Tensor-decomposition tools

This module contains functions for tensor decomposition methods.

calc_integrals_decomposition(EC::ECInfo)

Decompose $v_{pr}^{qs}$ as $v_p^{qL} v_r^{sL}$ and store as mmL.

eigen_decompose(T2mat, nvirt, nocc, tol=1e-6)

Eigenvector-decompose symmetric doubles T2[ai,bj] matrix: $T^{ij}_{ab} = U^{iX}_a T_{XY} U^{jY}_b δ_{XY}$. Return $U^iX_a$ as U[a,i,X] for $T_{XX}$ > tol

iter_svd_decompose(Amat, nvirt, nocc, naux)

Iteratively decompose A[ai,ξ] as $U^{iX}_a Σ_X δ_{XY} V^Y_ξ$. Return $U^{iX}_a$ as U[a,i,X] for first naux $Σ_X$

rotate_U2pseudocanonical(EC::ECInfo, UaiX)

Diagonalize ϵv - ϵo transformed with UaiX (for update). Return eigenvalues and rotated UaiX

svd_decompose(Amat, tol=1e-6)

SVD-decompose A[ξ,ξ'] as $U^{X}_{ξ} Σ_X δ_{XY} V^{Y}_{ξ'}$. Return $U^{X}_{ξ}$ as U[ξ,X] for $Σ_X$ > tol

svd_decompose(Amat, nvirt, nocc, tol=1e-6)

SVD-decompose A[ai,ξ] as $U^{iX}_a Σ_X δ_{XY} V^{Y}_{ξ}$. Return $U^{iX}_a$ as U[a,i,X] for $Σ_X$ > tol