gemseo / algos / linear_solvers

# 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: object

Representation of the linear equations’ system A.x = b.

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

Parameters
• lhs (ndarray | spmatrix | LinearOperator) – The left-hand side (matrix or linear operator) of the problem.

• rhs (ndarray | None) –

The right-hand side (vector) of the problem.

By default it is set to None.

• solution (ndarray | None) –

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

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

plot_residuals()[source]

Plot the residuals’ convergence in log scale.

Returns

The matplotlib figure.

Raises

ValueError – When the residuals’ history is empty.

Return type

matplotlib.figure.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: ndarray | LinearOperator | spmatrix

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.