pymor.reductors.basic

Module Contents

class pymor.reductors.basic.DelayLTIPGReductor(fom, W, V, E_biorthonormal=False)

Bases: ProjectionBasedReductor

Petrov-Galerkin projection of an LinearDelayModel.

Parameters:

• fom – The full order Model to reduce.

• W – The basis of the test space.

• V – The basis of the ansatz space.

• E_biorthonormal – If True, no E matrix will be assembled for the reduced Model. Set to True if W and V are biorthonormal w.r.t. fom.E.

Methods

build_rom
extend_basis
project_operators
project_operators_to_subbasis
reconstruct	Reconstruct high-dimensional vector from reduced vector u.

build_rom(projected_operators, error_estimator)

abstract extend_basis(**kwargs)

project_operators()

project_operators_to_subbasis(dims)

reconstruct(u, basis='V')

Reconstruct high-dimensional vector from reduced vector u.

class pymor.reductors.basic.InstationaryRBReductor(fom, RB=None, product=None, initial_data_product=None, product_is_mass=False, check_orthonormality=None, check_tol=None)

Bases: ProjectionBasedReductor

Galerkin projection of an InstationaryModel.

Parameters:

• fom – The full order Model to reduce.

• RB – The basis of the reduced space onto which to project. If None an empty basis is used.

• product – Inner product Operator w.r.t. which RB is orthonormalized. If None, the the Euclidean inner product is used.

• initial_data_product – Inner product Operator w.r.t. which the initial_data of fom is orthogonally projected. If None, the Euclidean inner product is used.

• product_is_mass – If True, no mass matrix for the reduced Model is assembled. Set to True if RB is orthonormal w.r.t. the mass matrix of fom.

• check_orthonormality – See ProjectionBasedReductor.

• check_tol – See ProjectionBasedReductor.

Methods

build_rom
project_operators
project_operators_to_subbasis

build_rom(projected_operators, error_estimator)

project_operators()

project_operators_to_subbasis(dims)

class pymor.reductors.basic.LTIPGReductor(fom, W, V, E_biorthonormal=False)

Bases: ProjectionBasedReductor

Petrov-Galerkin projection of an LTIModel.

Parameters:

• fom – The full order Model to reduce.

• W – The basis of the test space.

• V – The basis of the ansatz space.

• E_biorthonormal – If True, no E matrix will be assembled for the reduced Model. Set to True if W and V are biorthonormal w.r.t. fom.E.

Methods

build_rom
extend_basis
project_operators
project_operators_to_subbasis
reconstruct	Reconstruct high-dimensional vector from reduced vector u.

build_rom(projected_operators, error_estimator)

abstract extend_basis(**kwargs)

project_operators()

project_operators_to_subbasis(dims)

reconstruct(u, basis='V')

Reconstruct high-dimensional vector from reduced vector u.

class pymor.reductors.basic.ProjectionBasedReductor(fom, bases, products={}, check_orthonormality=True, check_tol=0.001)

Bases: pymor.core.base.BasicObject

Generic projection based reductor.

Parameters:

• fom – The full order Model to reduce.

• bases – A dict of VectorArrays of basis vectors.

• products – A dict of inner product Operators w.r.t. which the corresponding bases are orthonormalized. A value of None corresponds to orthonormalization of the basis w.r.t. the Euclidean inner product.

• check_orthonormality – If True, check if bases which have a corresponding entry in the products dict are orthonormal w.r.t. the given inner product. After each basis extension, orthonormality is checked again.

• check_tol – If check_orthonormality is True, the numerical tolerance with which the checks are performed.

Methods

assemble_error_estimator
assemble_error_estimator_for_subbasis
build_rom
extend_basis
project_operators
project_operators_to_subbasis
reconstruct	Reconstruct high-dimensional vector from reduced vector u.
reduce

assemble_error_estimator()

assemble_error_estimator_for_subbasis(dims)

abstract build_rom(projected_operators, error_estimator)

extend_basis(U, basis='RB', method='gram_schmidt', pod_modes=1, pod_orthonormalize=True, copy_U=True)

abstract project_operators()

abstract project_operators_to_subbasis(dims)

reconstruct(u, basis='RB')

Reconstruct high-dimensional vector from reduced vector u.

reduce(dims=None)

class pymor.reductors.basic.SOLTIPGReductor(fom, W, V, M_biorthonormal=False)

Bases: ProjectionBasedReductor

Petrov-Galerkin projection of an SecondOrderModel.

Parameters:

• fom – The full order Model to reduce.

• W – The basis of the test space.

• V – The basis of the ansatz space.

• E_biorthonormal – If True, no E matrix will be assembled for the reduced Model. Set to True if W and V are biorthonormal w.r.t. fom.E.

Methods

build_rom
extend_basis
project_operators
project_operators_to_subbasis
reconstruct	Reconstruct high-dimensional vector from reduced vector u.

build_rom(projected_operators, error_estimator)

abstract extend_basis(**kwargs)

project_operators()

project_operators_to_subbasis(dims)

reconstruct(u, basis='V')

Reconstruct high-dimensional vector from reduced vector u.

class pymor.reductors.basic.StationaryRBReductor(fom, RB=None, product=None, check_orthonormality=None, check_tol=None)

Bases: ProjectionBasedReductor

Galerkin projection of a StationaryModel.

Parameters:

• fom – The full order Model to reduce.

• RB – The basis of the reduced space onto which to project. If None an empty basis is used.

• product – Inner product Operator w.r.t. which RB is orthonormalized. If None, the Euclidean inner product is used.

• check_orthonormality – See ProjectionBasedReductor.

• check_tol – See ProjectionBasedReductor.

Methods

build_rom
project_operators
project_operators_to_subbasis

build_rom(projected_operators, error_estimator)

project_operators()

project_operators_to_subbasis(dims)

pymor.reductors.basic.extend_basis(U, basis, product=None, method='gram_schmidt', pod_modes=1, pod_orthonormalize=True, copy_U=True)