--- title: "mlab-numerics-numeric-trapezoid — Mova code model" description: "Mova code model of mlab/src/builtins/numeric.rs: components with their labels, obernants and the model text." url: "https://groupants.elamur.ai/free/en/mova/mlab/src/builtins/numeric.rs.groupant/numeric-trapezoid.groupant/" --- Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants** This page as HTML: # mlab-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 - **kind:** groupant_fragment - **status:** partial source bound model - **source:** [`mlab/src/builtins/numeric.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/numeric.rs) - **source SHA-256:** `f6fa5b4a76ef32af…` - **covers:** 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. (bytes 20309–21559) - **part of:** [mlab-numerics-numeric](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/numeric.rs.groupant/) - **repository folder:** [`mlab/src/builtins/numeric.rs.groupant/numeric-trapezoid.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/numeric.rs.groupant/numeric-trapezoid.groupant) - **repository commit:** `855da7bd4a7b` > **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](#approximant) | | **ast** | partial | `../syntax.json` | | **cost** | symbolic source derived | [invariant](#invariant) | | **descriptant** | present | [descriptant](#descriptant) | | **invariant** | partial | [invariant](#invariant) | | **tests** | executed bounded checks | [tests](#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](#behavior-complement) | | `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) | | `spacing_units` | spacing_units | partial source derived model | [spacing_units](#spacing-units) | | `length_gate` | length_gate | partial source derived model | [length_gate](#length-gate) | | `orientation` | orientation | partial source derived model | [orientation](#orientation) | | `complex_projection` | complex_projection | partial source derived model | [complex_projection](#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.