pymor.operators.block
¶
Module Contents¶
- class pymor.operators.block.BlockColumnOperator(blocks)[source]¶
Bases:
BlockOperatorBase
A column vector of arbitrary
Operators
.
- class pymor.operators.block.BlockDiagonalOperator(blocks)[source]¶
Bases:
BlockOperator
Block diagonal
Operator
of arbitraryOperators
.This is a specialization of
BlockOperator
for the block diagonal case.Methods
Apply the operator to a
VectorArray
.Apply the adjoint operator.
Apply the inverse operator.
Apply the inverse adjoint operator.
Assemble the operator for given
parameter values
.- apply(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_adjoint(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 left-multplication 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(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 solver-dependent 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_inverse_adjoint(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 solver-dependent 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(mu=None)[source]¶
Assemble the operator for given
parameter values
.The result of the method strongly depends on the given operator. For instance, a matrix-based operator will assemble its matrix, a
LincombOperator
will try to form the linear combination of its operators, whereas an arbitrary operator might simply return aFixedParameterOperator
. The only assured property of the assembled operator is that it no longer depends on aParameter
.Parameters
- mu
The
parameter values
for which to assemble the operator.
Returns
Parameter-independent, assembled
Operator
.
- class pymor.operators.block.BlockEmbeddingOperator(block_space, component)[source]¶
Bases:
BlockColumnOperator
A column vector of arbitrary
Operators
.
- class pymor.operators.block.BlockOperator(blocks)[source]¶
Bases:
BlockOperatorBase
A matrix of arbitrary
Operators
.This operator can be
applied
to a compatibleBlockVectorArrays
.Parameters
- blocks
Two-dimensional array-like where each entry is an
Operator
orNone
.
- class pymor.operators.block.BlockOperatorBase(blocks)[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.
Methods
Apply the operator to a
VectorArray
.Apply the adjoint operator.
Return a
VectorArray
representation of the operator in its range space.Return a
VectorArray
representation of the operator in its source space.Assemble the operator for given
parameter values
.Return the operator's derivative with respect to a given parameter.
- apply(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_adjoint(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 left-multplication 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.
- as_range_array(mu=None)[source]¶
Return a
VectorArray
representation of the operator in its range space.In the case of a linear operator with
NumpyVectorSpace
assource
, this method returns for givenparameter values
mu
aVectorArray
V
in the operator’srange
, such thatV.lincomb(U.to_numpy()) == self.apply(U, mu)
for all
VectorArrays
U
.Parameters
- mu
The
parameter values
for which to return theVectorArray
representation.
Returns
- V
The
VectorArray
defined above.
- as_source_array(mu=None)[source]¶
Return a
VectorArray
representation of the operator in its source space.In the case of a linear operator with
NumpyVectorSpace
asrange
, this method returns for givenparameter values
mu
aVectorArray
V
in the operator’ssource
, such thatself.range.make_array(V.inner(U).T) == self.apply(U, mu)
for all
VectorArrays
U
.Parameters
- mu
The
parameter values
for which to return theVectorArray
representation.
Returns
- V
The
VectorArray
defined above.
- assemble(mu=None)[source]¶
Assemble the operator for given
parameter values
.The result of the method strongly depends on the given operator. For instance, a matrix-based operator will assemble its matrix, a
LincombOperator
will try to form the linear combination of its operators, whereas an arbitrary operator might simply return aFixedParameterOperator
. The only assured property of the assembled operator is that it no longer depends on aParameter
.Parameters
- mu
The
parameter values
for which to assemble the operator.
Returns
Parameter-independent, assembled
Operator
.
- d_mu(parameter, index=0)[source]¶
Return the operator’s derivative with respect to a given parameter.
Parameters
- parameter
The parameter w.r.t. which to return the derivative.
- index
Index of the parameter’s component w.r.t which to return the derivative.
Returns
New
Operator
representing the partial derivative.
- class pymor.operators.block.BlockProjectionOperator(block_space, component)[source]¶
Bases:
BlockRowOperator
A row vector of arbitrary
Operators
.
- class pymor.operators.block.BlockRowOperator(blocks)[source]¶
Bases:
BlockOperatorBase
A row vector of arbitrary
Operators
.
- class pymor.operators.block.SecondOrderModelOperator(alpha, beta, A, B)[source]¶
Bases:
BlockOperator
BlockOperator appearing in SecondOrderModel.to_lti().
This represents a block operator
\[\begin{split}\mathcal{A} = \begin{bmatrix} \alpha I & \beta I \\ B & A \end{bmatrix},\end{split}\]which satisfies
\[\begin{split}\mathcal{A}^H &= \begin{bmatrix} \overline{\alpha} I & B^H \\ \overline{\beta} I & A^H \end{bmatrix}, \\ \mathcal{A}^{-1} &= \begin{bmatrix} (\alpha A - \beta B)^{-1} A & -\beta (\alpha A - \beta B)^{-1} \\ -(\alpha A - \beta B)^{-1} B & \alpha (\alpha A - \beta B)^{-1} \end{bmatrix}, \\ \mathcal{A}^{-H} &= \begin{bmatrix} A^H (\alpha A - \beta B)^{-H} & -B^H (\alpha A - \beta B)^{-H} \\ -\overline{\beta} (\alpha A - \beta B)^{-H} & \overline{\alpha} (\alpha A - \beta B)^{-H} \end{bmatrix}.\end{split}\]Methods
Apply the operator to a
VectorArray
.Apply the adjoint operator.
Apply the inverse operator.
Apply the inverse adjoint operator.
Assemble the operator for given
parameter values
.- apply(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_adjoint(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 left-multplication 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(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 solver-dependent 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_inverse_adjoint(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 solver-dependent 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(mu=None)[source]¶
Assemble the operator for given
parameter values
.The result of the method strongly depends on the given operator. For instance, a matrix-based operator will assemble its matrix, a
LincombOperator
will try to form the linear combination of its operators, whereas an arbitrary operator might simply return aFixedParameterOperator
. The only assured property of the assembled operator is that it no longer depends on aParameter
.Parameters
- mu
The
parameter values
for which to assemble the operator.
Returns
Parameter-independent, assembled
Operator
.