pymor.reductors.mt

Module Contents

class pymor.reductors.mt.MTReductor(fom, mu=None)

Bases: pymor.core.base.BasicObject

Modal Truncation reductor.

See Section 9.2 in [Ant05].

Parameters:

• fom – The full-order LTIModel to reduce.

• mu – Parameter values.

Methods

reconstruct	Reconstruct high-dimensional vector from reduced vector u.
reduce	Modal Truncation.

reconstruct(u)

Reconstruct high-dimensional vector from reduced vector u.

reduce(r=None, decomposition='samdp', projection='orth', symmetric=False, which='NR', method_options=None, allow_complex_rom=False)

Modal Truncation.

Parameters:

• r – Order of the reduced model.

• decomposition –

  Algorithm used for the decomposition:

  • 'eig': scipy.linalg.eig algorithm

  • 'samdp': find dominant poles using samdp algorithm

• projection –

  Projection method used:

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

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

• symmetric – If True, assume A is symmetric and E is symmetric positive definite.

• which –

  A string specifying which r eigenvalues and eigenvectors to compute. Possible values are:

  • 'SM': select eigenvalues with smallest magnitude (only for decomposition with eig)

  • 'LR': select eigenvalues with largest real part (only for decomposition with eig)

  • 'NR': select eigenvalues with largest norm(residual) / abs(Re(pole))

  • 'NS': select eigenvalues with largest norm(residual) / abs(pole)

  • 'NM': select eigenvalues with largest norm(residual)

• method_options – Optional dict with more options for the samdp algorithm.

• allow_complex_rom – If True, the reduced model is complex when the poles of the reduced model are not closed under complex conjugation.

Returns:

rom – Reduced-order model.