Solving systems of linear equations with LAPACK

At a glance

Project structure

Source bundle/
└── Accelerate-Linear-Solvers/
    ├── main.swift
    ├── isPositiveDefinite.swift
    ├── leastSquares_nonsquare.swift
    ├── matrixVectorMultiply.swift
    ├── nonsymmetric_banded.swift
    ├── nonsymmetric_general.swift
    ├── nonsymmetric_nonsquare.swift
    ├── nonsymmetric_tridiagonal.swift
    ├── symmetric_indefinite_general.swift
    ├── symmetric_positiveDefinite_banded.swift
    ├── symmetric_positiveDefinite_general.swift
    └── symmetric_positiveDefinite_tridiagonal.swift

Structure observations

• Architecturally prominent files are ranked from entry points and role-named declarations; resource-only paths are omitted.
• Primary languages: Swift.
• The verified tree contains 3 project/configuration file(s) and 0 source declaration(s).

Overall architecture

flowchart LR
    N1["main"]
    N2["Accelerate APIs"]
    N1 --> N2

Reference code

Accelerate-Linear-Solvers/main.swift:1 — architecture anchor

/*
See the LICENSE.txt file for this sample’s licensing information.

Abstract:
Main Swift file for LAPACK linear solvers sample.
*/

Interpretation

The arrows summarize the source-visible entry, role-named types or folders, and framework direction; when nodes come from structural folders, the sequence is a high-level interpretation rather than proof that every adjacent node calls the next. Ownership is claimed only where the next section cites a stored property or assignment. The diagram is intentionally limited to the dominant path into Accelerate.

Ownership and state

classDiagram
    main *-- Array : bValues
    main *-- Array : subdiagonalElements
    main *-- Array : diagonalElements
    main *-- Array : abValues

Ownership evidence

Accelerate-Linear-Solvers/main.swift:12 — stored dependency or nearest verified ownership anchor

let bValues: [Float] = [80, 180, 160,
                        800, 1800, 1600]

Composition arrows indicate a source-visible construction expression or locally owned value state; aggregation means the owner stores or receives a dependency without proving exclusive lifetime ownership.

Concurrency, scheduling, and thread safety

Evidence limit: actor isolation, async/await, or Task creation does not by itself prove background-thread execution; Sendable conformance alone does not prove thread-safe mutation.

No source-visible execution, scheduling, or synchronization boundary was found in the indexed source.

@MainActor/MainActor.run, DispatchQueue.main, and RunLoop.main are reported as distinct isolation, queue, and event-loop mechanisms. A plain Task is kept separate from Task.detached; neither is labeled as a background thread.

State propagation, frameworks, and dependencies

Evidence limit: an import proves a source-level compilation dependency at the cited line; it does not prove runtime use, architectural adoption, or whether a Swift package is a direct application dependency.

receive(on:) describes downstream delivery scheduling, while subscribe(on:) describes upstream subscription/request/cancel scheduling. An import Combine alone establishes neither behavior nor a Store, reducer, Redux, or other application architecture.

Class and protocol design

Accelerate-Linear-Solvers/isPositiveDefinite.swift:9 — representative type boundary

import Accelerate

No local protocol conformance is claimed as protocol-oriented design; external framework conformances are listed only as dependencies.

Access control

Reference code

Accelerate-Linear-Solvers/leastSquares_nonsquare.swift:9 — representative boundary

import Accelerate

Swift declarations without a modifier are internal; explicit private, fileprivate, private(set), public, or open entries above are interpreted by language semantics. Objective-C/C samples instead rely on header and implementation boundaries, which are not equivalent to Swift lexical privacy.

Logic ownership and placement

Design patterns

Naming conventions

• Types: feature-specific names rather than reusable layer suffixes.
• Protocols: no local protocol declaration in the scanned source.
• Methods: isPositiveDefinite, leastSquares_nonsquare, matrixVectorMultiply, nonsymmetric_banded, nonsymmetric_general, nonsymmetric_nonsquare, sgels, nonsymmetric_tridiagonal.
• Files: feature/project roles rather than a strict one-type-per-file rule.

Architecture takeaways

• main is the main source-visible entry or composition anchor for this sample.
• Framework work reaches Accelerate through a deliberately small high-level chain; the detailed API graph remains inside the cited implementation files.
• Stored-property evidence identifies lifecycle collaboration; it does not by itself prove exclusive object ownership.
• Access-control conclusions separate verified language visibility from the likely design rationale.
• The source does not justify labeling the design protocol-oriented.

Source map

• Official Apple documentation