pymor.bindings.pymess

Module Contents

class pymor.bindings.pymess.LyapunovEquation(opt, A, E, B)[source]

Bases: pymess.Equation

Lyapunov equation class for pymess.

Represents a (generalized) continuous-time algebraic Lyapunov equation:

  • if opt.type is pymess.MESS_OP_NONE and E is None:

    \[A X + X A^T + B B^T = 0,\]

  • if opt.type is pymess.MESS_OP_NONE and E is not None:

    \[A X E^T + E X A^T + B B^T = 0,\]

  • if opt.type is pymess.MESS_OP_TRANSPOSE and E is None:

    \[A^T X + X A + B^T B = 0,\]

  • if opt.type is pymess.MESS_OP_TRANSPOSE and E is not None:

    \[A^T X E + E^T X A + B^T B = 0.\]

Parameters

opt

pymess Options structure.

A

The non-parametric Operator A.

E

The non-parametric Operator E or None.

B

The operator B as a VectorArray from A.source.

Methods

ainv_apply

apeinv_apply

apex_apply

ax_apply

einv_apply

ex_apply

parameter

ainv_apply(op, y)[source]
apeinv_apply(op, p, idx_p, y)[source]
apex_apply(op, p, idx_p, y)[source]
ax_apply(op, y)[source]
einv_apply(op, y)[source]
ex_apply(op, y)[source]
parameter(arp_p, arp_m, B=None, K=None)[source]
class pymor.bindings.pymess.RiccatiEquation(opt, A, E, B, C)[source]

Bases: pymess.Equation

Riccati equation class for pymess.

Represents a Riccati equation

  • if opt.type is pymess.MESS_OP_NONE and E is None:

    \[A X + X A^T - X C^T C X + B B^T = 0,\]

  • if opt.type is pymess.MESS_OP_NONE and E is not None:

    \[A X E^T + E X A^T - E X C^T C X E^T + B B^T = 0,\]

  • if opt.type is pymess.MESS_OP_TRANSPOSE and E is None:

    \[A^T X + X A - X B B^T X + C^T C = 0,\]

  • if opt.type is pymess.MESS_OP_TRANSPOSE and E is not None:

    \[A^T X E + E^T X A - E X B B^T X E^T + C^T C = 0.\]

Parameters

opt

pymess Options structure.

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.

Methods

ainv_apply

apeinv_apply

apex_apply

ax_apply

einv_apply

ex_apply

parameter

ainv_apply(op, y)[source]
apeinv_apply(op, p, idx_p, y)[source]
apex_apply(op, p, idx_p, y)[source]
ax_apply(op, y)[source]
einv_apply(op, y)[source]
ex_apply(op, y)[source]
parameter(arp_p, arp_m, B=None, K=None)[source]
pymor.bindings.pymess.dense_nm_gmpcare_solver_options(linesearch=False, maxit=50, absres_tol=1e-11, relres_tol=1e-12, nrm=0)[source]

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

Also see lradi_solver_options.

Parameters

linesearch

See pymess.dense_nm_gmpcare.

maxit

See pymess.dense_nm_gmpcare.

absres_tol

See pymess.dense_nm_gmpcare.

relres_tol

See pymess.dense_nm_gmpcare.

nrm

See pymess.dense_nm_gmpcare.

Returns

A dict of available solvers with default solver options.

pymor.bindings.pymess.lradi_solver_options(adi_maxit=500, adi_memory_usage=pymess.MESS_MEMORY_MID, adi_output=1, adi_rel_change_tol=1e-10, adi_res2_tol=1e-10, adi_res2c_tol=1e-11, adi_shifts_arp_m=32, adi_shifts_arp_p=48, adi_shifts_b0=None, adi_shifts_l0=16, adi_shifts_p=None, adi_shifts_paratype=pymess.MESS_LRCFADI_PARA_ADAPTIVE_Z)[source]

Return available adi solver options with default values for the pymess backend.

Parameters

adi_maxit

See pymess.OptionsAdi.

adi_memory_usage

See pymess.OptionsAdi.

adi_output

See pymess.OptionsAdi.

adi_rel_change_tol

See pymess.OptionsAdi.

adi_res2_tol

See pymess.OptionsAdi.

adi_res2c_tol

See pymess.OptionsAdi.

adi_shifts_arp_m

See pymess.OptionsAdiShifts.

adi_shifts_arp_p

See pymess.OptionsAdiShifts.

adi_shifts_b0

See pymess.OptionsAdiShifts.

adi_shifts_l0

See pymess.OptionsAdiShifts.

adi_shifts_p

See pymess.OptionsAdiShifts.

adi_shifts_paratype

See pymess.OptionsAdiShifts.

Returns

A dict of available solvers with default solver options.

pymor.bindings.pymess.lrnm_solver_options(newton_gstep=0, newton_k0=None, newton_linesearch=0, newton_maxit=30, newton_output=1, newton_res2_tol=1e-10, newton_singleshifts=0)[source]

Return available adi solver options with default values for the pymess backend.

Parameters

newton_gstep

See pymess.OptionsNewton.

newton_k0

See pymess.OptionsNewton.

newton_linesearch

See pymess.OptionsNewton.

newton_maxit

See pymess.OptionsNewton.

newton_output

See pymess.OptionsNewton.

newton_res2_tol

See pymess.OptionsNewton.

newton_singleshifts

See pymess.OptionsNewton.

Returns

A dict of available solvers with default solver options.

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

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

Returns

A dict of available solvers with default solver options.

pymor.bindings.pymess.lyap_lrcf_solver_options()[source]

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

Also see lradi_solver_options.

Returns

A dict of available solvers with default solver options.

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

Return available positive Riccati solvers with default options for the pymess backend.

Returns

A dict of available solvers with default solver options.

pymor.bindings.pymess.ricc_lrcf_solver_options()[source]

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

Also see dense_nm_gmpcare_solver_options and lrnm_solver_options.

Returns

A dict of available solvers with default solver options.

pymor.bindings.pymess.solve_lyap_dense(A, E, B, trans=False, cont_time=True, options=None)[source]

Compute the solution of a Lyapunov equation.

See

for a general description.

This function uses pymess.glyap.

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. Only the continuous-time case is implemented.

options

The solver options to use (see lyap_dense_solver_options).

Returns

X

Lyapunov equation solution as a NumPy array.

pymor.bindings.pymess.solve_lyap_lrcf(A, E, B, trans=False, cont_time=True, options=None, default_solver=None)[source]

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

See

for a general description.

This function uses pymess.glyap and pymess.lradi. For both methods, to_numpy and from_numpy need to be implemented for A.source. Additionally, since glyap is a dense solver, it expects to_matrix to work for A and E.

If the solver is not specified using the options or default_solver arguments, glyap is used for small problems (smaller than defined with mat_eqn_sparse_min_size) and lradi for large problems.

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. Only the continuous-time case is implemented.

options

The solver options to use (see lyap_lrcf_solver_options).

default_solver

Default solver to use (pymess_lradi, pymess_glyap). If None, choose solver depending on the dimension of A.

Returns

Z

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

pymor.bindings.pymess.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 pymess.dense_nm_gmpcare.

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 pos_ricc_lrcf_solver_options).

Returns

Z

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

pymor.bindings.pymess.solve_ricc_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None, default_solver=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 pymess.dense_nm_gmpcare and pymess.lrnm. For both methods, to_numpy and from_numpy need to be implemented for A.source. Additionally, since dense_nm_gmpcare is a dense solver, it expects to_matrix to work for A and E.

If the solver is not specified using the options or default_solver arguments, dense_nm_gmpcare is used for small problems (smaller than defined with mat_eqn_sparse_min_size) and lrnm for large problems.

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).

default_solver

Default solver to use (pymess_lrnm, pymess_dense_nm_gmpcare). If None, chose solver depending on dimension A.

Returns

Z

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