pymor.operators.list

Module Contents

class pymor.operators.list.LinearComplexifiedListVectorArrayOperatorBase

Bases: ListVectorArrayOperatorBase

Base Operator for complexified ListVectorArrays.

class pymor.operators.list.ListVectorArrayOperatorBase

Bases: pymor.operators.interface.Operator

Base Operator for ListVectorArrays.

Methods

apply	Apply the operator to a VectorArray.
apply_adjoint	Apply the adjoint operator.
apply_inverse	Apply the inverse operator.
apply_inverse_adjoint	Apply the inverse adjoint operator.

apply(U, mu=None)

Apply the operator to a VectorArray.

Parameters:

• U – VectorArray of vectors to which the operator is applied.

• mu – The parameter values for which to evaluate the operator.

Returns:

|VectorArray| of the operator evaluations.

apply_adjoint(V, mu=None)

Apply the adjoint operator.

For any given linear Operator op, parameter values mu and VectorArrays U, V in the source resp. range we have:

op.apply_adjoint(V, mu).dot(U) == V.inner(op.apply(U, mu))

Thus, when op is represented by a matrix M, apply_adjoint is given by left-multiplication of (the complex conjugate of) M with V.

Parameters:

• V – VectorArray of vectors to which the adjoint operator is applied.

• mu – The parameter values for which to apply the adjoint operator.

Returns:

|VectorArray| of the adjoint operator evaluations.

apply_inverse(V, mu=None, initial_guess=None, least_squares=False)

Apply the inverse operator.

Parameters:

• V – VectorArray of vectors to which the inverse operator is applied.

• mu – The parameter values for which to evaluate the inverse operator.

• initial_guess – VectorArray with the same length as V containing initial guesses for the solution. Some implementations of apply_inverse may ignore this parameter. If None a solver-dependent default is used.

• least_squares –

  If True, solve the least squares problem:

  u = argmin ||op(u) - v||_2.
  

  Since for an invertible operator the least squares solution agrees with the result of the application of the inverse operator, setting this option should, in general, have no effect on the result for those operators. However, note that when no appropriate solver_options are set for the operator, most implementations will choose a least squares solver by default which may be undesirable.

Returns:

|VectorArray| of the inverse operator evaluations.

Raises:

InversionError – The operator could not be inverted.

apply_inverse_adjoint(U, mu=None, initial_guess=None, least_squares=False)

Apply the inverse adjoint operator.

Parameters:

• U – VectorArray of vectors to which the inverse adjoint operator is applied.

• mu – The parameter values for which to evaluate the inverse adjoint operator.

• initial_guess – VectorArray with the same length as U containing initial guesses for the solution. Some implementations of apply_inverse_adjoint may ignore this parameter. If None a solver-dependent default is used.

• least_squares –

  If True, solve the least squares problem:

  v = argmin ||op^*(v) - u||_2.
  

  Since for an invertible operator the least squares solution agrees with the result of the application of the inverse operator, setting this option should, in general, have no effect on the result for those operators. However, note that when no appropriate solver_options are set for the operator, most operator implementations will choose a least squares solver by default which may be undesirable.

Returns:

|VectorArray| of the inverse adjoint operator evaluations.

Raises:

InversionError – The operator could not be inverted.

class pymor.operators.list.NumpyListVectorArrayMatrixOperator(matrix, solver_options=None, name=None)

Bases: ListVectorArrayOperatorBase, pymor.operators.numpy.NumpyMatrixOperator

Variant of NumpyMatrixOperator using ListVectorArray instead of NumpyVectorArray.

This class is mainly intended for performance tests of ListVectorArray. In general NumpyMatrixOperator should be used instead of this class.

Parameters:

• matrix – The NumPy array which is to be wrapped.

• solver_options – The solver_options for the operator.

• name – Name of the operator.

Methods

apply_adjoint	Apply the adjoint operator.
apply_inverse_adjoint	Apply the inverse adjoint operator.

apply_adjoint(V, mu=None)

Apply the adjoint operator.

For any given linear Operator op, parameter values mu and VectorArrays U, V in the source resp. range we have:

op.apply_adjoint(V, mu).dot(U) == V.inner(op.apply(U, mu))

Thus, when op is represented by a matrix M, apply_adjoint is given by left-multiplication of (the complex conjugate of) M with V.

Parameters:

• V – VectorArray of vectors to which the adjoint operator is applied.

• mu – The parameter values for which to apply the adjoint operator.

Returns:

|VectorArray| of the adjoint operator evaluations.

apply_inverse_adjoint(U, mu=None, initial_guess=None, least_squares=False)

Apply the inverse adjoint operator.

Parameters:

• U – VectorArray of vectors to which the inverse adjoint operator is applied.

• mu – The parameter values for which to evaluate the inverse adjoint operator.

• initial_guess – VectorArray with the same length as U containing initial guesses for the solution. Some implementations of apply_inverse_adjoint may ignore this parameter. If None a solver-dependent default is used.

• least_squares –

  If True, solve the least squares problem:

  v = argmin ||op^*(v) - u||_2.
  

  Since for an invertible operator the least squares solution agrees with the result of the application of the inverse operator, setting this option should, in general, have no effect on the result for those operators. However, note that when no appropriate solver_options are set for the operator, most operator implementations will choose a least squares solver by default which may be undesirable.

Returns:

|VectorArray| of the inverse adjoint operator evaluations.

Raises:

InversionError – The operator could not be inverted.