Options for Linear solver algorithms¶
BICG¶
Module: 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/BICG.html.
Here are the options available in GEMSEO:
- 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.
inner_m (int)
By default it is set to 30.
max_iter (int)
The maximum number of iterations.
By default it is set to 1000.
outer_k (int)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
outer_v (Optional[List[Tuple]])
The data used to augment the Krylov subspace.
By default it is set to None.
preconditioner (Optional[Union[ndarray,)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
prepend_outer_v (bool)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
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.
store_outer_av (bool)
By default it is set to True.
store_residuals (bool)
Whether to store the residuals convergence history.
By default it is set to False.
tol (float)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
use_ilu_precond (bool)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
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.
BICGSTAB¶
Module: 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 GEMSEO:
- 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.
inner_m (int)
By default it is set to 30.
max_iter (int)
The maximum number of iterations.
By default it is set to 1000.
outer_k (int)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
outer_v (Optional[List[Tuple]])
The data used to augment the Krylov subspace.
By default it is set to None.
preconditioner (Optional[Union[ndarray,)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
prepend_outer_v (bool)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
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.
store_outer_av (bool)
By default it is set to True.
store_residuals (bool)
Whether to store the residuals convergence history.
By default it is set to False.
tol (float)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
use_ilu_precond (bool)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
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.
DEFAULT¶
Module: 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 GEMSEO:
- 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.
inner_m (int)
By default it is set to 30.
max_iter (int)
The maximum number of iterations.
By default it is set to 1000.
outer_k (int)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
outer_v (Optional[List[Tuple]])
The data used to augment the Krylov subspace.
By default it is set to None.
preconditioner (Optional[Union[ndarray,)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
prepend_outer_v (bool)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
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.
store_outer_av (bool)
By default it is set to True.
store_residuals (bool)
Whether to store the residuals convergence history.
By default it is set to False.
tol (float)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
use_ilu_precond (bool)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
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.
GMRES¶
Module: 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 GEMSEO:
- 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.
inner_m (int)
By default it is set to 30.
max_iter (int)
The maximum number of iterations.
By default it is set to 1000.
outer_k (int)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
outer_v (Optional[List[Tuple]])
The data used to augment the Krylov subspace.
By default it is set to None.
preconditioner (Optional[Union[ndarray,)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
prepend_outer_v (bool)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
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.
store_outer_av (bool)
By default it is set to True.
store_residuals (bool)
Whether to store the residuals convergence history.
By default it is set to False.
tol (float)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
use_ilu_precond (bool)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
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.
LGMRES¶
Module: 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 GEMSEO:
- 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.
inner_m (int)
By default it is set to 30.
max_iter (int)
The maximum number of iterations.
By default it is set to 1000.
outer_k (int)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
outer_v (Optional[List[Tuple]])
The data used to augment the Krylov subspace.
By default it is set to None.
preconditioner (Optional[Union[ndarray,)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
prepend_outer_v (bool)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
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.
store_outer_av (bool)
By default it is set to True.
store_residuals (bool)
Whether to store the residuals convergence history.
By default it is set to False.
tol (float)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
use_ilu_precond (bool)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
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.
QMR¶
Module: 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 GEMSEO:
- 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.
inner_m (int)
By default it is set to 30.
max_iter (int)
The maximum number of iterations.
By default it is set to 1000.
outer_k (int)
The number of vectors to carry between inner GMRES iterations.
By default it is set to 3.
outer_v (Optional[List[Tuple]])
The data used to augment the Krylov subspace.
By default it is set to None.
preconditioner (Optional[Union[ndarray,)
The preconditionner, approximation of RHS^-1. If None, no preconditioner is used.
By default it is set to None.
prepend_outer_v (bool)
Whether to put outer_v augmentation vectors before the Krylov iterates.
By default it is set to False.
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.
store_outer_av (bool)
By default it is set to True.
store_residuals (bool)
Whether to store the residuals convergence history.
By default it is set to False.
tol (float)
The relative tolerance for convergence, norm(RHS.dot(sol)) <= max(tol*norm(LHS), atol).
By default it is set to 1e-12.
use_ilu_precond (bool)
Whether to use superLU to compute an incomplete LU factorization as preconditioner.
By default it is set to True.
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.