solve_cgs_lagrange#

sectionproperties.analysis.solver.solve_cgs_lagrange(k_lg: csc_matrix, f: ndarray[Any, dtype[float64]], m: LinearOperator | None = None, tol: float = 1e-05) → ndarray[Any, dtype[float64]][source]#

Solves a linear system using the CGS iterative method (Lagrangian multiplier).

Parameters:

  • k_lg (csc_matrix) – (N+1) x (N+1) Lagrangian multiplier matrix of the linear system

  • f (ndarray[Any, dtype[float64]]) – N x 1 right hand side of the linear system

  • m (LinearOperator | None) – Preconditioner for the linear matrix approximating the inverse of k

  • tol (float) – Tolerance for the solver to achieve. The algorithm terminates when either the relative or the absolute residual is below tol

Returns:

The solution vector to the linear system of equations

Raises:

RuntimeError – If the CGS iterative method does not converge or the error from the Lagrangian multiplier method exceeds the tolerance

Return type:

ndarray[Any, dtype[float64]]