Elamur Groupantsmlab-numerics-numeric-quadrature
The groupant beside mlab/src/builtins/numeric.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 |
finite_map | finite_map | partial source derived model | finite_map |
infinite_map | infinite_map | partial source derived model | infinite_map |
retry_effect | retry_effect | partial source derived model | retry_effect |
option_order | option_order | partial source derived model | option_order |
Model text
descriptant
mlab-numerics-numeric-quadrature
map_point supplies x(t) and positive quadrature weight; gk15 samples symmetric15 nodes, forms K15 and embedded G7, returns hK and abs(h(K-G)). integral orders endpoints, sets sign, starts10 intervals and splits maximum estimated error until tolerance or650.
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
map_point supplies x(t) and positive quadrature weight; gk15 samples symmetric15 nodes, forms K15 and embedded G7, returns hK and abs(h(K-G)). integral orders endpoints, sets sign, starts10 intervals and splits maximum estimated error until tolerance or650.
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
Finite map endpoints x(-1)=a,x(1)=b, zero derivative endpoints. Error estimate is not an analytical bound; finite nonpathological parameters assumed.
Cost
O(I²+15Icallback cost) worst interval scans for I<=650, O(I) interval storage plus15 nodes.
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-numeric-quadrature
behavior_complement
No endpoint callback in the embedded rule; equal integral bounds exclude all samples after options. Exhaustion does not exclude returned value: it emits warning. Nonfinite q returns immediately.
reverse_reconstruction
A finite quadrature result constrains weighted sample sums; integrands agreeing at sampled nodes or differing in nullspace of those weights can share result. Mapping antecedent t is unique only on interior monotone finite/right domains; Left reverses orientation with positive weight.
finite_map
a2,b6,t0→x4,w3; Jacobian is cubic map derivative.
infinite_map
Right2,t.5→3,4; Left2,t.5→1,4; Both0→0,1.
retry_effect
Vectorized nonnumeric/wrong-shape/complex result or error falls back to scalar calls after its effects.
option_order
Unknown paired option errors before lo==hi shortcut; unpaired trailing option is ignored by loop condition.
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/numeric.rs.groupant/numeric-quadrature.groupant/