pymor.bindings.slycot

Module Contents

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

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

Returns:

A dict of available solvers with default solver options.

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

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

Returns:

A dict of available solvers with default solver options.

pymor.bindings.slycot.ricc_dense_solver_options()[source]

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

Returns:

A dict of available solvers with default solver options.

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

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

Returns:

A dict of available solvers with default solver options.

pymor.bindings.slycot.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 slycot.sb03md (if E is None) and slycot.sg03ad (if E is not None), which are based on the Bartels-Stewart algorithm.

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 matrix 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.slycot.solve_lyap_lrcf(A, E, B, trans=False, cont_time=True, options=None)[source]

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

See

for a general description.

This function uses slycot.sb03md (if E is None) and slycot.sg03ad (if E is not None), which are dense solvers based on the Bartels-Stewart algorithm. Therefore, we assume A and E can be converted to NumPy arrays using to_matrix and that B.to_numpy is implemented.

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.slycot.solve_pos_ricc_dense(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

Compute the solution of a Riccati equation.

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

This function uses slycot.sb02md (if E is None and S is None) which is based on the Schur vector approach, and slycot.sb02od (if E is None and S is not None) or slycot.sg02ad (if E is not None) which are both based on the method of deflating subspaces.

Parameters:
Returns:

X – Riccati equation solution as a NumPy array.

pymor.bindings.slycot.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 slycot.sb02md (if E is None) or slycot.sg03ad (if E is not None), which are dense solvers. Therefore, we assume all Operators and VectorArrays can be converted to NumPy arrays using to_matrix and to_numpy.

Parameters:
Returns:

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

pymor.bindings.slycot.solve_ricc_dense(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

Compute the solution of a Riccati equation.

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

This function uses slycot.sb02md (if E is None and S is None) which is based on the Schur vector approach, and slycot.sb02od (if E is None and S is not None) or slycot.sg02ad (if E is not None) which are both based on the method of deflating subspaces.

Parameters:
Returns:

X – Riccati equation solution as a NumPy array.

pymor.bindings.slycot.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 slycot.sb02md (if E is None) or slycot.sg03ad (if E is not None), which are dense solvers. Therefore, we assume all Operators and VectorArrays can be converted to NumPy arrays using to_matrix and to_numpy.

Parameters:
Returns:

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