def _run_sdc_with_problem(problem, core, num_time_steps, dt, num_nodes, max_iter, precision):
thresh = ThresholdCheck(max_threshold=max_iter + 1, conditions=('error', 'residual', 'solution reduction', 'error reduction', 'iterations'),
min_threshold=1e-7)
_comm = ForwardSendingMessaging()
_sdc = ParallelSdc(communicator=_comm)
_comm.link_solvers(previous=_comm, next=_comm)
_comm.write_buffer(value=problem.initial_value, time_point=problem.time_start)
_sdc.init(integrator=SdcIntegrator, threshold=thresh, problem=problem, num_time_steps=num_time_steps, num_nodes=num_nodes)
_solution = _sdc.run(core, dt=dt)
# for _node_index in range(0, len(_solution.solution(-1))):
# print("Node {}: {} <-> {}".format(_node_index, _solution.solution(-1)[_node_index].value, problem.exact(_solution.solution(-1)[_node_index].time_point)))
# assert_numpy_array_almost_equal(_solution.solution(-1)[_node_index].value,
# problem.exact(_solution.solution(-1)[_node_index].time_point),
# places=2)
assert_true(len(frozenset(thresh.has_reached()).intersection(frozenset(('error', 'solution reduction', 'error reduction', 'residual')))) > 0,
"Termination criteria should be 'error' or 'residual'.")
assert_not_in('iterations', thresh.has_reached(), "Maximum Number of iterations should not be reached.")
class ThresholdCheckTest(unittest.TestCase):
def setUp(self):
self._default = ThresholdCheck()
def test_has_default_thresholds(self):
self.assertIs(self._default.max_iterations, 10)
self.assertEqual(self._default.min_solution_reduction, 1e-7)
self.assertIsNone(self._default.min_error)
self.assertIsNone(self._default.min_error_reduction)
self.assertIsNone(self._default.min_residual)
self.assertIsNone(self._default.has_reached())
def test_prints_conditions(self):
self.assertRegex(self._default.print_conditions(), "iterations=10")
class MlSdc(IIterativeTimeSolver, IParallelSolver):
"""
See Also
--------
:py:class:`.IIterativeTimeSolver` :
implemented interface
:py:class:`.IParallelSolver` :
mixed-in interface
"""
def __init__(self, **kwargs):
super(MlSdc, self).__init__(**kwargs)
IParallelSolver.__init__(self, **kwargs)
del self._state
del self._integrator
self.threshold = ThresholdCheck(min_threshold=1e-7, max_threshold=10, conditions=("residual", "iterations"))
self.timer = TimerBase()
self._dt = 0.0
self._ml_provider = None
self.__nodes_type = GaussLobattoNodes
self.__weights_type = PolynomialWeightFunction
self.__exact = np.zeros(0)
self.__deltas = None # deltas between nodes as array; for each level (0: coarsest)
self.__time_points = None # time points of nodes as array; for each level
def init(self, problem, **kwargs):
"""Initializes MLSDC solver with given problem, integrator and multi-level provider.
Parameters
----------
ml_provider : :py:class:`.MultiLevelProvider`
*(required)*
handler for the different levels to use
num_nodes : :py:class:`int`
*(otional)*
number of nodes per time step
nodes_type : :py:class:`.INodes`
*(optional)*
Type of integration nodes to be used (class name, **NOT instance**).
weights_type : :py:class:`.IWeightFunction`
*(optional)*
Integration weights function to be used (class name, **NOT instance**).
Raises
------
ValueError :
* if given problem is not an :py:class:`.IInitialValueProblem`
* if number of nodes per time step is not given; neither through ``num_nodes``, ``nodes_type`` nor
``integrator``
* if no :py:class:`.MultiLevelProvider` is given
See Also
--------
:py:meth:`.IIterativeTimeSolver.init`
overridden method (with further parameters)
:py:meth:`.IParallelSolver.init`
mixed in overridden method (with further parameters)
"""
assert_is_instance(problem, IInitialValueProblem, descriptor="Initial Value Problem", checking_obj=self)
assert_named_argument('ml_provider', kwargs, types=MultiTimeLevelProvider,
descriptor='Multi Time Level Provider', checking_obj=self)
self._ml_provider = kwargs['ml_provider']
super(MlSdc, self).init(problem, **kwargs)
# TODO: need to store the exact solution somewhere else
self.__exact = np.zeros(self.ml_provider.integrator(-1).num_nodes, dtype=np.object)
def run(self, core, **kwargs):
"""Applies SDC solver to the initialized problem setup.
Solves the given problem with the explicit SDC algorithm.
Parameters
----------
core : :py:class:`.SdcSolverCore`
core solver stepping method
dt : :py:class:`float`
width of the interval to work on; this is devided into the number of given
time steps this solver has been initialized with
See Also
--------
:py:meth:`.IIterativeTimeSolver.run` : overridden method
"""
super(MlSdc, self).run(core, **kwargs)
assert_named_argument('dt', kwargs, types=float, descriptor="Width of Interval", checking_obj=self)
self._dt = kwargs['dt']
self._print_header()
# start iterations
# TODO: exact solution storage handling
self.__exact[0] = self.problem.initial_value
_has_work = True
_previous_flag = Message.SolverFlag.none
_current_flag = Message.SolverFlag.none
__work_loop_count = 1
while _has_work:
# LOG.debug("Work Loop: %d" % __work_loop_count)
_previous_flag = _current_flag
_current_flag = Message.SolverFlag.none
# receive dedicated message
_msg = self._communicator.receive(tag=(self.ml_provider.num_levels - 1))
if _msg.flag == Message.SolverFlag.failed:
# previous solver failed
# --> pass on the failure and abort
_current_flag = Message.SolverFlag.failed
_has_work = False
# LOG.debug("Previous Solver Failed")
else:
if _msg.flag == Message.SolverFlag.time_adjusted:
# the previous solver has adjusted its interval
# --> we need to recompute our interval
_current_flag = self._adjust_interval_width()
# we don't immediately start the computation of the newly computed interval
# but try to pass the new interval end to the next solver as soon as possible
# (this should avoid throwing away useless computation)
# LOG.debug("Previous Solver Adjusted Time")
else:
if _previous_flag in \
[Message.SolverFlag.none, Message.SolverFlag.converged, Message.SolverFlag.finished,
Message.SolverFlag.time_adjusted]:
# we just started or finished our previous interval
# --> start a new interval
_has_work = self._init_new_interval(_msg.time_point)
if _has_work:
# set initial values
self.state.initial.value = _msg.value.copy()
self.state.initial.solution.time_point = _msg.time_point
self.state.initial.done()
# LOG.debug("New Interval Initialized")
# start logging output
self._print_interval_header()
# start global timing (per interval)
self.timer.start()
else:
# LOG.debug("No New Interval Available")
pass
elif _previous_flag == Message.SolverFlag.iterating:
# LOG.debug("Next Iteration")
pass
else:
# LOG.warn("WARNING!!! Something went wrong here")
pass
if _has_work:
# we are still on the same interval or have just successfully initialized a new interval
# --> do the real computation
# LOG.debug("Starting New Solver Main Loop")
# initialize a new iteration state
self.state.proceed()
if _msg.time_point == self.state.initial.time_point:
if _previous_flag == Message.SolverFlag.iterating:
# LOG.debug("Updating initial value")
# if the previous solver has a new initial value for us, we use it
self.state.current_iteration.initial.value = _msg.value.copy()
_current_flag = self._main_solver_loop()
if _current_flag in \
[Message.SolverFlag.converged, Message.SolverFlag.finished, Message.SolverFlag.failed]:
_log_msgs = {'': OrderedDict()}
if self.state.last_iteration_index <= self.threshold.max_iterations:
_group = 'Converged after %d iteration(s)' % (self.state.last_iteration_index + 1)
_log_msgs[''][_group] = OrderedDict()
_log_msgs[''][_group] = self.threshold.has_reached(log=True)
_log_msgs[''][_group]['Final Residual'] = "{:.3e}"\
.format(supremum_norm(self.state.last_iteration.final_step.solution.residual))
_log_msgs[''][_group]['Solution Reduction'] = "{:.3e}"\
.format(supremum_norm(self.state.solution
.solution_reduction(self.state.last_iteration_index)))
if problem_has_exact_solution(self.problem, self):
_log_msgs[''][_group]['Error Reduction'] = "{:.3e}"\
.format(supremum_norm(self.state.solution
.error_reduction(self.state.last_iteration_index)))
else:
warnings.warn("{}: Did not converged: {:s}".format(self._core.name, self.problem))
_group = "FAILED: After maximum of {:d} iteration(s)"\
.format(self.state.last_iteration_index + 1)
_log_msgs[''][_group] = OrderedDict()
_log_msgs[''][_group]['Final Residual'] = "{:.3e}"\
.format(supremum_norm(self.state.last_iteration.final_step.solution.residual))
_log_msgs[''][_group]['Solution Reduction'] = "{:.3e}"\
.format(supremum_norm(self.state.solution
.solution_reduction(self.state.last_iteration_index)))
if problem_has_exact_solution(self.problem, self):
_log_msgs[''][_group]['Error Reduction'] = "{:.3e}"\
.format(supremum_norm(self.state.solution
.error_reduction(self.state.last_iteration_index)))
LOG.warn(" {} Failed: Maximum number iterations reached without convergence."
.format(self._core.name))
print_logging_message_tree(_log_msgs)
elif _previous_flag in [Message.SolverFlag.converged, Message.SolverFlag.finished]:
# LOG.debug("Solver Finished.")
self.timer.stop()
self._print_footer()
else:
# something went wrong
# --> we failed
# LOG.warn("Solver failed.")
_current_flag = Message.SolverFlag.failed
self._communicator.send(value=self.state.current_iteration.finest_level.final_step.value,
time_point=self.state.current_iteration.finest_level.final_step.time_point,
flag=_current_flag)
__work_loop_count += 1
# end while:has_work is None
# LOG.debug("Solver Main Loop Done")
return [_s.solution for _s in self._states]
@property
def state(self):
"""Read-only accessor for the sovler's state
Returns
-------
state : :py:class:`.ISolverState`
"""
if len(self._states) > 0:
return self._states[-1]
else:
return None
@property
def ml_provider(self):
"""Read-only accessor for the multi level provider
Returns
-------
multi_level_provider : :py:class:`.MultiLevelProvider`
"""
return self._ml_provider
def _main_solver_loop(self):
# initialize iteration timer of same type as global timer
_iter_timer = self.timer.__class__()
# initialize solver states for this iteration
self._init_new_iteration()
self._print_iteration(self.state.current_iteration_index + 1)
# iterate on time steps
_iter_timer.start()
self._level()
_iter_timer.stop()
# check termination criteria
self.threshold.check(self.state)
# log this iteration's summary
if self.state.is_first_iteration:
# on first iteration we do not have comparison values
self._print_iteration_end(None, None, None, _iter_timer.past())
else:
if problem_has_exact_solution(self.problem, self) and not self.state.is_first_iteration:
# we could compute the correct error of our current solution
self._print_iteration_end(self.state.solution.solution_reduction(self.state.current_iteration_index),
self.state.solution.error_reduction(self.state.current_iteration_index),
self.state.current_step.solution.residual,
_iter_timer.past())
else:
self._print_iteration_end(self.state.solution.solution_reduction(self.state.current_iteration_index),
None,
self.state.current_step.solution.residual,
_iter_timer.past())
# finalize this iteration (i.e. TrajectorySolutionData.finalize())
self.state.current_iteration.finalize()
_reason = self.threshold.has_reached()
if _reason is None:
# LOG.debug("solver main loop done: no reason")
return Message.SolverFlag.iterating
elif _reason == ['iterations']:
# LOG.debug("solver main loop done: iterations")
_dim = list(self.problem.spacial_dim)
_dim.insert(0, self.ml_provider.integrator(self.state.last.current_level_index).num_nodes)
LOG.debug("-->\n%s" % (self.state.last.current_level.values.reshape(tuple(_dim)).tolist()))
self.state.finalize()
return Message.SolverFlag.finished
else:
# LOG.debug("solver main loop done: other")
_dim = list(self.problem.spacial_dim)
_dim.insert(0, self.ml_provider.integrator(self.state.last.current_level_index).num_nodes)
LOG.debug("-->\n%s" % (self.state.last.current_level.values.reshape(tuple(_dim)).tolist()))
self.state.finalize()
return Message.SolverFlag.converged
def _init_new_state(self):
"""Initialize a new state for a work task
Usually, this starts a new work task.
The previous state, if applicable, is stored in a stack.
"""
if self.state:
# print("Finished a State")
# finalize the current state
self.state.finalize()
# print("Stating a new state")
# initialize solver state
self._states.append(MlSdcSolverState(num_level=self.ml_provider.num_levels))
def _init_new_interval(self, start):
"""Initializes a new work interval
Parameters
----------
start : :py:class:`float`
start point of new interval
Returns
-------
has_work : :py:class:`bool`
:py:class:`True` if new interval have been initialized;
:py:class:`False` if no new interval have been initialized (i.e. new interval end would exceed end of time
given by problem)
"""
assert_is_instance(start, float, descriptor="Time Point", checking_obj=self)
if start + self._dt > self.problem.time_end:
return False
if self.state and start == self.state.initial.time_point:
return False
self._init_new_state()
# set width of current interval
self.state.initial.solution.time_point = start
self.state.initial.value = self.problem.initial_value.copy()
self.state.delta_interval = self._dt
self.__time_points = np.zeros(self.ml_provider.num_levels, dtype=np.object)
self.__deltas = np.zeros(self.ml_provider.num_levels, dtype=np.object)
# make sure the integrators are all set up correctly for the different levels
for _level in range(0, self.ml_provider.num_levels):
_integrator = self.ml_provider.integrator(_level)
_integrator.transform_interval(self.state.interval)
# print("nodes: %s" % _integrator.nodes)
self.__time_points[_level] = np.zeros(_integrator.num_nodes, dtype=np.float)
self.__deltas[_level] = np.zeros(_integrator.num_nodes, dtype=np.float)
for _node in range(0, _integrator.num_nodes - 1):
self.__time_points[_level] = deepcopy(_integrator.nodes)
self.__deltas[_level][_node + 1] = _integrator.nodes[_node + 1] - _integrator.nodes[_node]
# print("Time Points: %s" % self.__time_points)
return True
def _init_new_iteration(self):
_current_state = self.state.current_iteration
_previous_iteration = self.state.previous_iteration
# set initial values
for _level_index in range(0, self.ml_provider.num_levels):
_current_state.add_finer_level(self.ml_provider.integrator(_level_index).num_nodes - 1)
_level = _current_state.finest_level
assert_condition(len(_level) == self.ml_provider.integrator(_level_index).num_nodes - 1,
RuntimeError, "Number of Steps on Level %d not correct (%d)"
% (len(_level), self.ml_provider.integrator(_level_index).num_nodes - 1),
checking_obj=self)
_level.initial = deepcopy(self.state.initial)
if _previous_iteration is None:
_level.broadcast(_level.initial.value)
for _step_index in range(0, len(_level)):
_level[_step_index].delta_tau = self.__deltas[_level_index][_step_index + 1]
_level[_step_index].solution.time_point = self.__time_points[_level_index][_step_index + 1]
if _previous_iteration is not None:
_level[_step_index].value = _previous_iteration[_level_index][_step_index].value.copy()
assert_condition(len(self.state.current_iteration) == self.ml_provider.num_levels,
RuntimeError, "Number of levels in current state not correct."
" (this shouldn't have happend)",
checking_obj=self)
def _adjust_interval_width(self):
"""Adjust width of time interval
"""
raise NotImplementedError("Time Adaptivity not yet implemented.")
# return Message.SolverFlag.time_adjusted
def _compute_fas_correction(self, q_rhs_fine, fas_fine, q_rhs_coarse, fine_lvl):
# add fas correction of finer level if available
_fine_data = q_rhs_fine + fas_fine if fas_fine is not None else q_rhs_fine
# 1. restringate fine data
_restringated_fine = self.ml_provider.restringate(_fine_data, fine_lvl)
# LOG.debug("R x (Q_fine x F_fine + FAS_fine):\n %s\n = R(%s)\n = R(%s + %s)"
# % (_restringated_fine, _fine_data, q_rhs_fine, fas_fine))
assert_condition(q_rhs_coarse.shape == _restringated_fine.shape,
ValueError,
message='Dimensions of coarse data and restringated fine data do not match: %s != %s'
% (q_rhs_coarse.shape, _restringated_fine.shape),
checking_obj=self)
# 2. compute difference
self.state.current_iteration.current_level.fas_correction = _restringated_fine - q_rhs_coarse
# LOG.debug("FAS Correction:\n %s\n = %s - %s"
# % (self.state.current_iteration.current_level.fas_correction, _restringated_fine, q_rhs_coarse))
def _recompute_rhs_for_level(self, level):
if level.rhs is None:
if not level.initial.rhs_evaluated:
level.initial.rhs = self.problem.evaluate_wrt_time(level.initial.time_point, level.initial.value)
for step in level:
if not step.rhs_evaluated:
step.rhs = self.problem.evaluate_wrt_time(step.time_point, step.value)
def _compute_residual(self, finalize=False):
LOG.debug("Computing Residual")
self._print_step(1, None, self.state.current_level.initial.time_point,
supremum_norm(self.state.current_level.initial.value),
None, None)
_full_integral = 0.0
self._recompute_rhs_for_level(self.state.current_level)
for _step_index in range(0, len(self.state.current_level)):
_step = self.state.current_level[_step_index]
if not _step.integral_available:
_step.integral = \
self.ml_provider \
.integrator(self.state.current_level_index) \
.evaluate(self.state.current_level.rhs, from_node=_step_index, target_node=_step_index + 1)
_full_integral += _step.integral
self._core.compute_residual(self.state, step=_step, integral=_full_integral)
if finalize:
# finalize this step (i.e. StepSolutionData.finalize())
_step.done()
for _step_index in range(0, len(self.state.current_level)):
_step = self.state.current_level[_step_index]
if _step_index > 0:
_previous_time = self.state.current_level[_step_index - 1].time_point
else:
_previous_time = self.state.current_level.initial.time_point
_fas = _step.fas_correction if not self.state.current_iteration.on_finest_level else None
_cc = _step.coarse_correction if not self.state.current_iteration.on_finest_level else None
if problem_has_exact_solution(self.problem, self):
self._print_step(_step_index + 2,
_previous_time,
_step.time_point,
supremum_norm(_step.value),
_step.solution.residual,
_step.solution.error,
_fas,
_cc)
else:
self._print_step(_step_index + 2,
_previous_time,
_step.time_point,
supremum_norm(_step.value),
_step.solution.residual,
None,
_fas,
_cc)
self._print_sweep_end()
if finalize:
LOG.debug("Finalizing Level %d" % self.state.current_iteration.current_level_index)
self.state.current_iteration.current_level.finalize()
def _level(self):
_current_level = self.state.current_iteration.current_level
_finer_level = self.state.current_iteration.finer_level
_coarser_level = self.state.current_iteration.coarser_level
_msg = self.comm.receive(tag=self.state.current_level_index)
if _msg and _msg.time_point == self.state.initial.time_point:
_current_level.initial.definalize()
_current_level.initial.value = _msg.value
_current_level.initial.done()
# LOG.debug("Level %d initial values: %s"
# % (self.state.current_iteration.current_level_index, _current_level.values))
self._print_level_header()
self._recompute_rhs_for_level(_current_level)
# LOG.debug("Level %d RHS values: %s"
# % (self.state.current_iteration.current_level_index, _current_level.rhs))
if not self.state.current_iteration.on_finest_level:
# compute FAS Correction
_q_rhs_coarse = \
np.concatenate(
(np.array([np.zeros(self.problem.dim_for_time_solver, dtype=self.problem.numeric_type)]),
np.array([
self.ml_provider
.integrator(self.state.current_iteration.current_level_index)
.evaluate(_current_level.rhs, target_node=_step_i+1)
for _step_i in range(0, len(_current_level))
], dtype=self.problem.numeric_type)),
axis=0)
self._recompute_rhs_for_level(_finer_level)
_q_rhs_fine = \
np.concatenate(
(np.array([np.zeros(self.problem.dim_for_time_solver, dtype=self.problem.numeric_type)]),
np.array([
self.ml_provider
.integrator(self.state.current_iteration.finer_level_index)
.evaluate(_finer_level.rhs, target_node=_step_i+1)
for _step_i in range(0, len(_finer_level))
], dtype=self.problem.numeric_type)),
axis=0)
self._compute_fas_correction(_q_rhs_fine, _finer_level.fas_correction, _q_rhs_coarse,
fine_lvl=self.state.current_iteration.finer_level_index)
if (not self.state.current_iteration.on_base_level and not self.state.current_iteration.on_finest_level) or \
(self.state.current_iteration.on_finest_level and self.state.is_first_iteration):
# pre-sweep
LOG.debug("pre-sweep")
self._sdc_sweep(copy=self.state.current_iteration.on_finest_level, with_residual=True)
if not self.state.current_iteration.on_base_level:
# restrict
_coarser_level.values = \
self.ml_provider.restringate(_current_level.values,
fine_level=self.state.current_iteration.current_level_index,
coarse_level=self.state.current_iteration.coarser_level_index)
# call next coarser level
self.state.current_iteration.step_down()
# RECURSION HERE!
self._level()
# -> coarser level is done; coming up again
# coarse correction
# TODO: correct RHS evaluations; not values
_prolongated_coarse_correction = \
self.ml_provider.prolongate(_coarser_level.coarse_corrections,
fine_level=self.state.current_iteration.current_level_index,
coarse_level=self.state.current_iteration.coarser_level_index)
# LOG.debug("Apply Coarse Correction\n ==> %s\n = %s + %s"
# % ((_current_level.values + _prolongated_coarse_correction),
# _current_level.values.flatten(), _prolongated_coarse_correction))
_corrected_values = _current_level.values + _prolongated_coarse_correction
for _step_index in range(0, len(_current_level)):
_current_level[_step_index].intermediate.value = _corrected_values[_step_index + 1]
# LOG.debug("Recompute Errors")
for _step_index in range(0, len(_current_level)):
self._core.compute_error(self.state, step_index=_step_index, problem=self.problem)
# post-sweep
LOG.debug("post-sweep with coarse-corrected intermediate")
self._sdc_sweep(use_intermediate=True, copy=False, with_residual=False)
else:
# post-sweep
LOG.debug("post-sweep")
self._sdc_sweep(use_intermediate=False, copy=False, with_residual=False)
if not self.state.current_iteration.on_finest_level:
# compute coarse correction
# LOG.debug("Computing Coarse Correction")
_restringated_values = \
self.ml_provider\
.restringate(_finer_level.values,
self.state.current_iteration.finer_level_index,
self.state.current_iteration.current_level_index)
for _step_index in range(0, len(_current_level)):
_step = _current_level[_step_index]
_step.coarse_correction = _step.value - _restringated_values[_step_index + 1]
# LOG.debug(" %d: %s = %s - %s"
# % (_step_index, _step.coarse_correction, _step.value, _restringated_values[_step_index + 1]))
self._compute_residual(finalize=True)
self.comm.send(tag=self.state.current_level_index,
value=_current_level.final_step.value,
time_point=_current_level.final_step.time_point)
self._print_level_end()
# LOG.debug("Level %d final values:\n%s"
# % (self.state.current_iteration.current_level_index, _current_level.values))
if not self.state.current_iteration.on_finest_level:
# pass on to next finer level
self.state.current_iteration.step_up()
def _sdc_sweep(self, use_intermediate=False, copy=True, with_residual=False):
"""
Parameters
----------
copy : :py:class:`bool`
passed on to :py:meth:`._sdc_step`
with_residual : :py:class:`bool`
whether to compute the residual at the end or not; *note: when the residual is computed, the sweep will be
logged*
"""
LOG.debug("Sweeping on level %d ..." % self.state.current_level_index)
self.state.current_iteration.current_level.reset_to_start()
_integrator = self.ml_provider.integrator(self.state.current_iteration.current_level_index)
_num_nodes = _integrator.num_nodes
# compute integral
self.state.current_iteration.current_level.integral = 0.0
if not self.state.current_iteration.current_level.initial.rhs_evaluated:
self.state.current_iteration.current_level.initial.rhs = \
self.problem.evaluate_wrt_time(self.state.current_iteration.current_level.initial.time_point,
self.state.current_iteration.current_level.initial.value)
_integrate_values = np.array([self.state.current_iteration.current_level.initial.rhs],
dtype=self.problem.numeric_type)
for _step_index in range(0, len(self.state.current_iteration.current_level)):
# TODO: clean up this conditional
if self.state.current_iteration.on_finest_level and self.state.is_first_iteration and not use_intermediate:
# LOG.debug("On First Iteration on Finest Level. Taking breadcasted initial value.")
_integrate_values = \
np.append(_integrate_values,
np.array([self.state.current_iteration.current_level.initial.rhs],
dtype=self.problem.numeric_type),
axis=0)
elif not self.state.current_iteration.on_finest_level:
# LOG.debug("Not on Finest Level. Taking current intermediate value.")
_step = self.state.current_iteration.current_level[_step_index]
if use_intermediate:
if not _step.intermediate.rhs_evaluated:
_step.intermediate.rhs = self.problem.evaluate_wrt_time(_step.time_point,
_step.intermediate.value)
_integrate_values = \
np.append(_integrate_values,
np.array([_step.intermediate.rhs], dtype=self.problem.numeric_type),
axis=0)
else:
if not _step.rhs_evaluated:
_step.rhs = self.problem.evaluate_wrt_time(_step.time_point, _step.value)
_integrate_values = \
np.append(_integrate_values,
np.array([_step.rhs], dtype=self.problem.numeric_type),
axis=0)
elif use_intermediate:
# LOG.debug("On Finest Level. Using intermediate value.")
_step = self.state.current_iteration.current_level[_step_index]
if not _step.intermediate.rhs_evaluated:
_step.intermediate.rhs = self.problem.evaluate_wrt_time(_step.time_point, _step.intermediate.value)
_integrate_values = \
np.append(_integrate_values,
np.array([_step.intermediate.rhs], dtype=self.problem.numeric_type),
axis=0)
else:
# LOG.debug("On Finest Level. Taking previous iteration's value.")
_step = self.state.previous_iteration[self.state.current_iteration.current_level_index][_step_index]
if use_intermediate:
if not _step.intermediate.rhs_evaluated:
_step.intermediate.rhs = self.problem.evaluate_wrt_time(_step.time_point,
_step.intermediate.value)
_integrate_values = \
np.append(_integrate_values,
np.array([_step.intermediate.rhs], dtype=self.problem.numeric_type),
axis=0)
else:
if not _step.rhs_evaluated:
_step.rhs = self.problem.evaluate_wrt_time(_step.time_point, _step.value)
_integrate_values = \
np.append(_integrate_values,
np.array([_step.rhs], dtype=self.problem.numeric_type),
axis=0)
assert_condition(_integrate_values.shape[0] == _num_nodes,
ValueError, message="Number of integration values not correct: %d != %d"
% (_integrate_values.shape[0], _num_nodes),
checking_obj=self)
# LOG.debug("Integration Values: %s" % _integrate_values)
# if use_intermediate:
# LOG.debug("Values Before (intermediate): %s"
# % ([_step.intermediate.value for _step in self.state.current_level]))
# else:
# LOG.debug("Values Before: %s" % self.state.current_iteration.current_level.values)
# do the actual SDC steps of this SDC sweep
for _step_index in range(0, len(self.state.current_iteration.current_level)):
# LOG.debug("Step %d:" % _step_index)
_current_step = self.state.current_iteration.current_level[_step_index]
# if not _current_step.integral_available:
# TODO: fix unneccessary recomputation of integrals
_current_step.integral = _integrator.evaluate(_integrate_values,
from_node=_step_index, target_node=_step_index + 1)
# we successively compute the full integral
# LOG.debug(" Full Integral up to %d: %s = %s + %s"
# % (_step_index + 1, self.state.current_iteration.current_level.integral + _current_step.integral,
# self.state.current_iteration.current_level.integral, _current_step.integral))
self.state.current_iteration.current_level.integral += _current_step.integral
# do the SDC step of this sweep
self._sdc_step(use_intermediate=use_intermediate, copy=copy)
if self.state.current_level.current_step != self.state.current_level.final_step:
self.state.current_level.proceed()
del _integrate_values
# LOG.debug("Values After: %s" % self.state.current_iteration.current_level.values)
if with_residual:
self._compute_residual()
def _sdc_step(self, use_intermediate=False, copy=True):
"""
Parameters
----------
copy : :py:class:`bool`
whether to copy value from previous iteration to this one or just assume the value of the current iteration
have been set before
"""
if copy:
# copy solution of previous iteration to this one
if self.state.is_first_iteration:
if use_intermediate:
# LOG.debug("Coppying Initial Value to step %d intermediate" % self.state.current_step_index)
self.state.current_step.intermediate.value = self.state.current_level.initial.value.copy()
else:
# LOG.debug("Coppying Initial Value to step %d" % self.state.current_step_index)
self.state.current_step.value = self.state.current_level.initial.value.copy()
else:
if use_intermediate:
# LOG.debug("Coppying Previous Iteration's Value to step %d intermediate"
# % self.state.current_step_index)
self.state.current_step.intermediate.value = \
self.state.previous_iteration[self.state.current_level_index][self.state.current_step_index].value.copy()
else:
# LOG.debug("Coppying Previous Iteration's Value to step %d" % self.state.current_step_index)
self.state.current_step.value = \
self.state.previous_iteration[self.state.current_level_index][self.state.current_step_index].value.copy()
# compute step
self._core.run(self.state, problem=self.problem, use_intermediate=use_intermediate)
# calculate error
self._core.compute_error(self.state, problem=self.problem)
# step gets finalized after computation of residual
def print_lines_for_log(self):
_lines = super(MlSdc, self).print_lines_for_log()
return _lines
def _print_interval_header(self):
LOG.info("%s%s" % (VERBOSITY_LVL1, SEPARATOR_LVL3))
LOG.info("{} Interval: [{:.3f}, {:.3f}]"
.format(VERBOSITY_LVL1, self.state.initial.time_point, self.state.initial.time_point + self._dt))
self._print_output_tree_header()
def _print_output_tree_header(self):
LOG.info("%s iter" % VERBOSITY_LVL1)
LOG.info("%s \\" % VERBOSITY_LVL2)
LOG.info("%s |- level nodes" % VERBOSITY_LVL2)
LOG.info("%s | \\" % VERBOSITY_LVL3)
LOG.info("%s | |- step t_0 t_1 phi(t_1) resid err fas coar.corr" % VERBOSITY_LVL3)
LOG.info("%s | \\_" % VERBOSITY_LVL2)
LOG.info("%s \\_ sol r.red err r.red resid time" % VERBOSITY_LVL1)
def _print_iteration(self, _iter):
_iter = self._output_format(_iter, 'int', width=4)
LOG.info("%s %s" % (VERBOSITY_LVL1, _iter))
LOG.info("%s \\" % VERBOSITY_LVL2)
def _print_level_header(self):
_lvl = self._output_format(self.state.current_level_index, 'int', width=2)
_nodes = self._output_format(self.ml_provider.integrator(self.state.current_level_index).num_nodes,
'int', width=2)
LOG.info("%s %s|- %s %s" % (VERBOSITY_LVL2, ('| ' * (self.ml_provider.num_levels - self.state.current_level_index - 1)),
_lvl, _nodes))
LOG.info("%s %s| \\" % (VERBOSITY_LVL3, ('| ' * (self.ml_provider.num_levels - self.state.current_level_index - 1))))
def _print_level_end(self):
LOG.info("%s %s| \\_" % (VERBOSITY_LVL2, ('| ' * (self.ml_provider.num_levels - self.state.current_level_index - 1))))
def _print_iteration_end(self, solred, errred, resid, time):
_solred = self._output_format(solred, 'exp')
_errred = self._output_format(errred, 'exp')
_resid = self._output_format(resid, 'exp')
_time = self._output_format(time, 'float', width=6.3)
LOG.info("%s \\_ %s %s %s %s" % (VERBOSITY_LVL1, _solred, _errred, _resid, _time))
def _print_step(self, step, t0, t1, phi, resid, err, fas=None, cc=None):
_step = self._output_format(step, 'int', width=2)
_t0 = self._output_format(t0, 'float', width=6.3)
_t1 = self._output_format(t1, 'float', width=6.3)
_phi = self._output_format(phi, 'float', width=6.3)
_resid = self._output_format(resid, 'exp')
_err = self._output_format(err, 'exp')
_fas = self._output_format(fas, 'exp') if fas is not None else self._output_format(None, 'str')
_cc = self._output_format(cc, 'exp') if cc is not None else self._output_format(None, 'str')
LOG.info("%s %s|- %s %s %s %s %s %s %s %s"
% (VERBOSITY_LVL3, ('| ' * (self.ml_provider.num_levels - self.state.current_level_index)),
_step, _t0, _t1, _phi, _resid, _err, _fas, _cc))
def _print_sweep_end(self):
LOG.info("%s %s| \\_"
% (VERBOSITY_LVL3, ('| ' * (self.ml_provider.num_levels - self.state.current_level_index))))
def _output_format(self, value, _type, width=None):
def _value_to_numeric(val):
if isinstance(val, np.ndarray):
if val.size > 1 or val.dtype == np.complex:
return supremum_norm(val)
else:
return val[0]
elif isinstance(val, IDiagnosisValue):
if val.value.shape != (1,):
return supremum_norm(val)
else:
return val.value[0]
else:
return val
if _type and width is None:
if _type == 'float':
width = 10.3
elif _type == 'int':
width = 10
elif _type == 'exp':
width = 9.2
else:
width = 10
if value is None:
_outstr = "{: ^{width}s}".format('na', width=int(width))
else:
if _type == 'float':
_outstr = "{: {width}f}".format(_value_to_numeric(value), width=width)
elif _type == 'int':
_outstr = "{: {width}d}".format(_value_to_numeric(value), width=width)
elif _type == 'exp':
_outstr = "{: {width}e}".format(_value_to_numeric(value), width=width)
else:
_outstr = "{: >{width}s}".format(value, width=width)
return _outstr
class ParallelSdc(IIterativeTimeSolver, IParallelSolver):
"""*Spectral Deferred Corrections* method for solving first order ODEs.
The *Spectral Deferred Corrections* (SDC) method is described in [Minion2003]_ (Equation 2.7)
Default Values:
* :py:class:`.ThresholdCheck`
* ``max_threshold``: 10
* ``min_threshold``: 1e-7
* ``conditions``: ``('residual', 'iterations')``
* :py:attr:`.num_time_steps`: 1
* :py:attr:`.num_nodes`: 3
Given the total number of time steps :math:`T_{max}`, number of integration nodes per time
step :math:`N`, current time step :math:`t \\in [0,T_{max})` and the next integration node
to consider :math:`n \\in [0, N)`.
Let :math:`[a,b]` be the total time interval to integrate over.
For :math:`T_{max}=3` and :math:`N=4`, this can be visualized as::
a b
| |
| . . | . . | . . |
t 0 0 0 0 1 1 1 2 2 2
n 0 1 2 3 1 2 3 1 2 3
i 0 1 2 3 4 5 6 7 8 9
In general, the value at :math:`a` (i.e. :math:`t=n=i=0`) is the initial value.
See Also
--------
:py:class:`.IIterativeTimeSolver` :
implemented interface
:py:class:`.IParallelSolver` :
mixed-in interface
"""
def __init__(self, **kwargs):
super(ParallelSdc, self).__init__(**kwargs)
IParallelSolver.__init__(self, **kwargs)
del self._state
self.threshold = ThresholdCheck(min_threshold=1e-7, max_threshold=10, conditions=("residual", "iterations"))
self.timer = TimerBase()
self._num_time_steps = 1
self._dt = 0.0
self._deltas = {"t": 0.0, "n": np.zeros(0)}
self._classic = True
self.__nodes_type = GaussLobattoNodes
self.__weights_type = PolynomialWeightFunction
self.__num_nodes = 3
self.__exact = np.zeros(0)
self.__time_points = {"steps": np.zeros(0), "nodes": np.zeros(0)}
def init(self, problem, integrator, **kwargs):
"""Initializes SDC solver with given problem and integrator.
Parameters
----------
num_time_steps : :py:class:`int`
Number of time steps to be used within the time interval of the problem.
num_nodes : :py:class:`int`
*(otional)*
number of nodes per time step
nodes_type : :py:class:`.INodes`
*(optional)*
Type of integration nodes to be used (class name, **NOT instance**).
weights_type : :py:class:`.IWeightFunction`
*(optional)*
Integration weights function to be used (class name, **NOT instance**).
classic : :py:class:`bool`
*(optional)*
Flag for specifying the type of the SDC sweep.
:py:class:`True`: *(default)* For the classic SDC as known from the literature;
:py:class:`False`: For the modified SDC as developed by Torbjörn Klatt.
Raises
------
ValueError :
* if given problem is not an :py:class:`.IInitialValueProblem`
* if number of nodes per time step is not given; neither through ``num_nodes``, ``nodes_type`` nor
``integrator``
See Also
--------
:py:meth:`.IIterativeTimeSolver.init`
overridden method (with further parameters)
:py:meth:`.IParallelSolver.init`
mixed in overridden method (with further parameters)
"""
assert_is_instance(problem, IInitialValueProblem, descriptor="Initial Value Problem", checking_obj=self)
assert_condition(
issubclass(integrator, IntegratorBase),
ValueError,
message="Integrator must be an IntegratorBase: NOT %s" % integrator.__mro__[-2].__name__,
checking_obj=self,
)
super(ParallelSdc, self).init(problem, integrator=integrator, **kwargs)
if "num_time_steps" in kwargs:
self._num_time_steps = kwargs["num_time_steps"]
if "num_nodes" in kwargs:
self.__num_nodes = kwargs["num_nodes"]
elif "nodes_type" in kwargs and kwargs["nodes_type"].num_nodes is not None:
self.__num_nodes = kwargs["nodes_type"].num_nodes
elif integrator.nodes_type is not None and integrator.nodes_type.num_nodes is not None:
self.__num_nodes = integrator.nodes_type.num_nodes
else:
raise ValueError(func_name(self) + "Number of nodes per time step not given.")
if "notes_type" in kwargs:
self.__nodes_type = kwargs["notes_type"]
if "weights_type" in kwargs:
self.__weights_type = kwargs["weights_type"]
if "classic" in kwargs:
assert_is_instance(kwargs["classic"], bool, descriptor="Classic Flag", checking_obj=self)
self._classic = kwargs["classic"]
# TODO: need to store the exact solution somewhere else
self.__exact = np.zeros(self.num_time_steps * (self.__num_nodes - 1) + 1, dtype=np.object)
def run(self, core, **kwargs):
"""Applies SDC solver to the initialized problem setup.
Solves the given problem with the explicit SDC algorithm.
Parameters
----------
core : :py:class:`.SdcSolverCore`
core solver stepping method
dt : :py:class:`float`
width of the interval to work on; this is devided into the number of given
time steps this solver has been initialized with
See Also
--------
:py:meth:`.IIterativeTimeSolver.run` : overridden method
"""
super(ParallelSdc, self).run(core, **kwargs)
assert_named_argument("dt", kwargs, types=float, descriptor="Width of Interval", checking_obj=self)
self._dt = kwargs["dt"]
self._print_header()
# start iterations
# TODO: exact solution storage handling
self.__exact[0] = self.problem.initial_value
_has_work = True
_previous_flag = Message.SolverFlag.none
_current_flag = Message.SolverFlag.none
__work_loop_count = 1
while _has_work:
LOG.debug("Work Loop: %d" % __work_loop_count)
_previous_flag = _current_flag
_current_flag = Message.SolverFlag.none
# receive dedicated message
_msg = self._communicator.receive()
if _msg.flag == Message.SolverFlag.failed:
# previous solver failed
# --> pass on the failure and abort
_current_flag = Message.SolverFlag.failed
_has_work = False
LOG.debug("Previous Solver Failed")
else:
if _msg.flag == Message.SolverFlag.time_adjusted:
# the previous solver has adjusted its interval
# --> we need to recompute our interval
_current_flag = self._adjust_interval_width()
# we don't immediately start the computation of the newly computed interval
# but try to pass the new interval end to the next solver as soon as possible
# (this should avoid throwing away useless computation)
LOG.debug("Previous Solver Adjusted Time")
else:
if _previous_flag in [
Message.SolverFlag.none,
Message.SolverFlag.converged,
Message.SolverFlag.finished,
Message.SolverFlag.time_adjusted,
]:
# we just started or finished our previous interval
# --> start a new interval
_has_work = self._init_new_interval(_msg.time_point)
if _has_work:
# set initial values
self.state.initial.solution.value = _msg.value.copy()
self.state.initial.solution.time_point = _msg.time_point
self.state.initial.done()
LOG.debug("New Interval Initialized")
# start logging output
self._print_interval_header()
# start global timing (per interval)
self.timer.start()
else:
# pass
LOG.debug("No New Interval Available")
elif _previous_flag == Message.SolverFlag.iterating:
LOG.debug("Next Iteration")
else:
LOG.warn("WARNING!!! Something went wrong here")
if _has_work:
# we are still on the same interval or have just successfully initialized a new interval
# --> do the real computation
LOG.debug("Starting New Solver Main Loop")
# initialize a new iteration state
self.state.proceed()
if _msg.time_point == self.state.initial.time_point:
if _previous_flag == Message.SolverFlag.iterating:
LOG.debug("Updating initial value")
# if the previous solver has a new initial value for us, we use it
self.state.current_iteration.initial.solution.value = _msg.value.copy()
_current_flag = self._main_solver_loop()
if _current_flag in [
Message.SolverFlag.converged,
Message.SolverFlag.finished,
Message.SolverFlag.failed,
]:
_log_msgs = {"": OrderedDict()}
if self.state.last_iteration_index <= self.threshold.max_iterations:
_group = "Converged after %d iteration(s)" % (self.state.last_iteration_index + 1)
_log_msgs[""][_group] = OrderedDict()
_log_msgs[""][_group] = self.threshold.has_reached(log=True)
_log_msgs[""][_group]["Final Residual"] = "{:.3e}".format(
supremum_norm(self.state.last_iteration.final_step.solution.residual)
)
_log_msgs[""][_group]["Solution Reduction"] = "{:.3e}".format(
supremum_norm(
self.state.solution.solution_reduction(self.state.last_iteration_index)
)
)
if problem_has_exact_solution(self.problem, self):
_log_msgs[""][_group]["Error Reduction"] = "{:.3e}".format(
supremum_norm(
self.state.solution.error_reduction(self.state.last_iteration_index)
)
)
else:
warnings.warn("{}: Did not converged: {:s}".format(self._core.name, self.problem))
_group = "FAILED: After maximum of {:d} iteration(s)".format(
self.state.last_iteration_index + 1
)
_log_msgs[""][_group] = OrderedDict()
_log_msgs[""][_group]["Final Residual"] = "{:.3e}".format(
supremum_norm(self.state.last_iteration.final_step.solution.residual)
)
_log_msgs[""][_group]["Solution Reduction"] = "{:.3e}".format(
supremum_norm(
self.state.solution.solution_reduction(self.state.last_iteration_index)
)
)
if problem_has_exact_solution(self.problem, self):
_log_msgs[""][_group]["Error Reduction"] = "{:.3e}".format(
supremum_norm(
self.state.solution.error_reduction(self.state.last_iteration_index)
)
)
LOG.warn(
" {} Failed: Maximum number iterations reached without convergence.".format(
self._core.name
)
)
print_logging_message_tree(_log_msgs)
elif _previous_flag in [Message.SolverFlag.converged, Message.SolverFlag.finished]:
LOG.debug("Solver Finished.")
self.timer.stop()
self._print_footer()
else:
# something went wrong
# --> we failed
LOG.warn("Solver failed.")
_current_flag = Message.SolverFlag.failed
self._communicator.send(
value=self.state.current_iteration.final_step.solution.value,
time_point=self.state.current_iteration.final_step.time_point,
flag=_current_flag,
)
__work_loop_count += 1
# end while:has_work is None
LOG.debug("Solver Main Loop Done")
return [_s.solution for _s in self._states]
@property
def state(self):
"""Read-only accessor for the sovler's state
Returns
-------
state : :py:class:`.ISolverState`
"""
if len(self._states) > 0:
return self._states[-1]
else:
return None
@property
def num_time_steps(self):
"""Accessor for the number of time steps within the interval.
Returns
-------
number_time_steps : :py:class:`int`
Number of time steps within the problem-given time interval.
"""
return self._num_time_steps
@property
def num_nodes(self):
"""Accessor for the number of integration nodes per time step.
Returns
-------
number_of_nodes : :py:class:`int`
Number of integration nodes used within one time step.
"""
return self.__num_nodes
@property
def classic(self):
"""Read-only accessor for the type of SDC
Returns
-------
is_classic : :py:class:`bool`
:py:class:`True` if it's the classic SDC as known from papers;
:py:class:`False` if it's the modified SDC by Torbjörn Klatt
"""
return self._classic
def _init_new_state(self):
"""Initialize a new state for a work task
Usually, this starts a new work task.
The previous state, if applicable, is stored in a stack.
"""
if self.state:
# finalize the current state
self.state.finalize()
# initialize solver state
self._states.append(SdcSolverState(num_nodes=self.num_nodes - 1, num_time_steps=self.num_time_steps))
def _init_new_interval(self, start):
"""Initializes a new work interval
Parameters
----------
start : :py:class:`float`
start point of new interval
Returns
-------
has_work : :py:class:`bool`
:py:class:`True` if new interval have been initialized;
:py:class:`False` if no new interval have been initialized (i.e. new interval end would exceed end of time
given by problem)
"""
assert_is_instance(start, float, descriptor="Time Point", checking_obj=self)
if start + self._dt > self.problem.time_end:
return False
if self.state and start == self.state.initial.time_point:
return False
self._init_new_state()
# set width of current interval
self.state.delta_interval = self._dt
# compute time step and node distances
self._deltas["t"] = self.state.delta_interval / self.num_time_steps # width of a single time step (equidistant)
# start time points of time steps
self.__time_points["steps"] = np.linspace(start, start + self._dt, self.num_time_steps + 1)
# initialize and transform integrator for time step width
self._integrator.init(
self.__nodes_type,
self.__num_nodes,
self.__weights_type,
interval=np.array([self.__time_points["steps"][0], self.__time_points["steps"][1]], dtype=np.float),
)
self.__time_points["nodes"] = np.zeros((self.num_time_steps, self.num_nodes), dtype=np.float)
_deltas_n = np.zeros(self.num_time_steps * (self.num_nodes - 1) + 1)
# copy the node provider so we do not alter the integrator's one
_nodes = deepcopy(self._integrator.nodes_type)
for _t in range(0, self.num_time_steps):
# transform Nodes (copy) onto new time step for retrieving actual integration nodes
_nodes.interval = np.array([self.__time_points["steps"][_t], self.__time_points["steps"][_t + 1]])
self.__time_points["nodes"][_t] = _nodes.nodes.copy()
for _n in range(0, self.num_nodes - 1):
_i = _t * (self.num_nodes - 1) + _n
_deltas_n[_i + 1] = _nodes.nodes[_n + 1] - _nodes.nodes[_n]
self._deltas["n"] = _deltas_n[1:].copy()
return True
def _adjust_interval_width(self):
"""Adjust width of time interval
"""
raise NotImplementedError("Time Adaptivity not yet implemented.")
# return Message.SolverFlag.time_adjusted
def _main_solver_loop(self):
# initialize iteration timer of same type as global timer
_iter_timer = self.timer.__class__()
self._print_iteration(self.state.current_iteration_index + 1)
# iterate on time steps
_iter_timer.start()
for _current_time_step in self.state.current_iteration:
# run this time step
self._time_step()
if self.state.current_time_step_index < len(self.state.current_iteration) - 1:
self.state.current_iteration.proceed()
_iter_timer.stop()
# check termination criteria
self.threshold.check(self.state)
# log this iteration's summary
if self.state.is_first_iteration:
# on first iteration we do not have comparison values
self._print_iteration_end(None, None, None, _iter_timer.past())
else:
if problem_has_exact_solution(self.problem, self) and not self.state.is_first_iteration:
# we could compute the correct error of our current solution
self._print_iteration_end(
self.state.solution.solution_reduction(self.state.current_iteration_index),
self.state.solution.error_reduction(self.state.current_iteration_index),
self.state.current_step.solution.residual,
_iter_timer.past(),
)
else:
self._print_iteration_end(
self.state.solution.solution_reduction(self.state.current_iteration_index),
None,
self.state.current_step.solution.residual,
_iter_timer.past(),
)
# finalize this iteration (i.e. TrajectorySolutionData.finalize())
self.state.current_iteration.finalize()
_reason = self.threshold.has_reached()
if _reason is None:
# LOG.debug("solver main loop done: no reason")
return Message.SolverFlag.iterating
elif _reason == ["iterations"]:
# LOG.debug("solver main loop done: iterations")
self.state.finalize()
return Message.SolverFlag.finished
else:
# LOG.debug("solver main loop done: other")
self.state.finalize()
return Message.SolverFlag.converged
def _time_step(self):
self.state.current_time_step.delta_time_step = self._deltas["t"]
for _step in range(0, len(self.state.current_time_step)):
_node_index = self.state.current_time_step_index * (self.num_nodes - 1) + _step
self.state.current_time_step[_step].delta_tau = self._deltas["n"][_node_index]
self.state.current_time_step[_step].solution.time_point = self.__time_points["nodes"][
self.state.current_time_step_index
][_step + 1]
self._print_time_step(
self.state.current_time_step_index + 1,
self.state.current_time_step.initial.time_point,
self.state.current_time_step.last.time_point,
self.state.current_time_step.delta_time_step,
)
# for classic SDC compute integral
_integral = 0.0
_integrate_values = None
if self.classic:
if not self.state.current_time_step.initial.rhs_evaluated:
self.state.current_time_step.initial.rhs = self.problem.evaluate_wrt_time(
self.state.current_time_step.initial.time_point, self.state.current_time_step.initial.value
)
_integrate_values = np.array([self.state.current_time_step.initial.rhs], dtype=self.problem.numeric_type)
for _step_index in range(0, len(self.state.current_time_step)):
if self.state.is_first_iteration:
_integrate_values = np.append(
_integrate_values,
np.array([self.state.current_time_step.initial.rhs], dtype=self.problem.numeric_type),
axis=0,
)
else:
_step = self.state.previous_iteration[self.state.current_time_step_index][_step_index]
if not _step.rhs_evaluated:
_step.rhs = self.problem.evaluate_wrt_time(_step.time_point, _step.value)
_integrate_values = np.append(
_integrate_values, np.array([_step.rhs], dtype=self.problem.numeric_type), axis=0
)
assert_condition(
_integrate_values.shape[0] == self.num_nodes,
ValueError,
message="Number of integration values not correct: {:d} != {:d}".format(
_integrate_values.shape[0], self.num_nodes
),
checking_obj=self,
)
_full_integral = 0.0
# do the actual SDC steps of this SDC sweep
for _step_index in range(0, len(self.state.current_time_step)):
_current_step = self.state.current_time_step[_step_index]
if self.classic:
_integral = self._integrator.evaluate(
_integrate_values, from_node=_step_index, target_node=_step_index + 1
)
# we successively compute the full integral, which is used for the residual at the end
_full_integral += _integral
_current_step.integral = _integral.copy()
# do the SDC step of this sweep
self._sdc_step()
if self.state.current_step_index < len(self.state.current_time_step) - 1:
self.state.current_time_step.proceed()
del _integrate_values
# compute residual and print step details
for _step_index in range(0, len(self.state.current_time_step)):
_step = self.state.current_time_step[_step_index]
self._core.compute_residual(self.state, step=_step, integral=_full_integral)
# finalize this step (i.e. StepSolutionData.finalize())
_step.done()
if _step_index > 0:
_previous_time = self.state.current_time_step[_step_index - 1].time_point
else:
_previous_time = self.state.current_time_step.initial.time_point
if problem_has_exact_solution(self.problem, self):
self._print_step(
_step_index + 2,
_previous_time,
_step.time_point,
supremum_norm(_step.value),
_step.solution.residual,
_step.solution.error,
)
else:
self._print_step(
_step_index + 2,
_previous_time,
_step.time_point,
supremum_norm(_step.value),
_step.solution.residual,
None,
)
self._print_time_step_end()
# finalizing the current time step (i.e. TrajectorySolutionData.finalize)
self.state.current_time_step.finalize()
def _sdc_step(self):
# helper variables
_current_time_step_index = self.state.current_time_step_index
_current_step_index = self.state.current_step_index
# copy solution of previous iteration to this one
if self.state.is_first_iteration:
self.state.current_step.value = self.state.initial.value.copy()
else:
self.state.current_step.value = self.state.previous_iteration[_current_time_step_index][
_current_step_index
].value.copy()
# TODO: review the custom modification
# if not self.classic:
# # gather values for integration and evaluate problem at given points
# # initial value for this time step
# _integrate_values = \
# np.array(
# [self.problem.evaluate_wrt_time(self.state.current_time_step.initial.time_point,
# self.state.current_time_step.initial.value.copy())
# ], dtype=self.problem.numeric_type)
#
# if _current_step_index > 0:
# # values from this iteration (already calculated)
# _from_current_iteration_range = range(0, _current_step_index)
# for _index in _from_current_iteration_range:
# _integrate_values = \
# np.append(_integrate_values,
# np.array(
# [self.problem.evaluate_wrt_time(self.state.current_time_step[_index].solution.time_point,
# self.state.current_time_step[_index].solution.value.copy())
# ], dtype=self.problem.numeric_type
# ), axis=0)
#
# # values from previous iteration
# _from_previous_iteration_range = range(_current_step_index, self.num_nodes - 1)
# for _index in _from_previous_iteration_range:
# if self.state.is_first_iteration:
# _this_value = self.problem.initial_value
# else:
# _this_value = self.state.previous_iteration[_current_time_step_index][_index].solution.value.copy()
# _integrate_values = \
# np.append(_integrate_values,
# np.array(
# [self.problem.evaluate_wrt_time(self.state.current_time_step[_index].solution.time_point,
# _this_value)
# ], dtype=self.problem.numeric_type
# ), axis=0)
# assert_condition(_integrate_values.shape[0] == self.num_nodes,
# ValueError, message="Number of integration values not correct: {:d} != {:d}"
# .format(_integrate_values.shape[0], self.num_nodes),
# checking_obj=self)
#
# # integrate
# self.state.current_step.integral = self._integrator.evaluate(_integrate_values,
# from_node=_current_step_index,
# target_node=_current_step_index + 1)
# del _integrate_values
# # END if not self.classic
# compute step
self._core.run(self.state, problem=self.problem)
# calculate error
self._core.compute_error(self.state, problem=self.problem)
# step gets finalized after computation of residual
def print_lines_for_log(self):
_lines = super(ParallelSdc, self).print_lines_for_log()
if "Number Nodes per Time Step" not in _lines["Integrator"]:
_lines["Integrator"]["Number Nodes per Time Step"] = "%d" % self.__num_nodes
if "Number Time Steps" not in _lines["Integrator"]:
_lines["Integrator"]["Number Time Steps"] = "%d" % self._num_time_steps
return _lines
def _print_interval_header(self):
LOG.info("%s%s" % (VERBOSITY_LVL1, SEPARATOR_LVL3))
LOG.info(
"{} Interval: [{:.3f}, {:.3f}]".format(
VERBOSITY_LVL1, self.state.initial.time_point, self.state.initial.time_point + self._dt
)
)
self._print_output_tree_header()
def _print_output_tree_header(self):
LOG.info("%s iter" % VERBOSITY_LVL1)
LOG.info("%s \\" % VERBOSITY_LVL2)
LOG.info("%s |- time start end delta" % VERBOSITY_LVL2)
LOG.info("%s | \\" % VERBOSITY_LVL3)
LOG.info("%s | |- step t_0 t_1 phi(t_1) resid err" % VERBOSITY_LVL3)
LOG.info("%s | \\_" % VERBOSITY_LVL2)
LOG.info("%s \\_ sol r.red err r.red resid time" % VERBOSITY_LVL1)
def _print_iteration(self, _iter):
_iter = self._output_format(_iter, "int", width=5)
LOG.info("%s %s" % (VERBOSITY_LVL1, _iter))
LOG.info("%s \\" % VERBOSITY_LVL2)
def _print_iteration_end(self, solred, errred, resid, time):
_solred = self._output_format(solred, "exp")
_errred = self._output_format(errred, "exp")
_resid = self._output_format(resid, "exp")
_time = self._output_format(time, "float", width=6.3)
LOG.info("%s \\_ %s %s %s %s" % (VERBOSITY_LVL1, _solred, _errred, _resid, _time))
def _print_time_step(self, time_step, start, end, delta):
_time_step = self._output_format(time_step, "int", width=3)
_start = self._output_format(start, "float", width=6.3)
_end = self._output_format(end, "float", width=6.3)
_delta = self._output_format(delta, "float", width=6.3)
LOG.info("%s |- %s %s %s %s" % (VERBOSITY_LVL2, _time_step, _start, _end, _delta))
LOG.info("%s | \\" % VERBOSITY_LVL3)
self._print_step(
1,
None,
self.state.current_time_step.initial.time_point,
supremum_norm(self.state.current_time_step.initial.solution.value),
None,
None,
)
def _print_time_step_end(self):
LOG.info("%s | \\_" % VERBOSITY_LVL2)
def _print_step(self, step, t0, t1, phi, resid, err):
_step = self._output_format(step, "int", width=2)
_t0 = self._output_format(t0, "float", width=6.3)
_t1 = self._output_format(t1, "float", width=6.3)
_phi = self._output_format(phi, "float", width=6.3)
_resid = self._output_format(resid, "exp")
_err = self._output_format(err, "exp")
LOG.info(
"%s | |- %s %s %s %s %s %s"
% (VERBOSITY_LVL3, _step, _t0, _t1, _phi, _resid, _err)
)
def _output_format(self, value, _type, width=None):
def _value_to_numeric(val):
if isinstance(val, (np.ndarray, IDiagnosisValue)):
return supremum_norm(val)
else:
return val
if _type and width is None:
if _type == "float":
width = 10.3
elif _type == "int":
width = 10
elif _type == "exp":
width = 9.2
else:
width = 10
if value is None:
_outstr = "{: ^{width}s}".format("na", width=int(width))
else:
if _type == "float":
_outstr = "{: {width}f}".format(_value_to_numeric(value), width=width)
elif _type == "int":
_outstr = "{: {width}d}".format(_value_to_numeric(value), width=width)
elif _type == "exp":
_outstr = "{: {width}e}".format(_value_to_numeric(value), width=width)
else:
_outstr = "{: >{width}s}".format(value, width=width)
return _outstr