def residual(self, iteration):
"""Accessor for the residuals of a specific iteration.
Parameters
----------
iteration : :py:class:`int`
0-based index of the iteration.
``-1`` means last iteration.
Returns
-------
residual : instance of :py:attr:`.Residual`
or :py:class:`None` if no solutions are stored.
Raises
------
ValueError :
If given ``iteration`` index is not in the valid range.
"""
if len(self._data) > 0:
assert_condition(iteration in range(-1, len(self._data)), ValueError,
message="Iteration index not within valid range: {:d} not in [-1, {:d}"
.format(iteration, len(self._data)),
checking_obj=self)
if self._data_type == StepSolutionData:
return np.array(self._data[iteration].residual, dtype=np.object)
else:
return self._data[iteration].residuals
else:
return None
def value(self, value):
assert_condition(not self.finalized, AttributeError,
message="Cannot change this solution data storage any more.", checking_obj=self)
assert_is_instance(value, np.ndarray, descriptor="Values", checking_obj=self)
self._dim = value.shape
self._numeric_type = value.dtype
self._data = value
def write_buffer(self, tag=None, **kwargs):
"""Writes data into this communicator's buffer
Parameters
----------
value :
data values to be send to the next solver
time_point : :py:class:`float`
time point of the data values
flag : :py:class:`.Message.SolverFlag`
message flag
Raises
------
ValueError
* if no arguments are given
* if ``time_point`` is not a :py:class:`float`
"""
assert_condition(len(kwargs) > 0, ValueError, "At least one argument must be given.", self)
if tag not in self._buffer:
self._buffer[tag] = Message()
self.write_buffer(tag=tag, **kwargs)
if "value" in kwargs:
self._buffer[tag].value = deepcopy(kwargs["value"])
if "time_point" in kwargs:
assert_is_instance(kwargs["time_point"], float, descriptor="Time Point", checking_obj=self)
self._buffer[tag].time_point = deepcopy(kwargs["time_point"])
if "flag" in kwargs:
self._buffer[tag].flag = deepcopy(kwargs["flag"])
def evaluate(self, data, **kwargs):
"""Applies this integrator to given data in specified time interval.
Parameters
----------
data : :py:class:`numpy.ndarray`
Data vector of the values at given time points.
Its length must equal the number of integration nodes.
time_start : :py:class:`float`
*(optional)*
Begining of the time interval to integrate over.
time_end : :py:class:`float`
*(optional)*
End of the time interval to integrate over.
Raises
------
ValueError :
* if ``data`` is not a :py:class:`numpy.ndarray`
* if either ``time_start`` or ``time_end`` are not given
* if ``time_start`` is larger or equals ``time_end``
"""
assert_is_instance(data, np.ndarray, descriptor="Data to integrate", checking_obj=self)
assert_condition("time_start" in kwargs or "time_end" in kwargs,
ValueError, message="Either start or end of time interval need to be given.",
checking_obj=self)
assert_condition(kwargs["time_start"] < kwargs["time_end"],
ValueError,
message="Time interval need to be non-zero positive: [{:f}, {:f}]"
.format(kwargs["time_start"], kwargs["time_end"]),
checking_obj=self)
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 finalize(self):
assert_condition(not self.finalized, RuntimeError,
message="This {} is already done.".format(class_name(self)),
checking_obj=self)
self._solution = self.finest_level.solution
self._current_index = 0
self._finalized = True
def values(self, values):
assert_condition(values.shape[0] == (len(self) + 1), ValueError,
"Number of values does not match number of nodes: %d != %d"
% (values.shape[0], (len(self) + 1)),
checking_obj=self)
for _step in range(0, len(self)):
self[_step].value = values[_step + 1].copy()
def __init__(self, **kwargs):
"""
Parameters
----------
solution_class : :py:class:`.ISolution`, :py:class:`.StepSolutionData` or :py:class:`.TrajectorySolutionData`
element_type : :py:class:`.IStepState` or :py:class:`.IStateItertor`
num_states : :py:class:`int`
*(optional)*
Raises
------
ValueError
if ``num_states`` is not a non-zero positive integer
"""
assert_named_argument('solution_class', kwargs, descriptor="Solution Type", checking_obj=self)
assert_named_argument('element_type', kwargs, descriptor="Element Type", checking_obj=self)
self._solution = kwargs['solution_class']()
del kwargs['solution_class']
self._element_type = kwargs['element_type']
del kwargs['element_type']
self._states = []
self._current_index = 0
self._finalized = False
if 'num_states' in kwargs:
_num_states = kwargs['num_states']
assert_condition(isinstance(_num_states, int) and _num_states > 0,
ValueError, message="Number of states must be a non-zero positive integer: NOT {}"
.format(_num_states),
checking_obj=self)
self._states = [self._element_type(**kwargs) for i in range(0, _num_states)]
def construct_space_tensor(self, number_of_points_list, stencil=None):
"""Constructs the Spacetensor which is important for the evaluation in the case of Dirichlet boundary conditions
Parameters
----------
number_of_points_list : :py:class:`int` or :py:class:`numpy.ndarray`
Number of points which will be distributed equiv-spaced on the grid
"""
if isinstance(number_of_points_list, (int, float, complex)):
assert_is_instance(stencil, Stencil, descriptor="Stencil", checking_obj=self)
npoints = int(number_of_points_list)
# LOG.debug("Your number %s was modified to %s" % (number_of_points_list, npoints))
assert_condition(npoints > max(stencil.arr.shape), ValueError,
message="Not enough points for the stencil", checking_obj=self)
npoints = np.asarray([npoints] * len(self.spacial_dim))
elif isinstance(number_of_points_list, np.ndarray):
assert_condition(len(number_of_points_list.shape) == 1 and number_of_points_list.size == len(self.spacial_dim),
ValueError, message="The number_of_points list is wrong", checking_obj=self)
npoints = np.floor(number_of_points_list)
else:
raise ValueError("Wrong number of points list")
# first we assign the memory using numpy
# spt(npoints,dim)
self._act_npoints = npoints
lspc = []
for i in range(len(self.spacial_dim)):
lspc.append(np.linspace(self._geometry[i, 0], self._geometry[i, 1], npoints[i]))
if len(self.spacial_dim) > 1:
space_tensor = np.asarray(np.meshgrid(*lspc))
else:
space_tensor = np.linspace(self._geometry[0, 0], self._geometry[0, 1], npoints)
return space_tensor
def _add_iteration(self):
assert_condition(self.num_level > 0,
ValueError,
message="Number of number of levels and nodes per level must be larger 0: NOT {}"
.format(self.num_level),
checking_obj=self)
self._states.append(self._element_type(num_level=self.num_level))
def fas_correction(self, fas_correction):
assert_condition(fas_correction.shape[0] == (len(self) + 1), ValueError,
"Number of FAS Corrections does not match number of nodes: %d != %d"
% (fas_correction.shape[0], (len(self) + 1)),
checking_obj=self)
for _step in range(0, len(self)):
self[_step].fas_correction = fas_correction[_step + 1] - fas_correction[_step]
def coarse_corrections(self, coarse_correction):
assert_condition(coarse_correction.shape[0] == (len(self) + 1), ValueError,
"Number of Coarse Corrections does not match number of nodes: %d != %d"
% (coarse_correction.shape[0], (len(self) + 1)),
checking_obj=self)
for _step in range(0, len(self)):
self[_step].coarse_correction = coarse_correction[_step + 1]
def _add_iteration(self):
assert_condition(self.num_time_steps > 0 and self.num_nodes > 0,
ValueError, message="Number of time steps and nodes per time step must be larger 0: NOT {}, {}"
.format(self.num_time_steps, self.num_nodes),
checking_obj=self)
self._states.append(self._element_type(num_states=self.num_nodes,
num_time_steps=self.num_time_steps))
def add_coefficient(self, coefficient, power):
"""Adds or sets the coefficient :math:`c` of :math:`cx^p` for a specific :math:`p`.
The polynomial gets automatically extended to hold the new coefficient in case it didn't included the specified
power previously.
Unset, but skipped powers have a coefficient of zero by default.
Parameters
----------
coefficient : :py:class:`float`
Coefficient :math:`c` of :math:`cx^p`.
power : :py:class:`int`
Power :math:`p` of :math:`cx^p`.
Examples
--------
>>> polyWeights = PolynomialWeightFunction()
>>> # To set the coefficient of x^3 to 3.14 use:
>>> polyWeights.add_coefficient(3.14, 3)
>>> # Similar, to set the constant coefficient 42, e.i. 42*x^0, use:
>>> polyWeights.add_coefficient(42, 0)
"""
assert_is_instance(power, int, descriptor="Power", checking_obj=self)
assert_condition(power >= 0, ValueError,
message="Power must be zero or positive: {:d}".format(power), checking_obj=self)
if self._coefficients.size <= power + 1:
self._coefficients = np.resize(self._coefficients, (power + 1))
self._coefficients[power] = coefficient
def solution(self, iteration):
"""Accessor for the solution of a specific iteration.
Parameters
----------
iteration : :py:class:`int`
0-based index of the iteration.
``-1`` means last iteration.
Returns
-------
solution : instance of :py:attr:`.data_storage_type`
or :py:class:`None` if no solutions are stored.
Raises
------
ValueError :
If given ``iteration`` index is not in the valid range.
"""
if len(self._data) > 0:
assert_condition(iteration in range(-1, len(self._data)), ValueError,
message="Iteration index not within valid range: {:d} not in [-1, {:d}"
.format(iteration, len(self._data)),
checking_obj=self)
return self._data[iteration]
else:
return None
def time_interval(self, value):
assert_is_instance(value, np.ndarray, descriptor="Time Interval", checking_obj=self)
assert_condition(value.size == 2, ValueError,
message="Time Interval must have two values: NOT %d" % value.size)
self.validate_time_interval(start=value[0], end=value[1])
self.time_start = value[0]
self.time_end = value[1]
def link_solvers(self, *args, **kwargs):
"""Links the given communicators with this communicator
Parameters
----------
previous : :py:class:`.ForwardSendingMessaging`
communicator of the previous solver
next : :py:class:`.ForwardSendingMessaging`
communicator of the next solver
Raises
------
ValueError
if one of the two communicators of the specified type is not given
"""
super(ForwardSendingMessaging, self).link_solvers(*args, **kwargs)
assert_condition(len(kwargs) == 2,
ValueError, message="Exactly two communicators must be given: NOT %d" % len(kwargs),
checking_obj=self)
assert_named_argument('previous', kwargs, types=ForwardSendingMessaging, descriptor="Previous Communicator",
checking_obj=self)
self._previous = kwargs['previous']
assert_named_argument('next', kwargs, types=ForwardSendingMessaging, descriptor="Next Communicator",
checking_obj=self)
self._next = kwargs['next']
def __init__(self, fine_level, coarse_level, rst_stencil, ipl_stencil):
assert_is_instance(fine_level, MultigridLevel1D, "Not an MultigridLevel1D")
assert_is_instance(coarse_level, MultigridLevel1D, "Not an MultigridLevel1D")
self.fl = fine_level
self.cl = coarse_level
assert_is_instance(ipl_stencil, InterpolationByStencilListIn1D)
assert_is_instance(rst_stencil, RestrictionStencilPure)
assert_condition(rst_stencil.ndim == 1,
ValueError, "Restriction Stencil"
+ "has not the dimension 1")
self.ipl = ipl_stencil
self.rst = rst_stencil
self.ipl_fine_views = []
self.ipl_coarse_views = []
# collect the views which are needed,
if self.ipl.mode == "own":
self.ipl_fine_views.append(self.fl.evaluable_view(
self.ipl.stencil_list[0]))
self.ipl_coarse_views(self.cl.mid)
elif self.ipl.mode == "list":
for stencil in self.ipl.stencil_list:
self.ipl_fine_views.append(self.fl.evaluable_view(stencil))
self.ipl_coarse_views.append(self.cl.mid)
else:
raise NotImplementedError("What do you have in mind?")
self.rst_fine_view = self.fl.evaluable_view(self.rst)
self.rst_coarse_view = self.cl.mid
def __eq__(self, other):
assert_condition(isinstance(other, self.__class__), TypeError,
message="Can not compare {} with {}".format(self.__class__, class_name(other)),
checking_obj=self)
return (
self.numeric_type == other.numeric_type
and np.array_equal(self.value, other.value)
)
def used_iterations(self, used_iterations):
assert_condition(not self.finalized, ValueError,
message="Solution cannot be changed any more.", checking_obj=self)
assert_condition(used_iterations > 0, ValueError,
message="Number of used iterations must be non-zero positive: NOT {:d}"
.format(used_iterations),
checking_obj=self)
self._used_iterations = used_iterations
def validate_time_interval(self, start=None, end=None):
if start is None:
start = self.time_start
if end is None:
end = self.time_end
assert_condition(start < end, ValueError,
message="Start Time must be smaller than End Time: NOT %s >= %s" % (start, end),
checking_obj=self)
return True
def add_solution_data(self, *args, **kwargs):
"""Appends solution of a new time point to the trajectory.
Parameters
----------
step_data : :py:class:`.StepSolutionData`
*(optional)*
In case a single unnamed argument is given, this is required to be an instance of
:py:class:`.StepSolutionData`.
If no named argument is given, the following two parameters are *not* optional.
values : :py:class:`numpy.ndarray`
*(optional)*
Solution values.
Passed on to constructor of :py:class:`.StepSolutionData`.
time_point : :py:class:`float`
*(optional)*
Time point of the solution.
Passed on to constructor of :py:class:`.StepSolutionData`.
Raises
------
ValueError
* if construction of :py:class:`.StepSolutionData` fails
* if internal consistency check fails (see :py:meth:`._check_consistency`)
"""
assert_condition(
not self.finalized,
AttributeError,
message="Cannot change this solution data storage any more.",
checking_obj=self,
)
_old_data = self._data # backup for potential rollback
if len(args) == 1 and isinstance(args[0], StepSolutionData):
assert_condition(
args[0].time_point is not None, ValueError, message="Time point must not be None.", checking_obj=self
)
self._data = np.append(self._data, np.array([args[0]], dtype=np.object))
else:
self._data = np.append(self._data, np.array([StepSolutionData(*args, **kwargs)], dtype=np.object))
try:
self._check_consistency()
except ValueError as err:
# consistency check failed, thus removing recently added solution data storage
warnings.warn("Consistency Check failed with:\n\t\t{}\n\tNot adding this solution.".format(*err.args))
self._data = _old_data.copy() # rollback
raise err
finally:
# everything ok
pass
if self._data.size == 1:
self._dim = self._data[-1].dim
self._numeric_type = self._data[-1].numeric_type
def initial_value(self, initial_value):
assert_is_instance(initial_value, np.ndarray, descriptor="Initial Value", checking_obj=self)
assert_condition(
initial_value.shape == self.dim_for_time_solver,
ValueError,
message="Initial Values shape must match problem DOFs: %s != %s"
% (initial_value.shape, self.dim_for_time_solver),
checking_obj=self,
)
self._initial_value = initial_value
def __contains__(self, item):
assert_condition(
isinstance(item, StepSolutionData),
TypeError,
message="Item must be a StepSolutionData: NOT {}".format(class_name(item)),
checking_obj=self,
)
for elem in self._data:
if elem == item:
return True
return False
def finalize(self):
"""Locks this storage data instance.
Raises
------
ValueError :
If it has already been locked.
"""
assert_condition(not self.finalized, AttributeError,
message="This solution data storage is already finalized.", checking_obj=self)
self._finalized = True
def __init__(self, *args, **kwargs):
super(self.__class__, self).__init__(*args, **kwargs)
assert_condition(kwargs['num_fine_points'] % 2 != 0, ValueError,
message="Number of fine level points needs to be odd: %d" % kwargs['num_fine_points'],
checking_obj=self)
self._n_coarse_points = int((self.num_fine_points + 1) / 2)
self.restringation_operator = np.zeros([self.num_coarse_points, self.num_fine_points])
self.prolongation_operator = np.zeros([self.num_fine_points, self.num_coarse_points])
self._construct_transform_matrices()
LOG.debug("Restringation operator: {}".format(self.restringation_operator))
LOG.debug("Prolongation operator: {}".format(self.prolongation_operator))
def finalize(self):
"""Finalizes the whole solver state.
This copies the :py:class:`.TrajectorySolutionData` objects from the :py:class:`.IIterationState` instances of
this sequence to the main :py:class:`.IterativeSolution` object and finalizes it.
"""
assert_condition(not self.finalized, RuntimeError,
message="This {} is already done.".format(class_name(self)),
checking_obj=self)
for _iter in self:
self.solution.add_solution(_iter.solution)
# self.solution.finalize()
self._current_index = 0
def embed(self, ue):
"""
Summary
_______
checks if u fits then embeds it
Parameters
----------
ue : ndarray
numpy array to embed
"""
assert_condition(ue.size == self._mid_points, ValueError,
"Array to embed has the wrong size")
self[self.borders[0]:-self.borders[1]] = ue
def embed(self, ue):
"""
Summary
_______
checks if u fits then embeds it
Parameters
----------
ue : ndarray
numpy array to embed
"""
assert_condition(ue.shape == self.mid.shape, ValueError,
"Array to embed has the wrong size")
self.mid = ue
def _check_consistency(self):
"""Check consistency of stored solution data objects.
Raises
------
ValueError :
If the time points of at least two solution data storage objects differ.
"""
if len(self._data) > 0:
_time_points = self._data[0].time_points
for iteration in range(1, len(self._data)):
assert_condition(np.array_equal(_time_points, self._data[iteration].time_points), ValueError,
message="Time points of one or more stored solution data objects do not match.",
checking_obj=self)