Elamur Groupantsmlab-numerics-numeric-trapezoid
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 |
spacing_units | spacing_units | partial source derived model | spacing_units |
length_gate | length_gate | partial source derived model | length_gate |
orientation | orientation | partial source derived model | orientation |
complex_projection | complex_projection | partial source derived model | complex_projection |
Model text
descriptant
mlab-numerics-numeric-trapezoid
trapz chooses row-vector or column slices; optional scalar X is uniform step, other X must have slice length. Each output sums (X[t]-X[t-1])*(Y[t]+Y[t-1])/2 or default spacing1.
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
trapz chooses row-vector or column slices; optional scalar X is uniform step, other X must have slice length. Each output sums (X[t]-X[t-1])*(Y[t]+Y[t-1])/2 or default spacing1.
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
Output scalar for one slice, row for multiple; zero/one-length slices accumulate0. Nonmonotone X gives signed widths without error.
Cost
O(N) sampled cells, O(columns) output.
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-trapezoid
behavior_complement
Wrong non-scalar X length excludes accumulation. A single sample excludes nonzero contribution regardless scalar step. Imaginary components cannot influence this real-only implementation.
reverse_reconstruction
For fixed X, output defines one linear weighted-sum constraint per Y slice; arbitrary perturbations in its nullspace produce same result. Uniform scaling of X and inverse scaling of Y preserve integral absent rounding.
spacing_units
trapz(2,[1,3,5])=2*(1+3)/2+2*(3+5)/2=12.
length_gate
X length2 with Y row length3 errors before data indexing.
orientation
row1 uses cols as length and one output; other matrices integrate columns.
complex_projection
Only re vectors are read, so this scope does not implement complex integration.
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-trapezoid.groupant/