---
title: "mlab-numerics-numeric-quadrature — 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-quadrature.groupant/"
---
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# mlab-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

- **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:** map_point supplies x(t) and positive quadrature weight; gk15 samples symmetric15 nodes, forms K15 and embedded G7, returns h*K and abs(h*(K-G)). integral orders endpoints, sets sign, starts10 intervals and splits maximum estimated error until tolerance or650. (bytes 531–6743)
- **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-quadrature.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/numeric.rs.groupant/numeric-quadrature.groupant)
- **repository commit:** `48f2e6f74146`

> **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) |
| `finite_map` | finite_map | partial source derived model | [finite_map](#finite-map) |
| `infinite_map` | infinite_map | partial source derived model | [infinite_map](#infinite-map) |
| `retry_effect` | retry_effect | partial source derived model | [retry_effect](#retry-effect) |
| `option_order` | option_order | partial source derived model | [option_order](#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 h*K 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 h*K 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+15*I*callback 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.