linear_problem module¶

Linear equations problem.

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: BaseProblem

Representation of the linear equations’ system \(Ax = b\).

It also contains the solution, and some properties of the system such as the symmetry or positive definiteness.

Parameters:

lhs (ArrayType | LinearOperator) – The left-hand side (matrix or linear operator) of the problem.
rhs (ndarray | None) – The right-hand side (vector) of the problem.
solution (ndarray | None) – The current solution.
is_symmetric (bool) –
Whether to assume that the LHS is symmetric.

By default it is set to False.
is_positive_def (bool) –
Whether to assume that the LHS is positive definite.

By default it is set to False.
is_converged (bool | None) – Whether the solution is converged to the specified tolerance. If False, the algorithm stopped before convergence. If None, no run was performed.

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 (bool) –
If True, return norm(lhs.solution-rhs)/norm(rhs), else return norm(lhs.solution-rhs).

By default it is set to True.
store (bool) –
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.

Returns:

The residuals value.

Raises:

ValueError – If solution is None and current_x is None.

Return type:

ndarray

plot_residuals()[source]¶

Plot the residuals’ convergence in log scale.

Returns:: The matplotlib figure.
Raises:: ValueError – When the residuals’ history is empty.
Return type:: Figure

convergence_info: int | str¶: The information provided by the solver if convergence occurred or not.

is_converged: bool¶: If the solution is_converged.

is_lhs_linear_operator: bool¶: Whether the LHS is symmetric.

is_positive_def: bool¶: Whether the LHS is positive definite.

is_symmetric: bool¶: Whether the LHS is symmetric.

lhs: LinearOperator | SparseArrayType¶

The left-hand side of the equation.

If None, the problem can’t be solved and the user has to set it after init.

residuals_history: list[float]¶: The convergence history of residuals.

rhs: ndarray¶: The right-hand side of the equation.

solution: ndarray¶: The current solution of the problem.

solver_name: str¶: The solver name.

solver_options: dict[str, Any]¶: The options passed to the solver.