Elamur Groupantsmlab-numerics-poly-fit-roots
The groupant beside mlab/src/builtins/poly.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 |
leading_trim | leading_trim | partial source derived model | leading_trim |
trailing_roots | trailing_roots | partial source derived model | trailing_roots |
finite_gate | finite_gate | partial source derived model | finite_gate |
caller_join | caller_join | partial source derived model | caller_join |
Model text
descriptant
mlab-numerics-poly-fit-roots
polyfit parses x,y,n then rejects extra outputs, unequal lengths, invalid degree; constructs Vandermonde and calls SVD. roots rejects complex/nonfinite, removes leading zeros, records trailing zeros, constructs companion first row -c[j+1]/c0 and subdiagonal1 then calls eig.
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
polyfit parses x,y,n then rejects extra outputs, unequal lengths, invalid degree; constructs Vandermonde and calls SVD. roots rejects complex/nonfinite, removes leading zeros, records trailing zeros, constructs companion first row -c[j+1]/c0 and subdiagonal1 then calls eig.
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
Highest-degree coefficient first. Degree cast to usize/powi i32 not range-certified; eig result ordering is backend-dependent.
Cost
Vandermonde O(Md), SVD O(Md min(M,d)); companion O(dĀ²) storage/O(dĀ³) eig.
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-poly-fit-roots
behavior_complement
No roots eig call for constant/all-zero polynomial. polyfit's nargout error excludes further length/degree decision after initial argument parsing. Imaginary x/y cannot affect fitted Vandermonde in current code.
reverse_reconstruction
Given monic roots, coefficient families differ by nonzero scale and leading zeros; trailing root zeros remain visible. Least-squares coefficients are compatible with residuals orthogonal to retained SVD column space, not a unique y.
leading_trim
[0,1,-3,2] and [1,-3,2] yield same companion.
trailing_roots
[1,-2,0] evaluates eig for residual degree1 then appends zero root.
finite_gate
Any NaN/Inf coefficient errors before trimming, including nominal leading zeros around it.
caller_join
roots uses it.call_function("eig",...,1); overridden/missing dispatch and non-Mat result are not backend proofs.
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 ā https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/poly.rs.groupant/poly-fit-roots.groupant/