Source code for gemseo.algos.linear_solvers.linear_problem

# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
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# Lesser General Public License for more details.
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# You should have received a copy of the GNU Lesser General Public License
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# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - API and implementation and/or documentation
#        :author: Francois Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""Linear equations problem."""
from __future__ import annotations

import logging
from typing import Any

import matplotlib.pyplot as plt
from matplotlib.figure import Figure
from numpy import ndarray
from numpy.linalg import norm
from scipy.sparse import spmatrix
from scipy.sparse.linalg import LinearOperator

LOGGER = logging.getLogger(__name__)


[docs]class LinearProblem: """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. """ rhs: ndarray """The right-hand side of the equation.""" 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.""" solution: ndarray """The current solution of the problem.""" is_converged: bool """If the solution is_converged.""" convergence_info: int | str """The information provided by the solver if convergence occurred or not.""" is_symmetric: bool """Whether the LHS is symmetric.""" is_positive_def: bool """Whether the LHS is positive definite.""" is_lhs_linear_operator: bool """Whether the LHS is symmetric.""" solver_options: dict[str, Any] """The options passed to the solver.""" solver_name: str """The solver name.""" residuals_history: list[float] """The convergence history of residuals.""" def __init__( self, lhs: ndarray | spmatrix | LinearOperator, rhs: ndarray | None = None, solution: ndarray | None = None, is_symmetric=False, is_positive_def=False, is_converged=None, ) -> None: """ Args: lhs: The left-hand side (matrix or linear operator) of the problem. rhs: The right-hand side (vector) of the problem. solution: The current solution. is_symmetric: Whether to assume that the LHS is symmetric. is_positive_def: Whether to assume that the LHS is positive definite. is_converged: Whether the solution is converged to the specified tolerance. If False, the algorithm stopped before convergence. If None, no run was performed. """ self.rhs = rhs self.lhs = lhs self.solution = solution self.is_converged = is_converged self.convergence_info = None self.is_symmetric = is_symmetric self.is_positive_def = is_positive_def if isinstance(lhs, LinearOperator): self.is_lhs_linear_operator = True else: self.is_lhs_linear_operator = False self.solver_options = None self.solver_name = None self.residuals_history = None
[docs] def compute_residuals( self, relative_residuals=True, store=False, current_x=None, ) -> ndarray: """Compute the L2 norm of the residuals of the problem. Args: relative_residuals: If True, return norm(lhs.solution-rhs)/norm(rhs), else return norm(lhs.solution-rhs). store: Whether to store the residuals value in the residuals_history attribute. current_x: Compute the residuals associated with current_x, If None, compute then from the solution attribute. Returns: The residuals value. Raises: ValueError: If self.solution is None and current_x is None. """ if self.rhs is None: raise ValueError("Missing RHS.") if current_x is None: current_x = self.solution if self.solution is None: raise ValueError("Missing solution.") res = norm(self.lhs.dot(current_x) - self.rhs) if relative_residuals: res /= norm(self.rhs) if store: if self.residuals_history is None: self.residuals_history = [] self.residuals_history.append(res) return res
[docs] def plot_residuals(self) -> Figure: """Plot the residuals' convergence in log scale. Returns: The matplotlib figure. Raises: ValueError: When the residuals' history is empty. """ if self.residuals_history is None or len(self.residuals_history) == 0: raise ValueError( "Residuals history is empty. " " Use the 'store_residuals' option for the solver." ) fig = plt.figure(figsize=(11.0, 6.0)) plt.plot(self.residuals_history, color="black", lw=2) ax1 = fig.gca() ax1.set_yscale("log") ax1.set_title(f"Linear solver '{self.solver_name}' convergence") ax1.set_ylabel("Residuals norm (log)") ax1.set_xlabel("Iterations") return fig
[docs] def check(self) -> None: """Check the consistency of the dimensions of the LHS and RHS. Raises: ValueError: When the shapes are inconsistent. """ lhs_shape = self.lhs.shape rhs_shape = self.rhs.shape if ( (len(lhs_shape) != 2) or (lhs_shape[0] != rhs_shape[0]) or (len(rhs_shape) != 1 and rhs_shape[-1] != 1) ): raise ValueError( "Incompatible dimensions in linear system Ax=b," " A shape is %s and b shape is %s", self.lhs.shape, self.rhs.shape, )