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Future Updates Roadmap

This document outlines planned features, improvements, and long-term goals for LinAlgKit.

🎯 Version 0.2.0 (Planned)

Target: Q1 2025

New Features

Matrix Inverse

  • inverse() — Compute matrix inverse using LU decomposition
  • solve(b) — Solve linear system Ax = b
  • Pseudo-inverse for non-square matrices

Matrix Decompositions

  • lu() — LU decomposition with partial pivoting
  • qr() — QR decomposition using Householder reflections
  • cholesky() — Cholesky decomposition for positive-definite matrices

Eigenvalue Operations

  • eigenvalues() — Compute eigenvalues
  • eigenvectors() — Compute eigenvectors
  • eig() — Combined eigenvalue/eigenvector computation

Enhancements

Broadcasting Support

# Planned: element-wise operations with broadcasting
A = lk.Matrix(3, 3, 1.0)
B = A + 5  # Add scalar to all elements

Slicing Support

# Planned: NumPy-style slicing
A = lk.Matrix.identity(5)
sub = A[1:4, 1:4]  # Extract 3x3 submatrix

In-place Operations

# Planned: memory-efficient in-place operations
A += B  # In-place addition
A *= 2  # In-place scalar multiplication

🎯 Version 0.3.0 (Planned)

Target: Q2 2025

Sparse Matrix Support

New Classes

  • SparseMatrix — CSR (Compressed Sparse Row) format
  • SparseCOO — Coordinate format for construction
  • SparseDiag — Diagonal sparse matrix

Features

# Planned API
S = lk.SparseMatrix.from_csr(data, indices, indptr, shape)
S = lk.SparseMatrix.from_dense(dense_matrix, threshold=1e-10)
dense = S.to_dense()

Matrix Norms

Frobenius Norm

# Planned
norm_f = A.norm('fro')  # sqrt(sum of squares)

Operator Norms

# Planned
norm_1 = A.norm(1)      # Maximum column sum
norm_inf = A.norm('inf')  # Maximum row sum
norm_2 = A.norm(2)      # Spectral norm (largest singular value)

Condition Number

# Planned
cond = A.condition_number()  # Ratio of largest to smallest singular value

🎯 Version 0.4.0 (Planned)

Target: Q3 2025

Singular Value Decomposition (SVD)

# Planned API
U, S, Vt = A.svd()
U, S, Vt = A.svd(full_matrices=False)  # Reduced SVD

Low-Rank Approximation

# Planned
A_approx = A.low_rank_approximation(rank=5)

Matrix Functions

Matrix Exponential

# Planned
exp_A = A.exp()  # e^A using Padé approximation

Matrix Logarithm

# Planned
log_A = A.log()

Matrix Power

# Planned
A_n = A.power(5)      # A^5
A_half = A.power(0.5)  # Matrix square root

🎯 Version 0.5.0 (Planned)

Target: Q4 2025

GPU Acceleration (Optional Backend)

# Planned API
import LinAlgKit as lk
lk.set_backend('cuda')  # Use GPU

A = lk.Matrix.from_numpy(large_array)
B = A * A  # Computed on GPU

Supported Operations

  • All basic arithmetic
  • Matrix multiplication
  • Decompositions (LU, QR, SVD)
  • Eigenvalue computation

Parallel CPU Operations

# Planned
lk.set_threads(8)  # Use 8 CPU threads for operations

🎯 Version 1.0.0 (Long-term Goal)

Target: 2026

Feature Complete Release

  • All planned features implemented and stable
  • Comprehensive test coverage (>95%)
  • Performance benchmarks against NumPy/SciPy
  • Complete documentation with tutorials

API Stability

  • Stable API with backwards compatibility guarantees
  • Semantic versioning strictly enforced
  • Deprecation warnings for any breaking changes

Additional Goals

  • SciPy interoperability
  • Jupyter notebook integration
  • Interactive documentation

🔧 Technical Improvements (Ongoing)

Performance

  • Optimize memory layout for cache efficiency
  • Implement SIMD operations for element-wise functions
  • Add optional Numba JIT compilation
  • Benchmark suite with automated performance regression tests

Testing

  • Property-based testing with Hypothesis
  • Numerical accuracy tests against reference implementations
  • Cross-platform CI (ARM, M1/M2 Mac)
  • Memory leak detection

Documentation

  • Interactive API examples (Jupyter notebooks)
  • Video tutorials
  • Comparison guides (vs NumPy, SciPy, TensorFlow)
  • Academic paper / citation

Developer Experience

  • Type stubs for mypy
  • VS Code extension for matrix visualization
  • Pre-commit hooks
  • Contribution guidelines expansion

💡 Community Requested Features

Have a feature request? Open an issue on GitHub: https://github.com/SciComputeOrg/LinAlgKit/issues

Under Consideration

  • Complex number support (MatrixC)
  • Quaternion matrices for 3D graphics
  • Symbolic matrix operations
  • Interval arithmetic for verified computing
  • Integration with SymPy

📊 Version Comparison

Feature 0.1.0 0.2.0 0.3.0 0.4.0 0.5.0 1.0.0
Basic ops ✅ ✅ ✅ ✅ ✅ ✅
NumPy interop ✅ ✅ ✅ ✅ ✅ ✅
Inverse/Solve ❌ ✅ ✅ ✅ ✅ ✅
Decompositions ❌ ✅ ✅ ✅ ✅ ✅
Sparse matrices ❌ ❌ ✅ ✅ ✅ ✅
SVD ❌ ❌ ❌ ✅ ✅ ✅
GPU support ❌ ❌ ❌ ❌ ✅ ✅
Stable API ❌ ❌ ❌ ❌ ❌ ✅

Contributing

We welcome contributions! See CONTRIBUTING.md for guidelines.

Priority areas:

  1. Bug fixes and documentation improvements
  2. Test coverage expansion
  3. Performance optimizations
  4. Feature implementations from this roadmap

Last updated: December 2025