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pao_param_methods.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Common routines for PAO parametrizations.
!> \author Ole Schuett
! **************************************************************************************************
MODULE pao_param_methods
USE cp_control_types, ONLY: dft_control_type
USE cp_dbcsr_api, ONLY: &
dbcsr_add, dbcsr_complete_redistribute, dbcsr_create, dbcsr_get_block_p, dbcsr_get_info, &
dbcsr_iterator_blocks_left, dbcsr_iterator_next_block, dbcsr_iterator_start, &
dbcsr_iterator_stop, dbcsr_iterator_type, dbcsr_multiply, dbcsr_p_type, dbcsr_release, &
dbcsr_reserve_diag_blocks, dbcsr_scale, dbcsr_type
USE cp_log_handling, ONLY: cp_to_string
USE dm_ls_scf_qs, ONLY: matrix_decluster
USE dm_ls_scf_types, ONLY: ls_mstruct_type,&
ls_scf_env_type
USE kinds, ONLY: dp
USE message_passing, ONLY: mp_comm_type
USE pao_types, ONLY: pao_env_type
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_rho_types, ONLY: qs_rho_get,&
qs_rho_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'pao_param_methods'
PUBLIC :: pao_calc_grad_lnv_wrt_U, pao_calc_AB_from_U, pao_calc_grad_lnv_wrt_AB
CONTAINS
! **************************************************************************************************
!> \brief Helper routine, calculates partial derivative dE/dU
!> \param qs_env ...
!> \param ls_scf_env ...
!> \param matrix_M_diag the derivate wrt U, matrix uses pao%diag_distribution
! **************************************************************************************************
SUBROUTINE pao_calc_grad_lnv_wrt_U(qs_env, ls_scf_env, matrix_M_diag)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(ls_scf_env_type), TARGET :: ls_scf_env
TYPE(dbcsr_type) :: matrix_M_diag
CHARACTER(len=*), PARAMETER :: routineN = 'pao_calc_grad_lnv_wrt_U'
INTEGER :: handle
REAL(KIND=dp) :: filter_eps
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: matrix_s
TYPE(dbcsr_type) :: matrix_M, matrix_Ma, matrix_Mb, matrix_NM
TYPE(ls_mstruct_type), POINTER :: ls_mstruct
TYPE(pao_env_type), POINTER :: pao
CALL timeset(routineN, handle)
ls_mstruct => ls_scf_env%ls_mstruct
pao => ls_scf_env%pao_env
filter_eps = ls_scf_env%eps_filter
CALL get_qs_env(qs_env, matrix_s=matrix_s)
CALL pao_calc_grad_lnv_wrt_AB(qs_env, ls_scf_env, matrix_Ma, matrix_Mb)
! Calculation uses distr. of matrix_s, afterwards we redistribute to pao%diag_distribution.
CALL dbcsr_create(matrix_M, template=matrix_s(1)%matrix, matrix_type="N")
CALL dbcsr_reserve_diag_blocks(matrix_M)
CALL dbcsr_create(matrix_NM, template=ls_mstruct%matrix_A, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, pao%matrix_N_inv, matrix_Ma, &
1.0_dp, matrix_NM, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "N", 1.0_dp, pao%matrix_N, matrix_Mb, &
1.0_dp, matrix_NM, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "T", 1.0_dp, matrix_NM, pao%matrix_Y, &
1.0_dp, matrix_M, filter_eps=filter_eps)
!---------------------------------------------------------------------------
! redistribute using pao%diag_distribution
CALL dbcsr_create(matrix_M_diag, &
name="PAO matrix_M", &
matrix_type="N", &
dist=pao%diag_distribution, &
template=matrix_s(1)%matrix)
CALL dbcsr_reserve_diag_blocks(matrix_M_diag)
CALL dbcsr_complete_redistribute(matrix_M, matrix_M_diag)
!---------------------------------------------------------------------------
! cleanup:
CALL dbcsr_release(matrix_M)
CALL dbcsr_release(matrix_Ma)
CALL dbcsr_release(matrix_Mb)
CALL dbcsr_release(matrix_NM)
CALL timestop(handle)
END SUBROUTINE pao_calc_grad_lnv_wrt_U
! **************************************************************************************************
!> \brief Takes current matrix_X and calculates the matrices A and B.
!> \param pao ...
!> \param qs_env ...
!> \param ls_scf_env ...
!> \param matrix_U_diag ...
! **************************************************************************************************
SUBROUTINE pao_calc_AB_from_U(pao, qs_env, ls_scf_env, matrix_U_diag)
TYPE(pao_env_type), POINTER :: pao
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(ls_scf_env_type), TARGET :: ls_scf_env
TYPE(dbcsr_type) :: matrix_U_diag
CHARACTER(len=*), PARAMETER :: routineN = 'pao_calc_AB_from_U'
INTEGER :: acol, arow, handle, iatom
LOGICAL :: found
REAL(dp), DIMENSION(:, :), POINTER :: block_A, block_B, block_N, block_N_inv, &
block_U, block_Y
TYPE(dbcsr_iterator_type) :: iter
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: matrix_s
TYPE(dbcsr_type) :: matrix_U
TYPE(ls_mstruct_type), POINTER :: ls_mstruct
CALL timeset(routineN, handle)
CALL get_qs_env(qs_env, matrix_s=matrix_s)
ls_mstruct => ls_scf_env%ls_mstruct
! --------------------------------------------------------------------------------------------
! sanity check matrix U
CALL pao_assert_unitary(pao, matrix_U_diag)
! --------------------------------------------------------------------------------------------
! redistribute matrix_U_diag from diag_distribution to distribution of matrix_s
CALL get_qs_env(qs_env, matrix_s=matrix_s)
CALL dbcsr_create(matrix_U, matrix_type="N", template=matrix_s(1)%matrix)
CALL dbcsr_reserve_diag_blocks(matrix_U)
CALL dbcsr_complete_redistribute(matrix_U_diag, matrix_U)
! --------------------------------------------------------------------------------------------
! calculate matrix A and B from matrix U
! Multiplying diagonal matrices is a local operation.
! To take advantage of this we're using an iterator instead of calling dbcsr_multiply().
!$OMP PARALLEL DEFAULT(NONE) SHARED(pao,ls_mstruct,matrix_U) &
!$OMP PRIVATE(iter,arow,acol,iatom,block_U,block_Y,block_A,block_B,block_N,block_N_inv,found)
CALL dbcsr_iterator_start(iter, matrix_U)
DO WHILE (dbcsr_iterator_blocks_left(iter))
CALL dbcsr_iterator_next_block(iter, arow, acol, block_U)
iatom = arow; CPASSERT(arow == acol)
CALL dbcsr_get_block_p(matrix=pao%matrix_Y, row=iatom, col=iatom, block=block_Y, found=found)
CPASSERT(ASSOCIATED(block_Y))
CALL dbcsr_get_block_p(matrix=ls_mstruct%matrix_A, row=iatom, col=iatom, block=block_A, found=found)
CALL dbcsr_get_block_p(matrix=pao%matrix_N_inv, row=iatom, col=iatom, block=block_N_inv, found=found)
CPASSERT(ASSOCIATED(block_A) .AND. ASSOCIATED(block_N_inv))
CALL dbcsr_get_block_p(matrix=ls_mstruct%matrix_B, row=iatom, col=iatom, block=block_B, found=found)
CALL dbcsr_get_block_p(matrix=pao%matrix_N, row=iatom, col=iatom, block=block_N, found=found)
CPASSERT(ASSOCIATED(block_B) .AND. ASSOCIATED(block_N))
block_A = MATMUL(MATMUL(block_N_inv, block_U), block_Y)
block_B = MATMUL(MATMUL(block_N, block_U), block_Y)
END DO
CALL dbcsr_iterator_stop(iter)
!$OMP END PARALLEL
CALL dbcsr_release(matrix_U)
CALL timestop(handle)
END SUBROUTINE pao_calc_AB_from_U
! **************************************************************************************************
!> \brief Debugging routine, check unitaryness of U
!> \param pao ...
!> \param matrix_U ...
! **************************************************************************************************
SUBROUTINE pao_assert_unitary(pao, matrix_U)
TYPE(pao_env_type), POINTER :: pao
TYPE(dbcsr_type) :: matrix_U
CHARACTER(len=*), PARAMETER :: routineN = 'pao_assert_unitary'
INTEGER :: acol, arow, group_handle, handle, i, &
iatom, M, N
INTEGER, DIMENSION(:), POINTER :: blk_sizes_pao, blk_sizes_pri
REAL(dp) :: delta_max
REAL(dp), DIMENSION(:, :), POINTER :: block_test, tmp1, tmp2
TYPE(dbcsr_iterator_type) :: iter
TYPE(mp_comm_type) :: group
IF (pao%check_unitary_tol < 0.0_dp) RETURN ! no checking
CALL timeset(routineN, handle)
delta_max = 0.0_dp
CALL dbcsr_get_info(pao%matrix_Y, row_blk_size=blk_sizes_pri, col_blk_size=blk_sizes_pao)
!$OMP PARALLEL DEFAULT(NONE) SHARED(pao,matrix_U,blk_sizes_pri,blk_sizes_pao,delta_max) &
!$OMP PRIVATE(iter,arow,acol,iatom,N,M,block_test,tmp1,tmp2)
CALL dbcsr_iterator_start(iter, matrix_U)
DO WHILE (dbcsr_iterator_blocks_left(iter))
CALL dbcsr_iterator_next_block(iter, arow, acol, block_test)
iatom = arow; CPASSERT(arow == acol)
N = blk_sizes_pri(iatom) ! size of primary basis
M = blk_sizes_pao(iatom) ! size of pao basis
! we only need the upper left "PAO-corner" to be unitary
ALLOCATE (tmp1(N, M), tmp2(M, M))
tmp1 = block_test(:, 1:M)
tmp2 = MATMUL(TRANSPOSE(tmp1), tmp1)
DO i = 1, M
tmp2(i, i) = tmp2(i, i) - 1.0_dp
END DO
!$OMP ATOMIC
delta_max = MAX(delta_max, MAXVAL(ABS(tmp2)))
DEALLOCATE (tmp1, tmp2)
END DO
CALL dbcsr_iterator_stop(iter)
!$OMP END PARALLEL
CALL dbcsr_get_info(matrix_U, group=group_handle)
CALL group%set_handle(group_handle)
CALL group%max(delta_max)
IF (pao%iw > 0) WRITE (pao%iw, *) 'PAO| checked unitaryness, max delta:', delta_max
IF (delta_max > pao%check_unitary_tol) &
CPABORT("Found bad unitaryness:"//cp_to_string(delta_max))
CALL timestop(handle)
END SUBROUTINE pao_assert_unitary
! **************************************************************************************************
!> \brief Helper routine, calculates partial derivative dE/dA and dE/dB.
!> As energy functional serves the definition by LNV (Li, Nunes, Vanderbilt).
!> \param qs_env ...
!> \param ls_scf_env ...
!> \param matrix_Ma the derivate wrt A, matrix uses s_matrix-distribution.
!> \param matrix_Mb the derivate wrt B, matrix uses s_matrix-distribution.
! **************************************************************************************************
SUBROUTINE pao_calc_grad_lnv_wrt_AB(qs_env, ls_scf_env, matrix_Ma, matrix_Mb)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(ls_scf_env_type), TARGET :: ls_scf_env
TYPE(dbcsr_type) :: matrix_Ma, matrix_Mb
CHARACTER(len=*), PARAMETER :: routineN = 'pao_calc_grad_lnv_wrt_AB'
INTEGER :: handle, nspin
INTEGER, DIMENSION(:), POINTER :: pao_blk_sizes
REAL(KIND=dp) :: filter_eps
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: matrix_ks, matrix_s, rho_ao
TYPE(dbcsr_type) :: matrix_HB, matrix_HPS, matrix_M, matrix_M1, matrix_M1_dc, matrix_M2, &
matrix_M2_dc, matrix_M3, matrix_M3_dc, matrix_PA, matrix_PH, matrix_PHP, matrix_PSP, &
matrix_SB, matrix_SP
TYPE(dft_control_type), POINTER :: dft_control
TYPE(ls_mstruct_type), POINTER :: ls_mstruct
TYPE(pao_env_type), POINTER :: pao
TYPE(qs_rho_type), POINTER :: rho
CALL timeset(routineN, handle)
ls_mstruct => ls_scf_env%ls_mstruct
pao => ls_scf_env%pao_env
CALL get_qs_env(qs_env, &
rho=rho, &
matrix_ks=matrix_ks, &
matrix_s=matrix_s, &
dft_control=dft_control)
CALL qs_rho_get(rho, rho_ao=rho_ao)
nspin = dft_control%nspins
filter_eps = ls_scf_env%eps_filter
CALL dbcsr_get_info(ls_mstruct%matrix_A, col_blk_size=pao_blk_sizes)
IF (nspin /= 1) CPABORT("open shell not yet implemented")
!TODO: handle openshell case properly
! Notation according to equation (4.6) on page 50 from:
! https://dx.doi.org/10.3929%2Fethz-a-010819495
!---------------------------------------------------------------------------
! calculate need products in pao basis
CALL dbcsr_create(matrix_PH, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, ls_scf_env%matrix_p(1), ls_scf_env%matrix_ks(1), &
0.0_dp, matrix_PH, filter_eps=filter_eps)
CALL dbcsr_create(matrix_PHP, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_PH, ls_scf_env%matrix_p(1), &
0.0_dp, matrix_PHP, filter_eps=filter_eps)
CALL dbcsr_create(matrix_SP, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, ls_scf_env%matrix_s, ls_scf_env%matrix_p(1), &
0.0_dp, matrix_SP, filter_eps=filter_eps)
IF (nspin == 1) CALL dbcsr_scale(matrix_SP, 0.5_dp)
CALL dbcsr_create(matrix_HPS, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_multiply("N", "T", 1.0_dp, ls_scf_env%matrix_ks(1), matrix_SP, &
0.0_dp, matrix_HPS, filter_eps=filter_eps)
CALL dbcsr_create(matrix_PSP, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, ls_scf_env%matrix_p(1), matrix_SP, &
0.0_dp, matrix_PSP, filter_eps=filter_eps)
!---------------------------------------------------------------------------
! M1 = dE_lnv / dP_pao
CALL dbcsr_create(matrix_M1, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_multiply("N", "T", 3.0_dp, ls_scf_env%matrix_ks(1), matrix_SP, &
1.0_dp, matrix_M1, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "N", 3.0_dp, matrix_SP, ls_scf_env%matrix_ks(1), &
1.0_dp, matrix_M1, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "T", -2.0_dp, matrix_HPS, matrix_SP, &
1.0_dp, matrix_M1, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "N", -2.0_dp, matrix_SP, matrix_HPS, &
1.0_dp, matrix_M1, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "T", -2.0_dp, matrix_SP, matrix_HPS, &
1.0_dp, matrix_M1, filter_eps=filter_eps)
! reverse possible molecular clustering
CALL dbcsr_create(matrix_M1_dc, &
template=matrix_s(1)%matrix, &
row_blk_size=pao_blk_sizes, &
col_blk_size=pao_blk_sizes)
CALL matrix_decluster(matrix_M1_dc, matrix_M1, ls_mstruct)
!---------------------------------------------------------------------------
! M2 = dE_lnv / dH
CALL dbcsr_create(matrix_M2, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_add(matrix_M2, matrix_PSP, 1.0_dp, 3.0_dp)
CALL dbcsr_multiply("N", "N", -2.0_dp, matrix_PSP, matrix_SP, &
1.0_dp, matrix_M2, filter_eps=filter_eps)
! reverse possible molecular clustering
CALL dbcsr_create(matrix_M2_dc, &
template=matrix_s(1)%matrix, &
row_blk_size=pao_blk_sizes, &
col_blk_size=pao_blk_sizes)
CALL matrix_decluster(matrix_M2_dc, matrix_M2, ls_mstruct)
!---------------------------------------------------------------------------
! M3 = dE_lnv / dS
CALL dbcsr_create(matrix_M3, template=ls_scf_env%matrix_s, matrix_type="N")
CALL dbcsr_add(matrix_M3, matrix_PHP, 1.0_dp, 3.0_dp)
CALL dbcsr_multiply("N", "N", -2.0_dp, matrix_PHP, matrix_SP, &
1.0_dp, matrix_M3, filter_eps=filter_eps)
CALL dbcsr_multiply("N", "T", -2.0_dp, matrix_PSP, matrix_PH, &
1.0_dp, matrix_M3, filter_eps=filter_eps)
! reverse possible molecular clustering
CALL dbcsr_create(matrix_M3_dc, &
template=matrix_s(1)%matrix, &
row_blk_size=pao_blk_sizes, &
col_blk_size=pao_blk_sizes)
CALL matrix_decluster(matrix_M3_dc, matrix_M3, ls_mstruct)
!---------------------------------------------------------------------------
! assemble Ma and Mb
! matrix_Ma = dE_lnv / dA = P * A * M1
! matrix_Mb = dE_lnv / dB = H * B * M2 + S * B * M3
CALL dbcsr_create(matrix_Ma, template=ls_mstruct%matrix_A, matrix_type="N")
CALL dbcsr_reserve_diag_blocks(matrix_Ma)
CALL dbcsr_create(matrix_Mb, template=ls_mstruct%matrix_B, matrix_type="N")
CALL dbcsr_reserve_diag_blocks(matrix_Mb)
!---------------------------------------------------------------------------
! combine M1 with matrices from primary basis
CALL dbcsr_create(matrix_PA, template=ls_mstruct%matrix_A, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, rho_ao(1)%matrix, ls_mstruct%matrix_A, &
0.0_dp, matrix_PA, filter_eps=filter_eps)
! matrix_Ma = P * A * M1
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_PA, matrix_M1_dc, &
0.0_dp, matrix_Ma, filter_eps=filter_eps)
!---------------------------------------------------------------------------
! combine M2 with matrices from primary basis
CALL dbcsr_create(matrix_HB, template=ls_mstruct%matrix_B, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_ks(1)%matrix, ls_mstruct%matrix_B, &
0.0_dp, matrix_HB, filter_eps=filter_eps)
! matrix_Mb = H * B * M2
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_HB, matrix_M2_dc, &
0.0_dp, matrix_Mb, filter_eps=filter_eps)
!---------------------------------------------------------------------------
! combine M3 with matrices from primary basis
CALL dbcsr_create(matrix_SB, template=ls_mstruct%matrix_B, matrix_type="N")
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_s(1)%matrix, ls_mstruct%matrix_B, &
0.0_dp, matrix_SB, filter_eps=filter_eps)
IF (nspin == 1) CALL dbcsr_scale(matrix_SB, 0.5_dp)
! matrix_Mb += S * B * M3
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_SB, matrix_M3_dc, &
1.0_dp, matrix_Mb, filter_eps=filter_eps)
IF (nspin == 1) CALL dbcsr_scale(matrix_Ma, 2.0_dp)
IF (nspin == 1) CALL dbcsr_scale(matrix_Mb, 2.0_dp)
!---------------------------------------------------------------------------
! cleanup: TODO release matrices as early as possible
CALL dbcsr_release(matrix_PH)
CALL dbcsr_release(matrix_PHP)
CALL dbcsr_release(matrix_SP)
CALL dbcsr_release(matrix_HPS)
CALL dbcsr_release(matrix_PSP)
CALL dbcsr_release(matrix_M)
CALL dbcsr_release(matrix_M1)
CALL dbcsr_release(matrix_M2)
CALL dbcsr_release(matrix_M3)
CALL dbcsr_release(matrix_M1_dc)
CALL dbcsr_release(matrix_M2_dc)
CALL dbcsr_release(matrix_M3_dc)
CALL dbcsr_release(matrix_PA)
CALL dbcsr_release(matrix_HB)
CALL dbcsr_release(matrix_SB)
CALL timestop(handle)
END SUBROUTINE pao_calc_grad_lnv_wrt_AB
END MODULE pao_param_methods