pymor.reductors.bt
¶
Module Contents¶
- class pymor.reductors.bt.BRBTReductor(fom, gamma=1, mu=None, solver_options=None)[source]¶
Bases:
GenericBTReductor
Bounded Real (BR) Balanced Truncation reductor.
See [Ant05] (Section 7.5.3) and [OJ88].
Parameters
- fom
The full-order
LTIModel
to reduce.- gamma
Upper bound for the \(\mathcal{H}_\infty\)-norm.
- mu
- solver_options
The solver options to use to solve the positive Riccati equations.
Methods
Returns error bounds for all possible reduced orders.
- class pymor.reductors.bt.BTReductor(fom, mu=None)[source]¶
Bases:
GenericBTReductor
Standard (Lyapunov) Balanced Truncation reductor.
See Section 7.3 in [Ant05].
Parameters
- fom
The full-order
LTIModel
to reduce.- mu
Methods
Returns error bounds for all possible reduced orders.
- class pymor.reductors.bt.FDBTReductor(fom, ast_pole_data=None, mu=None, solver_options=None)[source]¶
Bases:
GenericBTReductor
Balanced Truncation reductor using frequency domain representation of Gramians.
See [ZSW99].
Parameters
- fom
The full-order
LTIModel
to reduce.- ast_pole_data
Can be:
dictionary of parameters for
eigs
,list of anti-stable eigenvalues (scalars),
tuple
(lev, ew, rev)
whereew
contains the anti-stable eigenvalues andlev
andrev
areVectorArrays
representing the eigenvectors.None
if anti-stable eigenvalues should be computed via dense methods.
- mu
Methods
L-infinity error bounds for reduced order models.
- class pymor.reductors.bt.GenericBTReductor(fom, mu=None)[source]¶
Bases:
pymor.core.base.BasicObject
Generic Balanced Truncation reductor.
Parameters
- fom
The full-order
LTIModel
to reduce.- mu
Methods
Returns error bounds for all possible reduced orders.
Reconstruct high-dimensional vector from reduced vector
u
.Generic Balanced Truncation.
- reduce(r=None, tol=None, projection='bfsr')[source]¶
Generic Balanced Truncation.
Parameters
- r
Order of the reduced model if
tol
isNone
, maximum order iftol
is specified.- tol
Tolerance for the error bound if
r
isNone
.- projection
Projection method used:
'sr'
: square root method'bfsr'
: balancing-free square root method (default, since it avoids scaling by singular values and orthogonalizes the projection matrices, which might make it more accurate than the square root method)'biorth'
: like the balancing-free square root method, except it biorthogonalizes the projection matrices (usinggram_schmidt_biorth
)
Returns
- rom
Reduced-order model.
- class pymor.reductors.bt.LQGBTReductor(fom, mu=None, solver_options=None)[source]¶
Bases:
GenericBTReductor
Linear Quadratic Gaussian (LQG) Balanced Truncation reductor.
See Section 3 in [MG91].
Parameters
- fom
The full-order
LTIModel
to reduce.- mu
- solver_options
The solver options to use to solve the Riccati equations.
Methods
Returns error bounds for all possible reduced orders.