pymor.reductors.sobt

Module Contents

class pymor.reductors.sobt.GenericSOBTpvReductor(fom, mu=None)

Bases: pymor.core.base.BasicObject

Generic Second-Order Balanced Truncation position/velocity reductor.

See [RS08].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.

Methods

reconstruct	Reconstruct high-dimensional vector from reduced vector u.
reduce	Reduce using GenericSOBTpv.

reconstruct(u)

Reconstruct high-dimensional vector from reduced vector u.

reduce(r, projection='bfsr')

Reduce using GenericSOBTpv.

Parameters

r

Order of the reduced model.

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

Returns

rom

Reduced-order SecondOrderModel.

class pymor.reductors.sobt.SOBTReductor(fom, mu=None)

Bases: pymor.core.base.BasicObject

Second-Order Balanced Truncation reductor.

See [CLVVD06].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.

Methods

reconstruct	Reconstruct high-dimensional vector from reduced vector u.
reduce	Reduce using SOBT.

reconstruct(u)

Reconstruct high-dimensional vector from reduced vector u.

reduce(r, projection='bfsr')

Reduce using SOBT.

Parameters

r

Order of the reduced model.

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

Returns

rom

Reduced-order SecondOrderModel.

class pymor.reductors.sobt.SOBTfvReductor(fom, mu=None)

Bases: pymor.core.base.BasicObject

Free-velocity Second-Order Balanced Truncation reductor.

See [MS96].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.

Methods

reconstruct	Reconstruct high-dimensional vector from reduced vector u.
reduce	Reduce using SOBTfv.

reconstruct(u)

Reconstruct high-dimensional vector from reduced vector u.

reduce(r, projection='bfsr')

Reduce using SOBTfv.

Parameters

r

Order of the reduced model.

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

Returns

rom

Reduced-order SecondOrderModel.

class pymor.reductors.sobt.SOBTpReductor(fom, mu=None)

Bases: GenericSOBTpvReductor

Second-Order Balanced Truncation position reductor.

See [RS08].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.

class pymor.reductors.sobt.SOBTpvReductor(fom, mu=None)

Bases: GenericSOBTpvReductor

Second-Order Balanced Truncation position-velocity reductor.

See [RS08].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.

class pymor.reductors.sobt.SOBTvReductor(fom, mu=None)

Bases: GenericSOBTpvReductor

Second-Order Balanced Truncation velocity reductor.

See [RS08].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.

class pymor.reductors.sobt.SOBTvpReductor(fom, mu=None)

Bases: GenericSOBTpvReductor

Second-Order Balanced Truncation velocity-position reductor.

See [RS08].

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Parameter values.