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laprust

laprust solves dense linear assignment problems with a native Rust implementation and a NumPy API. Python 3.9 or newer is required. It exposes two solvers: lapjv and lapjv_batch.

laprust 1.0.0 derives from the lapjvr solver in LAPX 0.11.1. Future solver development is led by lapcpp for C++ and laprust for Rust; LAPX will incorporate their fixes and improvements.

It solves rectangular problems directly and handles unmatched rows and columns implicitly when a finite cost_limit is supplied, without allocating an expanded square cost matrix. The square path uses Jonker–Volgenant initialization, reduction, and shortest augmenting paths. This package is independent of LAPX and imports as laprust.

Installation

Once available on PyPI:

python -m pip install laprust

A source build requires a C++17 compiler and, for laprust, Rust/Cargo 1.83+ with a compatible target. Build dependencies (NumPy, Cython, setuptools) are installed automatically by pip. NumPy is the only Python runtime dependency. An installed wheel needs no compiler or Rust toolchain.

Quick start

import numpy as np
import laprust

cost = np.array([[3., 1.], [1., 4.]])
total, rows, cols = laprust.lapjv(cost)
# total = 2.0; rows = [0, 1]; cols = [1, 0]

costs = np.stack([cost, cost])  # (batch, rows, columns)
totals, rows, cols = laprust.lapjv_batch(costs, n_threads=2)
# totals = [2., 2.]; rows and cols are lists of arrays, one per problem

rectangular = np.array([[.1, .8, .9], [.9, .7, .8]], dtype=np.float32)
total, rows, cols = laprust.lapjv(rectangular, cost_limit=.5)
# Only (0, 0) is selected; total is about .1, excluding rejection penalties.

API

lapjv(cost, extend_cost=False, cost_limit=np.inf, return_cost=True,
      *, precision="native", output="indices")
lapjv_batch(costs, extend_cost=False, cost_limit=np.inf, return_cost=True,
            n_threads=0, *, precision="native", output="indices")
Option Behavior
cost / costs Real numeric arrays with shape (N, M) / (B, N, M).
extend_cost=True Allows rectangular inputs when the limit is infinite; no square padding is used.
cost_limit A finite value permits unmatched endpoints, each charged cost_limit / 2 rounded to the selected cost dtype. Finite limits also permit rectangles and apply to square inputs.
return_cost Defaults to True; totals sum selected original costs in float64 and exclude rejection penalties. False omits totals and skips the sum.
precision "native" preserves float32/float64; other real numeric inputs use float64. Explicit "float32" / "float64" select working costs.
output "indices" returns aligned row/column arrays; "pairs" returns (K, 2) arrays.
n_threads Batch only. 0 / None selects automatically; negative values use one worker; positive values are capped by batch size.

Rows are sorted and all returned indices are int64. They identify the selected pairs; unmatched items are absent. Batch results contain lists because each problem may select a different number of pairs. Equal-cost optima may return different assignments across solvers or precisions.

All solver paths retain the selected float32 or float64 cost storage and use float64 potentials, distances, and reduced-cost arithmetic. Finite-limit half-penalties are still rounded in the selected cost dtype. This improves robustness when small assignment differences coexist with large finite costs; extreme dynamic ranges and input conversion can still hide differences.

With a finite limit L, define h = cost_dtype(L/2), where cost_dtype is the cost storage dtype selected by precision. The optimized objective is sum(selected represented costs) + (N + M - 2*K) * h, where N and M are the input dimensions and K is the number of selected pairs. Represented costs are the input values after conversion to that cost dtype.

The reported total separately sums the selected original-input values in float64 and excludes rejection penalties. It can differ from the represented-cost sum when conversion rounds input values. Joint rejection is different from solving a full assignment and then filtering high-cost pairs. See API details for numerical and memory behavior.

Development and checks

python -m pip install -e ".[dev]"
cd tests
python -m pytest -q -m "not cross_package"
cd ..
python -m pytest -q .github/tests -m "not editable"
python -m build

The test suite covers SciPy and exhaustive-reference comparisons, rectangular and finite-limit cases, float32/float64, precision conversion, forbidden edges, empty inputs, invalid arguments, repeated workspaces, batch thread counts, concurrent calls, package independence, and type annotations. Historical LAPX regressions, cross-package concurrency, and isolated editable installs are also covered. See the solver test inventory, build and packaging checks, and CONTRIBUTING.md for commands and coverage.

Benchmarks

All three benchmark scripts compare SciPy (baseline), lapcpp, laprust, LAPX lapjvxa and LAPX lapjvsa. The LAPX candidates represent the JVX and JVS families using pair outputs, including their batch APIs. Once lapcpp and laprust are available on PyPI, install the dependencies below. Clone or download this repository for the scripts and run them from the repository root.

python -m pip install --upgrade lapcpp laprust "lapx==0.11.1" scipy
python benchmarks/benchmark_single.py --quick --repeats 3
python benchmarks/benchmark_batch.py --quick --threads 4 --repeats 3
python benchmarks/benchmark_tracking.py --quick --repeats 3

Use --json benchmark-results/run.json to save measurements and environment details. Each solver is warmed right before its own sample, and calls repeat until a sample lasts at least 10 ms; --reference-timing restores the pinned LAPX timing. See benchmark methodology for full workloads, reference LAPX settings, dedicated solver functions, tracking post-filtering, and timing boundaries. Tracking never passes its threshold as solver cost_limit.

Paper

The solver, its implicit rejection, and its performance against SciPy and other Jonker–Volgenant implementations are described in Native Rectangular Linear Assignment with Implicit Rejection: A Jonker–Volgenant Solver without Square Expansion, where laprust is labeled JVRUST. Read the PDF; its scripts, raw results, and reproduction steps are in the lap-paper repository.

Automation and license

GitHub workflows test supported Python versions on Windows, Linux and macOS, build and test source archives and wheels, and run the three benchmark modes. Wheel builds are also available manually. A version tag triggers the release workflow; PyPI publishing uses the repository's pypi environment and requires its Trusted Publisher configuration. No releases are published by local builds.

MIT licensed. See LICENSE, NOTICE, and native-source license for attribution.

Metadata

Release files for laprust 1.2.0

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

Source distribution for laprust 1.2.0
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Built distributions (wheels)

Table of built distributions (wheels) for laprust 1.2.0
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laprust-1.2.0-cp315-cp315-win_arm64.whl CPython 3.15 CPython 3.15 Windows ARM64 Details for laprust-1.2.0-cp315-cp315-win_arm64.whl
laprust-1.2.0-cp315-cp315-win_amd64.whl CPython 3.15 CPython 3.15 Windows x86-64 Details for laprust-1.2.0-cp315-cp315-win_amd64.whl
laprust-1.2.0-cp315-cp315-musllinux_1_2_x86_64.whl CPython 3.15 CPython 3.15 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp315-cp315-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp315-cp315-musllinux_1_2_aarch64.whl CPython 3.15 CPython 3.15 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp315-cp315-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp315-cp315-manylinux_2_31_armv7l.whl CPython 3.15 CPython 3.15 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp315-cp315-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp315-cp315-manylinux_2_28_x86_64.whl CPython 3.15 CPython 3.15 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp315-cp315-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp315-cp315-manylinux_2_28_aarch64.whl CPython 3.15 CPython 3.15 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp315-cp315-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp315-cp315-macosx_11_0_arm64.whl CPython 3.15 CPython 3.15 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp315-cp315-macosx_11_0_arm64.whl
laprust-1.2.0-cp315-cp315-macosx_10_15_x86_64.whl CPython 3.15 CPython 3.15 macOS 10.15+ x86-64 Details for laprust-1.2.0-cp315-cp315-macosx_10_15_x86_64.whl
laprust-1.2.0-cp314-cp314-win_arm64.whl CPython 3.14 CPython 3.14 Windows ARM64 Details for laprust-1.2.0-cp314-cp314-win_arm64.whl
laprust-1.2.0-cp314-cp314-win_amd64.whl CPython 3.14 CPython 3.14 Windows x86-64 Details for laprust-1.2.0-cp314-cp314-win_amd64.whl
laprust-1.2.0-cp314-cp314-musllinux_1_2_x86_64.whl CPython 3.14 CPython 3.14 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp314-cp314-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp314-cp314-musllinux_1_2_aarch64.whl CPython 3.14 CPython 3.14 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp314-cp314-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp314-cp314-manylinux_2_31_armv7l.whl CPython 3.14 CPython 3.14 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp314-cp314-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp314-cp314-manylinux_2_28_x86_64.whl CPython 3.14 CPython 3.14 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp314-cp314-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp314-cp314-manylinux_2_28_aarch64.whl CPython 3.14 CPython 3.14 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp314-cp314-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp314-cp314-macosx_11_0_arm64.whl CPython 3.14 CPython 3.14 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp314-cp314-macosx_11_0_arm64.whl
laprust-1.2.0-cp314-cp314-macosx_10_15_x86_64.whl CPython 3.14 CPython 3.14 macOS 10.15+ x86-64 Details for laprust-1.2.0-cp314-cp314-macosx_10_15_x86_64.whl
laprust-1.2.0-cp313-cp313-win_arm64.whl CPython 3.13 CPython 3.13 Windows ARM64 Details for laprust-1.2.0-cp313-cp313-win_arm64.whl
laprust-1.2.0-cp313-cp313-win_amd64.whl CPython 3.13 CPython 3.13 Windows x86-64 Details for laprust-1.2.0-cp313-cp313-win_amd64.whl
laprust-1.2.0-cp313-cp313-musllinux_1_2_x86_64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp313-cp313-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp313-cp313-musllinux_1_2_aarch64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp313-cp313-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp313-cp313-manylinux_2_31_armv7l.whl CPython 3.13 CPython 3.13 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp313-cp313-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp313-cp313-manylinux_2_28_x86_64.whl CPython 3.13 CPython 3.13 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp313-cp313-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp313-cp313-manylinux_2_28_aarch64.whl CPython 3.13 CPython 3.13 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp313-cp313-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp313-cp313-macosx_11_0_arm64.whl CPython 3.13 CPython 3.13 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp313-cp313-macosx_11_0_arm64.whl
laprust-1.2.0-cp313-cp313-macosx_10_13_x86_64.whl CPython 3.13 CPython 3.13 macOS 10.13+ x86-64 Details for laprust-1.2.0-cp313-cp313-macosx_10_13_x86_64.whl
laprust-1.2.0-cp312-cp312-win_arm64.whl CPython 3.12 CPython 3.12 Windows ARM64 Details for laprust-1.2.0-cp312-cp312-win_arm64.whl
laprust-1.2.0-cp312-cp312-win_amd64.whl CPython 3.12 CPython 3.12 Windows x86-64 Details for laprust-1.2.0-cp312-cp312-win_amd64.whl
laprust-1.2.0-cp312-cp312-musllinux_1_2_x86_64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp312-cp312-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp312-cp312-musllinux_1_2_aarch64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp312-cp312-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp312-cp312-manylinux_2_31_armv7l.whl CPython 3.12 CPython 3.12 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp312-cp312-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp312-cp312-manylinux_2_28_x86_64.whl CPython 3.12 CPython 3.12 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp312-cp312-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp312-cp312-manylinux_2_28_aarch64.whl CPython 3.12 CPython 3.12 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp312-cp312-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp312-cp312-macosx_11_0_arm64.whl CPython 3.12 CPython 3.12 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp312-cp312-macosx_11_0_arm64.whl
laprust-1.2.0-cp312-cp312-macosx_10_13_x86_64.whl CPython 3.12 CPython 3.12 macOS 10.13+ x86-64 Details for laprust-1.2.0-cp312-cp312-macosx_10_13_x86_64.whl
laprust-1.2.0-cp311-cp311-win_arm64.whl CPython 3.11 CPython 3.11 Windows ARM64 Details for laprust-1.2.0-cp311-cp311-win_arm64.whl
laprust-1.2.0-cp311-cp311-win_amd64.whl CPython 3.11 CPython 3.11 Windows x86-64 Details for laprust-1.2.0-cp311-cp311-win_amd64.whl
laprust-1.2.0-cp311-cp311-musllinux_1_2_x86_64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp311-cp311-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp311-cp311-musllinux_1_2_aarch64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp311-cp311-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp311-cp311-manylinux_2_31_armv7l.whl CPython 3.11 CPython 3.11 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp311-cp311-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp311-cp311-manylinux_2_28_x86_64.whl CPython 3.11 CPython 3.11 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp311-cp311-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp311-cp311-manylinux_2_28_aarch64.whl CPython 3.11 CPython 3.11 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp311-cp311-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp311-cp311-macosx_11_0_arm64.whl CPython 3.11 CPython 3.11 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp311-cp311-macosx_11_0_arm64.whl
laprust-1.2.0-cp311-cp311-macosx_10_12_x86_64.whl CPython 3.11 CPython 3.11 macOS 10.12+ x86-64 Details for laprust-1.2.0-cp311-cp311-macosx_10_12_x86_64.whl
laprust-1.2.0-cp310-cp310-win_arm64.whl CPython 3.10 CPython 3.10 Windows ARM64 Details for laprust-1.2.0-cp310-cp310-win_arm64.whl
laprust-1.2.0-cp310-cp310-win_amd64.whl CPython 3.10 CPython 3.10 Windows x86-64 Details for laprust-1.2.0-cp310-cp310-win_amd64.whl
laprust-1.2.0-cp310-cp310-musllinux_1_2_x86_64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp310-cp310-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp310-cp310-musllinux_1_2_aarch64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp310-cp310-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp310-cp310-manylinux_2_31_armv7l.whl CPython 3.10 CPython 3.10 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp310-cp310-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp310-cp310-manylinux_2_28_x86_64.whl CPython 3.10 CPython 3.10 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp310-cp310-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp310-cp310-manylinux_2_28_aarch64.whl CPython 3.10 CPython 3.10 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp310-cp310-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp310-cp310-macosx_11_0_arm64.whl CPython 3.10 CPython 3.10 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp310-cp310-macosx_11_0_arm64.whl
laprust-1.2.0-cp310-cp310-macosx_10_12_x86_64.whl CPython 3.10 CPython 3.10 macOS 10.12+ x86-64 Details for laprust-1.2.0-cp310-cp310-macosx_10_12_x86_64.whl
laprust-1.2.0-cp39-cp39-win_arm64.whl CPython 3.9 CPython 3.9 Windows ARM64 Details for laprust-1.2.0-cp39-cp39-win_arm64.whl
laprust-1.2.0-cp39-cp39-win_amd64.whl CPython 3.9 CPython 3.9 Windows x86-64 Details for laprust-1.2.0-cp39-cp39-win_amd64.whl
laprust-1.2.0-cp39-cp39-musllinux_1_2_x86_64.whl CPython 3.9 CPython 3.9 Linux musl 1.2+ x86-64 Details for laprust-1.2.0-cp39-cp39-musllinux_1_2_x86_64.whl
laprust-1.2.0-cp39-cp39-musllinux_1_2_aarch64.whl CPython 3.9 CPython 3.9 Linux musl 1.2+ ARM64 Details for laprust-1.2.0-cp39-cp39-musllinux_1_2_aarch64.whl
laprust-1.2.0-cp39-cp39-manylinux_2_31_armv7l.whl CPython 3.9 CPython 3.9 Linux glibc 2.31+ ARMv7l Details for laprust-1.2.0-cp39-cp39-manylinux_2_31_armv7l.whl
laprust-1.2.0-cp39-cp39-manylinux_2_28_x86_64.whl CPython 3.9 CPython 3.9 Linux glibc 2.28+ x86-64 Details for laprust-1.2.0-cp39-cp39-manylinux_2_28_x86_64.whl
laprust-1.2.0-cp39-cp39-manylinux_2_28_aarch64.whl CPython 3.9 CPython 3.9 Linux glibc 2.28+ ARM64 Details for laprust-1.2.0-cp39-cp39-manylinux_2_28_aarch64.whl
laprust-1.2.0-cp39-cp39-macosx_11_0_arm64.whl CPython 3.9 CPython 3.9 macOS 11.0+ ARM64 Details for laprust-1.2.0-cp39-cp39-macosx_11_0_arm64.whl
laprust-1.2.0-cp39-cp39-macosx_10_12_x86_64.whl CPython 3.9 CPython 3.9 macOS 10.12+ x86-64 Details for laprust-1.2.0-cp39-cp39-macosx_10_12_x86_64.whl

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