def visualize(self, U, codim=2, **kwargs):
"""Visualize scalar data associated to the grid as a patch plot.
Parameters
----------
U
|NumPy array| of the data to visualize. If `U.dim == 2 and len(U) > 1`, the
data is visualized as a time series of plots. Alternatively, a tuple of
|Numpy arrays| can be provided, in which case a subplot is created for
each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in `U` is attached to (either 0 or 2).
kwargs
See :func:`~pymor.gui.qt.visualize_patch`
"""
from pymor.gui.qt import visualize_patch
from pymor.vectorarrays.interfaces import VectorArrayInterface
from pymor.vectorarrays.numpy import NumpyVectorSpace, NumpyVectorArray
if isinstance(U, (np.ndarray, VectorArrayInterface)):
U = (U,)
assert all(isinstance(u, (np.ndarray, VectorArrayInterface)) for u in U)
U = tuple(NumpyVectorSpace.make_array(u) if isinstance(u, np.ndarray) else
u if isinstance(u, NumpyVectorArray) else
NumpyVectorSpace.make_array(u.data)
for u in U)
bounding_box = kwargs.pop('bounding_box', self.domain)
visualize_patch(self, U, codim=codim, bounding_box=bounding_box, **kwargs)
def projected(self, range_basis, source_basis, product=None, name=None):
assert source_basis is None or source_basis in self.source
assert range_basis is None or range_basis in self.range
assert product is None or product.source == product.range == self.range
if len(self.interpolation_dofs) == 0:
return ZeroOperator(self.source, self.range, self.name).projected(range_basis, source_basis, product, name)
elif not hasattr(self, 'restricted_operator') or source_basis is None:
return super().projected(range_basis, source_basis, product, name)
else:
name = name or self.name + '_projected'
if range_basis is not None:
if product is None:
projected_collateral_basis = NumpyVectorSpace.make_array(self.collateral_basis.dot(range_basis),
self.range.id)
else:
projected_collateral_basis = NumpyVectorSpace.make_array(product.apply2(self.collateral_basis,
range_basis),
self.range.id)
else:
projected_collateral_basis = self.collateral_basis
return ProjectedEmpiciralInterpolatedOperator(self.restricted_operator, self.interpolation_matrix,
NumpyVectorSpace.make_array(source_basis.components(self.source_dofs)),
projected_collateral_basis, self.triangular,
self.source.id, None, name)
def projected_to_subbasis(self, dim_range=None, dim_source=None, dim_collateral=None, name=None):
assert dim_source is None or dim_source <= self.source.dim
assert dim_range is None or dim_range <= self.range.dim
assert dim_collateral is None or dim_collateral <= self.restricted_operator.range.dim
if not isinstance(self.projected_collateral_basis.space, NumpyVectorSpace):
raise NotImplementedError
name = name or '{}_projected_to_subbasis'.format(self.name)
interpolation_matrix = self.interpolation_matrix[:dim_collateral, :dim_collateral]
if dim_collateral is not None:
restricted_operator, source_dofs = self.restricted_operator.restricted(np.arange(dim_collateral))
else:
restricted_operator = self.restricted_operator
old_pcb = self.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(old_pcb.data[:dim_collateral, :dim_range],
old_pcb.space.id)
old_sbd = self.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(old_sbd.data[:dim_source]) if dim_collateral is None \
else NumpyVectorSpace.make_array(old_sbd.data[:dim_source, source_dofs])
return ProjectedEmpiciralInterpolatedOperator(restricted_operator, interpolation_matrix,
source_basis_dofs, projected_collateral_basis, self.triangular,
self.source.id, solver_options=self.solver_options, name=name)
def save(self):
if not config.HAVE_PYVTK:
msg = QMessageBox(QMessageBox.Critical, 'Error', 'VTK output disabled. Pleas install pyvtk.')
msg.exec_()
return
filename = QFileDialog.getSaveFileName(self, 'Save as vtk file')[0]
base_name = filename.split('.vtu')[0].split('.vtk')[0].split('.pvd')[0]
if base_name:
if len(self.U) == 1:
write_vtk(self.grid, NumpyVectorSpace.make_array(self.U[0]), base_name, codim=self.codim)
else:
for i, u in enumerate(self.U):
write_vtk(self.grid, NumpyVectorSpace.make_array(u), '{}-{}'.format(base_name, i),
codim=self.codim)
def projected(self, range_basis, source_basis, product=None, name=None):
assert source_basis is None or source_basis in self.source
assert range_basis is None or range_basis in self.range
assert product is None or product.source == product.range == self.range
if range_basis is not None:
if product:
projected_value = NumpyVectorSpace.make_array(product.apply2(range_basis, self._value).T, self.range.id)
else:
projected_value = NumpyVectorSpace.make_array(range_basis.dot(self._value).T, self.range.id)
else:
projected_value = self._value
if source_basis is None:
return ConstantOperator(projected_value, self.source, name=self.name + '_projected')
else:
return ConstantOperator(projected_value, NumpyVectorSpace(len(source_basis), self.source.id),
name=self.name + '_projected')
class ComponentProjection(OperatorBase):
"""|Operator| representing the projection of a |VectorArray| on some of its components.
Parameters
----------
components
List or 1D |NumPy array| of the indices of the vector
:meth:`~pymor.vectorarrays.interfaces.VectorArrayInterface.components` that ar
to be extracted by the operator.
source
Source |VectorSpace| of the operator.
name
Name of the operator.
"""
linear = True
def __init__(self, components, source, name=None):
assert all(0 <= c < source.dim for c in components)
self.components = np.array(components, dtype=np.int32)
self.range = NumpyVectorSpace(len(components))
self.source = source
self.name = name
def apply(self, U, mu=None):
assert U in self.source
return self.range.make_array(U.components(self.components))
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
source_dofs = self.components[dofs]
return IdentityOperator(NumpyVectorSpace(len(source_dofs))), source_dofs
def with_cb_dim(self, dim):
assert dim <= self.restricted_operator.range.dim
interpolation_matrix = self.interpolation_matrix[:dim, :dim]
restricted_operator, source_dofs = self.restricted_operator.restricted(np.arange(dim))
old_pcb = self.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(old_pcb.to_numpy()[:dim, :])
old_sbd = self.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(old_sbd.to_numpy()[:, source_dofs])
return ProjectedEmpiciralInterpolatedOperator(restricted_operator, interpolation_matrix,
source_basis_dofs, projected_collateral_basis, self.triangular,
solver_options=self.solver_options, name=self.name)
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
if not self.transposed:
restricted_value = NumpyVectorSpace.make_array(self._array.components(dofs))
return VectorArrayOperator(restricted_value, False), np.arange(self.source.dim, dtype=np.int32)
else:
raise NotImplementedError
def action_ProjectedEmpiciralInterpolatedOperator(self, op):
if not isinstance(op.projected_collateral_basis.space, NumpyVectorSpace):
raise NotImplementedError
restricted_operator = op.restricted_operator
old_pcb = op.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(old_pcb.to_numpy()[:, :self.dim_range],
old_pcb.space.id)
old_sbd = op.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(old_sbd.to_numpy()[:self.dim_source])
return ProjectedEmpiciralInterpolatedOperator(restricted_operator, op.interpolation_matrix,
source_basis_dofs, projected_collateral_basis, op.triangular,
op.source.id, solver_options=op.solver_options, name=op.name)
def test_to_matrix():
np.random.seed(0)
A = np.random.randn(2, 2)
B = np.random.randn(3, 3)
C = np.random.randn(3, 3)
X = np.bmat([[np.eye(2) + A, np.zeros((2, 3))], [np.zeros((3, 2)), B.dot(C.T)]])
C = sps.csc_matrix(C)
Aop = NumpyMatrixOperator(A)
Bop = NumpyMatrixOperator(B)
Cop = NumpyMatrixOperator(C)
Xop = BlockDiagonalOperator([LincombOperator([IdentityOperator(NumpyVectorSpace(2)), Aop],
[1, 1]), Concatenation(Bop, AdjointOperator(Cop))])
assert np.allclose(X, to_matrix(Xop))
assert np.allclose(X, to_matrix(Xop, format='csr').toarray())
np.random.seed(0)
V = np.random.randn(10, 2)
Vva = NumpyVectorSpace.make_array(V.T)
Vop = VectorArrayOperator(Vva)
assert np.allclose(V, to_matrix(Vop))
Vop = VectorArrayOperator(Vva, transposed=True)
assert np.allclose(V, to_matrix(Vop).T)
def action_EmpiricalInterpolatedOperator(self, op):
range_basis, source_basis, product = self.range_basis, self.source_basis, self.product
if len(op.interpolation_dofs) == 0:
return self.apply(ZeroOperator(op.range, op.source, op.name))
elif not hasattr(op, 'restricted_operator') or source_basis is None:
raise RuleNotMatchingError('Has no restricted operator or source_basis is None')
else:
if range_basis is not None:
projected_collateral_basis = NumpyVectorSpace.make_array(op.collateral_basis.inner(range_basis,
product),
op.range.id)
else:
projected_collateral_basis = op.collateral_basis
return ProjectedEmpiciralInterpolatedOperator(op.restricted_operator, op.interpolation_matrix,
NumpyVectorSpace.make_array(source_basis.dofs(op.source_dofs)),
projected_collateral_basis, op.triangular,
op.source.id, None, op.name)
def reconstruct(self, U):
"""Reconstruct high-dimensional vector from reduced vector `U`."""
assert isinstance(U.space, NumpyVectorSpace)
UU = np.zeros((len(U), self.dim))
UU[:, :self.dim_subbasis] = U.data
UU = NumpyVectorSpace.make_array(UU, U.space.id)
if self.old_recontructor:
return self.old_recontructor.reconstruct(UU)
else:
return UU
def apply(self, U, mu=None):
mu = self.parse_parameter(mu)
if len(self.interpolation_dofs) == 0:
return self.range.zeros(len(U))
if hasattr(self, 'restricted_operator'):
U_dofs = NumpyVectorSpace.make_array(U.dofs(self.source_dofs))
AU = self.restricted_operator.apply(U_dofs, mu=mu)
else:
AU = NumpyVectorSpace.make_array(self.operator.apply(U, mu=mu).dofs(self.interpolation_dofs))
try:
if self.triangular:
interpolation_coefficients = solve_triangular(self.interpolation_matrix, AU.to_numpy().T,
lower=True, unit_diagonal=True).T
else:
interpolation_coefficients = solve(self.interpolation_matrix, AU.to_numpy().T).T
except ValueError: # this exception occurs when AU contains NaNs ...
interpolation_coefficients = np.empty((len(AU), len(self.collateral_basis))) + np.nan
return self.collateral_basis.lincomb(interpolation_coefficients)
def test_to_matrix_VectorArrayOperator():
np.random.seed(0)
V = np.random.randn(10, 2)
Vva = NumpyVectorSpace.make_array(V.T)
Vop = VectorArrayOperator(Vva)
assert_type_and_allclose(V, Vop, 'dense')
Vop = VectorArrayOperator(Vva, adjoint=True)
assert_type_and_allclose(V.T, Vop, 'dense')
def action_ConstantOperator(self, op):
range_basis, source_basis, product = self.range_basis, self.source_basis, self.product
if range_basis is not None:
projected_value = NumpyVectorSpace.make_array(range_basis.inner(op._value, product).T, op.range.id)
else:
projected_value = op._value
if source_basis is None:
return ConstantOperator(projected_value, op.source, name=op.name)
else:
return ConstantOperator(projected_value, NumpyVectorSpace(len(source_basis), op.source.id),
name=op.name)
def action_ConstantOperator(self, op):
range_basis, source_basis, product = self.range_basis, self.source_basis, self.product
if range_basis is not None:
projected_value = NumpyVectorSpace.make_array(
range_basis.inner(op._value, product).T, op.range.id)
else:
projected_value = op._value
if source_basis is None:
return ConstantOperator(projected_value, op.source, name=op.name)
else:
return ConstantOperator(projected_value,
NumpyVectorSpace(len(source_basis),
op.source.id),
name=op.name)
def action_ProjectedEmpiciralInterpolatedOperator(self, op):
if not isinstance(op.projected_collateral_basis.space,
NumpyVectorSpace):
raise NotImplementedError
restricted_operator = op.restricted_operator
old_pcb = op.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(
old_pcb.to_numpy()[:, :self.dim_range])
old_sbd = op.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(
old_sbd.to_numpy()[:self.dim_source])
return ProjectedEmpiciralInterpolatedOperator(
restricted_operator,
op.interpolation_matrix,
source_basis_dofs,
projected_collateral_basis,
op.triangular,
solver_options=op.solver_options,
name=op.name)
def with_cb_dim(self, dim):
assert dim <= self.restricted_operator.range.dim
interpolation_matrix = self.interpolation_matrix[:dim, :dim]
restricted_operator, source_dofs = self.restricted_operator.restricted(
np.arange(dim))
old_pcb = self.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(
old_pcb.to_numpy()[:dim, :])
old_sbd = self.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(
old_sbd.to_numpy()[:, source_dofs])
return ProjectedEmpiciralInterpolatedOperator(
restricted_operator,
interpolation_matrix,
source_basis_dofs,
projected_collateral_basis,
self.triangular,
solver_options=self.solver_options,
name=self.name)
def apply_inverse(self, V, mu=None, least_squares=False):
assert V in self.range
assert not self.functional and not self.vector
if V.dim == 0:
if self.source.dim == 0 and least_squares:
return self.source.make_array([np.zeros(0) for _ in range(len(V))])
else:
raise InversionError
op = NumpyMatrixOperator(self.matrix, solver_options=self.solver_options)
return self.source.make_array([op.apply_inverse(NumpyVectorSpace.make_array(v._array),
least_squares=least_squares).to_numpy().ravel()
for v in V._list])
class PyClawModel():
def __init__(self, claw):
self.claw = claw
self.num_eqn = claw.solution.state.q.shape[0]
self.mx = claw.solution.state.q.shape[1]
self.my = claw.solution.state.q.shape[2]
self.mz = claw.solution.state.q.shape[3]
self.solution_space = NumpyVectorSpace(claw.solution.state.q.size)
self.claw.start_frame = self.claw.solution.start_frame
def solve_manual(self, mu=None):
assert mu is None
use_claw_run = True
if use_claw_run:
status = self.claw.run()
else:
import copy
from clawpack.pyclaw.util import FrameCounter
frame = FrameCounter()
frame.set_counter(self.claw.start_frame)
self.claw.frames.append(copy.deepcopy(
self.claw.solution)) # initial solution
self.claw.solution.write(frame, self.claw.outdir,
self.claw.output_format,
self.claw.output_file_prefix,
self.claw.write_aux_always,
self.claw.output_options)
t = 0.0
t_increment = 10.0
for i in range(12):
self.claw.solver.evolve_to_time(self.claw.solution,
t + t_increment)
frame.increment()
self.claw.frames.append(copy.deepcopy(self.claw.solution))
self.claw.solution.write(frame, self.claw.outdir,
self.claw.output_format,
self.claw.output_file_prefix,
self.claw.write_aux_always,
self.claw.output_options)
self.claw.solution._start_frame = len(self.claw.frames)
t += t_increment
dim = self.claw.frames[0].q.size
print(dim)
qr = []
for f in range(len(self.claw.frames)):
qr.append(np.reshape(self.claw.frames[f].q, dim, order='F'))
return self.solution_space.make_array(qr)
def estimate(self, U, mu, d):
if len(U) > 1:
raise NotImplementedError
if not d.rhs.parametric:
CR = np.ones(1)
else:
CR = np.array(d.rhs.evaluate_coefficients(mu))
if not d.operator.parametric:
CO = np.ones(1)
else:
CO = np.array(d.operator.evaluate_coefficients(mu))
C = np.hstack((CR, np.dot(CO[..., np.newaxis], U.data).ravel()))
est = self.norm(NumpyVectorSpace.make_array(C))
if self.coercivity_estimator:
est /= self.coercivity_estimator(mu)
return est
def estimate(self, U, mu, m):
if len(U) > 1:
raise NotImplementedError
if not m.rhs.parametric:
CR = np.ones(1)
else:
CR = np.array(m.rhs.evaluate_coefficients(mu))
if not m.operator.parametric:
CO = np.ones(1)
else:
CO = np.array(m.operator.evaluate_coefficients(mu))
C = np.hstack((CR, np.dot(CO[..., np.newaxis], U.to_numpy()).ravel()))
est = self.norm(NumpyVectorSpace.make_array(C))
if self.coercivity_estimator:
est /= self.coercivity_estimator(mu)
return est
def calculate_csis(gq, lq):
spaces = gq["spaces"]
for space in spaces:
ldict = lq[space]
T = ldict["solution_matrix_robin"]
u_s = ldict["local_sol2"]
product = ldict["omega_star_product"]
norm = induced_norm(product)
if norm(u_s).real < 1e-14:
result = 1
else:
x = np.linalg.lstsq(T, u_s.data.T, rcond=None)[0]
y = T.dot(x)
y_p = NumpyVectorSpace.make_array(y.T)
y_p = y_p.lincomb(1 / norm(y_p).real)
result = np.sqrt(
norm(u_s).real[0]**2 /
(norm(u_s).real[0]**2 -
product.apply2(u_s, y_p).real[0][0]**2))
ldict["csi"] = result
print("calculated csis")
def _localizedly_project_functional(self, op):
if isinstance(op, LincombOperator):
ops = [
self._localizedly_project_functional(foo)
for foo in op.operators
]
return LincombOperator(ops, coefficients=op.coefficients)
assert op.linear and not op.parametric
v = op.as_vector()
def project_block(ids, basis):
o = self.l.localize_vector_array(v, ids)
if basis is None:
return o.data
else:
return basis.dot(o).T
mats = [
project_block(ids, basis)
for ids, basis in zip(self.range_spaces, self.range_bases)
]
return NumpyVectorSpace.make_array(np.concatenate(mats, axis=1))
class NumpyMatrixOperator(NumpyMatrixBasedOperator):
"""Wraps a 2D |NumPy Array| as an |Operator|.
Parameters
----------
matrix
The |NumPy array| which is to be wrapped.
source_id
The id of the operator's `source` |VectorSpace|.
range_id
The id of the operator's `range` |VectorSpace|.
solver_options
The |solver_options| for the operator.
name
Name of the operator.
"""
def __init__(self,
matrix,
source_id=None,
range_id=None,
solver_options=None,
name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
try:
matrix.setflags(write=False) # make numpy arrays read-only
except AttributeError:
pass
self.source = NumpyVectorSpace(matrix.shape[1], source_id)
self.range = NumpyVectorSpace(matrix.shape[0], range_id)
self.solver_options = solver_options
self.name = name
self.matrix = matrix
self.source_id = source_id
self.range_id = range_id
self.sparse = issparse(matrix)
@classmethod
def from_file(cls,
path,
key=None,
source_id=None,
range_id=None,
solver_options=None,
name=None):
from pymor.tools.io import load_matrix
matrix = load_matrix(path, key=key)
return cls(matrix,
solver_options=solver_options,
source_id=source_id,
range_id=range_id,
name=name or key or path)
@property
def H(self):
options = {
'inverse': self.solver_options.get('inverse_adjoint'),
'inverse_adjoint': self.solver_options.get('inverse')
} if self.solver_options else None
if self.sparse:
adjoint_matrix = self.matrix.transpose(copy=False).conj(copy=False)
elif np.isrealobj(self.matrix):
adjoint_matrix = self.matrix.T
else:
adjoint_matrix = self.matrix.T.conj()
return self.with_(matrix=adjoint_matrix,
source_id=self.range_id,
range_id=self.source_id,
solver_options=options,
name=self.name + '_adjoint')
def _assemble(self, mu=None):
pass
def assemble(self, mu=None):
return self
def as_range_array(self, mu=None):
return self.range.make_array(self.matrix.T.copy())
def as_source_array(self, mu=None):
return self.source.make_array(self.matrix.copy()).conj()
def apply(self, U, mu=None):
assert U in self.source
return self.range.make_array(self.matrix.dot(U.to_numpy().T).T)
def apply_adjoint(self, V, mu=None):
assert V in self.range
return self.H.apply(V, mu=mu)
@defaults('check_finite', 'default_sparse_solver_backend')
def apply_inverse(self,
V,
mu=None,
least_squares=False,
check_finite=True,
default_sparse_solver_backend='scipy'):
"""Apply the inverse operator.
Parameters
----------
V
|VectorArray| of vectors to which the inverse operator is applied.
mu
The |Parameter| for which to evaluate the inverse operator.
least_squares
If `True`, solve the least squares problem::
u = argmin ||op(u) - v||_2.
Since for an invertible operator the least squares solution agrees
with the result of the application of the inverse operator,
setting this option should, in general, have no effect on the result
for those operators. However, note that when no appropriate
|solver_options| are set for the operator, most implementations
will choose a least squares solver by default which may be
undesirable.
check_finite
Test if solution only contains finite values.
default_sparse_solver_backend
Default sparse solver backend to use (scipy, pyamg, generic).
Returns
-------
|VectorArray| of the inverse operator evaluations.
Raises
------
InversionError
The operator could not be inverted.
"""
assert V in self.range
if V.dim == 0:
if self.source.dim == 0 or least_squares:
return self.source.make_array(
np.zeros((len(V), self.source.dim)))
else:
raise InversionError
options = self.solver_options.get(
'inverse') if self.solver_options else None
assert self.sparse or not options
if self.sparse:
if options:
solver = options if isinstance(options,
str) else options['type']
backend = solver.split('_')[0]
else:
backend = default_sparse_solver_backend
if backend == 'scipy':
from pymor.bindings.scipy import apply_inverse as apply_inverse_impl
elif backend == 'pyamg':
if not config.HAVE_PYAMG:
raise RuntimeError('PyAMG support not enabled.')
from pymor.bindings.pyamg import apply_inverse as apply_inverse_impl
elif backend == 'generic':
logger = getLogger('pymor.bindings.scipy.scipy_apply_inverse')
logger.warning(
'You have selected a (potentially slow) generic solver for a NumPy matrix operator!'
)
from pymor.algorithms.genericsolvers import apply_inverse as apply_inverse_impl
else:
raise NotImplementedError
return apply_inverse_impl(self,
V,
options=options,
least_squares=least_squares,
check_finite=check_finite)
else:
if least_squares:
try:
R, _, _, _ = np.linalg.lstsq(self.matrix, V.to_numpy().T)
except np.linalg.LinAlgError as e:
raise InversionError(f'{str(type(e))}: {str(e)}')
R = R.T
else:
try:
R = np.linalg.solve(self.matrix, V.to_numpy().T).T
except np.linalg.LinAlgError as e:
raise InversionError(f'{str(type(e))}: {str(e)}')
if check_finite:
if not np.isfinite(np.sum(R)):
raise InversionError('Result contains non-finite values')
return self.source.make_array(R)
def apply_inverse_adjoint(self, U, mu=None, least_squares=False):
return self.H.apply_inverse(U, mu=mu, least_squares=least_squares)
def assemble_lincomb(self,
operators,
coefficients,
solver_options=None,
name=None):
if not all(
isinstance(op, (NumpyMatrixOperator, ZeroOperator,
IdentityOperator)) for op in operators):
return None
common_mat_dtype = reduce(
np.promote_types,
(op.matrix.dtype for op in operators if hasattr(op, 'matrix')))
common_coef_dtype = reduce(np.promote_types,
(type(c) for c in coefficients))
common_dtype = np.promote_types(common_mat_dtype, common_coef_dtype)
if coefficients[0] == 1:
matrix = operators[0].matrix.astype(common_dtype)
else:
matrix = operators[0].matrix * coefficients[0]
if matrix.dtype != common_dtype:
matrix = matrix.astype(common_dtype)
for op, c in zip(operators[1:], coefficients[1:]):
if type(op) is ZeroOperator:
continue
elif type(op) is IdentityOperator:
if c.imag == 0:
c = c.real
if operators[0].sparse:
try:
matrix += (scipy.sparse.eye(matrix.shape[0]) * c)
except NotImplementedError:
matrix = matrix + (scipy.sparse.eye(matrix.shape[0]) *
c)
else:
matrix += (np.eye(matrix.shape[0]) * c)
elif c == 1:
try:
matrix += op.matrix
except NotImplementedError:
matrix = matrix + op.matrix
elif c == -1:
try:
matrix -= op.matrix
except NotImplementedError:
matrix = matrix - op.matrix
else:
try:
matrix += (op.matrix * c)
except NotImplementedError:
matrix = matrix + (op.matrix * c)
return NumpyMatrixOperator(matrix,
source_id=self.source.id,
range_id=self.range.id,
solver_options=solver_options)
def __getstate__(self):
if hasattr(
self.matrix,
'factorization'): # remove unplicklable SuperLU factorization
del self.matrix.factorization
return self.__dict__
class NeuralNetworkModel(Model):
"""Class for models of stationary problems that use artificial neural networks.
This class implements a |Model| that uses a neural network for solving.
Parameters
----------
neural_network
The neural network that approximates the mapping from parameter space
to solution space. Should be an instance of
:class:`~pymor.models.neural_network.FullyConnectedNN` with input size that
matches the (total) number of parameters and output size equal to the
dimension of the reduced space.
output_functional
|Operator| mapping a given solution to the model output. In many applications,
this will be a |Functional|, i.e. an |Operator| mapping to scalars.
This is not required, however.
products
A dict of inner product |Operators| defined on the discrete space the
problem is posed on. For each product with key `'x'` a corresponding
attribute `x_product`, as well as a norm method `x_norm` is added to
the model.
error_estimator
An error estimator for the problem. This can be any object with
an `estimate_error(U, mu, m)` method. If `error_estimator` is
not `None`, an `estimate_error(U, mu)` method is added to the
model which will call `error_estimator.estimate_error(U, mu, self)`.
visualizer
A visualizer for the problem. This can be any object with
a `visualize(U, m, ...)` method. If `visualizer`
is not `None`, a `visualize(U, *args, **kwargs)` method is added
to the model which forwards its arguments to the
visualizer's `visualize` method.
name
Name of the model.
"""
def __init__(self, neural_network, output_functional=None, products=None,
error_estimator=None, visualizer=None, name=None):
super().__init__(products=products, error_estimator=error_estimator, visualizer=visualizer, name=name)
self.__auto_init(locals())
self.solution_space = NumpyVectorSpace(neural_network.output_dimension)
self.linear = output_functional is None or output_functional.linear
if output_functional is not None:
self.output_space = output_functional.range
def _solve(self, mu=None, return_output=False):
if not self.logging_disabled:
self.logger.info(f'Solving {self.name} for {mu} ...')
# convert the parameter `mu` into a form that is usable in PyTorch
converted_input = torch.from_numpy(mu.to_numpy()).double()
# obtain (reduced) coordinates by forward pass of the parameter values through the neural network
U = self.neural_network(converted_input).data.numpy()
# convert plain numpy array to element of the actual solution space
U = self.solution_space.make_array(U)
if return_output:
if self.output_functional is None:
raise ValueError('Model has no output')
return U, self.output_functional.apply(U, mu=mu)
else:
return U
class NumpyMatrixOperator(NumpyMatrixBasedOperator):
"""Wraps a 2D |NumPy Array| as an |Operator|.
Parameters
----------
matrix
The |NumPy array| which is to be wrapped.
name
Name of the operator.
"""
def __init__(self, matrix, source_id=None, range_id=None, solver_options=None, name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
try:
matrix.setflags(write=False) # make numpy arrays read-only
except AttributeError:
pass
self.source = NumpyVectorSpace(matrix.shape[1], source_id)
self.range = NumpyVectorSpace(matrix.shape[0], range_id)
self.solver_options = solver_options
self.name = name
self.matrix = matrix
self.source_id = source_id
self.range_id = range_id
self.sparse = issparse(matrix)
@classmethod
def from_file(cls, path, key=None, source_id=None, range_id=None, solver_options=None, name=None):
from pymor.tools.io import load_matrix
matrix = load_matrix(path, key=key)
return cls(matrix, solver_options=solver_options, source_id=source_id, range_id=range_id,
name=name or key or path)
@property
def H(self):
options = {'inverse': self.solver_options.get('inverse_adjoint'),
'inverse_adjoint': self.solver_options.get('inverse')} if self.solver_options else None
if self.sparse:
adjoint_matrix = self.matrix.transpose(copy=False).conj(copy=False)
elif np.isrealobj(self.matrix):
adjoint_matrix = self.matrix.T
else:
adjoint_matrix = self.matrix.T.conj()
return self.with_(matrix=adjoint_matrix, source_id=self.range_id, range_id=self.source_id,
solver_options=options, name=self.name + '_adjoint')
def _assemble(self, mu=None):
pass
def assemble(self, mu=None):
return self
def as_range_array(self, mu=None):
return self.range.make_array(self.matrix.T.copy())
def as_source_array(self, mu=None):
return self.source.make_array(self.matrix.copy()).conj()
def apply(self, U, mu=None):
assert U in self.source
return self.range.make_array(self.matrix.dot(U.to_numpy().T).T)
def apply_adjoint(self, V, mu=None):
assert V in self.range
return self.H.apply(V, mu=mu)
@defaults('check_finite', 'default_sparse_solver_backend')
def apply_inverse(self, V, mu=None, least_squares=False, check_finite=True,
default_sparse_solver_backend='scipy'):
"""Apply the inverse operator.
Parameters
----------
V
|VectorArray| of vectors to which the inverse operator is applied.
mu
The |Parameter| for which to evaluate the inverse operator.
least_squares
If `True`, solve the least squares problem::
u = argmin ||op(u) - v||_2.
Since for an invertible operator the least squares solution agrees
with the result of the application of the inverse operator,
setting this option should, in general, have no effect on the result
for those operators. However, note that when no appropriate
|solver_options| are set for the operator, most implementations
will choose a least squares solver by default which may be
undesirable.
check_finite
Test if solution only containes finite values.
default_solver
Default sparse solver backend to use (scipy, pyamg, generic).
Returns
-------
|VectorArray| of the inverse operator evaluations.
Raises
------
InversionError
The operator could not be inverted.
"""
assert V in self.range
if V.dim == 0:
if self.source.dim == 0 or least_squares:
return self.source.make_array(np.zeros((len(V), self.source.dim)))
else:
raise InversionError
options = self.solver_options.get('inverse') if self.solver_options else None
assert self.sparse or not options
if self.sparse:
if options:
solver = options if isinstance(options, str) else options['type']
backend = solver.split('_')[0]
else:
backend = default_sparse_solver_backend
if backend == 'scipy':
from pymor.bindings.scipy import apply_inverse as apply_inverse_impl
elif backend == 'pyamg':
if not config.HAVE_PYAMG:
raise RuntimeError('PyAMG support not enabled.')
from pymor.bindings.pyamg import apply_inverse as apply_inverse_impl
elif backend == 'generic':
logger = getLogger('pymor.bindings.scipy.scipy_apply_inverse')
logger.warning('You have selected a (potentially slow) generic solver for a NumPy matrix operator!')
from pymor.algorithms.genericsolvers import apply_inverse as apply_inverse_impl
else:
raise NotImplementedError
return apply_inverse_impl(self, V, options=options, least_squares=least_squares, check_finite=check_finite)
else:
if least_squares:
try:
R, _, _, _ = np.linalg.lstsq(self.matrix, V.to_numpy().T)
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
R = R.T
else:
try:
R = np.linalg.solve(self.matrix, V.to_numpy().T).T
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
if check_finite:
if not np.isfinite(np.sum(R)):
raise InversionError('Result contains non-finite values')
return self.source.make_array(R)
def apply_inverse_adjoint(self, U, mu=None, least_squares=False):
return self.H.apply_inverse(U, mu=mu, least_squares=least_squares)
def assemble_lincomb(self, operators, coefficients, solver_options=None, name=None):
if not all(isinstance(op, (NumpyMatrixOperator, ZeroOperator, IdentityOperator)) for op in operators):
return None
common_mat_dtype = reduce(np.promote_types,
(op.matrix.dtype for op in operators if hasattr(op, 'matrix')))
common_coef_dtype = reduce(np.promote_types, (type(c) for c in coefficients))
common_dtype = np.promote_types(common_mat_dtype, common_coef_dtype)
if coefficients[0] == 1:
matrix = operators[0].matrix.astype(common_dtype)
else:
matrix = operators[0].matrix * coefficients[0]
if matrix.dtype != common_dtype:
matrix = matrix.astype(common_dtype)
for op, c in zip(operators[1:], coefficients[1:]):
if type(op) is ZeroOperator:
continue
elif type(op) is IdentityOperator:
if c.imag == 0:
c = c.real
if operators[0].sparse:
try:
matrix += (scipy.sparse.eye(matrix.shape[0]) * c)
except NotImplementedError:
matrix = matrix + (scipy.sparse.eye(matrix.shape[0]) * c)
else:
matrix += (np.eye(matrix.shape[0]) * c)
elif c == 1:
try:
matrix += op.matrix
except NotImplementedError:
matrix = matrix + op.matrix
elif c == -1:
try:
matrix -= op.matrix
except NotImplementedError:
matrix = matrix - op.matrix
else:
try:
matrix += (op.matrix * c)
except NotImplementedError:
matrix = matrix + (op.matrix * c)
return NumpyMatrixOperator(matrix,
source_id=self.source.id,
range_id=self.range.id,
solver_options=solver_options)
def __getstate__(self):
if hasattr(self.matrix, 'factorization'): # remove unplicklable SuperLU factorization
del self.matrix.factorization
return self.__dict__
def transfer(va):
range_solution = localizer.to_space(
local_op.apply_inverse(
-rhsop.apply(NumpyVectorSpace.make_array(va))), training_space,
range_space)
return pou[range_space](range_solution).data
def _random_array(dims, length, seed):
np.random.seed(seed + mpi.rank)
dim = dims[mpi.rank] if len(dims) > 1 else dims[0]
array = NumpyVectorSpace.make_array(np.random.random((length, dim)))
obj_id = mpi.manage_object(array)
return obj_id
class ProjectedOperator(OperatorBase):
"""Generic |Operator| representing the projection of an |Operator| to a subspace.
This operator is implemented as the concatenation of the linear combination with
`source_basis`, application of the original `operator` and projection onto
`range_basis`. As such, this operator can be used to obtain a reduced basis
projection of any given |Operator|. However, no offline/online decomposition is
performed, so this operator is mainly useful for testing before implementing
offline/online decomposition for a specific application.
This operator is instantiated in :func:`pymor.algorithms.projection.project`
as a default implementation for parametric or nonlinear operators.
Parameters
----------
operator
The |Operator| to project.
range_basis
See :func:`pymor.algorithms.projection.project`.
source_basis
See :func:`pymor.algorithms.projection.project`.
product
See :func:`pymor.algorithms.projection.project`.
solver_options
The |solver_options| for the projected operator.
"""
linear = False
def __init__(self, operator, range_basis, source_basis, product=None, solver_options=None):
assert isinstance(operator, OperatorInterface)
assert source_basis is None or source_basis in operator.source
assert range_basis is None or range_basis in operator.range
assert (product is None
or (isinstance(product, OperatorInterface)
and range_basis is not None
and operator.range == product.source
and product.range == product.source))
self.build_parameter_type(operator)
self.source = NumpyVectorSpace(len(source_basis)) if source_basis is not None else operator.source
self.range = NumpyVectorSpace(len(range_basis)) if range_basis is not None else operator.range
self.solver_options = solver_options
self.name = operator.name
self.operator = operator
self.source_basis = source_basis.copy() if source_basis is not None else None
self.range_basis = range_basis.copy() if range_basis is not None else None
self.linear = operator.linear
self.product = product
@property
def H(self):
if self.product:
return super().H
else:
options = {'inverse': self.solver_options.get('inverse_adjoint'),
'inverse_adjoint': self.solver_options.get('inverse')} if self.solver_options else None
return ProjectedOperator(self.operator.H, self.source_basis, self.range_basis, solver_options=options)
def apply(self, U, mu=None):
mu = self.parse_parameter(mu)
if self.source_basis is None:
if self.range_basis is None:
return self.operator.apply(U, mu=mu)
elif self.product is None:
return self.range.make_array(self.operator.apply2(self.range_basis, U, mu=mu).T)
else:
V = self.operator.apply(U, mu=mu)
return self.range.make_array(self.product.apply2(V, self.range_basis))
else:
UU = self.source_basis.lincomb(U.to_numpy())
if self.range_basis is None:
return self.operator.apply(UU, mu=mu)
elif self.product is None:
return self.range.make_array(self.operator.apply2(self.range_basis, UU, mu=mu).T)
else:
V = self.operator.apply(UU, mu=mu)
return self.range.make_array(self.product.apply2(V, self.range_basis))
def jacobian(self, U, mu=None):
if self.linear:
return self.assemble(mu)
assert len(U) == 1
mu = self.parse_parameter(mu)
if self.source_basis is None:
J = self.operator.jacobian(U, mu=mu)
else:
J = self.operator.jacobian(self.source_basis.lincomb(U.to_numpy()), mu=mu)
from pymor.algorithms.projection import project
pop = project(J, range_basis=self.range_basis, source_basis=self.source_basis,
product=self.product, name=self.name + '_jacobian')
if self.solver_options:
options = self.solver_options.get('jacobian')
if options:
pop = pop.with_(solver_options=options)
return pop
def assemble(self, mu=None):
op = self.operator.assemble(mu=mu)
if op == self.operator: # avoid infinite recursion in apply_inverse default impl
return self
from pymor.algorithms.projection import project
pop = project(op, range_basis=self.range_basis, source_basis=self.source_basis,
product=self.product)
if self.solver_options:
pop = pop.with_(solver_options=self.solver_options)
return pop
def apply_adjoint(self, V, mu=None):
assert V in self.range
if self.range_basis is not None:
V = self.range_basis.lincomb(V.to_numpy())
U = self.operator.apply_adjoint(V, mu)
if self.source_basis is not None:
U = self.source.make_array(U.dot(self.source_basis))
return U
class NumpyMatrixOperator(NumpyMatrixBasedOperator):
"""Wraps a 2D |NumPy Array| as an |Operator|.
Parameters
----------
matrix
The |NumPy array| which is to be wrapped.
name
Name of the operator.
"""
def __init__(self, matrix, source_id=None, range_id=None, solver_options=None, name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
self.source = NumpyVectorSpace(matrix.shape[1], source_id)
self.range = NumpyVectorSpace(matrix.shape[0], range_id)
self.solver_options = solver_options
self.name = name
self._matrix = matrix
self.source_id = source_id
self.range_id = range_id
self.sparse = issparse(matrix)
@classmethod
def from_file(cls, path, key=None, source_id=None, range_id=None, solver_options=None, name=None):
from pymor.tools.io import load_matrix
matrix = load_matrix(path, key=key)
return cls(matrix, solver_options=solver_options, source_id=source_id, range_id=range_id,
name=name or key or path)
@property
def T(self):
options = {'inverse': self.solver_options.get('inverse_transpose'),
'inverse_transpose': self.solver_options.get('inverse')} if self.solver_options else None
return self.with_(matrix=self._matrix.T, source_id=self.range_id, range_id=self.source_id,
solver_options=options, name=self.name + '_transposed')
def _assemble(self, mu=None):
pass
def assemble(self, mu=None):
return self
def as_range_array(self, mu=None):
assert not self.sparse
return self.range.make_array(self._matrix.T.copy())
def as_source_array(self, mu=None):
assert not self.sparse
return self.source.make_array(self._matrix.copy())
def apply(self, U, mu=None):
assert U in self.source
return self.range.make_array(self._matrix.dot(U.data.T).T)
def apply_transpose(self, V, mu=None):
assert V in self.range
return self.source.make_array(self._matrix.T.dot(V.data.T).T)
@defaults('check_finite', 'default_sparse_solver_backend',
qualname='pymor.operators.numpy.NumpyMatrixOperator.apply_inverse')
def apply_inverse(self, V, mu=None, least_squares=False, check_finite=True,
default_sparse_solver_backend='scipy'):
"""Apply the inverse operator.
Parameters
----------
V
|VectorArray| of vectors to which the inverse operator is applied.
mu
The |Parameter| for which to evaluate the inverse operator.
least_squares
If `True`, solve the least squares problem::
u = argmin ||op(u) - v||_2.
Since for an invertible operator the least squares solution agrees
with the result of the application of the inverse operator,
setting this option should, in general, have no effect on the result
for those operators. However, note that when no appropriate
|solver_options| are set for the operator, most implementations
will choose a least squares solver by default which may be
undesirable.
check_finite
Test if solution only containes finite values.
default_solver
Default sparse solver backend to use (scipy, pyamg, generic).
Returns
-------
|VectorArray| of the inverse operator evaluations.
Raises
------
InversionError
The operator could not be inverted.
"""
assert V in self.range
if V.dim == 0:
if self.source.dim == 0 or least_squares:
return self.source.make_array(np.zeros((len(V), self.source.dim)))
else:
raise InversionError
options = self.solver_options.get('inverse') if self.solver_options else None
assert self.sparse or not options
if self.sparse:
if options:
solver = options if isinstance(options, str) else options['type']
backend = solver.split('_')[0]
else:
backend = default_sparse_solver_backend
if backend == 'scipy':
from pymor.bindings.scipy import apply_inverse as apply_inverse_impl
elif backend == 'pyamg':
if not config.HAVE_PYAMG:
raise RuntimeError('PyAMG support not enabled.')
from pymor.bindings.pyamg import apply_inverse as apply_inverse_impl
elif backend == 'generic':
logger = getLogger('pymor.bindings.scipy.scipy_apply_inverse')
logger.warn('You have selected a (potentially slow) generic solver for a NumPy matrix operator!')
from pymor.algorithms.genericsolvers import apply_inverse as apply_inverse_impl
else:
raise NotImplementedError
return apply_inverse_impl(self, V, options=options, least_squares=least_squares, check_finite=check_finite)
else:
if least_squares:
try:
R, _, _, _ = np.linalg.lstsq(self._matrix, V.data.T)
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
R = R.T
else:
try:
R = np.linalg.solve(self._matrix, V.data.T).T
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
if check_finite:
if not np.isfinite(np.sum(R)):
raise InversionError('Result contains non-finite values')
return self.source.make_array(R)
def apply_inverse_transpose(self, U, mu=None, least_squares=False):
options = {'inverse': self.solver_options.get('inverse_transpose') if self.solver_options else None}
transpose_op = NumpyMatrixOperator(self._matrix.T, source_id=self.range.id, range_id=self.source.id,
solver_options=options)
return transpose_op.apply_inverse(U, mu=mu, least_squares=least_squares)
def projected_to_subbasis(self, dim_range=None, dim_source=None, name=None):
"""Project the operator to a subbasis.
The purpose of this method is to further project an operator that has been
obtained through :meth:`~pymor.operators.interfaces.OperatorInterface.projected`
to subbases of the original projection bases, i.e. ::
op.projected(r_basis, s_basis, prod).projected_to_subbasis(dim_range, dim_source)
should be the same as ::
op.projected(r_basis[:dim_range], s_basis[:dim_source], prod)
For a |NumpyMatrixOperator| this amounts to extracting the upper-left
(dim_range, dim_source) corner of the matrix it wraps.
Parameters
----------
dim_range
Dimension of the range subbasis.
dim_source
Dimension of the source subbasis.
name
optional name for the returned |Operator|
Returns
-------
The projected |Operator|.
"""
assert dim_source is None or dim_source <= self.source.dim
assert dim_range is None or dim_range <= self.range.dim
name = name or '{}_projected_to_subbasis'.format(self.name)
# copy instead of just slicing the matrix to ensure contiguous memory
return NumpyMatrixOperator(self._matrix[:dim_range, :dim_source].copy(),
source_id=self.source.id,
range_id=self.range.id,
solver_options=self.solver_options,
name=name)
def assemble_lincomb(self, operators, coefficients, solver_options=None, name=None):
if not all(isinstance(op, (NumpyMatrixOperator, ZeroOperator, IdentityOperator)) for op in operators):
return None
common_mat_dtype = reduce(np.promote_types,
(op._matrix.dtype for op in operators if hasattr(op, '_matrix')))
common_coef_dtype = reduce(np.promote_types, (type(c.real if c.imag == 0 else c) for c in coefficients))
common_dtype = np.promote_types(common_mat_dtype, common_coef_dtype)
if coefficients[0] == 1:
matrix = operators[0]._matrix.astype(common_dtype)
else:
if coefficients[0].imag == 0:
matrix = operators[0]._matrix * coefficients[0].real
else:
matrix = operators[0]._matrix * coefficients[0]
if matrix.dtype != common_dtype:
matrix = matrix.astype(common_dtype)
for op, c in zip(operators[1:], coefficients[1:]):
if type(op) is ZeroOperator:
continue
elif type(op) is IdentityOperator:
if operators[0].sparse:
try:
matrix += (scipy.sparse.eye(matrix.shape[0]) * c)
except NotImplementedError:
matrix = matrix + (scipy.sparse.eye(matrix.shape[0]) * c)
else:
matrix += (np.eye(matrix.shape[0]) * c)
elif c == 1:
try:
matrix += op._matrix
except NotImplementedError:
matrix = matrix + op._matrix
elif c == -1:
try:
matrix -= op._matrix
except NotImplementedError:
matrix = matrix - op._matrix
elif c.imag == 0:
try:
matrix += (op._matrix * c.real)
except NotImplementedError:
matrix = matrix + (op._matrix * c.real)
else:
try:
matrix += (op._matrix * c)
except NotImplementedError:
matrix = matrix + (op._matrix * c)
return NumpyMatrixOperator(matrix,
source_id=self.source.id,
range_id=self.range.id,
solver_options=solver_options)
def __getstate__(self):
if hasattr(self._matrix, 'factorization'): # remove unplicklable SuperLU factorization
del self._matrix.factorization
return self.__dict__
def as_vector(self, copy=True):
vec = self.matrix.AsVector().FV().NumPy()
return NumpyVectorSpace.make_array(vec.copy() if copy else vec)
def solve(va):
solution = local_op.apply_inverse(
-rhsop.apply(NumpyVectorSpace.make_array(va)))
return solution.data
class VectorArrayOperator(OperatorBase):
"""Wraps a |VectorArray| as an |Operator|.
If `transposed` is `False`, the operator maps from `NumpyVectorSpace(len(array))`
to `array.space` by forming linear combinations of the vectors in the array
with given coefficient arrays.
If `transposed == True`, the operator maps from `array.space` to
`NumpyVectorSpace(len(array))` by forming the inner products of the argument
with the vectors in the given array.
Parameters
----------
array
The |VectorArray| which is to be treated as an operator.
transposed
See description above.
name
The name of the operator.
"""
linear = True
def __init__(self, array, transposed=False, space_id=None, name=None):
self._array = array.copy()
if transposed:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
self.transposed = transposed
self.space_id = space_id
self.name = name
@property
def T(self):
return VectorArrayOperator(self._array, not self.transposed, self.space_id, self.name + '_transposed')
def apply(self, U, mu=None):
assert U in self.source
if not self.transposed:
return self._array.lincomb(U.data)
else:
return self.range.make_array(U.dot(self._array))
def apply_transpose(self, V, mu=None):
assert V in self.range
if not self.transposed:
return self.source.make_array(self._array.dot(V).T)
else:
return self._array.lincomb(V.data)
def apply_inverse_transpose(self, U, mu=None, least_squares=False):
transpose_op = VectorArrayOperator(self._array, transposed=not self.transposed)
return transpose_op.apply_inverse(U, mu=mu, least_squares=least_squares)
def assemble_lincomb(self, operators, coefficients, solver_options=None, name=None):
transposed = operators[0].transposed
if not all(isinstance(op, VectorArrayOperator) and op.transposed == transposed for op in operators):
return None
assert not solver_options
if coefficients[0] == 1:
array = operators[0]._array.copy()
else:
array = operators[0]._array * coefficients[0]
for op, c in zip(operators[1:], coefficients[1:]):
array.axpy(c, op._array)
return VectorArrayOperator(array, transposed=transposed, name=name)
def as_range_array(self, mu=None):
if not self.transposed:
return self._array.copy()
else:
super().as_range_array(mu)
def as_source_array(self, mu=None):
if self.transposed:
return self._array.copy()
else:
super().as_source_array(mu)
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
if not self.transposed:
restricted_value = NumpyVectorSpace.make_array(self._array.components(dofs))
return VectorArrayOperator(restricted_value, False), np.arange(self.source.dim, dtype=np.int32)
else:
raise NotImplementedError
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
restricted_value = NumpyVectorSpace.make_array(self._value.components(dofs))
return ConstantOperator(restricted_value, NumpyVectorSpace(len(dofs))), dofs
def solve(va):
g = localizer.to_space(NumpyVectorSpace.make_array(va), source_space,
omega_star_space)
solution = bilifo.apply_inverse(g)
return solution.data
def localize_problem(p,
coarse_grid_resolution,
fine_grid_resolution,
mus=None,
calT=False,
calTd=False,
calQ=False,
dof_codim=2,
localization_codim=2,
discretizer=None,
m=1):
assert coarse_grid_resolution > (m + 1) * 2
assert fine_grid_resolution % coarse_grid_resolution == 0
print("localizing problem")
global_quantities = {}
global_quantities["coarse_grid_resolution"] = coarse_grid_resolution
local_quantities = {}
# Diskretisierung auf dem feinen Gitter:
diameter = 1. / fine_grid_resolution
global_quantities["diameter"] = diameter
if discretizer is None:
discretizer = discretize_stationary_cg
d, data = discretizer(p, diameter=diameter)
grid = data["grid"]
global_quantities["d"] = d
global_quantities["data"] = data
global_operator = d.operator.assemble(mus)
global_quantities["op"] = global_operator
global_quantities["op_not_assembled"] = d.operator
global_rhs = d.rhs.assemble(mus)
global_quantities["rhs"] = global_rhs
op_fixed = copy.deepcopy(d.operator)
# Skalierung der Dirichlet-Freiheitsgrade:
try:
dirichlet_dofs = data['boundary_info'].dirichlet_boundaries(dof_codim)
for op in op_fixed.operators:
op.assemble(mus).matrix[dirichlet_dofs, dirichlet_dofs] *= 1e5
# d.rhs.assemble(mus)._matrix[:, dirichlet_dofs] *= 1e5
except KeyError:
pass
global_operator_fixed = op_fixed.assemble(mus)
global_quantities["op_fixed"] = global_operator_fixed
global_quantities["op_fixed_not_assembled"] = op_fixed
global_quantities["p"] = p
try:
dmask = data['boundary_info'].dirichlet_mask(dof_codim)
except KeyError:
dmask = None
# Konstruktion der Teilraeume:
subspaces, subspaces_per_codim = build_subspaces(
*partition_any_grid(grid,
num_intervals=(coarse_grid_resolution,
coarse_grid_resolution),
dmask=dmask,
codim=dof_codim))
global_quantities["subspaces"] = subspaces
global_quantities["subspaces_per_codim"] = subspaces_per_codim
localizer = NumpyLocalizer(d.solution_space, subspaces['dofs'])
global_quantities["localizer"] = localizer
def create_m_patch(xspace, m):
for i in range(m):
space = xspace
cspace = tuple(
set(i for k in space if subspaces[k]['codim'] == 0
for i in subspaces[k]['cpatch'] if i not in space))
xspace = tuple(
set(i for k in cspace if subspaces[k]['codim'] == 1
for i in subspaces[k]['env']) | set(space))
cxspace = tuple(
set(i for k in xspace if subspaces[k]['codim'] == 0
for i in subspaces[k]['cpatch'] if i not in xspace))
return xspace, cxspace
pou = localized_pou(subspaces, subspaces_per_codim, localizer,
coarse_grid_resolution, grid, localization_codim,
dof_codim)
global_quantities["pou"] = pou
spaces = [subspaces[s_id]["env"] for s_id in subspaces_per_codim[2]]
global_quantities["spaces"] = spaces
full_l2_product = d.products["l2"].assemble()
full_h1_semi_product = d.products["h1_semi"].assemble()
k_product = LincombOperator((full_h1_semi_product, full_l2_product),
(1, mus["k"]**2)).assemble()
global_quantities["full_norm"] = induced_norm(k_product)
global_quantities["k_product"] = k_product
for xpos in range(coarse_grid_resolution - 1):
for ypos in range(coarse_grid_resolution - 1):
# print "localizing..."
s_id = subspaces_per_codim[localization_codim][
ypos + xpos * (coarse_grid_resolution - 1)]
space = subspaces[s_id]["env"]
ldict = {}
local_quantities[space] = ldict
ldict["pos"] = (xpos, ypos)
# Konstruktion der lokalen Raeume:
range_space = subspaces[s_id]["env"]
ldict["range_space"] = range_space
omega_space = tuple(
sorted(
set(subspaces[s_id]['env'])
| set(subspaces[s_id]['cenv'])))
ldict["omega_space"] = omega_space
training_space, source_space = create_m_patch(range_space, m)
# source_space = subspaces[s_id]["cxenv"]
ldict["source_space"] = source_space
# training_space = subspaces[s_id]["xenv"]
ldict["training_space"] = training_space
omega_star_space = tuple(
sorted(set(training_space) | set(source_space)))
ldict["omega_star_space"] = omega_star_space
# lokale Shift-Loesung mit f(Dirichlet)
local_op = localizer.localize_operator(global_operator,
training_space,
training_space)
local_rhs = localizer.localize_operator(global_rhs, None,
training_space)
local_solution = local_op.apply_inverse(local_rhs.as_range_array())
local_solution = localizer.to_space(local_solution, training_space,
range_space)
local_solution = pou[range_space](local_solution)
ldict["local_solution_dirichlet"] = local_solution
# Dirichlet Transferoperator:
rhsop = localizer.localize_operator(global_operator,
training_space, source_space)
transop_dirichlet = create_dirichlet_transfer(
localizer, local_op, rhsop, source_space, training_space,
range_space, pou)
ldict["dirichlet_transfer"] = transop_dirichlet
# subgrid
xmin = max(0, xpos - m)
xsize = min(xpos + 2 + m, coarse_grid_resolution) - xmin
ymin = max(0, ypos - m)
ysize = min(ypos + 2 + m, coarse_grid_resolution) - ymin
ldict["posext"] = [(xmin / coarse_grid_resolution,
ymin / coarse_grid_resolution),
((xmin + xsize) / coarse_grid_resolution,
(ymin + ysize) / coarse_grid_resolution)]
mysubgrid = getsubgrid(grid,
xmin,
ymin,
coarse_grid_resolution,
xsize=xsize,
ysize=ysize)
mysubbi = SubGridBoundaryInfo(mysubgrid, grid,
data['boundary_info'], 'robin')
ld, ldata = discretizer(p, grid=mysubgrid, boundary_info=mysubbi)
lop = ld.operator.assemble(mus)
# index conversion
ndofsext = len(ldata['grid'].parent_indices(dof_codim))
global_dofnrsext = -100000000 * np.ones(
shape=(d.solution_space.dim, ))
global_dofnrsext[ldata['grid'].parent_indices(
dof_codim)] = np.array(range(ndofsext))
lvecext = localizer.localize_vector_array(
NumpyVectorSpace.make_array(global_dofnrsext),
omega_star_space).data[0]
# Robin Transferoperator:
bilifo = NumpyMatrixOperator(lop.matrix[:, lvecext][lvecext, :])
transop_robin = create_robin_transfer(localizer, bilifo,
source_space,
omega_star_space,
range_space, pou)
ldict["robin_transfer"] = transop_robin
# lokale Shift-Loesung mit f(Robin)
lrhs = ld.rhs.assemble(mus)
llrhs = NumpyMatrixOperator(lrhs.matrix[lvecext.astype(int)])
local_solution = bilifo.apply_inverse(llrhs.as_range_array())
ldict["local_sol2"] = local_solution
local_solution = localizer.to_space(local_solution,
omega_star_space, range_space)
local_solution_pou = pou[range_space](local_solution)
ldict["local_solution_robin"] = local_solution_pou
if calT:
# Transfer-Matrix:
ldict["transfer_matrix_robin"] = transop_robin.as_range_array(
).data.T
if calTd:
# Transfer-Matrix:
ldict[
"transfer_matrix_dirichlet"] = transop_dirichlet.as_range_array(
).data.T
# Konstruktion der Produkte:
range_k = localizer.localize_operator(k_product, range_space,
range_space)
omstar_k = LincombOperator((NumpyMatrixOperator(
ld.products["h1_semi"].assemble().matrix[:,
lvecext][lvecext, :]),
NumpyMatrixOperator(
ld.products["l2"].assemble(
).matrix[:, lvecext][lvecext, :])),
(1, mus["k"]**2)).assemble()
ldict["omega_star_product"] = omstar_k
ldict["range_product"] = range_k
if calQ:
# Loesungs-Matrix:
solution_op_robin = create_robin_solop(localizer, bilifo,
source_space,
omega_star_space)
Q_r = solution_op_robin.as_range_array()
ldict["solution_matrix_robin"] = Q_r.data.T
source_Q_r_product = NumpyMatrixOperator(
omstar_k.apply(Q_r).data.T)
ldict["source_product"] = source_Q_r_product
lproduct = localizer.localize_operator(full_l2_product,
source_space, source_space)
lmat = lproduct.matrix.tocoo()
lmat.data = np.array([
4. / 6. * diameter if (row == col) else diameter / 6.
for row, col in zip(lmat.row, lmat.col)
])
ldict["source_product"] = NumpyMatrixOperator(lmat.tocsc().astype(
np.cfloat))
return global_quantities, local_quantities
def localize_vector_array(self, va, ind):
assert isinstance(va, NumpyVectorArray)
subspace = self.join_spaces(ind)
a = va._array[:, subspace]
return NumpyVectorSpace.make_array(a)
class NumpyGenericOperator(OperatorBase):
"""Wraps an arbitrary Python function between |NumPy arrays| as an |Operator|.
Parameters
----------
mapping
The function to wrap. If `parameter_type` is `None`, the function is of
the form `mapping(U)` and is expected to be vectorized. In particular::
mapping(U).shape == U.shape[:-1] + (dim_range,).
If `parameter_type` is not `None`, the function has to have the signature
`mapping(U, mu)`.
adjoint_mapping
The adjoint function to wrap. If `parameter_type` is `None`, the function is of
the form `adjoint_mapping(U)` and is expected to be vectorized. In particular::
adjoint_mapping(U).shape == U.shape[:-1] + (dim_source,).
If `parameter_type` is not `None`, the function has to have the signature
`adjoint_mapping(U, mu)`.
dim_source
Dimension of the operator's source.
dim_range
Dimension of the operator's range.
linear
Set to `True` if the provided `mapping` and `adjoint_mapping` are linear.
parameter_type
The |ParameterType| of the |Parameters| the mapping accepts.
solver_options
The |solver_options| for the operator.
name
Name of the operator.
"""
def __init__(self,
mapping,
adjoint_mapping=None,
dim_source=1,
dim_range=1,
linear=False,
parameter_type=None,
source_id=None,
range_id=None,
solver_options=None,
name=None):
self.source = NumpyVectorSpace(dim_source, source_id)
self.range = NumpyVectorSpace(dim_range, range_id)
self.solver_options = solver_options
self.name = name
self._mapping = mapping
self._adjoint_mapping = adjoint_mapping
self.linear = linear
if parameter_type is not None:
self.build_parameter_type(parameter_type)
self.source_id = source_id # needed for with_
self.range_id = range_id
def apply(self, U, mu=None):
assert U in self.source
if self.parametric:
mu = self.parse_parameter(mu)
return self.range.make_array(self._mapping(U.to_numpy(), mu=mu))
else:
return self.range.make_array(self._mapping(U.to_numpy()))
def apply_adjoint(self, V, mu=None):
if self._adjoint_mapping is None:
raise ValueError(
'NumpyGenericOperator: adjoint mapping was not defined.')
assert V in self.range
V = V.to_numpy()
if self.parametric:
mu = self.parse_parameter(mu)
return self.source.make_array(self._adjoint_mapping(V, mu=mu))
else:
return self.source.make_array(self._adjoint_mapping(V))
class NeuralNetworkInstationaryModel(Model):
"""Class for models of instationary problems that use artificial neural networks.
This class implements a |Model| that uses a neural network for solving.
Parameters
----------
T
The final time T.
nt
The number of time steps.
neural_network
The neural network that approximates the mapping from parameter space
to solution space. Should be an instance of
:class:`~pymor.models.neural_network.FullyConnectedNN` with input size that
matches the (total) number of parameters and output size equal to the
dimension of the reduced space.
parameters
|Parameters| of the reduced order model (the same as used in the full-order
model).
output_functional
|Operator| mapping a given solution to the model output. In many applications,
this will be a |Functional|, i.e. an |Operator| mapping to scalars.
This is not required, however.
products
A dict of inner product |Operators| defined on the discrete space the
problem is posed on. For each product with key `'x'` a corresponding
attribute `x_product`, as well as a norm method `x_norm` is added to
the model.
error_estimator
An error estimator for the problem. This can be any object with
an `estimate_error(U, mu, m)` method. If `error_estimator` is
not `None`, an `estimate_error(U, mu)` method is added to the
model which will call `error_estimator.estimate_error(U, mu, self)`.
visualizer
A visualizer for the problem. This can be any object with
a `visualize(U, m, ...)` method. If `visualizer`
is not `None`, a `visualize(U, *args, **kwargs)` method is added
to the model which forwards its arguments to the
visualizer's `visualize` method.
name
Name of the model.
"""
def __init__(self,
T,
nt,
neural_network,
parameters={},
output_functional=None,
products=None,
error_estimator=None,
visualizer=None,
name=None):
super().__init__(products=products,
error_estimator=error_estimator,
visualizer=visualizer,
name=name)
self.__auto_init(locals())
self.solution_space = NumpyVectorSpace(
neural_network.output_dimension)
if output_functional is not None:
self.dim_output = output_functional.range.dim
def _compute_solution(self, mu=None, **kwargs):
U = self.solution_space.empty(reserve=self.nt)
dt = self.T / (self.nt - 1)
t = 0.
# iterate over time steps
for i in range(self.nt):
mu = mu.with_(t=t)
# convert the parameter `mu` into a form that is usable in PyTorch
converted_input = torch.from_numpy(mu.to_numpy()).double()
# obtain (reduced) coordinates by forward pass of the parameter values through the neural network
result_neural_network = self.neural_network(
converted_input).data.numpy()
# convert plain numpy array to element of the actual solution space
U.append(self.solution_space.make_array(result_neural_network))
t += dt
return U
def localize_operator(self, op, range_ind, source_ind):
if isinstance(op, VectorArrayOperator):
assert range_ind is None
source_ind = tuple(source_ind)
source_subspace = self.join_spaces(source_ind)
a = NumpyVectorSpace.make_array(op._array.data[:, source_subspace])
result = VectorArrayOperator(a,
transposed=op.transposed,
name='{}-{}-{}'.format(
op.name, source_ind, range_ind))
return result
if isinstance(op, NumpyMatrixOperator):
# special case for functionals
if range_ind is None:
source_ind = tuple(source_ind)
source_subspace = self.join_spaces(source_ind)
m = op.matrix[source_subspace]
result = NumpyMatrixOperator(m,
name='{}-{}-{}'.format(
op.name, source_ind,
range_ind))
return result
source_ind = tuple(source_ind)
range_ind = tuple(range_ind)
op_id = getattr(op, 'sid', op.uid)
identification_key = (op_id, source_ind, range_ind)
if identification_key in self._resultcache:
return self._resultcache[identification_key]
if op_id not in self._non_zeros:
# FIXME also handle dense case
M = op.matrix.tocoo()
incidences = np.empty(len(M.col),
dtype=[('row', np.int32),
('col', np.int32)])
incidences['row'] = self.subspace_map[M.row]
incidences['col'] = self.subspace_map[M.col]
incidences = np.unique(incidences)
self._non_zeros[op_id] = set(incidences.tolist())
non_zeros = self._non_zeros[op_id]
if all((ri, si) not in non_zeros
for si, ri in product(source_ind, range_ind)):
return None
source_subspace = self.join_spaces(source_ind)
range_subspace = self.join_spaces(range_ind)
if issparse(op.matrix):
m = op.matrix.tocsc()[:, source_subspace][range_subspace, :]
else:
m = op.matrix[:, source_subspace][range_subspace, :]
result = NumpyMatrixOperator(m,
name='{}-{}-{}'.format(
op.name, source_ind, range_ind))
self._resultcache[identification_key] = result
return result
elif isinstance(op, LincombOperator):
ops = [
self.localize_operator(o, range_ind, source_ind)
for o in op.operators
]
return LincombOperator(ops, op.coefficients)
else:
print("op is ", op)
raise NotImplementedError
class ProjectedOperator(OperatorBase):
"""Generic |Operator| representing the projection of an |Operator| to a subspace.
This operator is implemented as the concatenation of the linear combination with
`source_basis`, application of the original `operator` and projection onto
`range_basis`. As such, this operator can be used to obtain a reduced basis
projection of any given |Operator|. However, no offline/online decomposition is
performed, so this operator is mainly useful for testing before implementing
offline/online decomposition for a specific application.
This operator is instantiated in the default implementation of
:meth:`~pymor.operators.interfaces.OperatorInterface.projected` in
:class:`OperatorBase` for parametric or nonlinear operators.
Parameters
----------
operator
The |Operator| to project.
source_basis
See :meth:`~pymor.operators.interfaces.OperatorInterface.projected`.
range_basis
See :meth:`~pymor.operators.interfaces.OperatorInterface.projected`.
product
See :meth:`~pymor.operators.interfaces.OperatorInterface.projected`.
name
Name of the projected operator.
"""
linear = False
def __init__(self, operator, range_basis, source_basis, product=None, solver_options=None, name=None):
assert isinstance(operator, OperatorInterface)
assert source_basis is None or source_basis in operator.source
assert range_basis is None or range_basis in operator.range
assert product is None \
or (isinstance(product, OperatorInterface)
and range_basis is not None
and operator.range == product.source
and product.range == product.source)
self.build_parameter_type(operator)
self.source = NumpyVectorSpace(len(source_basis), operator.source.id) if source_basis is not None else operator.source
self.range = NumpyVectorSpace(len(range_basis), operator.range.id) if range_basis is not None else operator.range
self.solver_options = solver_options
self.name = name
self.operator = operator
self.source_basis = source_basis.copy() if source_basis is not None else None
self.range_basis = range_basis.copy() if range_basis is not None else None
self.linear = operator.linear
self.product = product
@property
def T(self):
if self.product:
return super().T
else:
options = {'inverse': self.solver_options.get('inverse_transpose'),
'inverse_transpose': self.solver_options.get('inverse')} if self.solver_options else None
return ProjectedOperator(self.operator.T, self.source_basis, self.range_basis,
solver_options=options, name=self.name + '_transposed')
def apply(self, U, mu=None):
mu = self.parse_parameter(mu)
if self.source_basis is None:
if self.range_basis is None:
return self.operator.apply(U, mu=mu)
elif self.product is None:
return self.range.make_array(self.operator.apply2(self.range_basis, U, mu=mu).T)
else:
V = self.operator.apply(U, mu=mu)
return self.range.make_array(self.product.apply2(V, self.range_basis))
else:
UU = self.source_basis.lincomb(U.data)
if self.range_basis is None:
return self.operator.apply(UU, mu=mu)
elif self.product is None:
return self.range.make_array(self.operator.apply2(self.range_basis, UU, mu=mu).T)
else:
V = self.operator.apply(UU, mu=mu)
return self.range.make_array(self.product.apply2(V, self.range_basis))
def projected_to_subbasis(self, dim_range=None, dim_source=None, name=None):
"""See :meth:`NumpyMatrixOperator.projected_to_subbasis`."""
assert dim_source is None or dim_source <= self.source.dim
assert dim_range is None or dim_range <= self.range.dim
assert dim_source is None or self.source_basis is not None, 'not implemented'
assert dim_range is None or self.range_basis is not None, 'not implemented'
name = name or '{}_projected_to_subbasis'.format(self.name)
source_basis = self.source_basis if dim_source is None \
else self.source_basis[:dim_source]
range_basis = self.range_basis if dim_range is None \
else self.range_basis[:dim_range]
return ProjectedOperator(self.operator, range_basis, source_basis, product=None,
solver_options=self.solver_options, name=name)
def jacobian(self, U, mu=None):
if self.linear:
return self.assemble(mu)
assert len(U) == 1
mu = self.parse_parameter(mu)
if self.source_basis is None:
J = self.operator.jacobian(U, mu=mu)
else:
J = self.operator.jacobian(self.source_basis.lincomb(U.data), mu=mu)
pop = J.projected(range_basis=self.range_basis, source_basis=self.source_basis,
product=self.product, name=self.name + '_jacobian')
if self.solver_options:
options = self.solver_options.get('jacobian')
if options:
pop = pop.with_(solver_options=options)
return pop
def assemble(self, mu=None):
op = self.operator.assemble(mu=mu)
pop = op.projected(range_basis=self.range_basis, source_basis=self.source_basis,
product=self.product, name=self.name + '_assembled')
if self.solver_options:
pop = pop.with_(solver_options=self.solver_options)
return pop
def discrete_multiply(va, function):
assert len(function.shape) == 1
return NumpyVectorSpace.make_array(va.data * function)
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
restricted_value = NumpyVectorSpace.make_array(self._value.dofs(dofs))
return ConstantOperator(restricted_value,
NumpyVectorSpace(len(dofs))), dofs
class NumpyGenericOperator(OperatorBase):
"""Wraps an arbitrary Python function between |NumPy arrays| as a an |Operator|.
Parameters
----------
mapping
The function to wrap. If `parameter_type` is `None`, the function is of
the form `mapping(U)` and is expected to be vectorized. In particular::
mapping(U).shape == U.shape[:-1] + (dim_range,).
If `parameter_type` is not `None`, the function has to have the signature
`mapping(U, mu)`.
adjoint_mapping
The adjoint function to wrap. If `parameter_type` is `None`, the function is of
the form `adjoint_mapping(U)` and is expected to be vectorized. In particular::
adjoint_mapping(U).shape == U.shape[:-1] + (dim_source,).
If `parameter_type` is not `None`, the function has to have the signature
`adjoint_mapping(U, mu)`.
dim_source
Dimension of the operator's source.
dim_range
Dimension of the operator's range.
linear
Set to `True` if the provided `mapping` and `adjoint_mapping` are linear.
parameter_type
The |ParameterType| of the |Parameters| the mapping accepts.
name
Name of the operator.
"""
def __init__(self, mapping, adjoint_mapping=None, dim_source=1, dim_range=1, linear=False, parameter_type=None,
source_id=None, range_id=None, solver_options=None, name=None):
self.source = NumpyVectorSpace(dim_source, source_id)
self.range = NumpyVectorSpace(dim_range, range_id)
self.solver_options = solver_options
self.name = name
self._mapping = mapping
self._adjoint_mapping = adjoint_mapping
self.linear = linear
if parameter_type is not None:
self.build_parameter_type(parameter_type)
self.source_id = source_id # needed for with_
self.range_id = range_id
def apply(self, U, mu=None):
assert U in self.source
if self.parametric:
mu = self.parse_parameter(mu)
return self.range.make_array(self._mapping(U.to_numpy(), mu=mu))
else:
return self.range.make_array(self._mapping(U.to_numpy()))
def apply_adjoint(self, V, mu=None):
if self._adjoint_mapping is None:
raise ValueError('NumpyGenericOperator: adjoint mapping was not defined.')
assert V in self.range
V = V.to_numpy()
if self.parametric:
mu = self.parse_parameter(mu)
return self.source.make_array(self._adjoint_mapping(V, mu=mu))
else:
return self.source.make_array(self._adjoint_mapping(V))
class VectorArrayOperator(OperatorBase):
"""Wraps a |VectorArray| as an |Operator|.
If `adjoint` is `False`, the operator maps from `NumpyVectorSpace(len(array))`
to `array.space` by forming linear combinations of the vectors in the array
with given coefficient arrays.
If `adjoint == True`, the operator maps from `array.space` to
`NumpyVectorSpace(len(array))` by forming the inner products of the argument
with the vectors in the given array.
Parameters
----------
array
The |VectorArray| which is to be treated as an operator.
adjoint
See description above.
space_id
Id of the `source` (`range`) |VectorSpace| in case `adjoint` is
`False` (`True`).
name
The name of the operator.
"""
linear = True
def __init__(self, array, adjoint=False, space_id=None, name=None):
self._array = array.copy()
if adjoint:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
self.adjoint = adjoint
self.space_id = space_id
self.name = name
@property
def H(self):
return VectorArrayOperator(self._array, not self.adjoint,
self.space_id, self.name + '_adjoint')
def apply(self, U, mu=None):
assert U in self.source
if not self.adjoint:
return self._array.lincomb(U.to_numpy())
else:
return self.range.make_array(self._array.dot(U).T)
def apply_adjoint(self, V, mu=None):
assert V in self.range
if not self.adjoint:
return self.source.make_array(self._array.dot(V).T)
else:
return self._array.lincomb(V.to_numpy())
def apply_inverse_adjoint(self, U, mu=None, least_squares=False):
adjoint_op = VectorArrayOperator(self._array, adjoint=not self.adjoint)
return adjoint_op.apply_inverse(U, mu=mu, least_squares=least_squares)
def as_range_array(self, mu=None):
if not self.adjoint:
return self._array.copy()
else:
return super().as_range_array(mu)
def as_source_array(self, mu=None):
if self.adjoint:
return self._array.copy()
else:
return super().as_source_array(mu)
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
if not self.adjoint:
restricted_value = NumpyVectorSpace.make_array(
self._array.dofs(dofs))
return VectorArrayOperator(restricted_value,
False), np.arange(self.source.dim,
dtype=np.int32)
else:
raise NotImplementedError
p = EllipticProblem(domain=RectDomain([[0, 0], [1, 1]]),
diffusion_functions=(ConstantFunction(1.,
dim_domain=2), ),
diffusion_functionals=(1., ),
rhs=ConstantFunction(1., dim_domain=2))
d, data = discretize_elliptic_cg(p, diameter=0.01)
grid = data["grid"]
subspaces, subspaces_per_codim = build_subspaces(*partition_any_grid(
grid, num_intervals=(coarse_grid_resolution, coarse_grid_resolution)))
localizer = NumpyLocalizer(d.solution_space, subspaces['dofs'])
images = d.solution_space.empty()
fdict = localized_pou(subspaces, subspaces_per_codim, localizer,
coarse_grid_resolution, grid)
for space in sorted(fdict):
lvec = localizer.localize_vector_array(
NumpyVectorSpace.make_array(np.ones(d.solution_space.dim)), space)
lvec = fdict[space](lvec)
gvec = localizer.globalize_vector_array(lvec, space)
images.append(gvec)
sum = d.solution_space.zeros()
for i in range(len(images)):
sum += images.copy(ind=i)
d.visualize(images)
assert np.abs(np.max(sum.data) - 1) < 1e-12
assert np.abs(np.min(sum.data) - 1) < 1e-12
def as_vector(self, copy=True):
vec = self.matrix.AsVector().FV().NumPy()
return NumpyVectorSpace.make_array(vec.copy() if copy else vec)
def _random_array(dims, length, seed):
np.random.seed(seed + mpi.rank)
dim = dims[mpi.rank] if len(dims) > 1 else dims[0]
array = NumpyVectorSpace.make_array(np.random.random((length, dim)))
obj_id = mpi.manage_object(array)
return obj_id
class VectorArrayOperator(OperatorBase):
"""Wraps a |VectorArray| as an |Operator|.
If `transposed` is `False`, the operator maps from `NumpyVectorSpace(len(array))`
to `array.space` by forming linear combinations of the vectors in the array
with given coefficient arrays.
If `transposed == True`, the operator maps from `array.space` to
`NumpyVectorSpace(len(array))` by forming the inner products of the argument
with the vectors in the given array.
Parameters
----------
array
The |VectorArray| which is to be treated as an operator.
transposed
See description above.
name
The name of the operator.
"""
linear = True
def __init__(self, array, transposed=False, space_id=None, name=None):
self._array = array.copy()
if transposed:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
self.transposed = transposed
self.space_id = space_id
self.name = name
@property
def T(self):
return VectorArrayOperator(self._array, not self.transposed,
self.space_id, self.name + '_transposed')
def apply(self, U, mu=None):
assert U in self.source
if not self.transposed:
return self._array.lincomb(U.data)
else:
return self.range.make_array(U.dot(self._array))
def apply_transpose(self, V, mu=None):
assert V in self.range
if not self.transposed:
return self.source.make_array(self._array.dot(V).T)
else:
return self._array.lincomb(V.data)
def apply_inverse_transpose(self, U, mu=None, least_squares=False):
transpose_op = VectorArrayOperator(self._array,
transposed=not self.transposed)
return transpose_op.apply_inverse(U,
mu=mu,
least_squares=least_squares)
def assemble_lincomb(self,
operators,
coefficients,
solver_options=None,
name=None):
transposed = operators[0].transposed
if not all(
isinstance(op, VectorArrayOperator)
and op.transposed == transposed for op in operators):
return None
assert not solver_options
if coefficients[0] == 1:
array = operators[0]._array.copy()
else:
array = operators[0]._array * coefficients[0]
for op, c in zip(operators[1:], coefficients[1:]):
array.axpy(c, op._array)
return VectorArrayOperator(array, transposed=transposed, name=name)
def as_range_array(self, mu=None):
if not self.transposed:
return self._array.copy()
else:
super().as_range_array(mu)
def as_source_array(self, mu=None):
if self.transposed:
return self._array.copy()
else:
super().as_source_array(mu)
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
if not self.transposed:
restricted_value = NumpyVectorSpace.make_array(
self._array.dofs(dofs))
return VectorArrayOperator(restricted_value,
False), np.arange(self.source.dim,
dtype=np.int32)
else:
raise NotImplementedError
class NumpyGenericOperator(Operator):
"""Wraps an arbitrary Python function between |NumPy arrays| as an |Operator|.
Parameters
----------
mapping
The function to wrap. If `parameters` is `None`, the function is of
the form `mapping(U)` and is expected to be vectorized. In particular::
mapping(U).shape == U.shape[:-1] + (dim_range,).
If `parameters` is not `None`, the function has to have the signature
`mapping(U, mu)`.
adjoint_mapping
The adjoint function to wrap. If `parameters` is `None`, the function is of
the form `adjoint_mapping(U)` and is expected to be vectorized. In particular::
adjoint_mapping(U).shape == U.shape[:-1] + (dim_source,).
If `parameters` is not `None`, the function has to have the signature
`adjoint_mapping(U, mu)`.
dim_source
Dimension of the operator's source.
dim_range
Dimension of the operator's range.
linear
Set to `True` if the provided `mapping` and `adjoint_mapping` are linear.
parameters
The |Parameters| the depends on.
solver_options
The |solver_options| for the operator.
name
Name of the operator.
"""
def __init__(self,
mapping,
adjoint_mapping=None,
dim_source=1,
dim_range=1,
linear=False,
parameters={},
source_id=None,
range_id=None,
solver_options=None,
name=None):
self.__auto_init(locals())
self.source = NumpyVectorSpace(dim_source, source_id)
self.range = NumpyVectorSpace(dim_range, range_id)
self.parameters_own = parameters
def apply(self, U, mu=None):
assert U in self.source
assert self.parameters.assert_compatible(mu)
if self.parametric:
return self.range.make_array(self.mapping(U.to_numpy(), mu=mu))
else:
return self.range.make_array(self.mapping(U.to_numpy()))
def apply_adjoint(self, V, mu=None):
if self.adjoint_mapping is None:
raise ValueError(
'NumpyGenericOperator: adjoint mapping was not defined.')
assert V in self.range
assert self.parameters.assert_compatible(mu)
V = V.to_numpy()
if self.parametric:
return self.source.make_array(self.adjoint_mapping(V, mu=mu))
else:
return self.source.make_array(self.adjoint_mapping(V))
