irrepx

Minimal O(3) irreducible representations with optional JAX support.

Install

pip install irrepx               # Light mode: representation algebra only
pip install irrepx[jax]          # Full mode: JAX (any platform, pre-installed)

One-step install with the right JAX backend:

pip install irrepx[jax-cpu]      # CPU
pip install irrepx[jax-cuda12]   # CUDA 12
pip install irrepx[jax-cuda13]   # CUDA 13
pip install irrepx[jax-tpu]      # TPU

Quick Start

from irrepx import Irrep, Irreps

# Structural algebra (no JAX needed)
irreps = Irreps("32x0e + 16x1o + 8x2e")
assert irreps.dim == 32 + 48 + 40
assert Irrep("2e") in Irrep("1o") * Irrep("1o")

With JAX installed:

import jax.numpy as jnp
from irrepx import IrrepsArray, spherical_harmonics

x = IrrepsArray("1o", jnp.array([[1.0, 0.0, 0.0]]))
sh = spherical_harmonics([0, 1, 2], x, normalize=True)
print(sh.irreps)  # 1x0e+1x1o+1x2e

Wigner D from direction

Compute Wigner D matrices from edge direction vectors (Gram-Schmidt → Euler angles → JD-seed formula). Available in both numpy (light) and JAX (full) modes.

import numpy as np
from irrepx import wigner_D_from_direction

edge = np.array([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]])  # (E, 3) unit vectors
D = wigner_D_from_direction(edge, l_range=[0, 1, 2])
# D[l] is (E, 2l+1, 2l+1)

With JAX, the same call is JIT-compatible and operates on jnp.ndarray.

Pre-computed constants

irrepx ships pre-computed Clebsch-Gordan coefficients, JD seed matrices, and spherical Bessel roots as npz files. These are loaded lazily on first access. The loaders take no arguments and return the full shipped table; callers slice or filter the subset they need.

from irrepx import load_cg, load_jd, load_sb_roots

cg = load_cg()         # dict keyed by "l1=N,l2=M", shipped lmax=7 (+SOC rows)
jd = load_jd()         # list of (2l+1, 2l+1) matrices, shipped lmax=13
sb = load_sb_roots()   # list of 1-D root arrays, shipped lmax=13

Inspect the shipped capacity with irrepx constants status. If your work needs larger tables than shipped, rebuild them with the CLI:

irrepx constants status
irrepx constants update --cg-lmax 10 --jd-lmax 15 --sb-lmax 20

For per-triplet CG access (used internally by spherical_harmonics and tensor_product), use the computational function:

from irrepx import clebsch_gordan

cg = clebsch_gordan(1, 1, 2)   # returns dense (3, 3, 5) array

License

GPL-3.0-or-later

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