approx-chol
Approximate Cholesky factorization for SDDM and graph Laplacian systems.
This package implements AC and AC(k), porting key algorithmic ideas from Laplacians.jl to make these algorithms accessible in Python.
AC(k) was introduced and analyzed by Gao, Kyng, and Spielman (2025), "AC(k): Robust Solution of Laplacian Equations by Randomized Approximate Cholesky Factorization" (SIAM Journal on Scientific Computing, November 2025, ISSN 1064-8275).
Install
pip install approx-chol
Usage
import numpy as np
from scipy.sparse import csr_array
from approx_chol import factorize
# 4-node path graph Laplacian (0-1-2-3)
row_ptrs = np.array([0, 2, 5, 8, 10], dtype=np.uint32)
col_indices = np.array([0, 1, 0, 1, 2, 1, 2, 3, 2, 3], dtype=np.uint32)
values = np.array([1.0, -1.0, -1.0, 2.0, -1.0, -1.0, 2.0, -1.0, -1.0, 1.0])
laplacian = csr_array((values, col_indices, row_ptrs), shape=(4, 4))
factor = factorize(laplacian)
# RHS must lie in the range of the Laplacian (sum to zero)
b = np.array([1.0, -1.0, 1.0, -1.0])
x = factor.solve(b)
Configuration
from approx_chol import Config, factorize
config = Config(seed=42, split=3)
factor = factorize(laplacian, config=config)
Low-level API
For direct control over CSR arrays without constructing a scipy sparse matrix:
from approx_chol import factorize_raw
factor = factorize_raw(row_ptrs, col_indices, values, n=4)
x = factor.solve(b)
API
factorize(matrix, config=None)— Factorize ascipy.sparse.csr_arrayorcsr_matrix.factorize_raw(row_ptrs, col_indices, values, n, config=None)— Factorize from raw CSR arrays.Factor.solve(b)— Solve LDL^T x = b, returning a new array.Factor.solve_into(b, out)— Solve in-place into a pre-allocated array.Config(seed=0, split=None, backend=None)— Configuration for the factorization.Backend.Approximate()/Backend.ExactBelow(max_dim, on_failure)— Which factorization each block gets; defaults toExactBelow(24, ExactFailure.FallBackToApproximate).Factor.fallbacks— Blocks routed to exact Cholesky and factored approximately anyway; also raises aRuntimeWarning.
Attribution
This package ports key algorithmic ideas from Laplacians.jl to make AC and AC(k) accessible in Python.
Laplacians.jl is licensed under the MIT License.
License
MIT — see LICENSE.
References
- Gao, Yuan; Kyng, Rasmus; Spielman, Daniel (2025). AC(k): Robust Solution of Laplacian Equations by Randomized Approximate Cholesky Factorization. SIAM Journal on Scientific Computing.
- Gao, Kyng & Spielman (2023). Robust and Practical Solution of Laplacian Equations by Approximate Elimination. https://arxiv.org/abs/2303.00709
- Kyng & Sachdeva (2016). Approximate Gaussian Elimination for Laplacians — Fast, Sparse, and Simple. https://arxiv.org/abs/1605.02353
1 maintainer
Metadata
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Transparency logRelease files / approx_chol-0.6.0-cp39-abi3-macosx_10_12_x86_64.whl
| Download URL | approx_chol-0.6.0-cp39-abi3-macosx_10_12_x86_64.whl |
|---|---|
| Size | 321.5 kB |
| Tags | CPython 3.9 abi3 macOS 10.12+ x86-64 |
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SHA-256 checksum How to use checksums |
9fdeef7072359337e653e061244ceafb9d8b228b04b01215723e6598964db8b6
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BLAKE2b-256 checksum How to use checksums |
64890e339b8fc15c6a8762b33f6d84103f486e30e57bdcfd3b62263e2c0dae7a
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| Upload date | |
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Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
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twine/7.0.0 CPython/3.13.14
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Provenance
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Transparency log
