blocksolver 0.8.0

Block Quasi-Minimal-Residual sparse linear solver

BLIT Python Bindings

Python interface for the BLIT (Block Iterative) sparse linear solver library.

Installation

Prerequisites

• Python >= 3.8
• NumPy
• Fortran compiler (gfortran, ifort)
• UMFPACK/SuiteSparse library
• BLAS/LAPACK

On Ubuntu/Debian:

sudo apt install gfortran libsuitesparse-dev libblas-dev liblapack-dev

On macOS (Homebrew):

brew install gcc suite-sparse openblas

Install

cd python
pip install .

For development:

pip install -e .

Usage

Basic Usage

import numpy as np
from blocksolver import blqmr_solve

# Define sparse matrix in CSC format (0-based indexing)
Ap = np.array([0, 2, 5, 9, 10, 12], dtype=np.int32)
Ai = np.array([0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4], dtype=np.int32)
Ax = np.array([2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.])
b = np.array([8.0, 45.0, -3.0, 3.0, 19.0])

# Solve
result = blqmr_solve(Ap, Ai, Ax, b, tol=1e-8)

print(f"Solution: {result.x}")
print(f"Converged: {result.converged}")
print(f"Iterations: {result.iter}")

With SciPy Sparse Matrices

from scipy.sparse import csc_matrix
from blocksolver import blqmr_scipy

A = csc_matrix([[4, 1, 0], [1, 3, 1], [0, 1, 2]])
b = np.array([1., 2., 3.])

x, flag = blqmr_scipy(A, b, tol=1e-10)

Multiple Right-Hand Sides

from blocksolver import blqmr_solve_multi

B = np.column_stack([b1, b2, b3])  # n x nrhs
result = blqmr_solve_multi(Ap, Ai, Ax, B)
# result.x is n x nrhs

API Reference

blqmr_solve(Ap, Ai, Ax, b, **kwargs) -> BLQMRResult

Solve sparse system Ax = b.

Parameters:

• Ap: Column pointers (int32, length n+1)
• Ai: Row indices (int32, length nnz)
• Ax: Non-zero values (float64, length nnz)
• b: Right-hand side (float64, length n)
• tol: Convergence tolerance (default: 1e-6)
• maxiter: Maximum iterations (default: n)
• droptol: ILU drop tolerance (default: 0.001)
• use_precond: Use ILU preconditioner (default: True)
• zero_based: Input uses 0-based indexing (default: True)

Returns: BLQMRResult with attributes:

• x: Solution vector
• flag: 0=converged, 1=maxiter, 2=precond fail, 3=stagnation
• iter: Iterations performed
• relres: Relative residual
• converged: Boolean property

Testing

make test
# or
pytest tests/ -v

License

BSD / LGPL / GPL - see LICENSE files in parent directory.