Small test for nonlinear_ODE_1 (#361)

* Added test for nonlinear ODE problem class

* End time needed to compute error, not starting time

pySDC/implementations/problem_classes/nonlinear_ODE_1.py

@@ -13,7 +13,7 @@ class nonlinear_ODE_1(ptype):
     given by
 
     .. math::
-        \frac{du(t)}{dt} = \sqrt(1 - u(t))
+        \frac{du(t)}{dt} = \sqrt{1 - u(t)}
 
     with initial condition :math:`u(0) = 0`. The exact solution is
 
@@ -30,6 +30,13 @@ class nonlinear_ODE_1(ptype):
         Tolerance for Newton's method to terminate.
     stop_at_nan : bool, optional
         Indicates that Newton solver has to stop if ``nan`` values arise.
+
+    Attributes
+    ----------
+    newton_itercount : int
+        Counts the Newton iterations.
+    newton_ncalls : int
+        Counts calls of Newton method.
     """
 
     dtype_u = mesh
@@ -42,6 +49,9 @@ def __init__(self, u0=0.0, newton_maxiter=200, newton_tol=5e-11, stop_at_nan=Tru
             'u0', 'newton_maxiter', 'newton_tol', 'stop_at_nan', localVars=locals(), readOnly=True
         )
 
+        self.newton_itercount = 0
+        self.newton_ncalls = 0
+
     def u_exact(self, t):
         r"""
         Routine to compute the exact solution at time :math:`t`.
@@ -125,12 +135,16 @@ def solve_system(self, rhs, dt, u0, t):
             # increase iteration count
             n += 1
 
+            self.newton_itercount += 1
+
         if np.isnan(res) and self.stop_at_nan:
             raise ProblemError('Newton got nan after %i iterations, aborting...' % n)
         elif np.isnan(res):
             self.logger.warning('Newton got nan after %i iterations...' % n)
 
         if n == self.newton_maxiter:
-            raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))
+            self.logger.warning('Newton did not converge after %i iterations, error is %s' % (n, res))
+
+        self.newton_ncalls += 1
 
         return u

pySDC/tests/test_problems/test_nonlinear_ODE_1.py

@@ -0,0 +1,95 @@
+import pytest
+
+
+@pytest.mark.base
+def test_singularity():
+    """
+    Test if the singularity occurs at correct time.
+    """
+
+    import numpy as np
+    from pySDC.implementations.problem_classes.nonlinear_ODE_1 import nonlinear_ODE_1
+
+    problem_params = {
+        'stop_at_nan': False,
+    }
+
+    nonlinear_ODE_class = nonlinear_ODE_1(**problem_params)
+    t_event = 2
+
+    u_event = nonlinear_ODE_class.u_exact(t_event)
+    f = nonlinear_ODE_class.eval_f(u_event, t_event)
+
+    assert f == 0, "Evaluation of right-hand side at singularity does not match with zero!"
+
+    dt = 1e-1
+    t0 = 1.9
+    u0 = nonlinear_ODE_class.u_exact(t0)
+    args = {
+        'rhs': u0,
+        'dt': dt,
+        'u0': u0,
+        't': t0,
+    }
+
+    sol = nonlinear_ODE_class.solve_system(**args)
+    assert abs(sol - 1) < 1e-14, f"Solution is not close enough to the value at singularity! Expected 1, got {sol}"
+    assert (
+        nonlinear_ODE_class.newton_itercount == nonlinear_ODE_class.newton_maxiter
+    ), f"Expected {nonlinear_ODE_class.newton_maxiter} Newton iterations, got {nonlinear_ODE_class.newton_itercount}"
+
+
+@pytest.mark.base
+def test_SDC_on_problem_class():
+    """
+    Test for SDC applied on problem class.
+    """
+
+    import numpy as np
+    from pySDC.implementations.problem_classes.nonlinear_ODE_1 import nonlinear_ODE_1
+    from pySDC.implementations.sweeper_classes.generic_implicit import generic_implicit
+    from pySDC.implementations.controller_classes.controller_nonMPI import controller_nonMPI
+
+    level_params = {
+        'restol': 1e-13,
+        'dt': 1e-3,
+    }
+
+    sweeper_params = {
+        'quad_type': 'LOBATTO',
+        'num_nodes': 3,
+        'QI': 'IE',
+    }
+
+    problem_params = {
+        'stop_at_nan': False,
+    }
+
+    step_params = {
+        'maxiter': 30,
+    }
+
+    controller_params = {
+        'logger_level': 30,
+    }
+
+    description = dict()
+    description['problem_class'] = nonlinear_ODE_1
+    description['problem_params'] = problem_params
+    description['sweeper_class'] = generic_implicit
+    description['sweeper_params'] = sweeper_params
+    description['level_params'] = level_params
+    description['step_params'] = step_params
+
+    controller = controller_nonMPI(num_procs=1, controller_params=controller_params, description=description)
+
+    t0 = 1.999
+    Tend = 2.0
+
+    P = controller.MS[0].levels[0].prob
+    uex = P.u_exact(Tend)
+
+    uend, _ = controller.run(u0=uex, t0=t0, Tend=Tend)
+
+    err = abs(uex - uend)
+    assert err < 1.968e-8, f"Error is too large! Got {err}"