipySolver(pybamm.OdeSolver):
     ----------
     method : str, optional
         The method to use in solve_ivp (default is "BDF")
-    tolerance : float, optional
-        The tolerance for the solver (default is 1e-8). Set as the both reltol and
-        abstol in solve_ivp.
+    rtol : float, optional
+        The relative tolerance for the solver (default is 1e-3).
+    atol : float, optional
+        The relative tolerance for the solver (default is 1e-6).
     """
 
-    def __init__(self, method="BDF", tol=1e-8):
-        super().__init__(method, tol)
+    def __init__(self, method="BDF", rtol=1e-3, atol=1e-6):
+        super().__init__(method, rtol, atol)
 
     def integrate(
         self, derivs, y0, t_eval, events=None, mass_matrix=None, jacobian=None
@@ -52,7 +53,7 @@ def integrate(
             various diagnostic messages.
 
         """
-        extra_options = {"rtol": self.tol, "atol": self.tol}
+        extra_options = {"rtol": self.rtol, "atol": self.atol}
 
         # check for user-supplied Jacobian
         implicit_methods = ["Radau", "BDF", "LSODA"]
@@ -90,12 +91,6 @@ def integrate(
                 termination = "final time"
                 t_event = None
                 y_event = np.array(None)
-            return pybamm.Solution(
-                sol.t,
-                sol.y,
-                t_event,
-                y_event,
-                termination
-            )
+            return pybamm.Solution(sol.t, sol.y, t_event, y_event, termination)
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/results/change_settings/change_solver_tolerances.py b/results/change_settings/change_solver_tolerances.py
new file mode 100644
index 0000000000..81261e796d
--- /dev/null
+++ b/results/change_settings/change_solver_tolerances.py
@@ -0,0 +1,52 @@
+#
+# Compare solution of li-ion battery models when changing solver tolerances
+#
+import numpy as np
+import pybamm
+
+pybamm.set_logging_level("INFO")
+
+# load model
+model = pybamm.lithium_ion.DFN()
+
+
+# process and discretise
+param = model.default_parameter_values
+param.process_model(model)
+geometry = model.default_geometry
+param.process_geometry(geometry)
+mesh = pybamm.Mesh(geometry, model.default_submesh_types, model.default_var_pts)
+disc = pybamm.Discretisation(mesh, model.default_spatial_methods)
+disc.process_model(model)
+
+# tolerances (rtol, atol)
+tols = [[1e-8, 1e-8], [1e-6, 1e-6], [1e-3, 1e-6], [1e-3, 1e-3]]
+
+# solve model
+solutions = [None] * len(tols)
+voltages = [None] * len(tols)
+voltage_rmse = [None] * len(tols)
+labels = [None] * len(tols)
+t_eval = np.linspace(0, 0.17, 100)
+for i, tol in enumerate(tols):
+    solver = pybamm.ScikitsDaeSolver(rtol=tol[0], atol=tol[1])
+    solutions[i] = solver.solve(model, t_eval)
+    voltages[i] = pybamm.ProcessedVariable(
+        model.variables["Terminal voltage [V]"],
+        solutions[i].t,
+        solutions[i].y,
+        mesh=mesh,
+    )(solutions[i].t)
+    voltage_rmse[i] = pybamm.rmse(voltages[0], voltages[i])
+    labels[i] = "rtol = {}, atol = {}".format(tol[0], tol[1])
+
+# print RMSE voltage errors vs tighest tolerance
+for i, tol in enumerate(tols):
+    print(
+        "rtol = {}, atol = {}, solve time = {} s, Voltage RMSE = {}".format(
+            tol[0], tol[1], solutions[i].solve_time, voltage_rmse[i]
+        )
+    )
+# plot
+plot = pybamm.QuickPlot([model] * len(solutions), mesh, solutions, labels=labels)
+plot.dynamic_plot()
diff --git a/results/change_settings/compare_var_pts.py b/results/change_settings/compare_var_pts.py
new file mode 100644
index 0000000000..2153a96f62
--- /dev/null
+++ b/results/change_settings/compare_var_pts.py
@@ -0,0 +1,68 @@
+#
+# Compare solution of li-ion battery models when varying the number of grid points
+#
+import numpy as np
+import pybamm
+import matplotlib.pyplot as plt
+
+pybamm.set_logging_level("INFO")
+
+# choose number of points per domain (all domains will have same npts)
+Npts = [30, 20, 10, 5]
+
+# create models
+models = [None] * len(Npts)
+for i, npts in enumerate(Npts):
+    models[i] = pybamm.lithium_ion.DFN(name="Npts = {}".format(npts))
+
+# load parameter values and process models and geometry
+param = models[0].default_parameter_values
+for model in models:
+    param.process_model(model)
+
+# set mesh
+meshes = [None] * len(models)
+
+# create geometry and discretise models
+var = pybamm.standard_spatial_vars
+for i, model in enumerate(models):
+    geometry = model.default_geometry
+    param.process_geometry(geometry)
+    var_pts = {
+        var.x_n: Npts[i],
+        var.x_s: Npts[i],
+        var.x_p: Npts[i],
+        var.r_n: Npts[i],
+        var.r_p: Npts[i],
+    }
+    meshes[i] = pybamm.Mesh(geometry, models[-1].default_submesh_types, var_pts)
+    disc = pybamm.Discretisation(meshes[i], model.default_spatial_methods)
+    disc.process_model(model)
+
+# solve model and plot voltage
+solutions = [None] * len(models)
+voltages = [None] * len(models)
+voltage_rmse = [None] * len(models)
+t_eval = np.linspace(0, 0.17, 100)
+for i, model in enumerate(models):
+    solutions[i] = model.default_solver.solve(model, t_eval)
+    voltages[i] = pybamm.ProcessedVariable(
+        model.variables["Terminal voltage [V]"],
+        solutions[i].t,
+        solutions[i].y,
+        mesh=meshes[i],
+    )(solutions[i].t)
+    voltage_rmse[i] = pybamm.rmse(voltages[0], voltages[i])
+    plt.plot(solutions[i].t, voltages[i], label=model.name)
+
+for i, npts in enumerate(Npts):
+    print(
+        "npts = {}, solve time = {} s, Voltage RMSE = {}".format(
+            npts, solutions[i].solve_time, voltage_rmse[i]
+        )
+    )
+
+plt.xlabel(r"$t$")
+plt.ylabel("Voltage [V]")
+plt.legend()
+plt.show()
diff --git a/tests/unit/test_processed_variable.py b/tests/unit/test_processed_variable.py
index 2f360180b0..d1933f04fc 100644
--- a/tests/unit/test_processed_variable.py
+++ b/tests/unit/test_processed_variable.py
@@ -383,7 +383,10 @@ def test_processed_variable_ode_pde_solution(self):
         model.rhs = {c: -c}
         model.initial_conditions = {c: 1}
         model.variables = {"c": c}
-        modeltest = tests.StandardModelTest(model)
+        solver = model.default_solver
+        solver.rtol = 1e-8
+        solver.atol = 1e-8
+        modeltest = tests.StandardModelTest(model, solver=solver)
         modeltest.test_all()
         t_sol, y_sol = modeltest.solution.t, modeltest.solution.y
         processed_vars = pybamm.post_process_variables(model.variables, t_sol, y_sol)
@@ -407,7 +410,10 @@ def test_processed_variable_ode_pde_solution(self):
             "c_s": c_s,
             "N_s": pybamm.grad(c_s),
         }
-        modeltest = tests.StandardModelTest(model)
+        solver = model.default_solver
+        solver.rtol = 1e-8
+        solver.atol = 1e-8
+        modeltest = tests.StandardModelTest(model, solver=solver)
         modeltest.test_all()
         # set up testing
         t_sol, y_sol = modeltest.solution.t, modeltest.solution.y
diff --git a/tests/unit/test_solvers/test_base_solver.py b/tests/unit/test_solvers/test_base_solver.py
index 000b01c6bd..9d0075e3ef 100644
--- a/tests/unit/test_solvers/test_base_solver.py
+++ b/tests/unit/test_solvers/test_base_solver.py
@@ -8,11 +8,14 @@
 
 class TestBaseSolver(unittest.TestCase):
     def test_base_solver_init(self):
-        solver = pybamm.BaseSolver(tol=1e-4)
-        self.assertEqual(solver.tol, 1e-4)
-
-        solver.tol = 1e-5
-        self.assertEqual(solver.tol, 1e-5)
+        solver = pybamm.BaseSolver(rtol=1e-2, atol=1e-4)
+        self.assertEqual(solver.rtol, 1e-2)
+        self.assertEqual(solver.atol, 1e-4)
+
+        solver.rtol = 1e-5
+        self.assertEqual(solver.rtol, 1e-5)
+        solver.rtol = 1e-7
+        self.assertEqual(solver.rtol, 1e-7)
 
         with self.assertRaises(NotImplementedError):
             solver.compute_solution(None, None)
diff --git a/tests/unit/test_solvers/test_scikits_solvers.py b/tests/unit/test_solvers/test_scikits_solvers.py
index 597ecf12ec..36b3cb21f8 100644
--- a/tests/unit/test_solvers/test_scikits_solvers.py
+++ b/tests/unit/test_solvers/test_scikits_solvers.py
@@ -13,7 +13,7 @@
 class TestScikitsSolvers(unittest.TestCase):
     def test_ode_integrate(self):
         # Constant
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth(t, y):
             return 0.5 * np.ones_like(y)
@@ -25,7 +25,7 @@ def constant_growth(t, y):
         np.testing.assert_allclose(0.5 * solution.t, solution.y[0])
 
         # Exponential decay
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8)
 
         def exponential_decay(t, y):
             return -0.1 * y
@@ -55,7 +55,7 @@ def sqrt_decay(t, y):
 
     def test_ode_integrate_with_event(self):
         # Constant
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_decay(t, y):
             return -2 * np.ones_like(y)
@@ -75,7 +75,7 @@ def y_equal_0(t, y):
         self.assertEqual(solution.termination, "event")
 
         # Expnonential growth
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8)
 
         def exponential_growth(t, y):
             return y
@@ -101,7 +101,7 @@ def ysq_eq_7(t, y):
 
     def test_ode_integrate_with_jacobian(self):
         # Linear
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8)
 
         def linear_ode(t, y):
             return np.array([0.5, 2 - y[0]])
@@ -134,7 +134,7 @@ def sparse_jacobian(t, y):
         )
         np.testing.assert_allclose(0.5 * solution.t, solution.y[0])
 
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8, linsolver="spgmr")
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8, linsolver="spgmr")
 
         solution = solver.integrate(linear_ode, y0, t_eval, jacobian=jacobian)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -152,7 +152,7 @@ def sparse_jacobian(t, y):
         np.testing.assert_allclose(0.5 * solution.t, solution.y[0])
 
         # Nonlinear exponential grwoth
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8)
 
         def exponential_growth(t, y):
             return np.array([y[0], (1.0 - y[0]) * y[1]])
@@ -182,7 +182,7 @@ def sparse_jacobian(t, y):
             np.exp(1 + solution.t - np.exp(solution.t)), solution.y[1], rtol=1e-4
         )
 
-        solver = pybamm.ScikitsOdeSolver(tol=1e-8, linsolver="spgmr")
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-8, atol=1e-8, linsolver="spgmr")
 
         solution = solver.integrate(exponential_growth, y0, t_eval, jacobian=jacobian)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -202,7 +202,7 @@ def sparse_jacobian(t, y):
 
     def test_dae_integrate(self):
         # Constant
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth_dae(t, y, ydot):
             return [0.5 * np.ones_like(y[0]) - ydot[0], 2 * y[0] - y[1]]
@@ -215,7 +215,7 @@ def constant_growth_dae(t, y, ydot):
         np.testing.assert_allclose(1.0 * solution.t, solution.y[1])
 
         # Exponential decay
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def exponential_decay_dae(t, y, ydot):
             return [-0.1 * y[0] - ydot[0], 2 * y[0] - y[1]]
@@ -228,7 +228,7 @@ def exponential_decay_dae(t, y, ydot):
         self.assertEqual(solution.termination, "final time")
 
     def test_dae_integrate_failure(self):
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth_dae(t, y, ydot):
             return [0.5 * np.ones_like(y[0]) - ydot[0], 2 * y[0] - y[1]]
@@ -240,7 +240,7 @@ def constant_growth_dae(t, y, ydot):
 
     def test_dae_integrate_bad_ics(self):
         # Constant
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth_dae(t, y, ydot):
             return [0.5 * np.ones_like(y[0]) - ydot[0], 2 * y[0] - y[1]]
@@ -265,7 +265,7 @@ def constant_growth_dae_algebraic(t, y):
         np.testing.assert_allclose(1.0 * solution.t, solution.y[1])
 
         # Exponential decay
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def exponential_decay_dae(t, y, ydot):
             return [-0.1 * y[0] - ydot[0], 2 * y[0] - y[1]]
@@ -278,7 +278,7 @@ def exponential_decay_dae(t, y, ydot):
 
     def test_dae_integrate_with_event(self):
         # Constant
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth_dae(t, y, ydot):
             return [0.5 * np.ones_like(y[0]) - ydot[0], 2 * y[0] - y[1]]
@@ -305,7 +305,7 @@ def y1_eq_5(t, y):
         self.assertEqual(solution.termination, "event")
 
         # Exponential decay
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def exponential_decay_dae(t, y, ydot):
             return np.array([-0.1 * y[0] - ydot[0], 2 * y[0] - y[1]])
@@ -334,7 +334,7 @@ def t_eq_0pt5(t, y):
 
     def test_dae_integrate_with_jacobian(self):
         # Constant
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth_dae(t, y, ydot):
             return np.array([0.5 * np.ones_like(y[0]) - ydot[0], 2.0 * y[0] - y[1]])
@@ -354,7 +354,7 @@ def jacobian(t, y):
         np.testing.assert_allclose(1.0 * solution.t, solution.y[1])
 
         # Nonlinear (tests when Jacobian a function of y)
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def nonlinear_dae(t, y, ydot):
             return np.array([0.5 * np.ones_like(y[0]) - ydot[0], 2 * y[0] ** 2 - y[1]])
@@ -375,7 +375,7 @@ def jacobian(t, y):
 
     def test_dae_integrate_with_non_unity_mass(self):
         # Constant
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         def constant_growth_dae(t, y, ydot):
             return np.array([0.5 * np.ones_like(y[0]) - 4 * ydot[0], 2.0 * y[0] - y[1]])
@@ -405,7 +405,7 @@ def test_model_solver_ode(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.ScikitsOdeSolver(tol=1e-9)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -431,7 +431,7 @@ def test_model_solver_ode_events(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.ScikitsOdeSolver(tol=1e-9)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
         t_eval = np.linspace(0, 10, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t))
@@ -474,7 +474,7 @@ def jacobian(t, y):
         model.jacobian = jacobian
 
         # Solve
-        solver = pybamm.ScikitsOdeSolver(tol=1e-9)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -503,7 +503,7 @@ def test_model_solver_dae(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -528,7 +528,7 @@ def test_model_solver_dae_bad_ics(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -552,7 +552,7 @@ def test_model_solver_dae_events(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
         t_eval = np.linspace(0, 5, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_less(solution.y[0], 1.5)
@@ -591,7 +591,7 @@ def jacobian(t, y):
         model.jacobian = jacobian
 
         # Solve
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -608,7 +608,7 @@ def test_solve_ode_model_with_dae_solver(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -624,7 +624,7 @@ def test_model_step_ode(self):
         disc = get_discretisation_for_testing()
         disc.process_model(model)
 
-        solver = pybamm.ScikitsOdeSolver(tol=1e-9)
+        solver = pybamm.ScikitsOdeSolver(rtol=1e-9, atol=1e-9)
 
         # Step once
         dt = 0.1
@@ -656,7 +656,7 @@ def test_model_step_dae(self):
         disc = get_discretisation_for_testing()
         disc.process_model(model)
 
-        solver = pybamm.ScikitsDaeSolver(tol=1e-8)
+        solver = pybamm.ScikitsDaeSolver(rtol=1e-8, atol=1e-8)
 
         # Step once
         dt = 0.1
diff --git a/tests/unit/test_solvers/test_scipy_solver.py b/tests/unit/test_solvers/test_scipy_solver.py
index cadc2d12b7..cef29c65e0 100644
--- a/tests/unit/test_solvers/test_scipy_solver.py
+++ b/tests/unit/test_solvers/test_scipy_solver.py
@@ -11,7 +11,7 @@
 class TestScipySolver(unittest.TestCase):
     def test_integrate(self):
         # Constant
-        solver = pybamm.ScipySolver(tol=1e-8, method="RK45")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="RK45")
 
         def constant_growth(t, y):
             return 0.5 * np.ones_like(y)
@@ -23,7 +23,7 @@ def constant_growth(t, y):
         np.testing.assert_allclose(0.5 * solution.t, solution.y[0])
 
         # Exponential decay
-        solver = pybamm.ScipySolver(tol=1e-8, method="BDF")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="BDF")
 
         def exponential_decay(t, y):
             return -0.1 * y
@@ -43,7 +43,7 @@ def sqrt_decay(t, y):
 
         y0 = np.array([1])
         t_eval = np.linspace(0, 3, 100)
-        solver = pybamm.ScipySolver(tol=1e-8, method="RK45")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="RK45")
         # Expect solver to fail when y goes negative
         with self.assertRaises(pybamm.SolverError):
             solver.integrate(sqrt_decay, y0, t_eval)
@@ -53,7 +53,7 @@ def sqrt_decay(t, y):
 
     def test_integrate_with_event(self):
         # Constant
-        solver = pybamm.ScipySolver(tol=1e-8, method="RK45")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="RK45")
 
         def constant_growth(t, y):
             return 0.5 * np.ones_like(y)
@@ -71,7 +71,7 @@ def y_eq_2(t, y):
         self.assertEqual(solution.termination, "event")
 
         # Exponential decay
-        solver = pybamm.ScipySolver(tol=1e-8, method="BDF")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="BDF")
 
         def exponential_growth(t, y):
             return y
@@ -97,7 +97,7 @@ def t_eq_6(t, y):
 
     def test_ode_integrate_with_jacobian(self):
         # Linear
-        solver = pybamm.ScipySolver(tol=1e-8, method="BDF")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="BDF")
 
         def linear_ode(t, y):
             return np.array([0.5 * np.ones_like(y[0]), 2.0 - y[0]])
@@ -115,7 +115,7 @@ def jacobian(t, y):
         )
 
         # Nonlinear exponential grwoth
-        solver = pybamm.ScipySolver(tol=1e-8, method="BDF")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="BDF")
 
         def exponential_growth(t, y):
             return np.array([y[0], (1.0 - y[0]) * y[1]])
@@ -147,7 +147,7 @@ def test_model_solver(self):
         disc = pybamm.Discretisation(mesh, spatial_methods)
         disc.process_model(model)
         # Solve
-        solver = pybamm.ScipySolver(tol=1e-8, method="RK45")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="RK45")
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -174,7 +174,7 @@ def test_model_solver_with_event(self):
         disc = pybamm.Discretisation(mesh, spatial_methods)
         disc.process_model(model)
         # Solve
-        solver = pybamm.ScipySolver(tol=1e-8, method="RK45")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="RK45")
         t_eval = np.linspace(0, 10, 100)
         solution = solver.solve(model, t_eval)
         self.assertLess(len(solution.t), len(t_eval))
@@ -219,7 +219,7 @@ def jacobian(t, y):
         model.jacobian = jacobian
 
         # Solve
-        solver = pybamm.ScipySolver(tol=1e-9)
+        solver = pybamm.ScipySolver(rtol=1e-9, atol=1e-9)
         t_eval = np.linspace(0, 1, 100)
         solution = solver.solve(model, t_eval)
         np.testing.assert_array_equal(solution.t, t_eval)
@@ -249,7 +249,7 @@ def test_model_step(self):
         disc = pybamm.Discretisation(mesh, spatial_methods)
         disc.process_model(model)
 
-        solver = pybamm.ScipySolver(tol=1e-8, method="RK45")
+        solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8, method="RK45")
 
         # Step once
         dt = 0.1

From 3a0dc1cc50edb147d96443fefbd6fcbf0ce677dc Mon Sep 17 00:00:00 2001
From: Robert Timms <timms@maths.ox.ac.uk>
Date: Thu, 3 Oct 2019 14:14:13 +0100
Subject: [PATCH 2/5] #644 tighter default tols for testing

---
 tests/integration/test_models/standard_model_tests.py |  4 ++++
 tests/unit/test_processed_variable.py                 | 10 ++--------
 2 files changed, 6 insertions(+), 8 deletions(-)

diff --git a/tests/integration/test_models/standard_model_tests.py b/tests/integration/test_models/standard_model_tests.py
index 09fcd23a25..6a37c4f94e 100644
--- a/tests/integration/test_models/standard_model_tests.py
+++ b/tests/integration/test_models/standard_model_tests.py
@@ -71,6 +71,10 @@ def test_solving(self, solver=None, t_eval=None):
         # Overwrite solver if given
         if solver is not None:
             self.solver = solver
+        else:
+            # use tighter default tolerances for testing
+            self.solver.rtol = 1e-8
+            self.solver.atol = 1e-8
         if t_eval is None:
             t_eval = np.linspace(0, 1, 100)
 
diff --git a/tests/unit/test_processed_variable.py b/tests/unit/test_processed_variable.py
index d1933f04fc..2f360180b0 100644
--- a/tests/unit/test_processed_variable.py
+++ b/tests/unit/test_processed_variable.py
@@ -383,10 +383,7 @@ def test_processed_variable_ode_pde_solution(self):
         model.rhs = {c: -c}
         model.initial_conditions = {c: 1}
         model.variables = {"c": c}
-        solver = model.default_solver
-        solver.rtol = 1e-8
-        solver.atol = 1e-8
-        modeltest = tests.StandardModelTest(model, solver=solver)
+        modeltest = tests.StandardModelTest(model)
         modeltest.test_all()
         t_sol, y_sol = modeltest.solution.t, modeltest.solution.y
         processed_vars = pybamm.post_process_variables(model.variables, t_sol, y_sol)
@@ -410,10 +407,7 @@ def test_processed_variable_ode_pde_solution(self):
             "c_s": c_s,
             "N_s": pybamm.grad(c_s),
         }
-        solver = model.default_solver
-        solver.rtol = 1e-8
-        solver.atol = 1e-8
-        modeltest = tests.StandardModelTest(model, solver=solver)
+        modeltest = tests.StandardModelTest(model)
         modeltest.test_all()
         # set up testing
         t_sol, y_sol = modeltest.solution.t, modeltest.solution.y

From 184515d9808bfd7b03c784a4dd8205ca18593650 Mon Sep 17 00:00:00 2001
From: Robert Timms <timms@maths.ox.ac.uk>
Date: Thu, 3 Oct 2019 15:24:02 +0100
Subject: [PATCH 3/5] #644 reduce rtol

---
 .../full_battery_models/lead_acid/base_lead_acid_model.py | 5 +++++
 pybamm/solvers/base_solver.py                             | 4 ++--
 pybamm/solvers/dae_solver.py                              | 4 ++--
 pybamm/solvers/ode_solver.py                              | 4 ++--
 pybamm/solvers/scikits_dae_solver.py                      | 4 ++--
 pybamm/solvers/scikits_ode_solver.py                      | 4 ++--
 pybamm/solvers/scipy_solver.py                            | 4 ++--
 .../test_lead_acid/test_asymptotics_convergence.py        | 8 +++++++-
 8 files changed, 24 insertions(+), 13 deletions(-)

diff --git a/pybamm/models/full_battery_models/lead_acid/base_lead_acid_model.py b/pybamm/models/full_battery_models/lead_acid/base_lead_acid_model.py
index 9f223ae9a3..cf753ddb4e 100644
--- a/pybamm/models/full_battery_models/lead_acid/base_lead_acid_model.py
+++ b/pybamm/models/full_battery_models/lead_acid/base_lead_acid_model.py
@@ -60,6 +60,11 @@ def default_geometry(self):
         elif self.options["dimensionality"] == 2:
             return pybamm.Geometry("2+1D macro")
 
+    @property
+    def default_var_pts(self):
+        var = pybamm.standard_spatial_vars
+        return {var.x_n: 30, var.x_s: 30, var.x_p: 30, var.y: 10, var.z: 10}
+
     def set_standard_output_variables(self):
         super().set_standard_output_variables()
         # Current
diff --git a/pybamm/solvers/base_solver.py b/pybamm/solvers/base_solver.py
index c98fa63e47..c4b59b062a 100644
--- a/pybamm/solvers/base_solver.py
+++ b/pybamm/solvers/base_solver.py
@@ -11,12 +11,12 @@ class BaseSolver(object):
     Parameters
     ----------
     rtol : float, optional
-        The relative tolerance for the solver (default is 1e-3).
+        The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     """
 
-    def __init__(self, method=None, rtol=1e-3, atol=1e-6):
+    def __init__(self, method=None, rtol=1e-6, atol=1e-6):
         self._method = method
         self._rtol = rtol
         self._atol = atol
diff --git a/pybamm/solvers/dae_solver.py b/pybamm/solvers/dae_solver.py
index 0828a819ea..f8970681aa 100644
--- a/pybamm/solvers/dae_solver.py
+++ b/pybamm/solvers/dae_solver.py
@@ -13,7 +13,7 @@ class DaeSolver(pybamm.BaseSolver):
     Parameters
     ----------
     rtol : float, optional
-        The relative tolerance for the solver (default is 1e-3).
+        The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
         The relative tolerance for the solver (default is 1e-6)
     root_method : str, optional
@@ -28,7 +28,7 @@ class DaeSolver(pybamm.BaseSolver):
     def __init__(
         self,
         method=None,
-        rtol=1e-3,
+        rtol=1e-6,
         atol=1e-6,
         root_method="lm",
         root_tol=1e-6,
diff --git a/pybamm/solvers/ode_solver.py b/pybamm/solvers/ode_solver.py
index 54d4c5e946..86e4be2a10 100644
--- a/pybamm/solvers/ode_solver.py
+++ b/pybamm/solvers/ode_solver.py
@@ -11,12 +11,12 @@ class OdeSolver(pybamm.BaseSolver):
     Parameters
     ----------
     rtol : float, optional
-        The relative tolerance for the solver (default is 1e-3).
+        The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     """
 
-    def __init__(self, method=None, rtol=1e-3, atol=1e-6):
+    def __init__(self, method=None, rtol=1e-6, atol=1e-6):
         super().__init__(method, rtol, atol)
 
     def compute_solution(self, model, t_eval):
diff --git a/pybamm/solvers/scikits_dae_solver.py b/pybamm/solvers/scikits_dae_solver.py
index d59e33f69c..b1f1f9cd39 100644
--- a/pybamm/solvers/scikits_dae_solver.py
+++ b/pybamm/solvers/scikits_dae_solver.py
@@ -23,7 +23,7 @@ class ScikitsDaeSolver(pybamm.DaeSolver):
     method : str, optional
         The method to use in solve_ivp (default is "BDF")
     rtol : float, optional
-        The relative tolerance for the solver (default is 1e-3).
+        The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     root_method : str, optional
@@ -38,7 +38,7 @@ class ScikitsDaeSolver(pybamm.DaeSolver):
     def __init__(
         self,
         method="ida",
-        rtol=1e-3,
+        rtol=1e-6,
         atol=1e-6,
         root_method="lm",
         root_tol=1e-6,
diff --git a/pybamm/solvers/scikits_ode_solver.py b/pybamm/solvers/scikits_ode_solver.py
index b0329d59ba..e501cd6cd9 100644
--- a/pybamm/solvers/scikits_ode_solver.py
+++ b/pybamm/solvers/scikits_ode_solver.py
@@ -27,14 +27,14 @@ class ScikitsOdeSolver(pybamm.OdeSolver):
     method : str, optional
         The method to use in solve_ivp (default is "BDF")
     rtol : float, optional
-        The relative tolerance for the solver (default is 1e-3).
+        The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     linsolver : str, optional
             Can be 'dense' (= default), 'lapackdense', 'spgmr', 'spbcgs', 'sptfqmr'
     """
 
-    def __init__(self, method="cvode", rtol=1e-3, atol=1e-6, linsolver="dense"):
+    def __init__(self, method="cvode", rtol=1e-6, atol=1e-6, linsolver="dense"):
         if scikits_odes_spec is None:
             raise ImportError("scikits.odes is not installed")
 
diff --git a/pybamm/solvers/scipy_solver.py b/pybamm/solvers/scipy_solver.py
index c1c97882be..4bd0553c25 100644
--- a/pybamm/solvers/scipy_solver.py
+++ b/pybamm/solvers/scipy_solver.py
@@ -15,12 +15,12 @@ class ScipySolver(pybamm.OdeSolver):
     method : str, optional
         The method to use in solve_ivp (default is "BDF")
     rtol : float, optional
-        The relative tolerance for the solver (default is 1e-3).
+        The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     """
 
-    def __init__(self, method="BDF", rtol=1e-3, atol=1e-6):
+    def __init__(self, method="BDF", rtol=1e-6, atol=1e-6):
         super().__init__(method, rtol, atol)
 
     def integrate(
diff --git a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_asymptotics_convergence.py b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_asymptotics_convergence.py
index 4d2405fac7..f7158abd85 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_asymptotics_convergence.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_asymptotics_convergence.py
@@ -47,13 +47,19 @@ def get_max_error(current):
             param.update_model(leading_order_model, loqs_disc)
             param.update_model(composite_model, comp_disc)
             param.update_model(full_model, full_disc)
-            # Solve, make sure times are the same
+            # Solve, make sure times are the same and use tight tolerances
             t_eval = np.linspace(0, 0.6)
             solver_loqs = leading_order_model.default_solver
+            solver_loqs.rtol = 1e-8
+            solver_loqs.atol = 1e-8
             solution_loqs = solver_loqs.solve(leading_order_model, t_eval)
             solver_comp = composite_model.default_solver
+            solver_comp.rtol = 1e-8
+            solver_comp.atol = 1e-8
             solution_comp = solver_comp.solve(composite_model, t_eval)
             solver_full = full_model.default_solver
+            solver_full.rtol = 1e-8
+            solver_full.atol = 1e-8
             solution_full = solver_full.solve(full_model, t_eval)
 
             # Post-process variables

From 752c72bdae3630f6b1b267994bbbff32f25afe2a Mon Sep 17 00:00:00 2001
From: Robert Timms <timms@maths.ox.ac.uk>
Date: Thu, 3 Oct 2019 16:33:59 +0100
Subject: [PATCH 4/5] #644 tino comments

---
 tests/integration/test_models/standard_model_tests.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/tests/integration/test_models/standard_model_tests.py b/tests/integration/test_models/standard_model_tests.py
index 6a37c4f94e..2b5afa1244 100644
--- a/tests/integration/test_models/standard_model_tests.py
+++ b/tests/integration/test_models/standard_model_tests.py
@@ -71,10 +71,10 @@ def test_solving(self, solver=None, t_eval=None):
         # Overwrite solver if given
         if solver is not None:
             self.solver = solver
-        else:
-            # use tighter default tolerances for testing
-            self.solver.rtol = 1e-8
-            self.solver.atol = 1e-8
+        # Use tighter default tolerances for testing
+        self.solver.rtol = 1e-8
+        self.solver.atol = 1e-8
+
         if t_eval is None:
             t_eval = np.linspace(0, 1, 100)
 

From 3da5c5d5292473dbd971140c56cabf26d3c12866 Mon Sep 17 00:00:00 2001
From: Robert Timms <timms@maths.ox.ac.uk>
Date: Fri, 4 Oct 2019 12:45:46 +0100
Subject: [PATCH 5/5] #644 fix atol docstring

---
 pybamm/solvers/base_solver.py        | 2 +-
 pybamm/solvers/dae_solver.py         | 2 +-
 pybamm/solvers/ode_solver.py         | 2 +-
 pybamm/solvers/scikits_dae_solver.py | 2 +-
 pybamm/solvers/scikits_ode_solver.py | 2 +-
 pybamm/solvers/scipy_solver.py       | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/pybamm/solvers/base_solver.py b/pybamm/solvers/base_solver.py
index c4b59b062a..ad1ad2b4a8 100644
--- a/pybamm/solvers/base_solver.py
+++ b/pybamm/solvers/base_solver.py
@@ -13,7 +13,7 @@ class BaseSolver(object):
     rtol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
-        The relative tolerance for the solver (default is 1e-6).
+        The absolute tolerance for the solver (default is 1e-6).
     """
 
     def __init__(self, method=None, rtol=1e-6, atol=1e-6):
diff --git a/pybamm/solvers/dae_solver.py b/pybamm/solvers/dae_solver.py
index f8970681aa..003403254f 100644
--- a/pybamm/solvers/dae_solver.py
+++ b/pybamm/solvers/dae_solver.py
@@ -15,7 +15,7 @@ class DaeSolver(pybamm.BaseSolver):
     rtol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
-        The relative tolerance for the solver (default is 1e-6)
+        The absolute tolerance for the solver (default is 1e-6).
     root_method : str, optional
         The method to use to find initial conditions (default is "lm")
     root_tol : float, optional
diff --git a/pybamm/solvers/ode_solver.py b/pybamm/solvers/ode_solver.py
index 86e4be2a10..db279b2577 100644
--- a/pybamm/solvers/ode_solver.py
+++ b/pybamm/solvers/ode_solver.py
@@ -13,7 +13,7 @@ class OdeSolver(pybamm.BaseSolver):
     rtol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
-        The relative tolerance for the solver (default is 1e-6).
+        The absolute tolerance for the solver (default is 1e-6).
     """
 
     def __init__(self, method=None, rtol=1e-6, atol=1e-6):
diff --git a/pybamm/solvers/scikits_dae_solver.py b/pybamm/solvers/scikits_dae_solver.py
index b1f1f9cd39..ee99d4602b 100644
--- a/pybamm/solvers/scikits_dae_solver.py
+++ b/pybamm/solvers/scikits_dae_solver.py
@@ -25,7 +25,7 @@ class ScikitsDaeSolver(pybamm.DaeSolver):
     rtol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
-        The relative tolerance for the solver (default is 1e-6).
+        The absolute tolerance for the solver (default is 1e-6).
     root_method : str, optional
         The method to use to find initial conditions (default is "lm")
     root_tol : float, optional
diff --git a/pybamm/solvers/scikits_ode_solver.py b/pybamm/solvers/scikits_ode_solver.py
index e501cd6cd9..542b15d19a 100644
--- a/pybamm/solvers/scikits_ode_solver.py
+++ b/pybamm/solvers/scikits_ode_solver.py
@@ -29,7 +29,7 @@ class ScikitsOdeSolver(pybamm.OdeSolver):
     rtol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
-        The relative tolerance for the solver (default is 1e-6).
+        The absolute tolerance for the solver (default is 1e-6).
     linsolver : str, optional
             Can be 'dense' (= default), 'lapackdense', 'spgmr', 'spbcgs', 'sptfqmr'
     """
diff --git a/pybamm/solvers/scipy_solver.py b/pybamm/solvers/scipy_solver.py
index 4bd0553c25..fd7afbf498 100644
--- a/pybamm/solvers/scipy_solver.py
+++ b/pybamm/solvers/scipy_solver.py
@@ -17,7 +17,7 @@ class ScipySolver(pybamm.OdeSolver):
     rtol : float, optional
         The relative tolerance for the solver (default is 1e-6).
     atol : float, optional
-        The relative tolerance for the solver (default is 1e-6).
+        The absolute tolerance for the solver (default is 1e-6).
     """
 
     def __init__(self, method="BDF", rtol=1e-6, atol=1e-6):