**atol** (*Optional[float]*)
The absolute tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to None.
.. raw:: html
**inner_m** (*int*)
By default it is set to 30.
.. raw:: html
**max_iter** (*int*)
The maximum number of iterations.
By default it is set to 1000.
.. raw:: html
**outer_k** (*int*)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
.. raw:: html
**outer_v** (*Optional[List[Tuple]]*)
The data used to augment the Krylov subspace.
By default it is set to None.
.. raw:: html
**preconditioner** (*Optional[Union[ndarray,*)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
.. raw:: html
**prepend_outer_v** (*bool*)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
.. raw:: html
**save_when_fail** (*bool*)
Whether to save the linear system to the disk when the solver failed to converge.
By default it is set to False.
.. raw:: html
**store_outer_av** (*bool*)
By default it is set to True.
.. raw:: html
**store_residuals** (*bool*)
Whether to store the residuals convergence history.
By default it is set to False.
.. raw:: html
**tol** (*float*)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
.. raw:: html
**use_ilu_precond** (*bool*)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
.. raw:: html
**x0** (*Optional[ndarray]*)
The initial guess for the solution. M{sparse matrix, dense matrix, LinearOperator}. If None, solvers usually start from the null vector. inner_m int: The number of inner GMRES iterations per outer iteration.
By default it is set to None.
.. raw:: html
.. _BICGSTAB_options:
BICGSTAB
--------
Module: :class:`gemseo.algos.linear_solvers.lib_scipy_linalg`
Linear solver implemented in the SciPy library.
More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/generated/BICGSTAB.html.
Here are the options available in |g|:
.. raw:: html
Options
**atol** (*Optional[float]*)
The absolute tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to None.
.. raw:: html
**inner_m** (*int*)
By default it is set to 30.
.. raw:: html
**max_iter** (*int*)
The maximum number of iterations.
By default it is set to 1000.
.. raw:: html
**outer_k** (*int*)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
.. raw:: html
**outer_v** (*Optional[List[Tuple]]*)
The data used to augment the Krylov subspace.
By default it is set to None.
.. raw:: html
**preconditioner** (*Optional[Union[ndarray,*)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
.. raw:: html
**prepend_outer_v** (*bool*)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
.. raw:: html
**save_when_fail** (*bool*)
Whether to save the linear system to the disk when the solver failed to converge.
By default it is set to False.
.. raw:: html
**store_outer_av** (*bool*)
By default it is set to True.
.. raw:: html
**store_residuals** (*bool*)
Whether to store the residuals convergence history.
By default it is set to False.
.. raw:: html
**tol** (*float*)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
.. raw:: html
**use_ilu_precond** (*bool*)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
.. raw:: html
**x0** (*Optional[ndarray]*)
The initial guess for the solution. M{sparse matrix, dense matrix, LinearOperator}. If None, solvers usually start from the null vector. inner_m int: The number of inner GMRES iterations per outer iteration.
By default it is set to None.
.. raw:: html
.. _DEFAULT_options:
DEFAULT
-------
Module: :class:`gemseo.algos.linear_solvers.lib_scipy_linalg`
This starts by LGMRES, but if it fails, switches to GMRES, then direct method super LU factorization.
More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/generated/DEFAULT.html.
Here are the options available in |g|:
.. raw:: html
Options
**atol** (*Optional[float]*)
The absolute tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to None.
.. raw:: html
**inner_m** (*int*)
By default it is set to 30.
.. raw:: html
**max_iter** (*int*)
The maximum number of iterations.
By default it is set to 1000.
.. raw:: html
**outer_k** (*int*)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
.. raw:: html
**outer_v** (*Optional[List[Tuple]]*)
The data used to augment the Krylov subspace.
By default it is set to None.
.. raw:: html
**preconditioner** (*Optional[Union[ndarray,*)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
.. raw:: html
**prepend_outer_v** (*bool*)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
.. raw:: html
**save_when_fail** (*bool*)
Whether to save the linear system to the disk when the solver failed to converge.
By default it is set to False.
.. raw:: html
**store_outer_av** (*bool*)
By default it is set to True.
.. raw:: html
**store_residuals** (*bool*)
Whether to store the residuals convergence history.
By default it is set to False.
.. raw:: html
**tol** (*float*)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
.. raw:: html
**use_ilu_precond** (*bool*)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
.. raw:: html
**x0** (*Optional[ndarray]*)
The initial guess for the solution. M{sparse matrix, dense matrix, LinearOperator}. If None, solvers usually start from the null vector. inner_m int: The number of inner GMRES iterations per outer iteration.
By default it is set to None.
.. raw:: html
.. _GMRES_options:
GMRES
-----
Module: :class:`gemseo.algos.linear_solvers.lib_scipy_linalg`
Linear solver implemented in the SciPy library.
More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/generated/GMRES.html.
Here are the options available in |g|:
.. raw:: html
Options
**atol** (*Optional[float]*)
The absolute tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to None.
.. raw:: html
**inner_m** (*int*)
By default it is set to 30.
.. raw:: html
**max_iter** (*int*)
The maximum number of iterations.
By default it is set to 1000.
.. raw:: html
**outer_k** (*int*)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
.. raw:: html
**outer_v** (*Optional[List[Tuple]]*)
The data used to augment the Krylov subspace.
By default it is set to None.
.. raw:: html
**preconditioner** (*Optional[Union[ndarray,*)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
.. raw:: html
**prepend_outer_v** (*bool*)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
.. raw:: html
**save_when_fail** (*bool*)
Whether to save the linear system to the disk when the solver failed to converge.
By default it is set to False.
.. raw:: html
**store_outer_av** (*bool*)
By default it is set to True.
.. raw:: html
**store_residuals** (*bool*)
Whether to store the residuals convergence history.
By default it is set to False.
.. raw:: html
**tol** (*float*)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
.. raw:: html
**use_ilu_precond** (*bool*)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
.. raw:: html
**x0** (*Optional[ndarray]*)
The initial guess for the solution. M{sparse matrix, dense matrix, LinearOperator}. If None, solvers usually start from the null vector. inner_m int: The number of inner GMRES iterations per outer iteration.
By default it is set to None.
.. raw:: html
.. _LGMRES_options:
LGMRES
------
Module: :class:`gemseo.algos.linear_solvers.lib_scipy_linalg`
Linear solver implemented in the SciPy library.
More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/generated/LGMRES.html.
Here are the options available in |g|:
.. raw:: html
Options
**atol** (*Optional[float]*)
The absolute tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to None.
.. raw:: html
**inner_m** (*int*)
By default it is set to 30.
.. raw:: html
**max_iter** (*int*)
The maximum number of iterations.
By default it is set to 1000.
.. raw:: html
**outer_k** (*int*)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
.. raw:: html
**outer_v** (*Optional[List[Tuple]]*)
The data used to augment the Krylov subspace.
By default it is set to None.
.. raw:: html
**preconditioner** (*Optional[Union[ndarray,*)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
.. raw:: html
**prepend_outer_v** (*bool*)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
.. raw:: html
**save_when_fail** (*bool*)
Whether to save the linear system to the disk when the solver failed to converge.
By default it is set to False.
.. raw:: html
**store_outer_av** (*bool*)
By default it is set to True.
.. raw:: html
**store_residuals** (*bool*)
Whether to store the residuals convergence history.
By default it is set to False.
.. raw:: html
**tol** (*float*)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
.. raw:: html
**use_ilu_precond** (*bool*)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
.. raw:: html
**x0** (*Optional[ndarray]*)
The initial guess for the solution. M{sparse matrix, dense matrix, LinearOperator}. If None, solvers usually start from the null vector. inner_m int: The number of inner GMRES iterations per outer iteration.
By default it is set to None.
.. raw:: html
.. _QMR_options:
QMR
---
Module: :class:`gemseo.algos.linear_solvers.lib_scipy_linalg`
Linear solver implemented in the SciPy library.
More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/generated/QMR.html.
Here are the options available in |g|:
.. raw:: html
Options
**atol** (*Optional[float]*)
The absolute tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to None.
.. raw:: html
**inner_m** (*int*)
By default it is set to 30.
.. raw:: html
**max_iter** (*int*)
The maximum number of iterations.
By default it is set to 1000.
.. raw:: html
**outer_k** (*int*)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
.. raw:: html
**outer_v** (*Optional[List[Tuple]]*)
The data used to augment the Krylov subspace.
By default it is set to None.
.. raw:: html
**preconditioner** (*Optional[Union[ndarray,*)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
.. raw:: html
**prepend_outer_v** (*bool*)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
.. raw:: html
**save_when_fail** (*bool*)
Whether to save the linear system to the disk when the solver failed to converge.
By default it is set to False.
.. raw:: html
**store_outer_av** (*bool*)
By default it is set to True.
.. raw:: html
**store_residuals** (*bool*)
Whether to store the residuals convergence history.
By default it is set to False.
.. raw:: html
**tol** (*float*)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
.. raw:: html
**use_ilu_precond** (*bool*)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
.. raw:: html
**x0** (*Optional[ndarray]*)
The initial guess for the solution. M{sparse matrix, dense matrix, LinearOperator}. If None, solvers usually start from the null vector. inner_m int: The number of inner GMRES iterations per outer iteration.
By default it is set to None.
.. raw:: html