|
| subroutine, public | bse_davidson::bse_davidson_tda (mv_env, bse_env, unit_nr, exc_ens, fm_x) |
| | Block Davidson with thick restart for the NUM_EXC_EN lowest solutions of sum_jb A_ia,jb X_jb^n = Ω^n X_ia^n. With the orthonormal basis Z_ia,m the reduced matrix is Ar_mn = sum_ia Z_ia,m (A Z)_ia,n with eigenpairs (θ_k, c_mk), X_ia^k = sum_m Z_ia,m c_mk, and the basis grows by the corrections t_ia,k = r_ia,k/(d_ia - θ_k) of the residuals r_ia,k = sum_m (A Z)_ia,m c_mk - θ_k X_ia^k, d_ia being the diagonal chosen by PRECONDITIONER. Arrays: Ar_mn (the reduced A) in fm_red_A on the process grid, c_mk in coef_ritz, θ_k c_mk in coef_ritz_theta.
|
| subroutine, public | bse_davidson::bse_davidson_abba_mk (mv_env, bse_env, unit_nr, exc_ens, fm_x, fm_y, abba_status, ab_margin, fm_x_tda) |
| | Block Davidson with thick restart for the NUM_EXC_EN lowest solutions of the full problem, written as sum_jb [(A+B)(A-B)]_ia,jb x_jb^n = (Ω^n)^2 x_ia^n with x^n = X^n - Y^n, which is symmetric in the inner product <u,v> = sum_ia,jb u_ia (A-B)_ia,jb v_jb. The basis V_ia,m is orthonormal in that inner product, W_ia,m = sum_jb (A-B)_ia,jb V_jb,m, and the reduced matrix Hr_mn = sum_ia,jb W_ia,m (A+B)_ia,jb W_jb,n has the eigenpairs ((Ω^k)^2, c_mk). Then x_ia^k = (Ω^k)^1/2 sum_m V_ia,m c_mk and y_ia^k = (X^k+Y^k)_ia = (Ω^k)^-1/2 sum_m W_ia,m c_mk obey sum_ia x_ia^k y_ia^k = 1, the residual is r_ia,k = sum_jb (A+B)_ia,jb y_jb^k - Ω^k x_ia^k and the correction t_ia,k = r_ia,k/(d_ia^2 - (Ω^k)^2), d_ia chosen by PRECONDITIONER. Arrays: Hr_mn in fm_red_M on the process grid, c_mk in coef_ritz, (Ω^k)^1/2 c_mk in coef_x, (Ω^k)^-1/2 c_mk in coef_y, Ω^k (Ω^k)^1/2 c_mk in coef_x_omega.
|
| subroutine, public | bse_davidson::bse_davidson_abba_os (mv_env, bse_env, unit_nr, exc_ens, fm_x, fm_y, abba_status, ab_margin, fm_x_tda) |
| | Block Davidson with thick restart for the NUM_EXC_EN lowest solutions of the full problem in the paired form of Olsen and Stratmann: with x^n = X^n - Y^n, y^n = X^n + Y^n, M = A+B and K = A-B, sum_jb M_ia,jb y_jb^n = Ω^n x_ia^n and sum_jb K_ia,jb x_jb^n = Ω^n y_ia^n. One orthonormal basis b_ia,m carries both vectors: Mr_mn = sum_ia b_ia,m (M b)_ia,n and Kr_mn = sum_ia b_ia,m (K b)_ia,n are solved by solve_reduced_paired for Ω^k, R_mk and L_mk with y_ia^k = sum_m b_ia,m R_mk, x_ia^k = sum_m b_ia,m L_mk and sum_ia x_ia^k y_ia^k = 1. The basis grows by the corrections t_ia,k = r_ia,k/(d_ia - Ω^k) of both residuals, rR_ia,k = sum_m (M b)_ia,m R_mk - Ω^k x_ia^k and rL_ia,k = sum_m (K b)_ia,m L_mk - Ω^k y_ia^k, d_ia chosen by PRECONDITIONER; the rR block enters before the rL block, which is nearly parallel to it for a small B. Arrays: Mr_mn and Kr_mn in fm_red_M and fm_red_K on the process grid, R_mk in coef_right, L_mk in coef_left.
|
| subroutine, public | bse_davidson::bse_davidson_refcheck (fm_a_explicit, exc_ens, fm_x, bse_env, unit_nr, fm_b_explicit, fm_y) |
| | Debug check of a Davidson result against the full diagonalization of the explicit matrices: energies, and per multiplet the smallest singular value of X_ref^T X for the TDA, or of X_ref^T X - Y_ref^T Y for ABBA. ABBA diagonalizes the Hermitian reduction C = (A-B)^1/2 (A+B) (A-B)^1/2 with C T^n = (Ω^n)^2 T^n, (X+Y)^n = (Ω^n)^-1/2 (A-B)^1/2 T^n, (X-Y)^n = (Ω^n)^1/2 (A-B)^-1/2 T^n. A failed reference solve aborts: this is debug output with nothing to fall back on.
|
1.15.0