scirs2-sparse 0.1.3

Sparse matrix module for SciRS2 (scirs2-sparse)
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# scirs2-sparse TODO

## Release Status: 0.1.0 (Stable Release)

This Stable Release continues the production-ready sparse matrix library with comprehensive platform testing and zero-warning code quality. Following the [SciRS2 POLICY](../SCIRS2_POLICY.md), the module provides comprehensive sparse matrix functionality with feature parity to SciPy's sparse module in key areas, enhanced GPU operations (from beta.4), and ecosystem consistency.

## Implemented Features ✅

### Core Sparse Matrix Formats
- **CSR (Compressed Sparse Row)** - Efficient row-wise operations
- **CSC (Compressed Sparse Column)** - Efficient column-wise operations  
- **COO (Coordinate)** - Simple triplet format, easy construction
- **DOK (Dictionary of Keys)** - Efficient incremental construction
- **LIL (List of Lists)** - Efficient row-wise incremental construction
- **DIA (Diagonal)** - Memory-efficient diagonal matrix storage
- **BSR (Block Sparse Row)** - Block-structured sparse matrices

### Matrix Operations
- Format conversions between all sparse formats
- Basic arithmetic operations (add, subtract, multiply, divide)
- Matrix multiplication (sparse-sparse, sparse-dense, sparse-vector)
- Transpose and conjugate transpose
- Element-wise operations (Hadamard product)
- Matrix norms (Frobenius, 1-norm, 2-norm, infinity norm)

### Construction Utilities
- Identity matrices (`eye`)
- Diagonal matrices (`diags`)
- Random sparse matrices (`random`)
- Kronecker products (`kron`)
- Kronecker sums (`kronsum`)
- Block matrices (`bmat`)
- Block diagonal matrices (`block_diag`)
- Matrix stacking (`hstack`, `vstack`)
- Triangular extraction (`tril`, `triu`)

### Specialized Formats
- Symmetric sparse matrices (SymCsrMatrix, SymCooMatrix)
- Enhanced index dtype handling with automatic optimization
- Safe index casting utilities

### Linear Algebra
- **Iterative Solvers**: CG, BiCG, BiCGSTAB, CGS, GMRES, LGMRES, MINRES, QMR
- **Preconditioners**: Jacobi, SSOR, Incomplete Cholesky (IC), Incomplete LU (ILU), SPAI
- **Matrix Functions**: Matrix exponential (expm), matrix powers, expm_multiply
- **Linear Operators**: Abstract linear operator interface with composition support

### Array-based API
- Modern array-focused API similar to SciPy 1.13+
- Support for NumPy-like array semantics
- Consistent element-wise and matrix multiplication operators

### Graph Algorithms (csgraph module)
- **Shortest Path Algorithms**: Dijkstra, Bellman-Ford, Floyd-Warshall with automatic selection
- **Connected Components**: Undirected, strongly connected, and weakly connected components
- **Graph Traversal**: BFS, DFS, topological sort, and reachability analysis
- **Laplacian Matrices**: Standard, normalized, and random walk Laplacians with algebraic connectivity
- **Minimum Spanning Trees**: Kruskal and Prim algorithms with validation utilities
- **Advanced Features**: Path reconstruction, component extraction, and graph validation

### Performance Optimizations
- **SIMD Acceleration**: Comprehensive SIMD optimization for matrix operations using `scirs2-core::simd_ops`
- **Parallel Processing**: Multi-threaded implementations using `scirs2-core::parallel_ops`
- **GPU Acceleration**: Multi-backend GPU support (CUDA, OpenCL, Metal) with automatic backend selection and CPU fallback
- **Memory Efficiency**: Out-of-core processing, cache-aware operations, and memory pooling
- **Platform Detection**: Automatic capability detection and algorithm selection

## Completed Features for 1.0.0 Release ✅

### High Priority - COMPLETED

- **Advanced Linear Algebra Enhancements**
  - ✅ Cholesky decomposition with pivoting for indefinite matrices
  - ✅ Enhanced pivoting strategies for LU decomposition (Partial, Scaled Partial, Threshold, Complete, Rook)
  - ✅ 2-norm estimation and condition number computation
  - ✅ Shift-and-invert eigenvalue mode for interior eigenvalues
  - ✅ Generalized eigenvalue problems (Ax = λBx)

### Medium Priority - COMPLETED

- **Enhanced Linear Operators**
  - ✅ Operator composition (addition, subtraction, multiplication)
  - ✅ Matrix-free operator implementations
  - ✅ Custom operator support with function operators
  - ✅ Transpose, adjoint, and power operators
  - ✅ Utility functions for operator manipulation

- **Specialized Formats**
  - ✅ Additional symmetric sparse formats (SymCsrArray, SymCooArray)
  - ✅ Banded matrix formats with specialized solvers
  - ✅ Block diagonal and other specialized formats

- **Advanced Solvers**
  - ✅ Least squares solvers (LSQR, LSMR)
  - ✅ Additional Krylov methods (GCROT, TFQMR)
  - ✅ Algebraic Multigrid (AMG) preconditioners

### Production Readiness Enhancements

- **Documentation and Examples**
  - ✅ Comprehensive documentation with examples for core types
  - ✅ Production-ready API documentation
  - ✅ Comprehensive tutorial showcasing all features
  - ✅ Clear performance characteristics documentation

- **Error Handling and Diagnostics**
  - ✅ Enhanced error messages with helpful suggestions
  - ✅ Context-aware error diagnostics
  - ✅ Recovery suggestions for common issues
  - ✅ User-friendly error descriptions

## Migration Guide

For users upgrading from earlier alpha versions:

1. **Array API Migration**: Prefer `_array` variants over legacy matrix formats
2. **Import Changes**: Use `scirs2_sparse::*` instead of individual format imports
3. **Error Handling**: Update error handling to use the new `SparseResult` type
4. **Deprecated Features**: Remove usage of deprecated matrix-specific operators

## Testing and Quality Assurance

All implemented features have been thoroughly tested with:
- ✅ Unit tests for individual components
- ✅ Integration tests for complex workflows  
- ✅ Numerical accuracy tests against SciPy reference implementations
- ✅ Performance benchmarks and regression tests
- ✅ Memory leak detection and profiling
- ✅ Cross-platform compatibility testing

## Production Readiness

This stable release is production-ready for:
- ✅ Core sparse matrix operations and formats
- ✅ Basic linear algebra computations with GPU acceleration
- ✅ Iterative solver applications with advanced preconditioners
- ✅ Format conversions and data manipulation
- ✅ Integration with other scirs2 modules
- ✅ Graph algorithms (csgraph module) with BFS, DFS, shortest paths, MST
- ✅ SIMD and parallel processing optimizations

**Note**: This 0.1.0 release maintains all sparse matrix GPU enhancements from beta.4 and continues with zero-warning code quality improvements from the workspace-wide quality initiative.