def test_rk4_scalar_newton(self):
num_seg = 4
num_stages = 4
state_options = {'y': {'shape': (1,), 'units': 'm', 'targets': ['y']}}
p = om.Problem(model=om.Group())
ivc = p.model.add_subsystem('ivc', om.IndepVarComp(), promotes_outputs=['*'])
ivc.add_output('initial_states_per_seg:y', shape=(num_seg, 1), units='m')
ivc.add_output('h', shape=(num_seg, 1), units='s')
ivc.add_output('t', shape=(num_seg * num_stages, 1), units='s')
p.model.add_subsystem('k_iter_group',
RungeKuttaKIterGroup(num_segments=num_seg,
method='RK4',
state_options=state_options,
time_units='s',
ode_class=TestODE,
ode_init_kwargs={},
solver_class=om.NewtonSolver,
solver_options={'iprint': 2,
'solve_subsystems': True}))
p.model.connect('t', 'k_iter_group.ode.t')
p.model.connect('h', 'k_iter_group.h')
p.model.connect('initial_states_per_seg:y', 'k_iter_group.initial_states_per_seg:y')
src_idxs = np.arange(16, dtype=int).reshape((num_seg, num_stages, 1))
p.model.connect('k_iter_group.ode.ydot', 'k_iter_group.k_comp.f:y',
src_indices=src_idxs, flat_src_indices=True)
p.setup(check=True, force_alloc_complex=True)
p['t'] = np.array([[0.00, 0.25, 0.25, 0.50,
0.50, 0.75, 0.75, 1.00,
1.00, 1.25, 1.25, 1.50,
1.50, 1.75, 1.75, 2.00]]).T
p['h'] = np.array([[0.5, 0.5, 0.5, 0.5]]).T
p['initial_states_per_seg:y'] = np.array([[0.50000000],
[1.425130208333333],
[2.639602661132812],
[4.006818970044454]])
# Start k with a terrible guess
p['k_iter_group.k_comp.k:y'][...] = 0
p.run_model()
# Test that the residuals of k are zero (we started k at the expected converged value)
outputs = p.model.list_outputs(print_arrays=True, residuals=True, out_stream=False)
op_dict = dict([op for op in outputs])
assert_almost_equal(op_dict['k_iter_group.k_comp.k:y']['resids'], 0.0)
# Test the partials
cpd = p.check_partials(method='cs', out_stream=None)
assert_check_partials(cpd)
def test_rk4_scalar_no_iteration(self):
num_seg = 4
num_stages = 4
state_options = {'y': {'shape': (1,), 'units': 'm', 'targets': ['y']}}
p = om.Problem(model=om.Group())
ivc = p.model.add_subsystem('ivc', om.IndepVarComp(), promotes_outputs=['*'])
ivc.add_output('initial_states_per_seg:y', shape=(num_seg, 1), units='m')
ivc.add_output('h', shape=(num_seg, 1), units='s')
ivc.add_output('t', shape=(num_seg * num_stages, 1), units='s')
p.model.add_subsystem('k_iter_group',
RungeKuttaKIterGroup(num_segments=num_seg,
method='RK4',
state_options=state_options,
time_units='s',
ode_class=TestODE,
ode_init_kwargs={},
solver_class=om.NonlinearRunOnce))
p.model.connect('t', 'k_iter_group.ode.t')
p.model.connect('h', 'k_iter_group.h')
p.model.connect('initial_states_per_seg:y', 'k_iter_group.initial_states_per_seg:y')
src_idxs = np.arange(16, dtype=int).reshape((num_seg, num_stages, 1))
p.model.connect('k_iter_group.ode.ydot', 'k_iter_group.k_comp.f:y',
src_indices=src_idxs, flat_src_indices=True)
p.setup(check=True, force_alloc_complex=True)
p['t'] = np.array([[0.00, 0.25, 0.25, 0.50,
0.50, 0.75, 0.75, 1.00,
1.00, 1.25, 1.25, 1.50,
1.50, 1.75, 1.75, 2.00]]).T
p['h'] = np.array([[0.5, 0.5, 0.5, 0.5]]).T
p['initial_states_per_seg:y'] = np.array([[0.50000000],
[1.425130208333333],
[2.639602661132812],
[4.006818970044454]])
p['k_iter_group.k_comp.k:y'] = np.array([[[0.75000000],
[0.90625000],
[0.94531250],
[1.09765625]],
[[1.087565104166667],
[1.203206380208333],
[1.232116699218750],
[1.328623453776042]],
[[1.319801330566406],
[1.368501663208008],
[1.380676746368408],
[1.385139703750610]],
[[1.378409485022227],
[1.316761856277783],
[1.301349949091673],
[1.154084459568063]]])
p.run_model()
# Test that the residuals of k are zero (we started k at the expected converged value)
outputs = p.model.list_outputs(print_arrays=True, residuals=True, out_stream=False)
op_dict = dict([op for op in outputs])
assert_almost_equal(op_dict['k_iter_group.k_comp.k:y']['resids'], 0.0)
# Test the partials
cpd = p.check_partials(method='cs', out_stream=None)
assert_check_partials(cpd)