Module solve 

The internal fields between two adjacent stacks: a certified Krylov or pivoted LU solve of (I - L1 U2) up = rhs, kept for the pullback.

Upstream: the numpy.linalg.solve inside treams.SMatrices.illuminate with a second S-matrix. The Krylov branch and its contraction test are treams-rs extensions.

L1 is the reflection of the lower stack for waves incident from the positive side (above) and U2 the reflection of the upper stack for waves incident from the negative side (below), so up holds the upgoing fields between the stacks.

Modules

saved 🔒

The original internal solve strategy and its numerical state, with a fixed factor slot that never builds a reflection product solely for serialization.

Structs

AdjointSolve 🔒

The adjoint solution of an internal system, beside its borrowed forward solution.

InternalSolve 🔒

The forward solution of the internal system and what its adjoint solve reuses.

Enums

InternalFactor 🔒

What the pullback reuses to solve the adjoint system.

Constants

ITERATIVE_MAX_COLUMNS 🔒

Most right-hand sides for which the Krylov solve is tried; wider batches factor.

ITERATIVE_MIN_ROWS 🔒

Rows from which a certified contraction tries the bounded Krylov solve before falling back to a dense LU factorization.

KRYLOV_STEPS 🔒

Krylov iterations, without restart, of one internal solve before the dense fallback.

Functions

absolute_row_sums 🔒

Positive row sums of (|re A| + |im A|) weights, rounded upward.

internal_iteration 🔒

The unrestarted Krylov solve of the operator, or of its adjoint, for a thin batch, or None when it fails numerically and the caller should factor the operator instead.

internal_operator 🔒

The internal operator I - lower upper.

is_contraction 🔒

Whether ||L U||_inf < 1 holds for the operator I - L U, which proves it invertible.

reflection_action 🔒

Apply I - L U, or its adjoint, using only thin products.

reflections_contract 🔒

Certify ||L U||_inf < 1 using |L| |U| 1, in quadratic work.