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

The groupant beside mlab/src/builtins/elem.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/elem.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/elem.rs)
- **source SHA-256:** `09570b244d52019b…`
- **covers:** map(m,f)=(rows,cols,f(re)); cmap applies f to (re,im_or_zeros) and narrows; map_parts separately transforms stored parts and narrows. csqrt(x,0) returns real sqrt if x>=0 else positive imaginary root; nonzero y uses hypot half-angle formula. (bytes 13655–14603)
- **part of:** [mlab-numerics-elem](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/elem.rs.groupant/)
- **repository folder:** [`mlab/src/builtins/elem.rs.groupant/elem-mapping.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/elem.rs.groupant/elem-mapping.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) |
| `branch_selection` | branch_selection | partial source derived model | [branch_selection](#branch-selection) |
| `narrowing` | narrowing | partial source derived model | [narrowing](#narrowing) |
| `shape_transport` | shape_transport | partial source derived model | [shape_transport](#shape-transport) |
| `nonfinite_gap` | nonfinite_gap | partial source derived model | [nonfinite_gap](#nonfinite-gap) |

## Model text


### descriptant

#### mlab-numerics-elem-mapping

map(m,f)=(rows,cols,f(re)); cmap applies f to (re,im_or_zeros) and narrows; map_parts separately transforms stored parts and narrows. csqrt(x,0) returns real sqrt if x>=0 else positive imaginary root; nonzero y uses hypot half-angle formula.

##### 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(m,f)=(rows,cols,f(re)); cmap applies f to (re,im_or_zeros) and narrows; map_parts separately transforms stored parts and narrows. csqrt(x,0) returns real sqrt if x>=0 else positive imaginary root; nonzero y uses hypot half-angle formula.

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

Same rows/cols and one result per valid real cell; malformed public vector lengths outside contract.

##### Cost

O(N) maps and temporary imaginary vector; csqrt O(1).

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-elem-mapping

### behavior_complement

map excludes imaginary dependence; cmap excludes index reordering. For finite x and y<0, csqrt excludes positive imaginary branch. A zero-imaginary result may narrow, so complex representation identity is not guaranteed.

### reverse_reconstruction

map preimage includes arbitrary imaginary arrays when re maps to output. cmap preimages are products of scalar f fibers subject to shape; principal csqrt reconstructs z by squaring only on admitted branch.

### branch_selection

(-9,0)→(0,3); (3,-4)→(2,-1); nonzero imaginary sign follows y.

### narrowing

map_parts invokes narrow after transforming im; a rounded-to-zero im array becomes real.

### shape_transport

Column-major index k is unchanged for every mapped cell.

### nonfinite_gap

hypot avoids some overflow but (r+x)/2 can still overflow; NaN and infinities are not certified.


### 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.