---
title: "mlab-numerics-reduce-order — Mova code model"
description: "Mova code model of mlab/src/builtins/reduce.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/mlab/src/builtins/reduce.rs.groupant/reduce-order.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**

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# mlab-numerics-reduce-order

The groupant beside mlab/src/builtins/reduce.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/reduce.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/reduce.rs)
- **source SHA-256:** `0f9cbbd92e1b1868…`
- **covers:** better ignores NaN best when candidate finite and uses strict >/<. minmax reduction scans slices in order; complex keys are modulus but returned cell keeps components. sort computes stable local index permutation by real/modulus keys, with NaNs last ascending and first descending. (bytes 6517–10628)
- **part of:** [mlab-numerics-reduce](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/reduce.rs.groupant/)
- **repository folder:** [`mlab/src/builtins/reduce.rs.groupant/reduce-order.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/reduce.rs.groupant/reduce-order.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) |
| `strict_tie` | strict_tie | partial source derived model | [strict_tie](#strict-tie) |
| `nan_sort` | nan_sort | partial source derived model | [nan_sort](#nan-sort) |
| `binary_dispatch` | binary_dispatch | partial source derived model | [binary_dispatch](#binary-dispatch) |
| `complex_key` | complex_key | partial source derived model | [complex_key](#complex-key) |

## Model text


### descriptant

#### mlab-numerics-reduce-order

better ignores NaN best when candidate finite and uses strict >/<. minmax reduction scans slices in order; complex keys are modulus but returned cell keeps components. sort computes stable local index permutation by real/modulus keys, with NaNs last ascending and first descending.

##### 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

better ignores NaN best when candidate finite and uses strict >/<. minmax reduction scans slices in order; complex keys are modulus but returned cell keeps components. sort computes stable local index permutation by real/modulus keys, with NaNs last ascending and first descending.

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

Coordinates are1-based local slice positions; sort preserves Class and complex storage, minmax casts Char/Logical result class to Double.

##### Cost

O(N+S) extrema; O(N log(max(L,2))+S) sort and O(N+S) index/scratch memory, including headers for empty slices.

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-reduce-order

### behavior_complement

Ties exclude winner replacement; sort excludes independent real/imag sorting. Empty0x0 minmax returns two empty values regardless nargout, while other empty slice shapes are unchecked.

### reverse_reconstruction

Extremum and position identify selected cell and constrain other keys; earlier equal keys are incompatible with later winner. Sorted values plus 1-based per-slice permutation recover original cells when the permutation is valid.

### strict_tie

[NaN,4,4] max index2, never3.

### nan_sort

Two NaNs compare equal in stable sort; descending moves NaNs before finite keys.

### binary_dispatch

Exactly2 arguments can take elementwise max/min even for empty second Mat; three-argument empty placeholder uses dim reduction.

### complex_key

Equal magnitudes retain first minmax cell without phase tiebreak; returned value may have different phase than another compatible winner.


### 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.