pymor.reductors.bt
¶
Module Contents¶
- class pymor.reductors.bt.BRBTReductor(fom, gamma=1, mu=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 –
Parameter values
.
Methods
Return 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 –
Parameter values
.
Methods
Return error bounds for all possible reduced orders.
- class pymor.reductors.bt.FDBTReductor(fom, mu=None)[source]¶
Bases:
GenericBTReductor
Balanced Truncation reductor using frequency domain representation of Gramians.
See [ZSW99].
- Parameters:
fom – The full-order
LTIModel
to reduce.mu –
Parameter values
.
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 –
Parameter values
.
Methods
Return 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)[source]¶
Bases:
GenericBTReductor
Linear Quadratic Gaussian (LQG) Balanced Truncation reductor.
See Section 3 in [MG91].
- Parameters:
fom – The full-order
LTIModel
to reduce.mu –
Parameter values
.
Methods
Return error bounds for all possible reduced orders.
- class pymor.reductors.bt.PRBTReductor(fom, mu=None)[source]¶
Bases:
GenericBTReductor
Positive Real (PR) Balanced Truncation reductor.
- Parameters:
fom – The full-order
LTIModel
to reduce.mu –
Parameter values
.
Methods
Return error bounds for all possible reduced orders.