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(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)