pymor.bindings.scipy

Module Contents

pymor.bindings.scipy.apply_inverse(op, V, initial_guess=None, options=None, least_squares=False, check_finite=True, default_solver='scipy_spsolve', default_least_squares_solver='scipy_least_squares_lsmr')

Solve linear equation system.

Applies the inverse of op to the vectors in V using SciPy.

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 (scipy_spsolve, scipy_bicgstab, scipy_bicgstab_spilu, scipy_lgmres, scipy_least_squares_lsmr, scipy_least_squares_lsqr).

• default_least_squares_solver – Default solver to use for least squares problems (scipy_least_squares_lsmr, scipy_least_squares_lsqr).

Returns:

|VectorArray| of the solution vectors.

pymor.bindings.scipy.lyap_dense_solver_options()

Return available dense Lyapunov solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.lyap_lrcf_solver_options()

Return available Lyapunov solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.matrix_astype_nocopy(matrix, dtype)

pymor.bindings.scipy.ricc_dense_solver_options()

Return available Riccati solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.ricc_lrcf_solver_options()

Return available Riccati solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.solve_lyap_dense(A, E, B, trans=False, cont_time=True, options=None)

Compute the solution of a Lyapunov equation.

See

• pymor.algorithms.lyapunov.solve_cont_lyap_dense

• pymor.algorithms.lyapunov.solve_disc_lyap_dense

for a general description.

This function uses scipy.linalg.solve_continuous_lyapunov or scipy.linalg.solve_discrete_lyapunov, which are dense solvers for Lyapunov equations with E=I.

Note

If E is not None, the problem will be reduced to a standard algebraic Lyapunov equation by inverting E.

Parameters:

• A – The matrix A as a 2D NumPy array.

• E – The matrix E as a 2D NumPy array or None.

• B – The matrix B as a 2D NumPy array.

• trans – Whether the first operator in the Lyapunov equation is transposed.

• cont_time – Whether the continuous- or discrete-time Lyapunov equation is solved.

• options – The solver options to use (see lyap_dense_solver_options).

Returns:

X – Lyapunov equation solution as a NumPy array.

pymor.bindings.scipy.solve_lyap_lrcf(A, E, B, trans=False, cont_time=True, options=None)

Compute an approximate low-rank solution of a Lyapunov equation.

See

• pymor.algorithms.lyapunov.solve_cont_lyap_lrcf

• pymor.algorithms.lyapunov.solve_disc_lyap_lrcf

for a general description.

This function uses scipy.linalg.solve_continuous_lyapunov or scipy.linalg.solve_discrete_lyapunov, which are dense solvers for Lyapunov equations with E=I. Therefore, we assume A and E can be converted to NumPy arrays using to_matrix and that B.to_numpy is implemented.

Note

If E is not None, the problem will be reduced to a standard algebraic Lyapunov equation by inverting E.

Parameters:

• A – The non-parametric Operator A.

• E – The non-parametric Operator E or None.

• B – The operator B as a VectorArray from A.source.

• trans – Whether the first Operator in the Lyapunov equation is transposed.

• cont_time – Whether the continuous- or discrete-time Lyapunov equation is solved.

• options – The solver options to use (see lyap_lrcf_solver_options).

Returns:

Z – Low-rank Cholesky factor of the Lyapunov equation solution, VectorArray from A.source.

pymor.bindings.scipy.solve_pos_ricc_dense(A, E, B, C, R=None, S=None, trans=False, options=None)

Compute the solution of a Riccati equation.

See pymor.algorithms.riccati.solve_pos_ricc_dense for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver.

Parameters:

• A – The matrix A as a 2D NumPy array.

• E – The matrix E as a 2D NumPy array or None.

• B – The matrix B as a 2D NumPy array.

• C – The matrix C as a 2D NumPy array.

• R – The matrix R as a 2D NumPy array or None.

• S – The matrix S as a 2D NumPy array or None.

• trans – Whether the first operator in the Riccati equation is transposed.

• options – The solver options to use (see ricc_dense_solver_options).

Returns:

X – Riccati equation solution as a NumPy array.

pymor.bindings.scipy.solve_pos_ricc_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None)

Compute an approximate low-rank solution of a positive Riccati equation.

See pymor.algorithms.riccati.solve_pos_ricc_lrcf for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver. Therefore, we assume all Operators and VectorArrays can be converted to NumPy arrays using to_matrix and to_numpy.

Parameters:

• A – The non-parametric Operator A.

• E – The non-parametric Operator E or None.

• B – The operator B as a VectorArray from A.source.

• C – The operator C as a VectorArray from A.source.

• R – The matrix R as a 2D NumPy array or None.

• S – The operator S as a VectorArray from A.source or None.

• trans – Whether the first Operator in the positive Riccati equation is transposed.

• options – The solver options to use (see ricc_lrcf_solver_options).

Returns:

Z – Low-rank Cholesky factor of the positive Riccati equation solution, VectorArray from A.source.

pymor.bindings.scipy.solve_ricc_dense(A, E, B, C, R=None, S=None, trans=False, options=None)

Compute the solution of a Riccati equation.

See pymor.algorithms.riccati.solve_ricc_dense for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver.

Parameters:

• A – The matrix A as a 2D NumPy array.

• E – The matrix E as a 2D NumPy array or None.

• B – The matrix B as a 2D NumPy array.

• C – The matrix C as a 2D NumPy array.

• R – The matrix R as a 2D NumPy array or None.

• S – The matrix S as a 2D NumPy array or None.

• trans – Whether the first operator in the Riccati equation is transposed.

• options – The solver options to use (see ricc_dense_solver_options).

Returns:

X – Riccati equation solution as a NumPy array.

pymor.bindings.scipy.solve_ricc_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None)

Compute an approximate low-rank solution of a Riccati equation.

See pymor.algorithms.riccati.solve_ricc_lrcf for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver. Therefore, we assume all Operators and VectorArrays can be converted to NumPy arrays using to_matrix and to_numpy.

Parameters:

• A – The non-parametric Operator A.

• E – The non-parametric Operator E or None.

• B – The operator B as a VectorArray from A.source.

• C – The operator C as a VectorArray from A.source.

• R – The matrix R as a 2D NumPy array or None.

• S – The operator S as a VectorArray from A.source or None.

• trans – Whether the first Operator in the Riccati equation is transposed.

• options – The solver options to use (see ricc_lrcf_solver_options).

Returns:

Z – Low-rank Cholesky factor of the Riccati equation solution, VectorArray from A.source.

pymor.bindings.scipy.solver_options(bicgstab_tol=1e-15, bicgstab_maxiter=None, spilu_drop_tol=0.0001, spilu_fill_factor=10, spilu_drop_rule=None, spilu_permc_spec='COLAMD', spsolve_permc_spec='COLAMD', spsolve_keep_factorization=True, 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 for the SciPy backend.

Parameters:

• bicgstab_tol – See scipy.sparse.linalg.bicgstab.

• bicgstab_maxiter – See scipy.sparse.linalg.bicgstab.

• spilu_drop_tol – See scipy.sparse.linalg.spilu.

• spilu_fill_factor – See scipy.sparse.linalg.spilu.

• spilu_drop_rule – See scipy.sparse.linalg.spilu.

• spilu_permc_spec – See scipy.sparse.linalg.spilu.

• spsolve_permc_spec – See scipy.sparse.linalg.spsolve.

• spsolve_keep_factorization – See scipy.sparse.linalg.spsolve.

• 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|.

pymor.bindings.scipy.svd_lapack_driver(driver='gesvd_unless_win_mkl')

pymor.bindings.scipy.SCIPY_1_14_OR_NEWER

pymor.bindings.scipy.sparray