---
title: "matrix-numerics — Mova code model"
description: "Mova code model of models/matrix-numerics.groupant: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/models/matrix-numerics.groupant/"
---
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# matrix-numerics

The groupant beside models/matrix-numerics.groupant 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_group
- **status:** partial descriptive instance
- **bound sources:** 7
- **repository folder:** [`models/matrix-numerics.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/matrix-numerics.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 | [forward](#forward) |
| **ast** | not materialized |  |
| **composition** | partial | [composition](#composition) |
| **cost** | symbolic source derived | [cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | see source local evidence | [checks](#checks) |

## 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) |
| `column-major-transport` | representation_transport | partial source derived model | [column-major-transport](#column-major-transport) |
| `rank-and-coefficients` | threshold_transport | partial source derived model | [rank-and-coefficients](#rank-and-coefficients) |
| `callback-effects` | effect_boundary | partial source derived model | [callback-effects](#callback-effects) |
| `error-observations` | residual_observation | partial source derived model | [error-observations](#error-observations) |

## Model text


### descriptant

#### matrix-numerics: wave30

polyfit→lstsq_svd joins real column-major Vandermonde with real y; roots/poly→Interp::call_function(eig) joins registry to linalg checks. ops routes matrix division to mldivide. elem cmap and FFT Mat::complex narrow zero im while explicit complex retains storage. FFT dim>=2 uses row slices, whereas reduce dims>2 use singleton slices. Local sort indices differ from global find indices. eval_nodes repeats callbacks after unsuitable vector attempt. Bench same column-major buffers feed both backends; main unexecuted.

This source-bound partial group organizes existing Mova code. Native evidence and excluded effects are recorded in source sidecars and the root wave30 report. Registration is not a universal proof or whole-system runtime claim.

### model

## matrix-numerics

### forward

Registry-bound matrix functions share column-major index k=j*rows+i. Element maps apply scalar real/complex functions; reductions aggregate dimension slices. FFT computes F_N(P_N(x)) and inverse F_N^-1/N over those slices. Polynomial Horner uses descending coefficients; polyfit creates V[i,j]=x_i^(d-j), returns retained-SVD V^+ y, while roots builds companion C and calls eig. Dense solve chooses LU/QR/SVD by shape/rank and records warning residuals. Numeric callbacks implement GK15, Brent, Nelder-Mead and Dormand-Prince; trapz sums adjacent sample averages times spacing. Bench data/best are a separate diagnostic path, not runtime dispatch.

### invariant

Well-formed Mat vectors match rows*cols and optional im length. Coordinates are column-major except explicit reshaping. FFT dim>=2 aliases dim2, unlike reduction singleton slices for dim>2. Finite fixtures preserve stated values/tolerances; warnings do not imply rejection. Long deconv division, executed nonempty diff steps, cumulative and trapz read real parts; deconv short-dividend remainder and diff order0/zero-length-axis branches clone input and preserve imaginary storage. Callback retry is not transactional.

### cost

Elementwise O(N); slice construction/reductions/cumulative O(N+S), S=number of slices, including shaped empties N0,S>0. Sort O(N log(max(L,2))+S); FFT O(S*N log N) plus planning. Horner O(PX), convolution O(PQ); fit/eigen/dense solves O(mn min(m,n)) or square O(n^3) plus residual products. GK at most650 intervals with O(I) scans, Brent1000 iterations, ODE1e6 attempts plus callback cost. Bench helpers use n² samples/three callbacks only. No timings or speed claims; dimension overflow and allocations remain explicit.

### composition

polyfit→lstsq_svd joins real column-major Vandermonde with real y; roots/poly→Interp::call_function(eig) joins registry to linalg checks. ops routes matrix division to mldivide. elem cmap and FFT Mat::complex narrow zero im while explicit complex retains storage. FFT dim>=2 uses row slices, whereas reduce dims>2 use singleton slices. Local sort indices differ from global find indices. eval_nodes repeats callbacks after unsuitable vector attempt. Bench same column-major buffers feed both backends; main unexecuted.

### domain

Bounded synthetic CPU matrices and functions, valid storage, finite small arithmetic where required; no network, corpus, teacher, GPU, benchmark main or held-out suites. Models describe broader source branches with explicitly partial execution.

### limitations

Backend faer/rustfft semantics are dependencies; lexical projections do not resolve macros/types. Public malformed Mat storage, huge dimensions, allocation failure, nonfinite convergence, callback side effects and arbitrary complex support are not certified. Native benchmark helper selection uses cargo --bin because this package has no library target.

### checks

- Eight exact named native tests, twice debug and twice release; same ordered named outcomes
- Seven production compiled mutants, one per owned source; expected assertion failure exit101, exact-byte restoration and positive rerun in both profiles
- Seven lexical syntax projections generated twice identically; fragments reference parent projection with SHA256 byte scopes
- Focused rustfmt on added inline test blocks only; guarded own-source commit

### catalog

### behavior-complement

Wrong shape/order adapters are incompatible with bounded transport fixtures. FFT inverse without1/N violates impulse reconstruction. Long deconv division and executed diff/trapz arithmetic do not preserve imaginary parts, but cloned passthrough branches do. Callback retry excludes exactly-once effects. Warning gates and fzero success flag1 do not exclude nonzero residual results.

### reverse-reconstruction

Fixed-N Fourier outputs identify padded/truncated slices up to rounding, leaving arbitrary truncated tails. Poly quotient/remainder plus real divisor reconstructs dividend via padded convolution; short dividends clone remainder. Least-squares B lies in AX plus residual orthogonal to retained columns. Sort values plus permutation recover slices; sums have zero-sum fibers. fzero output is compatible with bracket-width stopping or1000-iteration exhaustion and nonzero residual, even discontinuous functions without a root; only sampled fb==0 establishes an observed zero.

### column-major-transport

Mat k=j*r+i, faer view and Vandermonde columns share layout. FFT dim1 gathers s*r+t; all admitted dim>=2 gather t*r+s and change cols toN. reduce::slices dims>2 instead emits singleton slices. Layout adapters must preserve these distinct rules.

### rank-and-coefficients

polyfit uses lstsq_svd threshold max(m,n)*smax*eps; rank builtin uses spacing-based tolerance and therefore is not a certified identical rank selector. roots scaling to monic companion discards nonzero leading coefficient scale.

### callback-effects

eval_nodes vector attempt can mutate Interp before fallback; subsequent scalar calls add effects. Model callback count separately from mathematical integrand evaluation. Bench helper best similarly calls exactly3 times, returns last value and independent minimum time.

### error-observations

linalg gate tolerance1000*n*eps concerns selected residuals, not component relative error. GK embedded K-G is estimated error and its650-interval exit warns. These do not compose into a percent bound for roots/fit/numeric callbacks.