pymor.bindings package

Submodules

fenics module

ngsolve module

pyamg module

pymess module

scipy module


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

Solve linear equation system.

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

Parameters

op
The linear, non-parametric Operator to invert.
rhs
VectorArray of right-hand sides for the equation system.
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.

Defaults

check_finite, default_solver, default_least_squares_solver (see pymor.core.defaults)


pymor.bindings.scipy.lyap_dense_solver_options()[source]

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()[source]

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)[source]

pymor.bindings.scipy.pos_ricc_lrcf_solver_options()[source]

Return available positive 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()[source]

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, options=None)[source]

Compute the solution of a Lyapunov equation.

See pymor.algorithms.lyapunov.solve_lyap_dense for a general description.

This function uses scipy.linalg.solve_continuous_lyapunov, which is a dense solver for Lyapunov equations with E=I.

Note

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

Parameters

A
The operator A as a 2D NumPy array.
E
The operator E as a 2D NumPy array or None.
B
The operator B as a 2D NumPy array.
trans
Whether the first operator in the Lyapunov equation is transposed.
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, options=None)[source]

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

See pymor.algorithms.lyapunov.solve_lyap_lrcf for a general description.

This function uses scipy.linalg.solve_continuous_lyapunov, which is a dense solver 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 continuous-time 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.
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_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

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 operator 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 pos_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_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

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 operator 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)[source]

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.

Defaults

bicgstab_tol, bicgstab_maxiter, spilu_drop_tol, spilu_fill_factor, spilu_drop_rule, spilu_permc_spec, spsolve_permc_spec, spsolve_keep_factorization, lgmres_tol, lgmres_maxiter, lgmres_inner_m, lgmres_outer_k, least_squares_lsmr_damp, least_squares_lsmr_atol, least_squares_lsmr_btol, least_squares_lsmr_conlim, least_squares_lsmr_maxiter, least_squares_lsmr_show, least_squares_lsqr_atol, least_squares_lsqr_btol, least_squares_lsqr_conlim, least_squares_lsqr_iter_lim, least_squares_lsqr_show (see pymor.core.defaults)

slycot module