---
title: "algorithm-conjugate-gradient-tests — Mova code model"
description: "Mova code model of algorithms/src/conjugate_gradient/tests.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/conjugate_gradient/tests.rs.groupant/"
---
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# algorithm-conjugate-gradient-tests

The groupant beside algorithms/src/conjugate_gradient/tests.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
- **status:** partial descriptive instance
- **source:** [`algorithms/src/conjugate_gradient/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/conjugate_gradient/tests.rs)
- **source SHA-256:** `f5461c2081df0fa4…`
- **repository folder:** [`algorithms/src/conjugate_gradient/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/conjugate_gradient/tests.rs.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` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [approximant](#approximant) |
| **tests** | finite 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 relational specification | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial relational specification | [reverse_reconstruction](#reverse-reconstruction) |
| `independent_oracle` | independent_oracle | partial relational specification | [independent_oracle](#independent-oracle) |
| `mutation_sensitivity` | mutation_sensitivity | partial relational specification | [mutation_sensitivity](#mutation-sensitivity) |
| `boundary_partition` | boundary_partition | partial relational specification | [boundary_partition](#boundary-partition) |

## Model text


### descriptant

#### conjugate_gradient tests.rs

Original standard-library numerical implementation and finite tests. Prospective predictions were saved before code in ../prospective.md.

r=b-Ax, p initially r; alpha=(r'r)/(p'Ap), x_next=x+alpha*p; recompute fresh r and beta=(r_new'r_new)/(r_old'r_old), p_next=r_new+beta*p. Reject encountered nonpositive curvature. Exact arithmetic gives classical CG; recomputation and rounding lose exact conjugacy.

12 dense SPD matrices diag(1..n)+11' with independently constructed known solutions, directly recomputed residual, zero budget, zero residual, squared-norm underflow stagnation, asymmetry, negative curvature and arithmetic overflow.

Literature: Burden and Faires, Numerical Analysis (bisection); Kiefer (1953), Sequential minimax search for a maximum (golden section); Nocedal and Wright, Numerical Optimization, second edition, chapter 3 (gradient descent); Hestenes and Stiefel (1952), Methods of conjugate gradients for solving linear systems (CG). No source code was copied.

2026-10-30 epoch: scoped safe bounds and explicit failure statuses were retained; finite observations do not establish universal convergence.

### model

#### Mathematical combiner

Inputs: authoritative tests.rs, partial syntax projection, forward model, typed complement and reconstruction relations, and named finite observations. The combiner intersects accepted-domain constraints with update invariants, then partitions outputs by convergence, budget, stagnation or error. Cost is O(n²*k) arithmetic, O(n) auxiliary storage beyond caller matrix, checked vector reservations; symmetry precheck O(n²). Tests are sibling sources, never implementation children. Source hashes bind this descriptive epoch; syntax is not semantic AST or proof.

Observation retained: 12 dense SPD matrices diag(1..n)+11' with independently constructed known solutions, directly recomputed residual, zero budget, zero residual, squared-norm underflow stagnation, asymmetry, negative curvature and arithmetic overflow.

Limits: callback determinism/continuity/unimodality and global SPD are assumptions; residual stopping alone says nothing universal about solution error. Conditioning, underflow, finite rounding and callback cost remain material. No speed measurements or universal accuracy certificate are claimed.

### approximant

#### Forward approximant and invariant

Domain: Dimension 1..256, square exactly symmetric finite matrix, RHS and initial coordinates bounded by 1e100; caller assumes SPD; positive finite residual tolerance and budget <=100000.

r=b-Ax, p initially r; alpha=(r'r)/(p'Ap), x_next=x+alpha*p; recompute fresh r and beta=(r_new'r_new)/(r_old'r_old), p_next=r_new+beta*p. Reject encountered nonpositive curvature. Exact arithmetic gives classical CG; recomputation and rounding lose exact conjugacy.

Cost: O(n²*k) arithmetic, O(n) auxiliary storage beyond caller matrix, checked vector reservations; symmetry precheck O(n²).

Test source maps fixed fixtures to assertion success/failure. 12 dense SPD matrices diag(1..n)+11' with independently constructed known solutions, directly recomputed residual, zero budget, zero residual, squared-norm underflow stagnation, asymmetry, negative curvature and arithmetic overflow.

Numerical claims concern additive interval widths or absolute gradient/residual norms. A relative coordinate error has undefined behavior at zero without a separate convention and is not claimed. No supported 1/2/5/10% executable surrogate is attached: this exact API is already iterative, and no independently measured faster transformation with a useful certified metric is supplied.

### models

## Typed obernant family

### behavior_complement

Let U be all possible fixture outcomes and R the conjunction of the explicit assertions. U\R includes a wrong coordinate even if status looks plausible, false convergence, accepted invalid fixtures or exceeded callback count. Passing tests establishes membership only for these finite inputs, not all inputs.

### reverse_reconstruction

A passing assertion report maps back to all implementations agreeing on the finite fixtures. This is a large nonunique fiber: unsampled callbacks, matrix spectra and resource failures remain free. Domain: Dimension 1..256, square exactly symmetric finite matrix, RHS and initial coordinates bounded by 1e100; caller assumes SPD; positive finite residual tolerance and budget <=100000.

### independent_oracle

12 dense SPD matrices diag(1..n)+11' with independently constructed known solutions, directly recomputed residual, zero budget, zero residual, squared-norm underflow stagnation, asymmetry, negative curvature and arithmetic overflow.

### mutation_sensitivity

A compiled production mutation must fail the named assertion `dense coordinate oracle`; restoring exact source bytes must recover a passing focused suite. This shows local detection power only.

### boundary_partition

Partition observations by valid convergence, zero/exhausted budget, representational stagnation, and invalid inputs/nonfinite values. Allocation failure is modeled but not injected. Strict continuity/unimodality/SPD are not established by finite tests.


### tests

#### Checks

Run `cargo test -p mova-algorithms conjugate_gradient::tests` and its release equivalent. 12 dense SPD matrices diag(1..n)+11' with independently constructed known solutions, directly recomputed residual, zero budget, zero residual, squared-norm underflow stagnation, asymmetry, negative curvature and arithmetic overflow.

Compiled negative control must hit `dense coordinate oracle`. Full algorithms suite runs twice per profile; normalized ordered test outcomes are compared. Strict all-target Clippy and focused rustfmt check complete validation. See validation.md for observed evidence.

### validation

#### Validation evidence

2026-10-30. External records under `$MOVA_DATA/runs/octopus-wave19-solvers-2026-10-30/`. Two debug and two release runs each passed 501 library tests (12 new focused tests); sorted named outcomes agree across four runs. Strict algorithms all-target Clippy and focused rustfmt passed.

Source SHA-256: `f5461c2081df0fa44dd47ff3e840f71e9dc0705f14b52baa3c1e7e1833ae4c5e`. Negative production mutant failed `dense coordinate oracle`; restored bytes passed the focused suite.

- `negative-conjugate_gradient.log` SHA-256 `23b4b2c34030bee1b468aa16497e2f539bbb1d047f125d5641291cdc4ea333ca`
- `restored-conjugate_gradient.log` SHA-256 `eadca419529e42fb1088f6bb5ee6760ae151cb4f8b51e7a9fa85ab6d769ff617`
- `debug1.log` SHA-256 `61428a2e0c6dbc43cde2fa1cf9a4b021a6cebd75c04de1ecb3cf761fa95eccbf`
- `debug2.log` SHA-256 `73ffe6afebfbf497bd448639d77d254de8142e4c170e346e976eff376e95e496`
- `release1.log` SHA-256 `9a28e6d7f1af6cfbf056323b4ec824aca1899d9ed52b1635d30ed01ed8785afb`
- `release2.log` SHA-256 `17cdc616d33e1ca8add5062ebed8e5303eebab267338c981dbc2aecba57afd43`
- `clippy.log` SHA-256 `71ef179d48cc2d1e07e85d2e77009ed79e6e543be1e409886afdb92b50363422`

Partial syntax projection generated independently twice and compared byte-for-byte. These are finite checks; allocation exhaustion and arbitrary caller functions/matrices are not exhaustively verified.