Linear solvers#

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Warning

All the features of the wrapped libraries may not be exposed through GEMSEO.

Note

The algorithm settings can be passed to a function of the form

function(..., settings_model: AlgorithmSettings | None = None, **settings: Any)

either one by one:

function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

or using the argument name "settings_model" and the Pydantic model associated with the algorithm:

settings_model = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
function(..., settings_model=settings_model)

BICG#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

BI-Conjugate Gradient

Pydantic model of the settings for BICG#

from gemseo.settings.linear_solvers import BICG_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.bicg.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

BICGSTAB#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Bi-Conjugate Gradient STABilized

Pydantic model of the settings for BICGSTAB#

from gemseo.settings.linear_solvers import BICGSTAB_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.bicgstab.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

CG#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Conjugate Gradient

Pydantic model of the settings for CG#

from gemseo.settings.linear_solvers import CG_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.cg.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

CGS#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Conjugate Gradient Squared

Pydantic model of the settings for CGS#

from gemseo.settings.linear_solvers import CGS_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.cgs.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

DEFAULT#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Default solver (LGMRES)

Pydantic model of the settings for DEFAULT#

from gemseo.settings.linear_solvers import LGMRES_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lgmres.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
inner_m : <class 'int'>, optional

Number of inner GMRES iterations per each outer iteration.

By default it is set to 30.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
outer_k : <class 'int'>, optional

Number of vectors to carry between inner GMRES iterations.

By default it is set to 3.
outer_v : list[tuple[numpy.ndarray[typing.Any, numpy.dtype[numpy.number[typing.Any]]], numpy.ndarray[typing.Any, numpy.dtype[numpy.number[typing.Any]]]]], optional

List of tuples (v, Av) used to augment the Krylov subspace.

By default it is set to [].
prepend_outer_v : <class 'bool'>, optional

Whether to put outer_v augmentation vectors before Krylov iterates.

By default it is set to False.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_outer_Av : <class 'bool'>, optional

Whether A @ v should be additionnaly stored in outer_v list.

By default it is set to True.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

GCROT#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Generalized Conjugate Residual with Optimal Truncation

Pydantic model of the settings for GCROT#

from gemseo.settings.linear_solvers import GCROT_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.gcrotmk.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
CU : collections.abc.Iterable[tuple[numpy.ndarray[typing.Any, numpy.dtype[numpy.number[typing.Any]]], numpy.ndarray[typing.Any, numpy.dtype[numpy.number[typing.Any]]]]] | None, optional

List of tuples (c, u) required to form the matrices C and U.

If None start from empty matrices.

By default it is set to None.
discard_C : <class 'bool'>, optional

Whether to discard the C-vectors at the end.

By default it is set to True.
k : <class 'int'>, optional

Number of vectors to carry between inner FGMRES iterations.

If None use the same value as m.

By default it is set to 30.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
m : <class 'int'>, optional

Number of inner FGMRES iterations per each outer iteration.

By default it is set to 30.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
truncate : typing.Literal['oldest', 'smallest'], optional

The vectors from the previous cycle to drop.

By default it is set to oldest.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

GMRES#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Generalized Minimum RESidual

Pydantic model of the settings for GMRES#

from gemseo.settings.linear_solvers import GMRES_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.gmres.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
restart : <class 'int'>, optional

Number of iterations between restarts.

By default it is set to 20.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

LGMRES#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Loose Generalized Minimum RESidual

Pydantic model of the settings for LGMRES#

from gemseo.settings.linear_solvers import LGMRES_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lgmres.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
inner_m : <class 'int'>, optional

Number of inner GMRES iterations per each outer iteration.

By default it is set to 30.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
outer_k : <class 'int'>, optional

Number of vectors to carry between inner GMRES iterations.

By default it is set to 3.
outer_v : list[tuple[numpy.ndarray[typing.Any, numpy.dtype[numpy.number[typing.Any]]], numpy.ndarray[typing.Any, numpy.dtype[numpy.number[typing.Any]]]]], optional

List of tuples (v, Av) used to augment the Krylov subspace.

By default it is set to [].
prepend_outer_v : <class 'bool'>, optional

Whether to put outer_v augmentation vectors before Krylov iterates.

By default it is set to False.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_outer_Av : <class 'bool'>, optional

Whether A @ v should be additionnaly stored in outer_v list.

By default it is set to True.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

PETSC_BCGS#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_BCGS#

from gemseo.settings.linear_solvers import PETSC_BCGS_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPBCGS/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_BCGSL#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_BCGSL#

from gemseo.settings.linear_solvers import PETSC_BCGSL_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPBCGSL/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_BICG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_BICG#

from gemseo.settings.linear_solvers import PETSC_BICG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPBICG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_CG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_CG#

from gemseo.settings.linear_solvers import PETSC_CG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_CGLS#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_CGLS#

from gemseo.settings.linear_solvers import PETSC_CGLS_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPCGLS/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_CGNE#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_CGNE#

from gemseo.settings.linear_solvers import PETSC_CGNE_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPCGNE/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_CGS#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_CGS#

from gemseo.settings.linear_solvers import PETSC_CGS_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPCGS/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_CHEBYSHEV#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_CHEBYSHEV#

from gemseo.settings.linear_solvers import PETSC_CHEBYSHEV_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPCHEBYSHEV/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_CR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_CR#

from gemseo.settings.linear_solvers import PETSC_CR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPCR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_DGMRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_DGMRES#

from gemseo.settings.linear_solvers import PETSC_DGMRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPDGMRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_FBCGS#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_FBCGS#

from gemseo.settings.linear_solvers import PETSC_FBCGS_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPFBCGS/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_FBCGSR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_FBCGSR#

from gemseo.settings.linear_solvers import PETSC_FBCGSR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPFBCGSR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_FCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_FCG#

from gemseo.settings.linear_solvers import PETSC_FCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPFCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_FETIDP#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_FETIDP#

from gemseo.settings.linear_solvers import PETSC_FETIDP_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPFETIDP/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_FGMRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_FGMRES#

from gemseo.settings.linear_solvers import PETSC_FGMRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPFGMRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_GCR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_GCR#

from gemseo.settings.linear_solvers import PETSC_GCR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPGCR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_GLTR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_GLTR#

from gemseo.settings.linear_solvers import PETSC_GLTR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPGLTR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_GMRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_GMRES#

from gemseo.settings.linear_solvers import PETSC_GMRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPGMRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_GROPPCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_GROPPCG#

from gemseo.settings.linear_solvers import PETSC_GROPPCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPGROPPCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_HPDDM#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_HPDDM#

from gemseo.settings.linear_solvers import PETSC_HPDDM_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPHPDDM/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_IBCGS#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_IBCGS#

from gemseo.settings.linear_solvers import PETSC_IBCGS_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPIBCGS/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_LCD#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_LCD#

from gemseo.settings.linear_solvers import PETSC_LCD_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPLCD/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_LGMRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_LGMRES#

from gemseo.settings.linear_solvers import PETSC_LGMRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPLGMRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_LSQR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_LSQR#

from gemseo.settings.linear_solvers import PETSC_LSQR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPLSQR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_MINRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_MINRES#

from gemseo.settings.linear_solvers import PETSC_MINRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPMINRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_NASH#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_NASH#

from gemseo.settings.linear_solvers import PETSC_NASH_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPNASH/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PGMRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PGMRES#

from gemseo.settings.linear_solvers import PETSC_PGMRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPGMRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPEBCGS#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPEBCGS#

from gemseo.settings.linear_solvers import PETSC_PIPEBCGS_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPEBCGS/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPECG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPECG#

from gemseo.settings.linear_solvers import PETSC_PIPECG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPECG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPECG2#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPECG2#

from gemseo.settings.linear_solvers import PETSC_PIPECG2_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPECG2/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPECGRR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPECGRR#

from gemseo.settings.linear_solvers import PETSC_PIPECGRR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPECGRR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPECR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPECR#

from gemseo.settings.linear_solvers import PETSC_PIPECR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPECR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPEFCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPEFCG#

from gemseo.settings.linear_solvers import PETSC_PIPEFCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPEFCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPEFGMRES#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPEFGMRES#

from gemseo.settings.linear_solvers import PETSC_PIPEFGMRES_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPEFGMRES/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPEGCR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPEGCR#

from gemseo.settings.linear_solvers import PETSC_PIPEGCR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPEGCR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPELCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPELCG#

from gemseo.settings.linear_solvers import PETSC_PIPELCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPELCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PIPEPRCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PIPEPRCG#

from gemseo.settings.linear_solvers import PETSC_PIPEPRCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPIPEPRCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_PREONLY#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_PREONLY#

from gemseo.settings.linear_solvers import PETSC_PREONLY_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPPREONLY/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_QCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_QCG#

from gemseo.settings.linear_solvers import PETSC_QCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPQCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_RICHARDSON#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_RICHARDSON#

from gemseo.settings.linear_solvers import PETSC_RICHARDSON_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPRICHARDSON/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_STCG#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_STCG#

from gemseo.settings.linear_solvers import PETSC_STCG_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPSTCG/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_SYMMLQ#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_SYMMLQ#

from gemseo.settings.linear_solvers import PETSC_SYMMLQ_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPSYMMLQ/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_TCQMR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_TCQMR#

from gemseo.settings.linear_solvers import PETSC_TCQMR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPTCQMR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_TFQMR#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_TFQMR#

from gemseo.settings.linear_solvers import PETSC_TFQMR_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPTFQMR/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

PETSC_TSIRM#

Note

The plugin gemseo_petsc is required.

Module: gemseo_petsc.linear_solvers.petsc_ksp

Pydantic model of the settings for PETSC_TSIRM#

from gemseo.settings.linear_solvers import PETSC_TSIRM_Settings

More details about the algorithm and its settings on https://petsc.org/release/manualpages/KSP/KSPTSIRM/.

Optional settings

atol : <class 'float'>, optional

The absolute convergence tolerance.

Absolute tolerance of the (possibly preconditioned) residual norm. Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-50.
dtol : <class 'float'>, optional

The divergence tolerance.

The amount the (possibly preconditioned) residual norm can increase.

By default it is set to 100000.0.
ksp_pre_processor : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

A callback function that is called before calling ksp.solve().

The function is called with (KSP problem, options dict) as arguments. It allows the user to obtain an advanced configuration that is not supported by the current wrapper. If None, do not perform any call.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 100000.
monitor_residuals : <class 'bool'>, optional

Whether to store the residuals during convergence.

WARNING: as said in Petsc documentation,
"the routine is slow and should be used only for testing or convergence studies, not for timing."

By default it is set to False.
options_cmd : collections.abc.Mapping[str, typing.Any] | None, optional

The options to pass to the PETSc KSP solver.

If None, use the default options.

By default it is set to None.
preconditioner_type : gemseo_petsc.linear_solvers.settings.petsc_ksp_settings.PreconditionerType | None, optional

The type of the precondtioner.

If None, no preconditioning is applied. See [https://www.mcs.anl.gov/petsc/petsc4py-current/docs/apiref/petsc4py.PETSc.PC.Type-class.html]

By default it is set to ilu.
rtol : <class 'float'>, optional

The relative convergence tolerance.

Relative decrease in the (possibly preconditioned) residual norm.

By default it is set to 1e-05.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
set_from_options : <class 'bool'>, optional

Whether the options are set from sys.argv.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
view_config : <class 'bool'>, optional

Whether to view the configuration of the solver before run.

Configuration is viewed by calling ksp.view().

By default it is set to False.

TFQMR#

Module: gemseo.algos.linear_solvers.scipy_linalg.scipy_linalg

Transpose-Free Quasi-Minimal Residual

Pydantic model of the settings for TFQMR#

from gemseo.settings.linear_solvers import BaseSciPyLinalgSettingsBase

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.tfqmr.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 0.0.
callback : typing.Optional[typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional

The user-supplied function to call after each iteration.

It is called as callback(xk), where xk is the current solution vector. If None, no function is called.

By default it is set to None.
M : scipy.sparse.linalg._interface.LinearOperator | numpy.ndarray | scipy.sparse._base.sparray | None, optional

The preconditioner approximating the inverse of A.

By default it is set to None.
maxiter : <class 'int'>, optional

Maximum number of iterations.

By default it is set to 1000.
rtol : <class 'float'>, optional

The relative tolerance.

Algorithm stops if norm(b - A @ x) <= max(rtol*norm(b), atol).

By default it is set to 1e-12.
save_when_fail : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
store_residuals : <class 'bool'>, optional

Whether to store the residual norms at each iterations.

By default it is set to False.
use_ilu_precond : <class 'bool'>, optional

Whether to use an incomplete LU factorization as preconditioner.

By default it is set to False.
x0 : numpy.ndarray | None, optional

Starting guess for the solution.

If None, start from a matrix of zeros.

By default it is set to None.

Linear solvers#

BICG#

BICGSTAB#

CG#

CGS#

DEFAULT#

GCROT#

GMRES#

LGMRES#

PETSC_BCGS#

PETSC_BCGSL#

PETSC_BICG#

PETSC_CG#

PETSC_CGLS#

PETSC_CGNE#

PETSC_CGS#

PETSC_CHEBYSHEV#

PETSC_CR#

PETSC_DGMRES#

PETSC_FBCGS#

PETSC_FBCGSR#

PETSC_FCG#

PETSC_FETIDP#

PETSC_FGMRES#

PETSC_GCR#

PETSC_GLTR#

PETSC_GMRES#

PETSC_GROPPCG#

PETSC_HPDDM#

PETSC_IBCGS#

PETSC_LCD#

PETSC_LGMRES#

PETSC_LSQR#

PETSC_MINRES#

PETSC_NASH#

PETSC_PGMRES#

PETSC_PIPEBCGS#

PETSC_PIPECG#

PETSC_PIPECG2#

PETSC_PIPECGRR#

PETSC_PIPECR#

PETSC_PIPEFCG#

PETSC_PIPEFGMRES#

PETSC_PIPEGCR#

PETSC_PIPELCG#

PETSC_PIPEPRCG#

PETSC_PREONLY#

PETSC_QCG#

PETSC_RICHARDSON#

PETSC_STCG#

PETSC_SYMMLQ#

PETSC_TCQMR#

PETSC_TFQMR#

PETSC_TSIRM#

TFQMR#

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