symmray provides block-sparse arrays with abelian symmetries and fermionic signs. Its arrays follow the NumPy interface where possible and can store blocks using NumPy, PyTorch, JAX, or another autoray backend.

Key features include:

• sparse and flat storage layouts
• Z2, U1, Z2Z2, U1U1, and finite cyclic symmetries
• local fermionic phase handling for arbitrary tensor-network geometries
• contraction, fusion, reshaping, and blockwise linear algebra
• tensor-network and Hamiltonian constructors for quimb

import symmray as sr

# some U(1) indices
a, b, c, d, e = [
    sr.utils.rand_index("U1", size, dual=False, seed=seed)
    for seed, size in enumerate((4, 6, 8, 5, 7))
]

# some fermionic arrays
X = sr.utils.get_rand(
    "U1",
    shape=(a, b, c.conj()),
    fermionic=True,
    seed=6,
)
Y = sr.utils.get_rand(
    "U1",
    shape=(c, d.conj(), e.conj()),
    fermionic=True,
    seed=7,
)

# contract them
Z = sr.einsum("abc,cde->abde", X, Y)

# fuse into a matrix
matrix = Z.reshape((4 * 6, 5 * 7))

# decompose
U, s, VH = sr.linalg.svd(matrix)
print(U)
# U1FermionicArray(ndim=2, charge=0, indices=[
#     (24 = 2+4+6+6+4+2 : +[-2,-1,0,1,2,3])
#         -2 ; (2) : [(-1, -1)]
#         -1 ; (2+2) : [(-1, 0),(0, -1)]
#         0 ; (2+2+2) : [(-1, 1),(0, 0),(1, -1)]
#         1 ; (2+2+2) : [(0, 1),(1, 0),(2, -1)]
#         2 ; (2+2) : [(1, 1),(2, 0)]
#         3 ; (2) : [(2, 1)]
#     (23 = 2+4+5+6+4+2 : -[-2,-1,0,1,2,3])
# ], num_blocks=6, backend=numpy, dtype=float64)

See the documentation for installation, guides, examples, and the API reference. Contributions are welcome; see the development guide and GitHub issues.