Struct ComplexSparseSystem 

pub struct ComplexSparseSystem { /* private fields */ }

A complex sparse system whose sparsity pattern and values are both fixed across repeated solves, so the whole factorization — not merely the symbolic half — is computed once and reused.

This is the stronger guarantee RealSparseSystem cannot make: Newton’s Jacobian changes numerically every iteration, so only the ordering can be cached. The iterative-linear state estimator (gridoxide’s se::iterative) is different — its system matrix depends on the measurement set and on the assumption that voltage magnitudes stay near their initial values, so it is genuinely constant and only the right-hand side moves. That is exactly what makes the method cheaper per iteration than Newton-Raphson, and it is why this type exists.

Implementations

impl ComplexSparseSystem

pub fn new(n: usize, entries: &[(usize, usize, Complex<f64>)]) -> Option<Self>

Factorizes once. Returns None if the matrix is singular or malformed.

pub fn solve(&self, rhs: &[Complex<f64>]) -> Option<Vec<Complex<f64>>>

Solves A x = b against the cached factorization.

Singularity is checked on the result rather than reported by faer, which returns NaN-poisoned values instead of an error — the same contract solve_complex documents.

pub fn solve_adjoint(&self, rhs: &[Complex<f64>]) -> Option<Vec<Complex<f64>>>

Solves Aᴴ x = b — the conjugate transpose — against the same cached factorization.

No second factorization is involved, for the reason RealFactorization::solve_transpose documents: an LU = PAQ decomposition solves the transposed system by running the same triangular factors in the opposite order.

The conjugate transpose rather than the plain one, because that is the form the question comes in. A left eigenvector satisfies wᴴ A = λ wᴴ, i.e. Aᴴ w = λ̄ w, and left eigenvectors are what participation factors and eigenvalue sensitivities are built from (dynamics::smallsignal). faer offers it directly as solve_adjoint_in_place, so nothing here has to conjugate by hand.