Elamur Groupantsmlab-numerics-linalg-factors
The groupant beside mlab/src/builtins/linalg.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| cost | symbolic source derived | invariant |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | executed bounded checks | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
lu_output_arity | lu_output_arity | partial source derived model | lu_output_arity |
chol_failure | chol_failure | partial source derived model | chol_failure |
eigen_symmetry | eigen_symmetry | partial source derived model | eigen_symmetry |
residual_limits | residual_limits | partial source derived model | residual_limits |
Model text
descriptant
mlab-numerics-linalg-factors
lu returns packed L/U for <=1 output, P^T L and U for2, or L,U,P for3+. qr computes full/thin Q/R and zeros below R diagonal. chol symmetrizes upper input triangle, returning R with R^T R=upper-symmetric A or empty,status1 on two-output failure. eig dispatches exact symmetry then returns values or V,D and warning residuals.
Modeling epoch 2026-10-31
Prospective source reading preceded inline tests. This node records implementation behavior, not a complete MATLAB compatibility contract. Models retain limits discovered in source reading, including real-only projections and warning-only result gates. Synthetic CPU fixtures are independent of frozen suites. No external effects, teacher, corpora or benchmark main are executed.
approximant
Forward relation
lu returns packed L/U for <=1 output, P^T L and U for2, or L,U,P for3+. qr computes full/thin Q/R and zeros below R diagonal. chol symmetrizes upper input triangle, returning R with R^T R=upper-symmetric A or empty,status1 on two-output failure. eig dispatches exact symmetry then returns values or V,D and warning residuals.
Executable Rust surrogate gap: no calibrated replacement is attached. Exact test calls are evidence for the reference, not a fast approximant. Numerical approximants would need a named domain, zero convention and metric at supported caps 1/2/5/10%; categorical errors/effects have no percent surrogate here.
invariant
Invariants and cost
Factor shapes depend on nargout/economy. Gates use finite input and relative residual with explicit zero-reference behavior; no rejection on gate violation.
Cost
Decompositions O(n^3) square with O(n^2) storage; reconstruction gates add O(n^3); diagonal eigen scaling O(n^2).
Allocation failure, unchecked usize dimension arithmetic and IEEE nonfinite propagation are outside finite fixture guarantees. No measured throughput or global accuracy claim.
models
Typed source models: mlab-numerics-linalg-factors
behavior_complement
LU's two-output L excludes interpreting it as unit lower triangular without permutation. chol excludes lower-triangle influence. eig nonsquare/complex/nonfinite checks precede empty/backend evaluation.
reverse_reconstruction
Three-output LU reconstructs A=P^T L U; two-output factors reconstruct A=L2 U. chol R reconstructs symmetric upper-selected A but arbitrary lower-triangle input shares output. V,D reconstruct A only if V invertible; values-only fibers include similarity transforms.
lu_output_arity
nargout2 uses P^T L; nargout3 emits permutation matrix.
chol_failure
Positive-definite failure returns status1 if requested, otherwise MError; upper triangle defines the factorized symmetric matrix.
eigen_symmetry
Symmetric branch uses exact mirrored-cell equality; nonsymmetric vectors are normalized by Euclidean column norm.
residual_limits
Value-only eigen gate checks sum eigenvalues versus trace, which cannot detect trace-preserving errors.
tests
Evidence and limits
Selected wave30_tests exercise this source; fragment-specific limits are stated in its operators.
Native command specifications, numeric exits, profile-paired logs, compiled controls and exact-restoration receipts are retained externally in the wave30 numerics run. Tests exercise actual source, not a copied model. The selected finite fixtures do not prove full convergence, backend accuracy on all matrices, resource exhaustion or side-effectful callback behavior.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/linalg.rs.groupant/linalg-factors.groupant/