linear_problem module¶
Linear equations problem.
Classes:
|
Represent the linear equations system |
- class gemseo.algos.linear_solvers.linear_problem.LinearProblem(lhs, rhs=None, solution=None, is_symmetric=False, is_positive_def=False, is_converged=None)[source]¶
Bases:
objectRepresent the linear equations system
lhs.x = rhs.It also contains the solution, and some properties of the system such as the symmetry or positive definiteness.
- rhs¶
The right hand side of the equation.
- Type
ndarray
- lhs¶
The left hand side of the equation. If None, the problem can’t be solved and the user has to set it after init.
- Type
ndarray, LinearOperator, sparse
- solution¶
The current solution of the problem.
- Type
ndarray
- is_converged¶
If the solution is_converged.
- Type
bool
- convergence_info¶
The information provided by the solver if convergence occured or not.
- Type
int, str
- is_symmetric¶
Whether the LHS is symmetric.
- Type
bool
- is_positive_def¶
Whether the LHS is positive definite.
- Type
bool
- is_lhs_linear_operator¶
Whether the LHS is symmetric. XXX
- Type
bool
- solver_options¶
The options passed to the solver.
- Type
Dict[str, XXX]
- solver_name¶
The solver name.
- Type
str
- residuals_history¶
The convergence history of residuals.
- Type
List[float]
- Parameters
lhs (Union[ndarray, spmatrix, LinearOperator]) – The left hand side (matrix or linear operator) of the problem. If None, XXX.
rhs (Optional[ndarray]) –
The right hand side (vector) of the problem. If None, XXX.
By default it is set to None.
solution (Optional[ndarray]) –
The current solution.
By default it is set to None.
is_symmetric –
Whether to assume that the LHS is symmetric.
By default it is set to False.
is_positive_def –
Whether to assume that the LHS is positive definite.
By default it is set to False.
is_converged –
Whether the solution is converged to the specified tolerance. If False, the algorithm stopped before convergence. If None, no run was performed.
By default it is set to None.
- Return type
None
Methods:
check()Check the consistency of the dimensions of the LHS and RHS.
compute_residuals([relative_residuals, ...])Compute the L2 norm of the residuals of the problem.
Plot the residuals convergence in log scale.
- check()[source]¶
Check the consistency of the dimensions of the LHS and RHS.
- Raises
ValueError – When the shapes are inconsistent.
- Return type
None
- compute_residuals(relative_residuals=True, store=False, current_x=None)[source]¶
Compute the L2 norm of the residuals of the problem.
- Parameters
relative_residuals –
If True, return norm(lhs.solution-rhs)/norm(rhs), else return norm(lhs.solution-rhs).
By default it is set to True.
store –
Whether to store the residuals value in the residuals_history attribute.
By default it is set to False.
current_x –
Compute the residuals associated with current_x, If None, compute then from the solution attribute.
By default it is set to None.
- Returns
The residuals value.
- Raises
ValueError – If self.solution is None and current_x is None.
- Return type
numpy.ndarray