This release is a pre-release and may not be stable for production use.
🆕 What's new
- 2026/09/07: v0.10.0rc1 added Python 3.15 support and
lapmod_batch, with improved type hints, stability, and performance. 🚀
- 2025/10/31: v0.9.0 delivered a major stability and performance upgrade acrossmostall solvers.
- 2025/10/27: v0.8.0 addedlapjvx_batch,lapjvxa_batch,lapjvs_batch,lapjvsa_batchandlapjvsa.
- 2025/10/21: v0.7.0 addedlapjvs.
- 2025/10/16: v0.6.0 addedlapjvx,lapjvxa, andlapjvc.
- Looking for more? See GitHub releases.
lapx was initially created to maintain Tomas Kazmar's lap — a Jonker-Volgenant solver package, but has since evolved to offer much more; for details on all available solver functions, refer to the usage section.
Click to read more ...
All linear assignment problem solvers in lapx are based on Jonker-Volgenant algorithm for dense LAPJV ¹ or sparse LAPMOD ² matrices. Tomas Kazmar's lap implemented the core lapjv and lapmod from scratch based solely on the papers ¹˒² and the public domain Pascal implementation ³ provided by A. Volgenant.
¹ R. Jonker and A. Volgenant, "A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems", Computing 38, 325-340 (1987)
² A. Volgenant, "Linear and Semi-Assignment Problems: A Core Oriented Approach", Computer Ops Res. 23, 917-932 (1996)
³ http://www.assignmentproblems.com/LAPJV.htm | [archive.org]
💽 Installation
Install from PyPI:
pip install lapx
The pre-built wheels cover most platforms and architectures, see details.
🛠️ Other installation options
Install from GitHub repo (Requires C++ compiler):
pip install git+https://github.com/rathaROG/lapx.git
Build and install (Requires C++ compiler):
git clone https://github.com/rathaROG/lapx.git
cd lapx
pip install "setuptools>=67.8.0"
pip install wheel build
python -m build --wheel
cd dist
⚡ Extra performance
Since v0.9.1,
lapxenables safe (base) optimizations by default. For source builds, you can disable LAPX-added base optimizations or opt into extra flags via environment variables which might boost performance further:
LAPX_BASEOPTS=0— disables LAPX-added base optimization flags and LTO; other compiler defaults may still apply (switch available since v0.9.2)LAPX_FASTMATH=1— enables fast-math (may change numerical results and handling of NaN/infinity)LAPX_NATIVE=1— GCC/Clang only; tune for the CPU of the build machine (not suitable for sharing)LAPX_LTO=0— disables link-time optimization, including inherited LTO defaultsLTO is enabled by default when compilation and linking support it.
LAPX_BASEOPTS=0does not guarantee an unoptimized or debug build. Fast-math and native tuning are independent opt-ins, disabled by default; keep both disabled for portable release wheels.
See the setup.py for more details.
🧪 Usage
lapx was initially created as a drop‑in replacement to preserve the distribution of the original lap. While the package you install is lapx, the import name remains lap to avoid breaking existing code; use import lap to import lapx.
Show additional notes
Notes:
- Do not install both
lapandlapxat the same time; since both provide the same import name (lap), the one installed last will override the other.- If you only need
lapjvandlapmod, the originallapis sufficient; chooselapxif you want additional fixes, extended features (batch processing, flexible outputs, extra solvers), and—most importantly—improved stability and performance.
ℹ️ Cost values
lapjv, lapjvx, lapjvxa, lapjvs, lapjvsa, and their batch variants leave cost-value validation to the caller to keep repeated assignment calls lightweight. Prepare costs without NaN or negative infinity before calling these solvers; results with those values are undefined. Positive infinity (np.inf) can represent a forbidden assignment.
lapjvc treats NaN and either infinity as forbidden assignments. lapmod validates its sparse arrays and requires the stored costs to be finite, non-negative, and less than lap.LARGE.
Where available, cost_limit accepts a finite number or positive infinity. Returned total costs are accumulated in float64 from the original costs, including when the solver works in float32.
🅰️ Single-matrix Solvers 📄
1. The original function lapjv
lapjv supports both square and rectangular cost matrices. It returns the optimal assignments as mapping arrays x (size N) and y (size M) and optionally total cost if return_cost=True. See more details here.
import numpy as np, lap
# x, y = lap.lapjv(np.random.rand(100, 150), extend_cost=True, return_cost=False)
total_cost, x, y = lap.lapjv(np.random.rand(100, 150), extend_cost=True, return_cost=True)
valid = x >= 0
assignments = np.column_stack((np.arange(len(x))[valid], x[valid]))
# assignments = np.array([[y[i],i] for i in x if i >= 0]) # slower
Still need more explanation?
lapjv(C) returns two arrays x and y (also the total assignment cost if return_cost=True). If cost matrix C has shape NxM, then x is a size-N array specifying to which column each row is assigned, and y is a size-M array specifying to which row each column is assigned. For example, an output of x = [1, 0] indicates that row 0 is assigned to column 1 and row 1 is assigned to column 0. Similarly, an output of x = [2, 1, 0] indicates that row 0 is assigned to column 2, row 1 is assigned to column 1, and row 2 is assigned to column 0.
Notes:
- This function does not return two aligned index arrays as SciPy's
linear_sum_assignmentdoes; the final assignments can be done as shown in the example above; uselapjvxfor SciPy-style output.- See the original documentation of
lapjvat gatagat/lap.
2. The new function lapjvx
lapjvx basically is lapjv, but it matches the output style of SciPy's linear_sum_assignment with no additional overhead. See more details of lapjvx here.
import numpy as np, lap
# row_indices, col_indices = lap.lapjvx(np.random.rand(100, 150), extend_cost=True, return_cost=False)
total_cost, row_indices, col_indices = lap.lapjvx(np.random.rand(100, 150), extend_cost=True, return_cost=True)
assignments = np.column_stack((row_indices, col_indices))
# assignments = np.array(list(zip(row_indices, col_indices))) # slower
See how lapjvx compares to others in Object Tracking benchmark here.
Show lapjvxa
3. The new function lapjvxa
lapjvxa is essentially the same as lapjvx, but it returns assignments with shape (K, 2) directly — no additional/manual post-processing required. lapjvxa is optimized for applications that only need the final assignments and do not require control over the cost_limit parameter. See more details here.
import numpy as np, lap
# assignments = lap.lapjvxa(np.random.rand(100, 150), extend_cost=True, return_cost=False)
total_cost, assignments = lap.lapjvxa(np.random.rand(100, 150), extend_cost=True, return_cost=True)
Show lapjvc
4. The new function lapjvc
lapjvc is an enhanced version of Christoph Heindl's py-lapsolver. lapjvc is as fast as (if not faster than) other functions when the cost matrix is square, but it is much slower when the cost matrix is rectangular. This function adopts the output style of lapjvx — the same as SciPy's linear_sum_assignment. See more details here.
import numpy as np, lap
# row_indices, col_indices = lap.lapjvc(np.random.rand(100, 150), return_cost=False)
total_cost, row_indices, col_indices = lap.lapjvc(np.random.rand(100, 150), return_cost=True)
assignments = np.column_stack((row_indices, col_indices))
# assignments = np.array(list(zip(row_indices, col_indices))) # slower
Show lapjvs
5. The new function lapjvs
lapjvs is an enhanced version of Vadim Markovtsev's lapjv. While lapjvs does not use CPU special instruction sets like the original implementation, it still delivers comparable performance. It natively supports both square and rectangular cost matrices and can produce output either in SciPy's linear_sum_assignment style or mapping arrays x and y like lapjv. See more details here.
import numpy as np, lap
# row_indices, col_indices = lap.lapjvs(np.random.rand(100, 150), return_cost=False, jvx_like=True)
total_cost, row_indices, col_indices = lap.lapjvs(np.random.rand(100, 150), return_cost=True, jvx_like=True)
assignments = np.column_stack((row_indices, col_indices))
# assignments = np.array(list(zip(row_indices, col_indices))) # slower
Show lapjvsa
6. The new function lapjvsa
lapjvsa is essentially the same as lapjvs, but it returns assignments with shape (K, 2) directly — no additional/manual post-processing required. See more details here.
import numpy as np, lap
# assignments = lap.lapjvsa(np.random.rand(100, 150), return_cost=False)
total_cost, assignments = lap.lapjvsa(np.random.rand(100, 150), return_cost=True)
Show lapmod
7. The original function lapmod
See more details here.
import numpy as np, lap, time
n, m = 1000, 1000
cm = np.random.rand(n, m)
t0 = time.time()
c1, x1, y1 = lap.lapjv(cm, return_cost=True)
print(f"lapjv: cost={c1:.6f}, time={time.time()-t0:.4f}s")
cc, kk, ii = cm.ravel(), np.tile(np.arange(m), n), np.arange(0, n*m+1, m)
t1 = time.time()
c2, x2, y2 = lap.lapmod(n, cc, ii, kk, return_cost=True)
print(f"lapmod: cost={c2:.6f}, time={time.time()-t1:.4f}s")
print("Assignments identical?", (np.all(x1 == x2) and np.all(y1 == y2)))
🅱️ Batch Solvers 🗂️
1. The new function lapjvx_batch
lapjvx_batch is the batch version of lapjvx, accepting costs with shape (B, N, M). See more details here.
import numpy as np, lap, os
batch_costs = np.random.rand(500, 100, 150) # (B, N, M) # B is batch size
costs, rows, cols = lap.lapjvx_batch(batch_costs, extend_cost=True, return_cost=True, n_threads=os.cpu_count())
print(f"total costs = {costs.sum()}")
# access the assignments @ batch b = 7
assignments_7 = np.column_stack((rows[7], cols[7])) # (K_b, 2)
print(f"assignments_7.shape = {assignments_7.shape}")
Show lapjvxa_batch
2. The new function lapjvxa_batch
lapjvxa_batch is the batch version of lapjvxa, accepting costs with shape (B, N, M). See more details here.
import numpy as np, lap, os
batch_costs = np.random.rand(500, 100, 150) # (B, N, M) # B is batch size
costs, assignments = lap.lapjvxa_batch(batch_costs, extend_cost=True, return_cost=True, n_threads=os.cpu_count())
print(f"total costs = {costs.sum()}")
print(f"assignments[7].shape = {assignments[7].shape}") # assignments @ batch b = 7
Show lapjvs_batch
3. The new function lapjvs_batch
lapjvs_batch is the batch version of lapjvs, accepting costs with shape (B, N, M). See more details here.
import numpy as np, lap, os
batch_costs = np.random.rand(500, 100, 150) # (B, N, M) # B is batch size
costs, rows, cols = lap.lapjvs_batch(batch_costs, extend_cost=True, return_cost=True, n_threads=os.cpu_count())
print(f"total costs = {costs.sum()}")
# access the assignments @ batch b = 7
assignments_7 = np.column_stack((rows[7], cols[7])) # (K_b, 2)
print(f"assignments_7.shape = {assignments_7.shape}")
Show lapjvsa_batch
4. The new function lapjvsa_batch
lapjvsa_batch is the batch version of lapjvsa, accepting costs with shape (B, N, M). See more details here.
import numpy as np, lap, os
batch_costs = np.random.rand(500, 100, 150) # (B, N, M) # B is batch size
costs, assignments = lap.lapjvsa_batch(batch_costs, extend_cost=True, return_cost=True, n_threads=os.cpu_count())
print(f"total costs = {costs.sum()}")
print(f"assignments[7].shape = {assignments[7].shape}") # assignments @ batch b = 7
Show lapmod_batch
5. The new function lapmod_batch
lapmod_batch solves a sequence of sparse (n, cc, ii, kk) problems using the
same inputs and validation as lapmod. Each problem must be square, but sizes
and numbers of stored entries can differ. Results retain input order:
x_list[b] maps rows to columns and y_list[b] maps columns to rows for problem
b, with the same int32 arrays as the single solver.
import numpy as np
import lap
problems = [
(2, np.array([1., 4., 3., 2.]),
np.array([0, 2, 4]), np.array([0, 1, 0, 1])),
(3, np.array([4., 1., 3.]),
np.array([0, 1, 2, 3]), np.array([2, 0, 1])),
]
totals, x_list, y_list = lap.lapmod_batch(problems, n_threads=2)
print(totals) # [3. 8.]
print(x_list[1]) # [2 0 1]
# Skip total-cost calculation when only the assignments are needed.
x_list, y_list = lap.lapmod_batch(problems, return_cost=False, n_threads=2)
n_threads=0 or None uses the CPU count, capped to the batch size; n_threads=1
runs sequentially. Empty and single-item batches do not create a thread pool.
The default fast=True releases the GIL in the native solver so independent
problems can run concurrently. Python-side validation and total-cost calculation
can limit speedup; the fast=False Python fallback is largely GIL-bound.
fp_version selects the native path-search version, as in lapmod.
Keep input arrays unchanged while solving. Errors from an individual problem
propagate to the caller after the pool shuts down.
See the wrapper documentation for the full signature and return types.
🏆 Benchmark and Test
To run a quick benchmark or see some interesting results, please check here.
To run a full test suite, please check here.
📝 License
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