Decompositions

CP (CANDECOMP/PARAFAC) and Tucker (HOSVD) decompositions for compressing high-order tensors. Used in quantum chemistry for tensor hypercontraction (THC) and low-rank factorization of DF-coefficient tensors.

CP (PARAFAC)

cp_decompose(tensor, rank, *, max_iter=100, tol=1e-6) -> (factors, weights)

Decompose a tensor as T ≈ Σ_r w_r * a_r ⊗ b_r ⊗ c_r ⊗ ... via alternating least squares.

• factors: list of factor matrices, one per mode with shape (I_k, R)
• weights: (R,) tensor of component weights

factors, weights = trntensor.cp_decompose(T, rank=8, max_iter=20)
T_approx = trntensor.cp_reconstruct(factors, weights)

cp_reconstruct(factors, weights) -> torch.Tensor

Reconstruct the full tensor from CP factors.

Tucker (HOSVD)

tucker_decompose(tensor, ranks) -> (core, factors)

Higher-order SVD: T ≈ G ×_1 U_1 ×_2 U_2 ... Each factor matrix U_k is orthonormal by construction.

core, factors = trntensor.tucker_decompose(T, ranks=(4, 4, 4))
T_approx = trntensor.tucker_reconstruct(core, factors)

tucker_reconstruct(core, factors) -> torch.Tensor

Reconstruct from a Tucker decomposition.