pymor.operators.list
¶
Module Contents¶
Classes¶
Interface for 

Interface for 

Variant of 
 class pymor.operators.list.ListVectorArrayOperatorBase[source]¶
Bases:
pymor.operators.interface.Operator
Interface for
Parameter
dependent discrete operators.An operator in pyMOR is simply a mapping which for any given
parameter values
maps vectors from itssource
VectorSpace
to vectors in itsrange
VectorSpace
.Note that there is no special distinction between functionals and operators in pyMOR. A functional is simply an operator with
NumpyVectorSpace
(1)
as itsrange
VectorSpace
. solver_options[source]¶
If not
None
, a dict which can contain the following keys: ‘inverse’
solver options used for
apply_inverse
 ‘inverse_adjoint’
solver options used for
apply_inverse_adjoint
 ‘jacobian’
solver options for the operators returned by
jacobian
(has no effect for linear operators)
If
solver_options
isNone
or a dict entry is missing orNone
, default options are used. The interpretation of the given solver options is up to the operator at hand. In general, values insolver_options
should either be strings (indicating a solver type) or dicts of options, usually with an entry'type'
which specifies the solver type to use and further items which configure this solver.
 source[source]¶
The source
VectorSpace
.
 range[source]¶
The range
VectorSpace
.
 H[source]¶
The adjoint operator, i.e.
self.H.apply(V, mu) == self.apply_adjoint(V, mu)
for all V, mu.
 abstract _apply_inverse_one_vector(self, v, mu=None, initial_guess=None, least_squares=False, prepare_data=None)[source]¶
 abstract _apply_inverse_adjoint_one_vector(self, u, mu=None, initial_guess=None, least_squares=False, prepare_data=None)[source]¶
 apply(self, U, mu=None)[source]¶
Apply the operator to a
VectorArray
.Parameters
 U
VectorArray
of vectors to which the operator is applied. mu
The
parameter values
for which to evaluate the operator.
Returns
VectorArray
of the operator evaluations.
 apply_inverse(self, V, mu=None, initial_guess=None, least_squares=False)[source]¶
Apply the inverse operator.
Parameters
 V
VectorArray
of vectors to which the inverse operator is applied. mu
The
parameter values
for which to evaluate the inverse operator. initial_guess
VectorArray
with the same length asV
containing initial guesses for the solution. Some implementations ofapply_inverse
may ignore this parameter. IfNone
a solverdependent default is used. 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.
Returns
VectorArray
of the inverse operator evaluations.Raises
 InversionError
The operator could not be inverted.
 apply_adjoint(self, V, mu=None)[source]¶
Apply the adjoint operator.
For any given linear
Operator
op
,parameter values
mu
andVectorArrays
U
,V
in thesource
resp.range
we have:op.apply_adjoint(V, mu).dot(U) == V.inner(op.apply(U, mu))
Thus, when
op
is represented by a matrixM
,apply_adjoint
is given by leftmultplication of (the complex conjugate of)M
withV
.Parameters
 V
VectorArray
of vectors to which the adjoint operator is applied. mu
The
parameter values
for which to apply the adjoint operator.
Returns
VectorArray
of the adjoint operator evaluations.
 apply_inverse_adjoint(self, U, mu=None, initial_guess=None, least_squares=False)[source]¶
Apply the inverse adjoint operator.
Parameters
 U
VectorArray
of vectors to which the inverse adjoint operator is applied. mu
The
parameter values
for which to evaluate the inverse adjoint operator. initial_guess
VectorArray
with the same length asU
containing initial guesses for the solution. Some implementations ofapply_inverse_adjoint
may ignore this parameter. IfNone
a solverdependent default is used. least_squares
If
True
, solve the least squares problem:v = argmin op^*(v)  u_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 operator implementations will choose a least squares solver by default which may be undesirable.
Returns
VectorArray
of the inverse adjoint operator evaluations.Raises
 InversionError
The operator could not be inverted.
 class pymor.operators.list.LinearComplexifiedListVectorArrayOperatorBase[source]¶
Bases:
ListVectorArrayOperatorBase
Interface for
Parameter
dependent discrete operators.An operator in pyMOR is simply a mapping which for any given
parameter values
maps vectors from itssource
VectorSpace
to vectors in itsrange
VectorSpace
.Note that there is no special distinction between functionals and operators in pyMOR. A functional is simply an operator with
NumpyVectorSpace
(1)
as itsrange
VectorSpace
. solver_options[source]¶
If not
None
, a dict which can contain the following keys: ‘inverse’
solver options used for
apply_inverse
 ‘inverse_adjoint’
solver options used for
apply_inverse_adjoint
 ‘jacobian’
solver options for the operators returned by
jacobian
(has no effect for linear operators)
If
solver_options
isNone
or a dict entry is missing orNone
, default options are used. The interpretation of the given solver options is up to the operator at hand. In general, values insolver_options
should either be strings (indicating a solver type) or dicts of options, usually with an entry'type'
which specifies the solver type to use and further items which configure this solver.
 source[source]¶
The source
VectorSpace
.
 range[source]¶
The range
VectorSpace
.
 H[source]¶
The adjoint operator, i.e.
self.H.apply(V, mu) == self.apply_adjoint(V, mu)
for all V, mu.
 abstract _real_apply_inverse_one_vector(self, v, mu=None, initial_guess=None, least_squares=False, prepare_data=None)[source]¶
 abstract _real_apply_inverse_adjoint_one_vector(self, u, mu=None, initial_guess=None, least_squares=False, prepare_data=None)[source]¶
 class pymor.operators.list.NumpyListVectorArrayMatrixOperator(matrix, source_id=None, range_id=None, solver_options=None, name=None)[source]¶
Bases:
ListVectorArrayOperatorBase
,pymor.operators.numpy.NumpyMatrixOperator
Variant of
NumpyMatrixOperator
usingListVectorArray
instead ofNumpyVectorArray
.This class is mainly intended for performance tests of
ListVectorArray
. In generalNumpyMatrixOperator
should be used instead of this class.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.
 _apply_inverse_one_vector(self, v, mu=None, initial_guess=None, least_squares=False, prepare_data=None)[source]¶
 apply_adjoint(self, V, mu=None)[source]¶
Apply the adjoint operator.
For any given linear
Operator
op
,parameter values
mu
andVectorArrays
U
,V
in thesource
resp.range
we have:op.apply_adjoint(V, mu).dot(U) == V.inner(op.apply(U, mu))
Thus, when
op
is represented by a matrixM
,apply_adjoint
is given by leftmultplication of (the complex conjugate of)M
withV
.Parameters
 V
VectorArray
of vectors to which the adjoint operator is applied. mu
The
parameter values
for which to apply the adjoint operator.
Returns
VectorArray
of the adjoint operator evaluations.
 apply_inverse_adjoint(self, U, mu=None, initial_guess=None, least_squares=False)[source]¶
Apply the inverse adjoint operator.
Parameters
 U
VectorArray
of vectors to which the inverse adjoint operator is applied. mu
The
parameter values
for which to evaluate the inverse adjoint operator. initial_guess
VectorArray
with the same length asU
containing initial guesses for the solution. Some implementations ofapply_inverse_adjoint
may ignore this parameter. IfNone
a solverdependent default is used. least_squares
If
True
, solve the least squares problem:v = argmin op^*(v)  u_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 operator implementations will choose a least squares solver by default which may be undesirable.
Returns
VectorArray
of the inverse adjoint operator evaluations.Raises
 InversionError
The operator could not be inverted.
 _assemble_lincomb(self, operators, coefficients, identity_shift=0.0, solver_options=None, name=None)[source]¶
Try to assemble a linear combination of the given operators.
Returns a new
Operator
which represents the sumc_1*O_1 + ... + c_N*O_N + s*I
where
O_i
areOperators
,c_i
,s
scalar coefficients andI
the identity.This method is called in the
assemble
method ofLincombOperator
on the first of its operators. If an assembly of the given linear combination is possible, e.g. the linear combination of the system matrices of the operators can be formed, then the assembled operator is returned. Otherwise, the method returnsNone
to indicate that assembly is not possible.Parameters
 operators
List of
Operators
O_i
whose linear combination is formed. coefficients
List of the corresponding linear coefficients
c_i
. identity_shift
The coefficient
s
. solver_options
solver_options
for the assembled operator. name
Name of the assembled operator.
Returns
The assembled
Operator
if assembly is possible, otherwiseNone
.