The algebra module provides a comprehensive suite of tools for linear algebra, specifically designed to support both NumPy and JAX backends seamlessly. It is optimized for scientific computing tasks, including solving large sparse linear systems and eigenvalue problems.

• Automatically detects if JAX is available and prefers it for performance.
• Provides a unified interface through general_python.algebra.utils to access backend-specific functions (e.g., xp.sin, xp.linalg.norm).

A robust factory pattern (choose_solver) allows easy access to various iterative and direct solvers:

• Krylov Subspace Methods: Conjugate Gradient (CG), MINRES, MINRES-QLP.
• Direct Solvers: wrappers around scipy.linalg.solve and JAX equivalents.
• Eigenvalue Solvers: Interfaces for Arnoldi/Lanczos methods (via backend).

• ILU: Incomplete LU factorization (NumPy/SciPy only).
• LinearOperator support for custom preconditioners.

• Utilities to generate random symmetric, Hermitian, or sparse matrices for testing and simulation.

from general_python.algebra.solvers import choose_solver, SolverType
import numpy as np

# Create a random symmetric matrix
A = np.random.rand(100, 100)
A = A + A.T + 100 * np.eye(100)  # Make it diagonally dominant (positive definite)
b = np.random.rand(100)

# Use CG solver
solver = choose_solver(SolverType.CG, A=A)
result = solver.solve(b)

print(f"Converged: {result.success}")
print(f"Solution norm: {np.linalg.norm(result.x)}")