def problem_has_exact_solution(problem, checking_obj=None):
"""Convenience accessor for exact solution.
Parameters
----------
problem : :py:class:`.IProblem`
The problem to check for an exact solution function.
checking_obj : object
*(optional)*
The object calling this function for a meaningful error message.
For debugging purposes only.
Returns
-------
has_exact_solution : :py:class:`bool`
:py:class:`True` if exact solution was given, :py:class:`False` otherwise
Raises
------
ValueError :
If the given problem is not an instance of :py:class:`.IProblem`.
"""
assert_is_instance(
problem, IProblem, message="It needs to be a problem to have an exact solution.", checking_obj=checking_obj
)
return isinstance(problem, HasExactSolutionMixin)
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 __init__(self, restriction_stencil, decrease_in_points=None, center=None):
assert_is_instance(restriction_stencil, np.ndarray, "Not an ndarray")
self.rst_stencil = Stencil(restriction_stencil, center)
if decrease_in_points is None:
self.dip = np.asarray(self.rst_stencil.shape) - 1
elif isinstance(decrease_in_points, np.ndarray) and \
decrease_in_points.ndim == restriction_stencil.ndim:
self.dip = decrease_in_points
elif isinstance(decrease_in_points, int):
self.dip = np.asarray([decrease_in_points]*restriction_stencil.ndim)
else:
raise ValueError("Wrong decrease in points")
self.dim = restriction_stencil.ndim
if self.dim == 1:
self.eval = self.evalA_1D
elif self.dim == 2:
self.eval = self.evalA_2D
elif self.dim == 3:
self.eval = self.evalA_3D
else:
raise NotImplementedError("More than 3 dimensions " +
"are not implemented")
def __init__(self, *args, **kwargs):
"""
Parameters
----------
exact_function : :py:class:`callable`
*(optional)*
If given initializes the problem with the exact solution function.
"""
assert_is_instance(
self,
IProblem,
descriptor="Problem needs to be a IProblem first: NOT %s" % class_name(self),
checking_obj=self,
)
self._exact_function = None
if "exact_function" in kwargs:
self.exact_function = kwargs["exact_function"]
self._strings["exact"] = None
if "strings" in kwargs:
if "exact" in kwargs["strings"]:
assert_is_instance(
kwargs["strings"]["exact"],
str,
descriptor="String representation of Exact Function",
checking_obj=self,
)
self._strings["exact"] = kwargs["strings"]["exact"]
def add_level_transition(self, transitioner, coarse_level, fine_level):
"""Adds specialized level transitioner for specified levels.
Parameters
----------
transitioner : :py:class:`.ILevelTransitionProvider`
Special level transitioner for specified prolongation and restringation between given coarse and fine level.
coarse_level : :py:class:`int`
Coarse level of the transitioner.
fine_level : :py:class:`int`
Fine level of the transitioner.
Raises
------
ValueError
if ``transitioner`` is not an :py:class:`.ILevelTransitionProvider`
"""
assert_is_instance(transitioner, ILevelTransitionProvider, descriptor="Level Transitioner", checking_obj=self)
# extend/initialize level_transition_provider map if necessary
if coarse_level not in self._level_transitioners:
self._level_transitioners[coarse_level] = {}
self._level_transitioners[coarse_level][fine_level] = transitioner
def __init__(self, *args, **kwargs):
super(HeatEquation, self).__init__(*args, **kwargs)
# HasExactSolutionMixin.__init__(self, *args, **kwargs)
self._thermal_diffusivity = kwargs.get('thermal_diffusivity', 1.0)
if self.time_start is None:
self.time_start = 0.0
if self.time_end is None:
self.time_end = 1.0
if self.initial_value is None:
self.initial_value = np.zeros(self.dim_for_time_solver)
if isinstance(self.thermal_diffusivity, complex):
self.numeric_type = np.complex
self._mg_stencil = kwargs.get('mg_stencil')
self._mg_level = kwargs.get('mg_level')
self._direct_solvers = {}
if kwargs.get('delta_times_for_time_levels') is not None and self._mg_level is not None:
assert_is_instance(kwargs['delta_times_for_time_levels'], (list, np.ndarray),
descriptor="Delta Times for Time Levels", checking_obj=self)
for time_level in kwargs['delta_times_for_time_levels']:
assert_is_instance(kwargs['delta_times_for_time_levels'][time_level], (list, np.ndarray),
descriptor="Delta Times for Time Level %d" % time_level, checking_obj=self)
for delta_time in kwargs['delta_times_for_time_levels'][time_level]:
self.initialize_direct_space_solver(time_level, delta_time, kwargs['mg_level'])
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 __init__(self, stencil_list, center=None, *args, **kwargs):
"""init
"""
# in the case of just one stencil
if isinstance(stencil_list, np.ndarray) and stencil_list.ndim == 1:
self.mode = "own"
self.increase_of_points = 2
self.stencil_list = []
self.stencil_list.append(stencil_list)
self.center = []
if center is None:
self.center.append(np.floor(np.asarray(self.stencil[0].shape)*0.5))
elif isinstance(center, int) and center < self.stencil[0].size:
self.center.append(center)
else:
raise ValueError("Wrong argument")
# now the case of a stencil set
elif isinstance(stencil_list, list):
# check if each one is a nd.array
for stencil in stencil_list:
assert_is_instance(stencil, Stencil,
"not real stencil", self)
# each stencil
self.mode = "list"
self.stencil_list = stencil_list
self.increase_of_points = len(stencil_list)
if self.mode == "own":
self.eval = self.eval_own
elif self.mode == "list":
self.eval = self.eval_list
else:
raise RuntimeError("Something went terribly wrong")
super().__init__(*args, **kwargs)
def problem_has_direct_implicit(problem, checking_obj=None):
"""Convenience checker for existence of a direct implicit formulation of a problem.
Parameters
----------
problem : :py:class:`.IProblem`
The problem to check for a direct implicit formulation.
checking_obj : :py:class:`object`
*(optional)*
The object calling this function for a meaningful error message.
For debugging purposes only.
Returns
-------
has_direct_impl : :py:class:`bool`
:py:class:`True` if exact solution was given, :py:class:`False` otherwise
Raises
------
ValueError :
If the given problem is not an instance of :py:class:`.IProblem`.
"""
assert_is_instance(problem, IProblem,
message="It needs to be a problem to have a direct implicit formula.", checking_obj=checking_obj)
return isinstance(problem, HasDirectImplicitMixin)
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 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 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 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 find_root(fun, x0, method="hybr"):
"""Wrapper around SciPy's generic root finding algorithm to support complex numbers.
SciPy's generic root finding algorithm (``scipy.optimize.root``) is not able to deal with functions returning
and/or accepting arrays with complex numbers.
This wrapped call will first convert all arrays of complex numbers into arrays of floats while splitting each
complex number up into two floats.
Parameters
----------
fun : :py:class:`callable`
Complex function to find the root of
x0 : :py:class:`numpy.ndarray`
Initial guess.
method : :py:class:`str`
Root finding method to be used.
See ``scipy.optimize.root`` for details.
Returns
-------
Same solution object as ``scipy.optimize.root`` but with ``x`` being converted back including complex numbers.
Examples
--------
from pypint.plugins.implicit_solvers.find_root import find_root
import numpy
fun = lambda x: (-1.0 + 1.0j) * x
sol = find_root(fun, numpy.array([0.0]))
"""
assert_is_instance(x0, np.ndarray, descriptor="Initial Guess")
assert_is_callable(fun, descriptor="Function to find root of")
assert_is_instance(method, str, descriptor="Root finding method")
_value_map = {}
_transformed_size = 0
_transform_necessary = False
for i in range(0, x0.size):
if isinstance(x0[i], complex):
_value_map[i] = [_transformed_size, _transformed_size + 1]
_transformed_size += 2
_transform_necessary = True
else:
_value_map[i] = [_transformed_size]
_transformed_size += 1
if _transform_necessary:
_wrapped_func = \
lambda x_next: _transform_to_real(fun(_transform_to_complex(x_next, _value_map)),
_value_map, _transformed_size)
sol = root(fun=_wrapped_func, x0=_transform_to_real(x0, _value_map, _transformed_size), method=method)
else:
sol = root(fun=fun, x0=x0, method=method)
if sol.success and _transform_necessary:
sol.x = _transform_to_complex(sol.x, _value_map)
return sol
def implicit_solve(self, next_x, func, method="unused", **kwargs):
"""A solver for the implicit equations.
"""
assert_is_instance(next_x, np.ndarray, descriptor="Initial Guess", checking_obj=self)
assert_is_callable(func, descriptor="Function of RHS for Implicit Solver", checking_obj=self)
sol = scop.newton_krylov(func, next_x.reshape(-1))
assert_is_instance(sol, np.ndarray, descriptor="Solution", checking_obj=self)
return sol.reshape(self.dim_for_time_solver)
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 run(self, state, **kwargs):
"""Apply the solver core to the current state
Parameters
----------
state : :py:class:`.ISolverState`
Current state of the solver.
"""
assert_is_instance(state, ISolverState, descriptor="Solver's State", checking_obj=self)
def compute_error(self, state, **kwargs):
"""Computes the error of the current state
Parameters
----------
state : :py:class:`.ISolverState`
Current state of the solver.
"""
assert_is_instance(state, ISolverState, descriptor="Solver's State", checking_obj=self)
def __lt__(self, other):
assert_is_instance(other, StepSolutionData,
message="Can not compare StepSolutionData with {}".format(class_name(other)),
checking_obj=self)
return (
self.dim == other.dim
and self.numeric_type == other.numeric_type
and self.time_point < other.time_point
)
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 __init__(self, *args, **kwargs):
self._n = kwargs.get('n')
self._m = 2*self._n + 1
kwargs.update({"dim": (self._m, self._m, 1)})
super(AvilesGiga, self).__init__(*args, **kwargs)
# HasDirectImplicitMixin.__init__(self, *args, **kwargs)
self._epsilon = kwargs.get('epsilon', 1.0)
lspc = np.linspace(0, np.pi, self._m)
x = np.meshgrid(lspc, lspc)
if self.time_start is None:
self.time_start = 0.0
if self.time_end is None:
self.time_end = 1.0
if self.initial_value is None:
if kwargs.get("initial") is "rand":
self.initial_value = np.random.rand(self.dim_for_time_solver) * 1e-3
else:
self.initial_value = (np.sin(x[1])*np.sin(x[0])).reshape(self.dim_for_time_solver)
if isinstance(self.epsilon, complex):
self.numeric_type = np.complex
self._u = np.zeros((self._m, self._m), dtype=np.complex128)
# place to work on
self._u_x = self._u.copy()
self._u_y = self._u.copy()
self._u_f = self._u.copy()
self._u_angle = self._u.copy()
self._u_edens = self._u.copy()
self._B = self._u.copy()
# arrays to work in fourier space
self._k_od = np.hstack((np.arange(self._n+1, dtype=np.int64),
np.arange(self._n, dtype=np.int64)-self._n))
self._k_y = self._k_od
self._k_x = self._k_od.reshape(self._m, 1)
for i in range(self._m-1):
self._k_y = np.vstack((self._k_y, self._k_od))
self._k_x = np.hstack((self._k_x, self._k_od.reshape(self._m, 1)))
self._k_2 = self._k_x**2 + self._k_y**2
self._k_4 = self._k_2**2
if kwargs.get('delta_times_for_time_levels') is not None and self._mg_level is not None:
assert_is_instance(kwargs['delta_times_for_time_levels'], (list, np.ndarray),
descriptor="Delta Times for Time Levels", checking_obj=self)
for time_level in kwargs['delta_times_for_time_levels']:
assert_is_instance(kwargs['delta_times_for_time_levels'][time_level], (list, np.ndarray),
descriptor="Delta Times for Time Level %d" % time_level, checking_obj=self)
for delta_time in kwargs['delta_times_for_time_levels'][time_level]:
self.initialize_direct_space_solver(time_level, delta_time, kwargs['mg_level'])
def direct_implicit(self, *args, **kwargs):
"""Direct Implicit Formula for :math:`u'(t, \\phi_t) &= \\lambda u(t, \\phi_t)`
"""
assert_named_argument('phis_of_time', kwargs, checking_obj=self)
assert_named_argument('delta_node', kwargs, checking_obj=self)
assert_named_argument('integral', kwargs, checking_obj=self)
_phis = kwargs['phis_of_time']
assert_is_instance(_phis, list, message="Direct implicit formula needs multiple phis.", checking_obj=self)
assert_condition(len(_phis) == 3, ValueError, message="Need exactly three different phis.", checking_obj=self)
for _phi in _phis:
assert_condition(_phi.shape == self.dim_for_time_solver, ValueError,
message="Given phi is of wrong shape: %s != %s" % (_phi.shape, self.dim_for_time_solver),
checking_obj=self)
# _phis[0] : previous iteration -> previous step
# _phis[1] : previous iteration -> current step
# _phis[2] : current iteration -> previous step
_dn = kwargs['delta_node']
# TODO: make this numerics check more advanced (better warning for critical numerics)
if isinstance(self.lmbda, complex):
assert_condition(_dn * self.lmbda.real != 1.0,
ArithmeticError, "Direct implicit formula for lambda={:f} and dn={:f} not valid. "
.format(self.lmbda, _dn) + "Try implicit solver.",
self)
else:
assert_condition(_dn * self.lmbda != 1.0,
ArithmeticError, "Direct implicit formula for lambda={:f} and dn={:f} not valid. "
.format(self.lmbda, _dn) + "Try implicit solver.",
self)
_int = kwargs['integral']
_fas = kwargs['fas'] \
if 'fas' in kwargs and kwargs['fas'] is not None else 0.0
if 'core' in kwargs \
and (isinstance(kwargs['core'], (ImplicitSdcCore, ImplicitMlSdcCore))
or (isinstance(self.lmbda, complex) and isinstance(kwargs['core'], SemiImplicitMlSdcCore))):
_new = (_phis[2] - _dn * self.lmbda * _phis[1] + _int + _fas) / (1 - self.lmbda * _dn)
# LOG.debug("Implicit MLSDC Step:\n %s = (%s - %s * %s * %s + %s + %s) / (1 - %s * %s)"
# % (_new, _phis[2], _dn, self.lmbda, _phis[1], _int, _fas, self.lmbda, _dn))
return _new
else:
_new = \
(_phis[2]
+ _dn * (complex(0, self.lmbda.imag) * (_phis[2] - _phis[0]) - self.lmbda.real * _phis[1])
+ _int + _fas) \
/ (1 - self.lmbda.real * _dn)
# LOG.debug("Semi-Implicit MLSDC Step:\n %s = (%s + %s * (%s * (%s - %s) - %s * %s) + %s + %s) / (1 - %s * %s)"
# % (_new, _phis[2], _dn, complex(0, self.lmbda.imag), _phis[2], _phis[0], self.lmbda.real, _phis[1], _int, _fas, self.lmbda.real, _dn))
return _new
def __eq__(self, other):
assert_is_instance(other, StepSolutionData,
message="Can not compare StepSolutionData with {}".format(class_name(other)),
checking_obj=self)
return (
self.time_point == other.time_point
and self.dim == other.dim
and self.numeric_type == other.numeric_type
and np.array_equal(self.value, other.value)
and self.error == other.error
and self.residual == other.residual
)
def run(self, state, **kwargs):
"""Implicit Euler step method.
.. math::
u_{m+1}^{k+1} - \\Delta_\\tau F(t_{m+1}, u_{m+1}^{k+1}) =
u_m^{k+1} + \\Delta_\\tau F(t_{m+1}, u_{m+1}^k) + \\Delta_t I_m^{m+1} \\left( F(\\vec{u}^k) \\right)
Parameters
----------
solver_state : :py:class:`.SdcSolverState`
"""
super(ImplicitSdcCore, self).run(state, **kwargs)
assert_is_instance(state, SdcSolverState, descriptor="State", checking_obj=self)
assert_named_argument('problem', kwargs, types=IProblem, descriptor="Problem", checking_obj=self)
_problem = kwargs['problem']
_previous_iteration_current_step = self._previous_iteration_current_step(state)
if problem_has_direct_implicit(_problem, self):
_previous_iteration_previous_step = self._previous_iteration_previous_step(state)
_sol = _problem.direct_implicit(phis_of_time=[_previous_iteration_previous_step.value,
_previous_iteration_current_step.value,
state.current_time_step.previous_step.value],
delta_node=state.current_step.delta_tau,
integral=state.current_step.integral,
core=self)
else:
# using step-wise formula
# u_{m+1}^{k+1} - \Delta_\tau F(u_{m+1}^{k+1})
# = u_m^{k+1} - \Delta_\tau F(u_m^k) + \Delta_t I_m^{m+1}(F(u^k))
# Note: \Delta_t is always 1.0 as it's part of the integral
_expl_term = \
(state.current_time_step.previous_step.value
- state.current_step.delta_tau
* _problem.evaluate_wrt_time(state.current_step.time_point,
_previous_iteration_current_step.value)
+ state.current_step.integral).reshape(-1)
_func = lambda x_next: \
_expl_term \
+ state.current_step.delta_tau \
* _problem.evaluate_wrt_time(state.current_step.time_point,
x_next.reshape(_problem.dim_for_time_solver)).reshape(-1) \
- x_next
_sol = _problem.implicit_solve(state.current_step.value.reshape(-1), _func)
if type(state.current_step.value) == type(_sol):
state.current_step.value = _sol
else:
state.current_step.value = _sol[0]
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__(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 run(self, state, **kwargs):
"""Explicit Euler step method.
.. math::
u_{m+1}^{k+1} = u_m^{k+1} + \\Delta_\\tau \\left( F(t_m, u_m^{k+1}) - F(t_m, u_m^k) \\right)
+ \\Delta_t I_m^{m+1} \\left( F(\\vec{u}^k) \\right)
Parameters
----------
solver_state : :py:class:`.MlSdcSolverState`
"""
super(ExplicitMlSdcCore, self).run(state, **kwargs)
assert_is_instance(state, MlSdcSolverState, descriptor="State", checking_obj=self)
assert_named_argument('problem', kwargs, types=IProblem, descriptor="Problem", checking_obj=self)
_problem = kwargs['problem']
_previous_step = state.previous_step
if not state.current_iteration.on_finest_level:
LOG.debug("taking restringated or coarse-corrected value")
if state.current_step != state.current_level.first:
_previous_iteration_previous_step = state.current_iteration.current_level.previous_step.initial
else:
_previous_iteration_previous_step = state.current_iteration.current_level.initial
else:
_previous_iteration_previous_step = self._previous_iteration_previous_step(state)
if not _previous_step.rhs_evaluated:
_previous_step.rhs = _problem.evaluate_wrt_time(state.current_step.time_point, _previous_step.value)
if not _previous_iteration_previous_step.rhs_evaluated:
_previous_iteration_previous_step.rhs = \
_problem.evaluate_wrt_time(state.current_step.time_point, _previous_iteration_previous_step.value)
_fas = np.zeros(_previous_step.rhs.shape, dtype=_previous_step.rhs.dtype)
if _previous_step.has_fas_correction():
# LOG.debug(" previous step has FAS")
_fas = _previous_step.fas_correction
# Note: \Delta_t is always 1.0 as it's part of the integral
# using step-wise formula
# Formula:
# u_{m+1}^{k+1} = u_m^{k+1} + \Delta_\tau [ F(u_m^{k+1}) - F(u_m^k) ] + \Delta_t I_m^{m+1}(F(u^k))
state.current_step.value = \
(_previous_step.value
+ state.current_step.delta_tau * (_previous_step.rhs - _previous_iteration_previous_step.rhs)
+ state.current_step.integral + _fas)
def __init__(self, value):
"""
Parameters
----------
value : :py:class:`numpy.ndarray`
Raises
------
ValueError:
If ``value`` is not a :py:class:`numpy.ndarray`.
"""
assert_is_instance(value, np.ndarray, descriptor="Diagnosis Values", checking_obj=self)
self._data = value
self._numeric_type = self.value.dtype
def implicit_solve(self, next_x, func, method="hybr", **kwargs):
"""A solver for implicit equations.
Finds the implicitly defined :math:`x_{i+1}` for the given right hand side function :math:`f(x_{i+1})`, such
that :math:`x_{i+1}=f(x_{i+1})`.
Parameters
----------
next_x : :py:class:`numpy.ndarray`
A starting guess for the implicitly defined value.
rhs_call : :py:class:`callable`
The right hand side function depending on the implicitly defined new value.
method : :py:class:`str`
*(optional, default=``hybr``)*
Method fo the root finding algorithm. See `scipy.optimize.root
<http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root.html#scipy.optimize.root>` for
details.
Returns
-------
next_x : :py:class:`numpy.ndarray`
The calculated new value.
Raises
------
ValueError :
* if ``next_x`` is not a :py:class:`numpy.ndarray` of shape :py:attr:`.IProblem.dim`
* if ``fun`` is not :py:class:`callable`
* if computed solution is not a `:py:class:`numpy.ndarray`
UserWarning :
If the implicit solver did not converged, i.e. the solution object's ``success`` is not :py:class:`True`.
"""
assert_is_instance(next_x, np.ndarray, descriptor="Initial Guess", checking_obj=self)
assert_is_callable(func, descriptor="Function of RHS for Implicit Solver", checking_obj=self)
sol = find_root(fun=func, x0=next_x.reshape(-1), method=method)
if not sol.success:
warnings.warn("Implicit solver did not converged.")
LOG.debug("sol.x: %s" % sol.x)
LOG.error("Implicit solver failed: %s" % sol.message)
else:
assert_is_instance(sol.x, np.ndarray, descriptor="Solution", checking_obj=self)
return sol.x.reshape(self.dim_for_time_solver)
def initialize_direct_space_solver(self, time_level, delta_time, mg_level=None):
if mg_level is None:
mg_level = self._mg_level
assert_is_instance(mg_level, IMultigridLevel, descriptor="Multigrid Level", checking_obj=self)
_stencil = Stencil(self.mg_stencil(delta_time, mg_level.h))
# LOG.debug("Stencil for dt=%f, h=%f: %s" % (delta_time, mg_level.h, _stencil.arr))
time_level = str(time_level)
delta_time = str(delta_time)
if self._direct_solvers.get(time_level) is None:
# LOG.debug("Initializing Solvers for Time Level '%s'" % time_level)
self._direct_solvers[time_level] = {}
# LOG.debug(" Initializing Solver for Time Level '%s' and Delta Node '%s'" % (time_level, delta_time))
# LOG.debug(" shape: %s" % (mg_level.mid.shape))
self._direct_solvers[time_level][delta_time] = {
'mg_level': mg_level,
'stencil': _stencil,
'solver': _stencil.generate_direct_solver(mg_level.mid.shape)
}
