pymor.bindings.slycot
¶
Module Contents¶
Functions¶
Return available Lyapunov solvers with default options for the slycot backend. 

Compute an approximate lowrank solution of a Lyapunov equation. 

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

Compute the solution of a Lyapunov equation. 

Compute the solution of a Riccati equation. 

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

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

Compute an approximate lowrank solution of a Riccati equation. 

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

Compute an approximate lowrank solution of a positive Riccati equation. 
 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.solve_lyap_lrcf(A, E, B, trans=False, options=None)[source]¶
Compute an approximate lowrank solution of a Lyapunov equation.
See
pymor.algorithms.lyapunov.solve_lyap_lrcf
for a general description.This function uses
slycot.sb03md
(ifE is None
) andslycot.sg03ad
(ifE is not None
), which are dense solvers based on the BartelsStewart algorithm. Therefore, we assume A and E can be converted toNumPy arrays
usingto_matrix
and thatB.to_numpy
is implemented.Parameters
 A
The nonparametric
Operator
A. E
The nonparametric
Operator
E orNone
. B
The operator B as a
VectorArray
fromA.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
Lowrank Cholesky factor of the Lyapunov equation solution,
VectorArray
fromA.source
.
 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.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
slycot.sb03md
(ifE is None
) andslycot.sg03ad
(ifE is not None
), which are based on the BartelsStewart algorithm.Parameters
 A
The matrix A as a 2D
NumPy array
. E
The matrix E as a 2D
NumPy array
orNone
. B
The matrix B as a 2D
NumPy array
. trans
Whether the first matrix 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.slycot.solve_ricc_dense(A, E, B, C, R=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
(ifE is None
) which is based on the Schur vector approach andslycot.sg02ad
(ifE is not None
) which is based on the method of deflating subspaces.Parameters
 A
The matrix A as a 2D
NumPy array
. E
The matrix E as a 2D
NumPy array
orNone
. 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
orNone
. trans
Whether the first matrix 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.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_ricc_lrcf(A, E, B, C, R=None, trans=False, options=None)[source]¶
Compute an approximate lowrank solution of a Riccati equation.
See
pymor.algorithms.riccati.solve_ricc_lrcf
for a general description.This function uses
slycot.sb02md
(if E isNone
) orslycot.sg03ad
(if E is notNone
), which are dense solvers. Therefore, we assume allOperators
andVectorArrays
can be converted toNumPy arrays
usingto_matrix
andto_numpy
.Parameters
 A
The nonparametric
Operator
A. E
The nonparametric
Operator
E orNone
. B
The operator B as a
VectorArray
fromA.source
. C
The operator C as a
VectorArray
fromA.source
. R
The matrix R as a 2D
NumPy array
orNone
. trans
Whether the first
Operator
in the Riccati equation is transposed. options
The solver options to use (see
ricc_lrcf_solver_options
).
Returns
 Z
Lowrank Cholesky factor of the Riccati equation solution,
VectorArray
fromA.source
.
 pymor.bindings.slycot.pos_ricc_lrcf_solver_options()[source]¶
Return available positive Riccati solvers with default options for the slycot backend.
Returns
A dict of available solvers with default solver options.
 pymor.bindings.slycot.solve_pos_ricc_lrcf(A, E, B, C, R=None, trans=False, options=None)[source]¶
Compute an approximate lowrank 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 isNone
) orslycot.sg03ad
(if E is notNone
), which are dense solvers. Therefore, we assume allOperators
andVectorArrays
can be converted toNumPy arrays
usingto_matrix
andto_numpy
.Parameters
 A
The nonparametric
Operator
A. E
The nonparametric
Operator
E orNone
. B
The operator B as a
VectorArray
fromA.source
. C
The operator C as a
VectorArray
fromA.source
. R
The matrix R as a 2D
NumPy array
orNone
. 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
Lowrank Cholesky factor of the positive Riccati equation solution,
VectorArray
fromA.source
.