pymor.reductors.sor_irka¶

IRKA-type reductor for SecondOrderModels.

Module Contents¶

class pymor.reductors.sor_irka.SORIRKAReductor(fom, mu=None)[source]

SOR-IRKA reductor.

Parameters

fom

The full-order SecondOrderModel to reduce.

mu

Methods

 reduce Reduce using SOR-IRKA.
reduce(rom0_params, tol=0.0001, maxit=100, num_prev=1, force_sigma_in_rhp=False, projection='orth', conv_crit='sigma', compute_errors=False, irka_options=None)[source]

Reduce using SOR-IRKA.

It uses IRKA as the intermediate reductor, to reduce from 2r to r poles. See Section 5.3.2 in [Wya12].

Parameters

rom0_params

Can be:

• order of the reduced model (a positive integer),

• dict with 'sigma', 'b', 'c' as keys mapping to initial interpolation points (a 1D NumPy array), right tangential directions (VectorArray from fom.D.source), and left tangential directions (VectorArray from fom.D.range), all of the same length (the order of the reduced model),

• initial reduced-order model (LTIModel).

If the order of reduced model is given, initial interpolation data is generated randomly.

tol

Tolerance for the convergence criterion.

maxit

Maximum number of iterations.

num_prev

Number of previous iterations to compare the current iteration to. Larger number can avoid occasional cyclic behavior of IRKA.

force_sigma_in_rhp

If False, new interpolation are reflections of the current reduced order model’s poles. Otherwise, only the poles in the left half-plane are reflected.

projection

Projection method:

• 'orth': projection matrices are orthogonalized with respect to the Euclidean inner product

• 'biorth': projection matrices are biorthogolized with respect to the E product

conv_crit

Convergence criterion:

• 'sigma': relative change in interpolation points

• 'h2': relative $$\mathcal{H}_2$$ distance of reduced-order models

compute_errors

Should the relative $$\mathcal{H}_2$$-errors of intermediate reduced order models be computed.

Warning

Computing $$\mathcal{H}_2$$-errors is expensive. Use this option only if necessary.

irka_options

Dict of options for IRKAReductor.reduce.

Returns

rom

Reduced-order SecondOrderModel.