def __init__(self, rst_stencil, level_in, level_out, *args, pre_assign=None, **kwargs):
super(RestrictionByStencilForLevels, self).__init__(*args, **kwargs)
if pre_assign is None:
# no pre assignment function
self.pre_assign = lambda a, b: b
else:
assert_is_callable(pre_assign, "Pre assignment function is not callable")
self.pre_assign = pre_assign
assert_is_instance(rst_stencil, Stencil, "Not a Stencil")
assert_is_instance(level_in, IMultigridLevel, "Not a IMultigridLevel")
assert_is_instance(level_out, IMultigridLevel, "Not a IMultigridLevel")
self.l_in = level_in
self.l_out = level_out
self.rst_stencil = rst_stencil
# check if the number of points per level matches
self.dip = []
for i in range(rst_stencil.dim):
self.dip.append((level_in.mid.shape[i]-1)/(level_out.mid.shape[i]-1) - 1)
# print("in.shape[", i, "]: ", level_in.mid.shape[i])
# print("out.shape[", i, "]: ", level_out.mid.shape[i])
# print("dip[", i, "]: ", self.dip[-1])
if (self.dip[-1] % 1) != 0:
raise ValueError("The Level do not match in direction " + str(i))
# now just construct a slice tuple and the evaluable view from the finer grid
self.evaluable_view = level_in.evaluable_restriction_view(rst_stencil)
self.slices = []
for i in range(rst_stencil.dim):
self.slices.append(slice(None, None, self.dip[i]+1))
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__(self, level_in, level_out, stencil_list, *args, pre_assign=None, **kwargs):
"""init
"""
super(InterpolationByStencilForLevelsClassical, self).__init__(*args, **kwargs)
if pre_assign is None:
# no pre assignment function
self.pre_assign = lambda a, b: b
else:
assert_is_callable(pre_assign, "Pre assignment function is not callable")
self.pre_assign = pre_assign
# check if all parameters are fitting
assert_is_instance(stencil_list, list)
for st in stencil_list:
assert_is_instance(st[0], Stencil, "that is not a stencil")
self.stencil_list = stencil_list
assert_is_instance(level_in, IMultigridLevel, "Not a IMultigridLevel")
assert_is_instance(level_out, IMultigridLevel, "Not a IMultigridLevel")
self.level_in = level_in
self.level_out = level_out
# increase in points for each direction
self.iip = []
self.fits = False
for i in range(level_in.mid.ndim):
self.iip.append((level_out.mid.shape[i]-1)/(level_in.mid.shape[i]) - 1)
n = level_out.mid.shape[i]
m = level_in.mid.shape[i]
self.fits = False
while m <= n:
if m == n:
self.fits = True
break
else:
m = m*2+1
if not self.fits:
raise ValueError("The Levels do not match in direction " + str(i))
# compute evaluable views with the positions and slices
self.slices_out = []
for st, pos in stencil_list:
sl_out = []
for i in range(st.dim):
sl_out.append(slice(pos[i], None, self.iip[i]+1))
# print("Initial Position:", pos)
# print("Slice", sl_out)
self.slices_out.append(tuple(sl_out.copy()))
def __init__(self, residual_tolerance_dict, max_iteration_dict,
*args, **kwargs):
self.rtd = residual_tolerance_dict
self.mid = max_iteration_dict
if "res_comp_method" in kwargs.keys():
self.compute_residual = kwargs["res_comp_method"]
assert_is_callable(self.compute_residual,
"Residual computation method "
"should be callable ")
else:
self.compute_residual = self._standard_residual_computation
super(ResidualErrorControl, self).__init__(args, kwargs)
def __init__(self, stencil_list, level_in, level_out, *args, pre_assign=None, **kwargs):
"""init
"""
super(InterpolationByStencilForLevels, self).__init__(*args, **kwargs)
if pre_assign is None:
# no pre assignment function
self.pre_assign = lambda a, b: b
else:
assert_is_callable(pre_assign, "Pre assignment function is not callable")
self.pre_assign = pre_assign
# check if all parameters are fitting
assert_is_instance(stencil_list, list)
for st in stencil_list:
assert_is_instance(st[0], Stencil, "that is not a stencil")
self.stencil_list = stencil_list
assert_is_instance(level_in, IMultigridLevel, "Not a IMultigridLevel")
assert_is_instance(level_out, IMultigridLevel, "Not a IMultigridLevel")
self.level_in = level_in
self.level_out = level_out
# increase in points for each direction
self.iip = []
for i in range(level_in.mid.ndim):
self.iip.append((level_out.mid.shape[i]-1)/(level_in.mid.shape[i]-1) - 1)
# print("in.shape[", i, "]: ", level_in.mid.shape[i])
# print("out.shape[", i, "]: ", level_out.mid.shape[i])
# print("iip[", i, "]: ", self.iip[-1])
if (self.iip[-1] % 1) != 0:
raise ValueError("The Levels do not match in direction " + str(i))
# compute evaluable views with the positions and slices
self.evaluable_views = []
self.slices_out = []
self.slices_in = []
for st, pos in stencil_list:
sl_out = []
sl_in = []
for i in range(st.dim):
sl_out.append(slice(pos[i], None, self.iip[i]+1))
if pos[i] == 0:
sl_in.append(slice(None, None))
else:
sl_in.append(slice(0, -1))
# print("Stencilcenter : ", st.center)
# print("Stencilborder :", st.b)
self.evaluable_views.append(level_in.evaluable_interpolation_view(st))
# print("The view: \n", self.evaluable_views[-1])
self.slices_out.append(tuple(sl_out.copy()))
self.slices_in.append(tuple(sl_in.copy()))
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 init(self, problem, **kwargs):
"""Initializes the solver with a given problem and options.
Parameters
----------
problem : :py:class:`.IProblem`
The problem this solver should solve.
integrator : :py:class:`.IntegratorBase`
Integrator to be used by this solver.
threshold : :py:class:`.ThresholdCheck`
*(optional)*
see :py:attr:`.threshold`
"""
self._problem = problem
if 'integrator' in kwargs:
assert_is_callable(kwargs['integrator'], message="Integrator must be instantiable.", checking_obj=self)
self._integrator = kwargs['integrator']()
if "threshold" in kwargs and isinstance(kwargs["threshold"], ThresholdCheck):
self.threshold = kwargs["threshold"]
def exact(self, time):
"""Evaluates given exact solution function at given time and with given time-dependent data.
Parameters
----------
time : :py:class:`float`
Time point :math:`t`
Returns
-------
exact_solution : :py:class:`numpy.ndarray`
Raises
------
ValueError :
* if ``time`` is not a :py:class:`float`
* if ``phi_of_time`` is not a :py:class:`numpy.ndarray`
* if not exact function is given
"""
assert_is_instance(time, float, descriptor="Time Point", checking_obj=self)
assert_is_callable(self._exact_function, descriptor="Exact Function", checking_obj=self)
return self._exact_function(time)
def eval_f(self, u=None, function=None, space_tensor=None):
"""Evaluates the right hand side with the actual space tensor, and the current :math:`u`.
"""
assert_condition(self._act_space_tensor is not None, ValueError,
message="A current space tensor is needed", checking_obj=self)
if function is None:
if u is None:
return self.rhs_function_wrt_space(self._act_space_tensor)
else:
assert_is_instance(u, np.ndarray, "u is not an numpy array")
assert_condition(u.shape == self._act_space_tensor[1].shape,
"u has the wrong shape", self)
return self.rhs_function_wrt_space(u, self._act_space_tensor)
else:
if u is None:
assert_is_callable(function, "Function is not callable", self)
return function(self._act_space_tensor)
else:
assert_is_instance(u, np.ndarray, "u is not an numpy array")
assert_condition(u.shape == self._act_space_tensor[1].shape,
"u has the wrong shape", self)
return function(u, self._act_space_tensor)
def rhs_function_wrt_time(self, function):
assert_is_callable(function, descriptor="Function of the RHS w.r.t Time", checking_obj=self)
self._rhs_function_wrt_time = function
def exact_function(self, exact_function):
assert_is_callable(exact_function, descriptor="Exact Function", checking_obj=self)
self._exact_function = exact_function
def __init__(self, mg_prob, stencil_form, *args, **kwargs):
for keys in kwargs.keys():
print(keys)
# assert_condition(problem_is_multigrid_problem(mg_prob), ValueError, message="Not a multigrid Problem")
assert_is_callable(stencil_form, "StencilForm has to be a function")
self.mg_problem = mg_prob
self.levels = []
self.smoothers = []
self.stencils = []
self.rst_ops = []
self.ipl_ops = []
self.dim = kwargs["dim"]
self.n_pre = kwargs.get("n_pre", 3)
self.n_post = kwargs.get("n_post", 3)
self.num_levels = kwargs.get("num_levels", 3)
# append course level
shape = kwargs["shape_coarse"]
if kwargs.get("dim") == 1:
self.levels.append(MultigridLevel1D(shape, self.mg_problem,
max_borders=kwargs["max_borders"], role="CL"))
elif kwargs.get("dim") == 2:
self.levels.append(MultigridLevel2D(shape, self.mg_problem,
max_borders=kwargs["max_borders"], role="CL"))
#append course stencil
self.stencils.append(Stencil(*stencil_form(self.levels[-1])))
self.smoothers.append(DirectSolverSmoother(self.stencils[-1], self.levels[-1]))
for i in range(kwargs["num_levels"]-1):
if i == kwargs["num_levels"]-2:
role = "FL"
else:
role = "ML"
if kwargs.get("dim") == 1:
shape = shape*2+1
self.levels.append(MultigridLevel1D(shape, self.mg_problem,
max_borders=kwargs["max_borders"], role=role))
elif kwargs.get("dim") == 2:
shape = (shape[0]*2+1, shape[1]*2+1)
self.levels.append(MultigridLevel2D(shape, self.mg_problem,
max_borders=kwargs["max_borders"], role=role))
self.stencils.append(Stencil(*stencil_form(self.levels[-1])))
# append smoother
if kwargs["smoothing_type"] is "jacobi":
omega = kwargs["smooth_opts"]["omega"]
# l_plus = np.asarray([0, -2.0/omega, 0])
# l_minus = np.asarray([1.0, -2.0*(1.0 - 1.0/omega), 1.0])
l_plus = self.stencils[-1].l_plus_jacobi(omega)
l_minus = self.stencils[-1].l_minus_jacobi(omega)
self.smoothers.append(SplitSmoother(l_plus, l_minus, self.levels[-1]))
elif kwargs["smoothing_type"] is "ilu":
self.smoothers.append(ILUSmoother(self.stencils[-1], self.levels[-1], **kwargs["smooth_opts"]))
else:
raise ValueError("Wrong smoothing type")
# append interpolation
self.ipl_ops.append(kwargs["ipl_class"](self.levels[-2], self.levels[-1],
*kwargs.get("ipl_opts"), pre_assign=iadd))
self.rst_ops.append(kwargs["rst_class"](self.levels[-1], self.levels[-2],
*kwargs.get("rst_opts")))
def __init__(self, *args, **kwargs):
"""
Parameters
----------
rhs_function_wrt_space : :py:class:`callable`
function returning the space-dependent values for the right hand side as used by the space solver
boundaries : :py:class:`None` or :py:class:`list` of :py:class:`str`
*(optional)*
defaults to ``periodic`` for each dimension
boundary_functions : :py:class:`None` or :py:class:`list` of :py:class:`callable`
*(optional)*
functions defined on the boundaries of the geometry
geometry : :py:class:`None` or :py:class:`numpy.ndarray`
*(optional)*
specifying the dimension and extend of the geometry
"""
assert_is_instance(self, IProblem, message="This Mixin is only valid for IProblems.", checking_obj=self)
assert_named_argument('rhs_function_wrt_space', kwargs, descriptor="RHS for space solver", checking_obj=self)
assert_is_callable(kwargs['rhs_function_wrt_space'], descriptor="RHS for space solver", checking_obj=self)
self._rhs_function_wrt_space = kwargs['rhs_function_wrt_space']
# check if boundary conditions are specified
if kwargs.get('boundaries') is None:
self._boundaries = ['periodic'] * len(self.spacial_dim)
elif isinstance(kwargs['boundaries'], str) \
and kwargs['boundaries'] in MultigridProblemMixin.valid_boundary_conditions:
self._boundaries = [kwargs['boundaries']] * len(self.spacial_dim)
elif isinstance(kwargs['boundaries'], list):
check = 0
for bc in kwargs['boundaries']:
if bc in MultigridProblemMixin.valid_boundary_conditions:
check += 1
if check == len(self.spacial_dim) * 2:
self._boundaries = kwargs['boundaries']
else:
LOG.warning('Boundary specifications are not valid, will use periodic boundaries for each dimension.')
self._boundaries = ['periodic'] * len(self.spacial_dim)
else:
LOG.warning('Boundary specifications are not valid, will use periodic boundaries for each dimension')
self._boundaries = ['periodic'] * len(self.spacial_dim)
# assign according to the boundary conditions the right functions
if kwargs.get('boundary_functions') is None:
self._boundary_functions = [None] * len(self.spacial_dim)
else:
assert_is_instance(kwargs['boundary_functions'], list, descriptor="Boundary Functions", checking_obj=self)
check = 0
assert_condition(len(kwargs['boundary_functions']) == len(self.spacial_dim),
ValueError, message="Not enough boundary functions given.", checking_obj=self)
for ftpls in kwargs['boundary_functions']:
if ftpls is 'dirichlet':
assert_is_instance(ftpls, list, message="Dirichlet function list not available", checking_obj=self)
assert_condition(len(ftpls) == 2,
ValueError, message="Wrong number of functions", checking_obj=self)
assert_is_callable(ftpls[0], "Not a function", self)
assert_is_callable(ftpls[1], "Not a function", self)
check += 1
self._boundary_functions = kwargs['boundary_functions']
# construct or save the geometry
if kwargs.get('geometry') is None:
self._geometry = np.asarray([[0, 1]] * len(self.spacial_dim))
else:
assert_is_instance(kwargs['geometry'], np.ndarray, descriptor="Geometry", checking_obj=self)
assert_condition(len(kwargs["geometry"].shape) == 2, ValueError,
message="Numpy array has the wrong dimensions", checking_obj=self)
assert_condition(kwargs['geometry'].shape[0] == len(self.spacial_dim) and kwargs['geometry'].shape[1] == 2,
ValueError,
message="Numpy array has a wrong shape", checking_obj=self)
self._geometry = kwargs['geometry']
self._rhs_space_operators = {}
self._implicit_solve_method = kwargs.get('implicit_solve_method', 'direct')
self._mg_core = None
# the Space tensor which is actually used
self._act_space_tensor = None
self._act_grid_distances = None
# the points actually used
self._act_npoints = None
def mg_solve(self, next_x, method='direct', **kwargs):
"""Runs the multigrid solver
This is where all the magic happens on each call of the space solver from the iterative time solver, i.e. on
every iteration for each time-level in each sweep on each step.
Parameters
----------
method : :py:class:`str`
defaults to ``direct``
``mg``
for full multigrid cycles; additional keyword arguments passed to the multigrid solver can be given;
additional arguments required:
``mg_level``
``direct``
for using the a predefined multigrid smoother as a direct solver via :py:class:`.DirectSolverSmoother`;
additional arguments required:
``mg_level``
``stencil``
Raises
------
ValueError
if given ``method`` is not one of ``mg`` or ``direct``
Returns
-------
solution
"""
if method == 'mg':
assert_named_argument('stencil_fnc', kwargs, descriptor="Stencil Generation Function",
checking_obj=self)
assert_is_callable(kwargs['stencil_fnc'], descriptor="Stencil Generation Function", checking_obj=self)
# LOG.debug("Using Multigrid as implicit space solver.")
mg_core_options = {}
mg_core_options.update(MG_SMOOTHER_PRESETS["Jacobi"])
mg_core_options.update(MG_LEVEL_PRESETS["Standard-1D"])
mg_core_options.update(MG_RESTRICTION_PRESETS["Standard-1D"])
mg_core_options.update(MG_INTERPOLATION_PRESETS["Standard-1D"])
mg_core_options["shape_coarse"] = 4
mg_core_options["n_pre"] = 1
mg_core_options["n_post"] = 1
self.mg_core = MultiGridCore(self, lambda h: (kwargs['stencil_fnc'](h), np.array([1])), **mg_core_options)
self.mg_core.levels[-1].mid[:] = next_x.reshape(self.mg_core.levels[-1].mid.shape)
self.mg_core.levels[-1].rhs = kwargs['rhs'].reshape(self.mg_core.levels[-1].rhs.shape)
self.mg_core.pad(-1)
self.mg_core.modify_rhs(-1)
self.mg_core.v_cycle()
self.mg_core.v_cycle()
# LOG.debug("input: %s --> %s" % (next_x.shape, self._mg_core.levels[-1].mid.shape))
return self.mg_core.levels[-1].mid.reshape(next_x.shape)
elif method == 'direct':
if kwargs.get('solver') is None:
# assert_named_argument('mg_level', kwargs, types=IMultigridLevel, descriptor="Multigrid Level",
# checking_obj=self)
assert_named_argument('stencil', kwargs, types=Stencil, descriptor="MG Stencil", checking_obj=self)
solver_function = DirectSolverSmoother(kwargs['stencil'], kwargs['mg_level']).relax
else:
solver_function = kwargs['solver']
# LOG.debug("next_x.shape: {:s}".format(next_x.shape))
return solver_function(next_x)
else:
raise ValueError("Unknown method: '%s'" % method)
def rhs_function_wrt_space(self, function):
assert_is_callable(function, descriptor="Function of RHS w.r.t. Space", checking_obj=self)
self._rhs_function_wrt_space = function