https://github.com/murrellgroup/kabsch.jl
Kabsch algorithm for optimally aligning two paired sets of points
https://github.com/murrellgroup/kabsch.jl
gpu-accelerated julia kabsch rmsd static-arrays
Last synced: 4 months ago
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Kabsch algorithm for optimally aligning two paired sets of points
- Host: GitHub
- URL: https://github.com/murrellgroup/kabsch.jl
- Owner: MurrellGroup
- License: mit
- Created: 2025-06-07T21:22:58.000Z (5 months ago)
- Default Branch: main
- Last Pushed: 2025-06-14T22:14:31.000Z (5 months ago)
- Last Synced: 2025-06-16T19:19:41.336Z (5 months ago)
- Topics: gpu-accelerated, julia, kabsch, rmsd, static-arrays
- Language: Julia
- Homepage:
- Size: 235 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Kabsch.jl
[](https://MurrellGroup.github.io/Kabsch.jl/stable/)
[](https://MurrellGroup.github.io/Kabsch.jl/dev/)
[](https://github.com/MurrellGroup/Kabsch.jl/actions/workflows/CI.yml?query=branch%3Amain)
[](https://codecov.io/gh/MurrellGroup/Kabsch.jl)
A Julia implementation of the Kabsch algorithm for finding the optimal rotation between paired sets of points.
## Usage
```julia
using Kabsch, Manifolds
# Generate realistic test data
P = randn(3, 10)
R_true = rand(Rotations(3)) # Random rotation matrix
Q = R_true * centered(P) .+ randn(3) # Rotate and translate P
# Find optimal alignment
R, P_centroid, Q_centroid = kabsch(P, Q)
Q_aligned = superimposed(Q, P)
# Verify perfect alignment
@assert P ≈ Q_aligned
@assert rmsd(superimposed, Q, P) ≈ 0
```
### Batched Operations
Process multiple alignments simultaneously:
```julia
Ps = randn(3, 50, 8) # 8 reference point sets
Qs = randn(3, 50, 8) # 8 point sets to align, uncorrelated for ease of showcase
Rs, P_centroids, Q_centroids = kabsch(Ps, Qs)
Q_aligned_all = superimposed(Qs, Ps)
```
### Extensions
**StaticArrays:** Optimal performance for small point sets
```julia
using StaticArrays
P = @SMatrix randn(3, 5)
Q = @SMatrix randn(3, 5) # uncorrelated for ease of showcase
R, Pt, Qt = kabsch(P, Q)
```
**CUDA:** GPU acceleration for 3D case
```julia
using CUDA
P_gpu = CUDA.randn(3, 100, 1000) # 100 batches on GPU
Q_gpu = CUDA.randn(3, 100, 1000) # uncorrelated for ease of showcase
R_gpu, _, _ = kabsch(P_gpu, Q_gpu)
```
## See also
- [BioStructures.jl](https://github.com/BioJulia/BioStructures.jl) for `rmsd` and `superimpose!` on molecular structures (including residue alignment)