#LINEAR-ALGEBRA

#v0.3.0 - Shared Numeric Capability Alignment

#Package Positioning

• immut: Immutable, value-oriented Matrix, Vector, and MatrixFn types for persistent data and explicit copy-on-update semantics.
• mutable: Execution-oriented Matrix and Vector types with in-place updates, Transpose views, RowView / ColView, and backend-specific implementations for js, wasm, wasm-gc, and native.
• Shared Core, Different Execution Model: Constructors and core algebraic operators remain aligned across packages, but mutation and access semantics are intentionally different.

#What Defines v0.3.0

• Shared Square-Root Capability: Numerical matrix APIs now use Luna-Flow/arithmetic.Sqrt instead of a package-local trait. mutable re-exports the shared trait for source-level discoverability.
• Target-Side Integral Embedding: Generic integer conversions use IntegralHomomorphism::from_integral, matching the current Luna-Flow/luna-generic algebraic model.
• Ecosystem-Oriented Constraints: Custom scalar types can implement the shared Luna Flow traits once and use them across compatible ecosystem packages.
• Backend Consistency: Native, JS, Wasm, and Wasm GC matrix implementations use the same arithmetic capability identity and explicit trait invocation.
• Compatibility Boundary: Tolerance remains a mutable package trait in this release; it has not yet moved to arithmetic.

#API Guidance & Performance

• Core Algebraic API: Shared operations such as make, transpose, +, -, *, trace, and matrix/vector conversions are intended to stay semantically aligned across immut and mutable.
• Random Access: In mutable, for high-performance random access, prefer .get(i, j) and .set(i, j, val) directly.
• Structured Views: For repeated row or column work in mutable, prefer row_view() / col_view() instead of relying on matrix[row] convenience syntax.
• Strict Bounds: Public matrix, view, and transpose accessors consistently reject out-of-bounds indices, including 0xN and Nx0 edge cases.
• MatrixFn Alignment: immut.MatrixFn now shares the same non-negative dimension and empty-matrix semantics as the concrete matrix implementations.
• Public Surface: Internal decomposition helpers remain implementation details. Package users should rely on the documented public matrix methods instead.

#Key Features

• Mutable & Immutable Support: Full Matrix and Vector suites with distinct semantics for value-oriented and execution-oriented workloads.
• Advanced Operations: Includes determinant, inverse, rank, Cholesky decomposition, eigen-related routines, row elimination, transpose views, and matrix/vector conversions.
• Shared Data Model, Backend-Tuned Kernels: mutable still ships backend-tuned execution paths for Native, Wasm, JS, and Wasm GC targets, but the core matrix storage model is now unified.
• Benchmark Infrastructure: bench/, src/perf_support, and src/perf_runner now form a full steady-state benchmarking subsystem for backend comparison and diagnostic replay.
• Correctness First: Coverage now includes immutable laws, cross-package consistency checks, determinant/rank/inverse alignment, and regression tests for numerical behavior.
• Auditable Public Contracts: Bounds behavior, swap semantics, benchmark fixtures, and documentation are now tracked more explicitly as part of the repository’s correctness story.

#Benchmark Packages

• perf: Benchmark entry package used by moon bench for the steady-state matrix suite.
• perf_support: Public fixture metadata, case registry, runtime loaders, and checksum-oriented execution helpers for benchmark cases.
• perf_runner: Single-case diagnostic and sampling runner used for replay, local investigation, and richer benchmark artifact generation.

#Quick Start

let imm = @immut.Matrix::from_2d_array([[1, 2], [3, 4]])
let imm_updated = imm.set(0, 1, 9)

let m = @mutable.Matrix::from_2d_array([[1.0, 2.0], [3.0, 4.0]])
m.set(0, 1, 9.0)

let det = m.determinant()
let maybe_inv = m.inverse()
let row0 = m.row_view(0).to_array()

#Documentation

• 🇺🇸 English (doc/en_US)
• 🇨🇳 简体中文 (doc/zh_CN)
• 🇯🇵 日本語 (doc/ja_JP)

• 🇺🇸 README.md
• 🇨🇳 README.md
• 🇯🇵 README.md

#Version History

#Current Repository Highlights

• Current Release Narrative (0.3.0):
  • Square-root-dependent matrix algorithms now require the shared arithmetic.Sqrt capability.
  • mutable.Sqrt is a public re-export of arithmetic.Sqrt; the old package-local trait and scalar implementations were removed.
  • Integral test fixtures and conversion helpers now use target-side IntegralHomomorphism::from_integral.
  • Custom numeric types should implement capabilities in luna-generic and arithmetic rather than package-specific linear-algebra traits.

• Previous Release Narrative (0.2.12):
  • Public matrix, view, and transpose accessors enforce explicit bounds contracts, including zero-row and zero-column edge shapes.
  • immut.Matrix and mutable.Matrix are aligned on shared correctness semantics while preserving their value-vs-mutation execution split.
  • Benchmark diagnostics and the tracked correctness audit reflect the exported 0.2.12 surface.

• Earlier Release Narrative (0.2.11):
  • mutable.Matrix now combines the shared flat storage model from 0.2.10 with follow-up backend kernel optimizations and a dedicated wasm-gc implementation.
  • Public numerical signatures are aligned around Field / Num / Tolerance, and immutable determinant documentation matches the simplified post-0.2.10 constraint set.
  • The benchmark stack now includes runtime-loaded fixtures, expanded case metadata, richer summary reporting, a local dashboard, optional Rust comparison runs, and diagnostic replay via perf_runner.
  • The release checklist, benchmark docs, package overview, and localized READMEs are aligned to the 0.2.11 release story.

• Algorithms & Stability (0.2.8):
  • Added LU- and QR-related decomposition support used by determinant, inverse, rank, and eigen routines.
  • Shifted determinant and rank behavior toward more stable elimination-based implementations.

• Native Optimization (0.2.7):
  • Implemented transposition + dot-product strategy for Native matrix multiplication, outperforming naive implementations by more than 2x.
  • Optimized make, new, and transpose to remove expensive integer division in hot loops.

• Performance Overhaul (0.2.4):
  • Optimized secondary utilities such as mapi and each_row_col.
  • Improved hybrid matrix multiplication and vector linear-combination performance.

• Other Fixes & Renames:
  • map_row() / map_col() -> map_row_inplace() / map_col_inplace()
  • eachij() -> each_row_col()
  • Corrected determinant behavior for 0x0 matrices.
  • Fixed copy-on-conversion behavior between vectors and matrices.

#Development

moon fmt
moon check
moon test --enable-coverage
./run_test.sh

#Release Checklist

1. Bump moon.mod to the intended next release version before publishing.
2. Update README.md so the release notes and version history match the package contents.
3. Run moon check and ./run_test.sh; both are required before publishing.
4. Trigger publish-package; it will publish the version currently declared in moon.mod.