pymor.algorithms.genericsolvers

This module contains some iterative linear solvers which only use the Operator interface.

Module Contents

pymor.algorithms.genericsolvers.apply_inverse(op, V, initial_guess=None, options=None, least_squares=False, check_finite=True, default_solver='generic_lgmres', default_least_squares_solver='generic_least_squares_lsmr')

Solve linear equation system.

Applies the inverse of op to the vectors in V using a generic iterative solver.

Parameters:

• op – The linear, non-parametric Operator to invert.

• V – VectorArray of right-hand sides for the equation system.

• 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.

• options – The solver_options to use (see solver_options).

• least_squares – If True, return least squares solution.

• check_finite – Test if solution only contains finite values.

• default_solver – Default solver to use (generic_lgmres, generic_least_squares_lsmr, generic_least_squares_lsqr).

• default_least_squares_solver – Default solver to use for least squares problems (generic_least_squares_lsmr, generic_least_squares_lsqr).

Returns:

|VectorArray| of the solution vectors.

pymor.algorithms.genericsolvers.lgmres(A, b, x0=None, tol=1e-05, maxiter=1000, M=None, callback=None, inner_m=30, outer_k=3, outer_v=None, store_outer_Av=True)

pymor.algorithms.genericsolvers.lsmr(A, b, damp=0.0, atol=1e-06, btol=1e-06, conlim=100000000.0, maxiter=None, show=False)

pymor.algorithms.genericsolvers.lsqr(A, b, damp=0.0, atol=1e-08, btol=1e-08, conlim=100000000.0, iter_lim=None, show=False)

pymor.algorithms.genericsolvers.solver_options(lgmres_tol=1e-05, lgmres_maxiter=1000, lgmres_inner_m=39, lgmres_outer_k=3, least_squares_lsmr_damp=0.0, least_squares_lsmr_atol=1e-06, least_squares_lsmr_btol=1e-06, least_squares_lsmr_conlim=100000000.0, least_squares_lsmr_maxiter=None, least_squares_lsmr_show=False, least_squares_lsqr_damp=0.0, least_squares_lsqr_atol=1e-06, least_squares_lsqr_btol=1e-06, least_squares_lsqr_conlim=100000000.0, least_squares_lsqr_iter_lim=None, least_squares_lsqr_show=False)

Returns available solvers with default solver_options.

Parameters:

• lgmres_tol – See scipy.sparse.linalg.lgmres.

• lgmres_maxiter – See scipy.sparse.linalg.lgmres.

• lgmres_inner_m – See scipy.sparse.linalg.lgmres.

• lgmres_outer_k – See scipy.sparse.linalg.lgmres.

• least_squares_lsmr_damp – See scipy.sparse.linalg.lsmr.

• least_squares_lsmr_atol – See scipy.sparse.linalg.lsmr.

• least_squares_lsmr_btol – See scipy.sparse.linalg.lsmr.

• least_squares_lsmr_conlim – See scipy.sparse.linalg.lsmr.

• least_squares_lsmr_maxiter – See scipy.sparse.linalg.lsmr.

• least_squares_lsmr_show – See scipy.sparse.linalg.lsmr.

• least_squares_lsqr_damp – See scipy.sparse.linalg.lsqr.

• least_squares_lsqr_atol – See scipy.sparse.linalg.lsqr.

• least_squares_lsqr_btol – See scipy.sparse.linalg.lsqr.

• least_squares_lsqr_conlim – See scipy.sparse.linalg.lsqr.

• least_squares_lsqr_iter_lim – See scipy.sparse.linalg.lsqr.

• least_squares_lsqr_show – See scipy.sparse.linalg.lsqr.

Returns:

A dict of available solvers with default |solver_options|.