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cp2k/src/ct_methods.F
Ole Schütt 0afa151ef8 prettify
2024-05-30 09:53:28 +02:00

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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 Cayley transformation methods
!> \par History
!> 2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
MODULE ct_methods
USE cp_dbcsr_api, ONLY: &
dbcsr_add, dbcsr_add_on_diag, dbcsr_copy, dbcsr_create, dbcsr_desymmetrize, &
dbcsr_distribution_get, dbcsr_distribution_type, dbcsr_dot, dbcsr_filter, dbcsr_finalize, &
dbcsr_frobenius_norm, dbcsr_func_inverse, dbcsr_function_of_elements, dbcsr_get_diag, &
dbcsr_get_info, dbcsr_get_stored_coordinates, dbcsr_hadamard_product, &
dbcsr_iterator_blocks_left, dbcsr_iterator_next_block, dbcsr_iterator_start, &
dbcsr_iterator_stop, dbcsr_iterator_type, dbcsr_multiply, dbcsr_nblkcols_total, &
dbcsr_nblkrows_total, dbcsr_norm, dbcsr_norm_maxabsnorm, dbcsr_release, &
dbcsr_reserve_block2d, dbcsr_scale, dbcsr_set, dbcsr_set_diag, dbcsr_transposed, &
dbcsr_type, dbcsr_type_no_symmetry, dbcsr_work_create
USE cp_dbcsr_cholesky, ONLY: cp_dbcsr_cholesky_decompose,&
cp_dbcsr_cholesky_invert
USE cp_dbcsr_diag, ONLY: cp_dbcsr_syevd
USE cp_log_handling, ONLY: cp_get_default_logger,&
cp_logger_get_default_unit_nr,&
cp_logger_type
USE ct_types, ONLY: ct_step_env_type
USE input_constants, ONLY: &
cg_dai_yuan, cg_fletcher, cg_fletcher_reeves, cg_hager_zhang, cg_hestenes_stiefel, &
cg_liu_storey, cg_polak_ribiere, cg_zero, tensor_orthogonal, tensor_up_down
USE iterate_matrix, ONLY: matrix_sqrt_Newton_Schulz
USE kinds, ONLY: dp
USE machine, ONLY: m_walltime
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'ct_methods'
! Public subroutines
PUBLIC :: ct_step_execute, analytic_line_search, diagonalize_diagonal_blocks
CONTAINS
! **************************************************************************************************
!> \brief Performs Cayley transformation
!> \param cts_env ...
!> \par History
!> 2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE ct_step_execute(cts_env)
TYPE(ct_step_env_type) :: cts_env
CHARACTER(len=*), PARAMETER :: routineN = 'ct_step_execute'
INTEGER :: handle, n, preconditioner_type, unit_nr
REAL(KIND=dp) :: gap_estimate, safety_margin
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: evals
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_type) :: matrix_pp, matrix_pq, matrix_qp, &
matrix_qp_save, matrix_qq, oo1, &
oo1_sqrt, oo1_sqrt_inv, t_corr, tmp1, &
u_pp, u_qq
!TYPE(dbcsr_type) :: rst_x1, rst_x2
!REAL(KIND=dp) :: ener_tmp
!TYPE(dbcsr_iterator_type) :: iter
!INTEGER :: iblock_row,iblock_col,&
! iblock_row_size,iblock_col_size
!REAL(KIND=dp), DIMENSION(:,:), POINTER :: data_p
CALL timeset(routineN, handle)
logger => cp_get_default_logger()
IF (logger%para_env%is_source()) THEN
unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
ELSE
unit_nr = -1
END IF
! check if all input is in place and flags are consistent
IF (cts_env%update_q .AND. (.NOT. cts_env%update_p)) THEN
CPABORT("q-update is possible only with p-update")
END IF
IF (cts_env%tensor_type .EQ. tensor_up_down) THEN
CPABORT("riccati is not implemented for biorthogonal basis")
END IF
IF (.NOT. ASSOCIATED(cts_env%matrix_ks)) THEN
CPABORT("KS matrix is not associated")
END IF
IF (cts_env%use_virt_orbs .AND. (.NOT. cts_env%use_occ_orbs)) THEN
CPABORT("virtual orbs can be used only with occupied orbs")
END IF
IF (cts_env%use_occ_orbs) THEN
IF (.NOT. ASSOCIATED(cts_env%matrix_t)) THEN
CPABORT("T matrix is not associated")
END IF
IF (.NOT. ASSOCIATED(cts_env%matrix_qp_template)) THEN
CPABORT("QP template is not associated")
END IF
IF (.NOT. ASSOCIATED(cts_env%matrix_pq_template)) THEN
CPABORT("PQ template is not associated")
END IF
END IF
IF (cts_env%use_virt_orbs) THEN
IF (.NOT. ASSOCIATED(cts_env%matrix_v)) THEN
CPABORT("V matrix is not associated")
END IF
ELSE
IF (.NOT. ASSOCIATED(cts_env%matrix_p)) THEN
CPABORT("P matrix is not associated")
END IF
END IF
IF (cts_env%tensor_type .NE. tensor_up_down .AND. &
cts_env%tensor_type .NE. tensor_orthogonal) THEN
CPABORT("illegal tensor flag")
END IF
! start real calculations
IF (cts_env%use_occ_orbs) THEN
! create matrices for various ks blocks
CALL dbcsr_create(matrix_pp, &
template=cts_env%p_index_up, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_qp, &
template=cts_env%matrix_qp_template, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_qq, &
template=cts_env%q_index_up, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_pq, &
template=cts_env%matrix_pq_template, &
matrix_type=dbcsr_type_no_symmetry)
! create the residue matrix
CALL dbcsr_create(cts_env%matrix_res, &
template=cts_env%matrix_qp_template)
CALL assemble_ks_qp_blocks(cts_env%matrix_ks, &
cts_env%matrix_p, &
cts_env%matrix_t, &
cts_env%matrix_v, &
cts_env%q_index_down, &
cts_env%p_index_up, &
cts_env%q_index_up, &
matrix_pp, &
matrix_qq, &
matrix_qp, &
matrix_pq, &
cts_env%tensor_type, &
cts_env%use_virt_orbs, &
cts_env%eps_filter)
! create a matrix of single-excitation amplitudes
CALL dbcsr_create(cts_env%matrix_x, &
template=cts_env%matrix_qp_template)
IF (ASSOCIATED(cts_env%matrix_x_guess)) THEN
CALL dbcsr_copy(cts_env%matrix_x, &
cts_env%matrix_x_guess)
IF (cts_env%tensor_type .EQ. tensor_orthogonal) THEN
! bring x from contravariant-covariant representation
! to the orthogonal/cholesky representation
! use res as temporary storage
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%q_index_down, &
cts_env%matrix_x, 0.0_dp, cts_env%matrix_res, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%matrix_res, &
cts_env%p_index_up, 0.0_dp, &
cts_env%matrix_x, &
filter_eps=cts_env%eps_filter)
END IF
ELSE
! set amplitudes to zero
CALL dbcsr_set(cts_env%matrix_x, 0.0_dp)
END IF
!SELECT CASE (cts_env%preconditioner_type)
!CASE (prec_eigenvector_blocks,prec_eigenvector_full)
preconditioner_type = 1
safety_margin = 2.0_dp
gap_estimate = 0.0001_dp
SELECT CASE (preconditioner_type)
CASE (1, 2)
!RZK-warning diagonalization works only with orthogonal tensor!!!
! find a better basis by diagonalizing diagonal blocks
! first pp
CALL dbcsr_create(u_pp, template=matrix_pp, &
matrix_type=dbcsr_type_no_symmetry)
!IF (cts_env%preconditioner_type.eq.prec_eigenvector_full) THEN
IF (.TRUE.) THEN
CALL dbcsr_get_info(matrix_pp, nfullrows_total=n)
ALLOCATE (evals(n))
CALL cp_dbcsr_syevd(matrix_pp, u_pp, evals, &
cts_env%para_env, cts_env%blacs_env)
DEALLOCATE (evals)
ELSE
CALL diagonalize_diagonal_blocks(matrix_pp, u_pp)
END IF
! and now qq
CALL dbcsr_create(u_qq, template=matrix_qq, &
matrix_type=dbcsr_type_no_symmetry)
!IF (cts_env%preconditioner_type.eq.prec_eigenvector_full) THEN
IF (.TRUE.) THEN
CALL dbcsr_get_info(matrix_qq, nfullrows_total=n)
ALLOCATE (evals(n))
CALL cp_dbcsr_syevd(matrix_qq, u_qq, evals, &
cts_env%para_env, cts_env%blacs_env)
DEALLOCATE (evals)
ELSE
CALL diagonalize_diagonal_blocks(matrix_qq, u_qq)
END IF
! apply the transformation to all matrices
CALL matrix_forward_transform(matrix_pp, u_pp, u_pp, &
cts_env%eps_filter)
CALL matrix_forward_transform(matrix_qq, u_qq, u_qq, &
cts_env%eps_filter)
CALL matrix_forward_transform(matrix_qp, u_qq, u_pp, &
cts_env%eps_filter)
CALL matrix_forward_transform(matrix_pq, u_pp, u_qq, &
cts_env%eps_filter)
CALL matrix_forward_transform(cts_env%matrix_x, u_qq, u_pp, &
cts_env%eps_filter)
IF (cts_env%max_iter .GE. 0) THEN
CALL solve_riccati_equation( &
pp=matrix_pp, &
qq=matrix_qq, &
qp=matrix_qp, &
pq=matrix_pq, &
x=cts_env%matrix_x, &
res=cts_env%matrix_res, &
neglect_quadratic_term=cts_env%neglect_quadratic_term, &
conjugator=cts_env%conjugator, &
max_iter=cts_env%max_iter, &
eps_convergence=cts_env%eps_convergence, &
eps_filter=cts_env%eps_filter, &
converged=cts_env%converged)
IF (cts_env%converged) THEN
!IF (unit_nr>0) THEN
! WRITE(unit_nr,*)
! WRITE(unit_nr,'(T6,A)') &
! "RICCATI equations solved"
! CALL m_flush(unit_nr)
!ENDIF
ELSE
CPABORT("RICCATI: CG algorithm has NOT converged")
END IF
END IF
IF (cts_env%calculate_energy_corr) THEN
CALL dbcsr_dot(matrix_qp, cts_env%matrix_x, cts_env%energy_correction)
END IF
CALL dbcsr_release(matrix_pp)
CALL dbcsr_release(matrix_qp)
CALL dbcsr_release(matrix_qq)
CALL dbcsr_release(matrix_pq)
! back-transform to the original basis
CALL matrix_backward_transform(cts_env%matrix_x, u_qq, &
u_pp, cts_env%eps_filter)
CALL dbcsr_release(u_qq)
CALL dbcsr_release(u_pp)
!CASE (prec_cholesky_inverse)
CASE (3)
! RZK-warning implemented only for orthogonal tensors!!!
! generalization to up_down should be easy
CALL dbcsr_create(u_pp, template=matrix_pp, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_copy(u_pp, matrix_pp)
CALL dbcsr_scale(u_pp, -1.0_dp)
CALL dbcsr_add_on_diag(u_pp, &
ABS(safety_margin*gap_estimate))
CALL cp_dbcsr_cholesky_decompose(u_pp, &
para_env=cts_env%para_env, &
blacs_env=cts_env%blacs_env)
CALL cp_dbcsr_cholesky_invert(u_pp, &
para_env=cts_env%para_env, &
blacs_env=cts_env%blacs_env, &
upper_to_full=.TRUE.)
!CALL dbcsr_scale(u_pp,-1.0_dp)
CALL dbcsr_create(u_qq, template=matrix_qq, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_copy(u_qq, matrix_qq)
CALL dbcsr_add_on_diag(u_qq, &
ABS(safety_margin*gap_estimate))
CALL cp_dbcsr_cholesky_decompose(u_qq, &
para_env=cts_env%para_env, &
blacs_env=cts_env%blacs_env)
CALL cp_dbcsr_cholesky_invert(u_qq, &
para_env=cts_env%para_env, &
blacs_env=cts_env%blacs_env, &
upper_to_full=.TRUE.)
! transform all riccati matrices (left-right preconditioner)
CALL dbcsr_create(tmp1, template=matrix_qq, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, u_qq, &
matrix_qq, 0.0_dp, tmp1, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_copy(matrix_qq, tmp1)
CALL dbcsr_release(tmp1)
CALL dbcsr_create(tmp1, template=matrix_pp, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_pp, &
u_pp, 0.0_dp, tmp1, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_copy(matrix_pp, tmp1)
CALL dbcsr_release(tmp1)
CALL dbcsr_create(matrix_qp_save, template=matrix_qp, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_copy(matrix_qp_save, matrix_qp)
CALL dbcsr_create(tmp1, template=matrix_qp, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_qp, &
u_pp, 0.0_dp, tmp1, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, u_qq, tmp1, &
0.0_dp, matrix_qp, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_release(tmp1)
!CALL dbcsr_print(matrix_qq)
!CALL dbcsr_print(matrix_qp)
!CALL dbcsr_print(matrix_pp)
IF (cts_env%max_iter .GE. 0) THEN
CALL solve_riccati_equation( &
pp=matrix_pp, &
qq=matrix_qq, &
qp=matrix_qp, &
pq=matrix_pq, &
oo=u_pp, &
vv=u_qq, &
x=cts_env%matrix_x, &
res=cts_env%matrix_res, &
neglect_quadratic_term=cts_env%neglect_quadratic_term, &
conjugator=cts_env%conjugator, &
max_iter=cts_env%max_iter, &
eps_convergence=cts_env%eps_convergence, &
eps_filter=cts_env%eps_filter, &
converged=cts_env%converged)
IF (cts_env%converged) THEN
!IF (unit_nr>0) THEN
! WRITE(unit_nr,*)
! WRITE(unit_nr,'(T6,A)') &
! "RICCATI equations solved"
! CALL m_flush(unit_nr)
!ENDIF
ELSE
CPABORT("RICCATI: CG algorithm has NOT converged")
END IF
END IF
IF (cts_env%calculate_energy_corr) THEN
CALL dbcsr_dot(matrix_qp_save, cts_env%matrix_x, cts_env%energy_correction)
END IF
CALL dbcsr_release(matrix_qp_save)
CALL dbcsr_release(matrix_pp)
CALL dbcsr_release(matrix_qp)
CALL dbcsr_release(matrix_qq)
CALL dbcsr_release(matrix_pq)
CALL dbcsr_release(u_qq)
CALL dbcsr_release(u_pp)
CASE DEFAULT
CPABORT("illegal preconditioner type")
END SELECT ! preconditioner type
IF (cts_env%update_p) THEN
IF (cts_env%tensor_type .EQ. tensor_up_down) THEN
CPABORT("orbital update is NYI for this tensor type")
END IF
! transform occupied orbitals
! in a way that preserves the overlap metric
CALL dbcsr_create(oo1, &
template=cts_env%p_index_up, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(oo1_sqrt_inv, &
template=oo1)
CALL dbcsr_create(oo1_sqrt, &
template=oo1)
! Compute (1+tr(X).X)^(-1/2)_up_down
CALL dbcsr_multiply("T", "N", 1.0_dp, cts_env%matrix_x, &
cts_env%matrix_x, 0.0_dp, oo1, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_add_on_diag(oo1, 1.0_dp)
CALL matrix_sqrt_Newton_Schulz(oo1_sqrt, &
oo1_sqrt_inv, &
oo1, &
!if cholesky is used then sqrt
!guess cannot be provided
!matrix_sqrt_inv_guess=cts_env%p_index_up,&
!matrix_sqrt_guess=cts_env%p_index_down,&
threshold=cts_env%eps_filter, &
order=cts_env%order_lanczos, &
eps_lanczos=cts_env%eps_lancsoz, &
max_iter_lanczos=cts_env%max_iter_lanczos)
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%p_index_up, &
oo1_sqrt_inv, 0.0_dp, oo1, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, oo1, &
cts_env%p_index_down, 0.0_dp, oo1_sqrt, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_release(oo1)
CALL dbcsr_release(oo1_sqrt_inv)
! bring x to contravariant-covariant representation now
CALL dbcsr_create(matrix_qp, &
template=cts_env%matrix_qp_template, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%q_index_up, &
cts_env%matrix_x, 0.0_dp, matrix_qp, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_qp, &
cts_env%p_index_down, 0.0_dp, &
cts_env%matrix_x, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_release(matrix_qp)
! update T=T+X or T=T+V.X (whichever is appropriate)
CALL dbcsr_create(t_corr, template=cts_env%matrix_t)
IF (cts_env%use_virt_orbs) THEN
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%matrix_v, &
cts_env%matrix_x, 0.0_dp, t_corr, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_add(cts_env%matrix_t, t_corr, &
1.0_dp, 1.0_dp)
ELSE
CALL dbcsr_add(cts_env%matrix_t, cts_env%matrix_x, &
1.0_dp, 1.0_dp)
END IF
! adjust T so the metric is preserved: T=(T+X).(1+tr(X).X)^(-1/2)
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%matrix_t, oo1_sqrt, &
0.0_dp, t_corr, filter_eps=cts_env%eps_filter)
CALL dbcsr_copy(cts_env%matrix_t, t_corr)
CALL dbcsr_release(t_corr)
CALL dbcsr_release(oo1_sqrt)
ELSE ! do not update p
IF (cts_env%tensor_type .EQ. tensor_orthogonal) THEN
! bring x to contravariant-covariant representation
CALL dbcsr_create(matrix_qp, &
template=cts_env%matrix_qp_template, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%q_index_up, &
cts_env%matrix_x, 0.0_dp, matrix_qp, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_qp, &
cts_env%p_index_down, 0.0_dp, &
cts_env%matrix_x, &
filter_eps=cts_env%eps_filter)
CALL dbcsr_release(matrix_qp)
END IF
END IF
ELSE
CPABORT("illegal occ option")
END IF
CALL timestop(handle)
END SUBROUTINE ct_step_execute
! **************************************************************************************************
!> \brief computes oo, ov, vo, and vv blocks of the ks matrix
!> \param ks ...
!> \param p ...
!> \param t ...
!> \param v ...
!> \param q_index_down ...
!> \param p_index_up ...
!> \param q_index_up ...
!> \param pp ...
!> \param qq ...
!> \param qp ...
!> \param pq ...
!> \param tensor_type ...
!> \param use_virt_orbs ...
!> \param eps_filter ...
!> \par History
!> 2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE assemble_ks_qp_blocks(ks, p, t, v, q_index_down, &
p_index_up, q_index_up, pp, qq, qp, pq, tensor_type, use_virt_orbs, eps_filter)
TYPE(dbcsr_type), INTENT(IN) :: ks, p, t, v, q_index_down, p_index_up, &
q_index_up
TYPE(dbcsr_type), INTENT(OUT) :: pp, qq, qp, pq
INTEGER, INTENT(IN) :: tensor_type
LOGICAL, INTENT(IN) :: use_virt_orbs
REAL(KIND=dp), INTENT(IN) :: eps_filter
CHARACTER(len=*), PARAMETER :: routineN = 'assemble_ks_qp_blocks'
INTEGER :: handle
LOGICAL :: library_fixed
TYPE(dbcsr_type) :: kst, ksv, no, on, oo, q_index_up_nosym, &
sp, spf, t_or, v_or
CALL timeset(routineN, handle)
IF (use_virt_orbs) THEN
! orthogonalize the orbitals
CALL dbcsr_create(t_or, template=t)
CALL dbcsr_create(v_or, template=v)
CALL dbcsr_multiply("N", "N", 1.0_dp, t, p_index_up, &
0.0_dp, t_or, filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, v, q_index_up, &
0.0_dp, v_or, filter_eps=eps_filter)
! KS.T
CALL dbcsr_create(kst, template=t)
CALL dbcsr_multiply("N", "N", 1.0_dp, ks, t_or, &
0.0_dp, kst, filter_eps=eps_filter)
! pp=tr(T)*KS.T
CALL dbcsr_multiply("T", "N", 1.0_dp, t_or, kst, &
0.0_dp, pp, filter_eps=eps_filter)
! qp=tr(V)*KS.T
CALL dbcsr_multiply("T", "N", 1.0_dp, v_or, kst, &
0.0_dp, qp, filter_eps=eps_filter)
CALL dbcsr_release(kst)
! KS.V
CALL dbcsr_create(ksv, template=v)
CALL dbcsr_multiply("N", "N", 1.0_dp, ks, v_or, &
0.0_dp, ksv, filter_eps=eps_filter)
! tr(T)*KS.V
CALL dbcsr_multiply("T", "N", 1.0_dp, t_or, ksv, &
0.0_dp, pq, filter_eps=eps_filter)
! tr(V)*KS.V
CALL dbcsr_multiply("T", "N", 1.0_dp, v_or, ksv, &
0.0_dp, qq, filter_eps=eps_filter)
CALL dbcsr_release(ksv)
CALL dbcsr_release(t_or)
CALL dbcsr_release(v_or)
ELSE ! no virtuals, use projected AOs
! THIS PROCEDURE HAS NOT BEEN UPDATED FOR CHOLESKY p/q_index_up/down
CALL dbcsr_create(sp, template=q_index_down, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(spf, template=q_index_down, &
matrix_type=dbcsr_type_no_symmetry)
! qp=KS*T
CALL dbcsr_multiply("N", "N", 1.0_dp, ks, t, 0.0_dp, qp, &
filter_eps=eps_filter)
! pp=tr(T)*KS.T
CALL dbcsr_multiply("T", "N", 1.0_dp, t, qp, 0.0_dp, pp, &
filter_eps=eps_filter)
! sp=-S_*P
CALL dbcsr_multiply("N", "N", -1.0_dp, q_index_down, p, 0.0_dp, sp, &
filter_eps=eps_filter)
! sp=1/S^-S_.P
SELECT CASE (tensor_type)
CASE (tensor_up_down)
CALL dbcsr_add_on_diag(sp, 1.0_dp)
CASE (tensor_orthogonal)
CALL dbcsr_create(q_index_up_nosym, template=q_index_up, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_desymmetrize(q_index_up, q_index_up_nosym)
CALL dbcsr_add(sp, q_index_up_nosym, 1.0_dp, 1.0_dp)
CALL dbcsr_release(q_index_up_nosym)
END SELECT
! spf=(1/S^-S_.P)*KS
CALL dbcsr_multiply("N", "N", 1.0_dp, sp, ks, 0.0_dp, spf, &
filter_eps=eps_filter)
! qp=spf*T
CALL dbcsr_multiply("N", "N", 1.0_dp, spf, t, 0.0_dp, qp, &
filter_eps=eps_filter)
SELECT CASE (tensor_type)
CASE (tensor_up_down)
! pq=tr(qp)
CALL dbcsr_transposed(pq, qp, transpose_distribution=.FALSE.)
CASE (tensor_orthogonal)
! pq=sig^.tr(qp)
CALL dbcsr_multiply("N", "T", 1.0_dp, p_index_up, qp, 0.0_dp, pq, &
filter_eps=eps_filter)
library_fixed = .FALSE.
IF (library_fixed) THEN
CALL dbcsr_transposed(qp, pq, transpose_distribution=.FALSE.)
ELSE
CALL dbcsr_create(no, template=qp, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, qp, p_index_up, 0.0_dp, no, &
filter_eps=eps_filter)
CALL dbcsr_copy(qp, no)
CALL dbcsr_release(no)
END IF
END SELECT
! qq=spf*tr(sp)
CALL dbcsr_multiply("N", "T", 1.0_dp, spf, sp, 0.0_dp, qq, &
filter_eps=eps_filter)
SELECT CASE (tensor_type)
CASE (tensor_up_down)
CALL dbcsr_create(oo, template=pp, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(no, template=qp, &
matrix_type=dbcsr_type_no_symmetry)
! first index up
CALL dbcsr_multiply("N", "N", 1.0_dp, q_index_up, qq, 0.0_dp, spf, &
filter_eps=eps_filter)
CALL dbcsr_copy(qq, spf)
CALL dbcsr_multiply("N", "N", 1.0_dp, q_index_up, qp, 0.0_dp, no, &
filter_eps=eps_filter)
CALL dbcsr_copy(qp, no)
CALL dbcsr_multiply("N", "N", 1.0_dp, p_index_up, pp, 0.0_dp, oo, &
filter_eps=eps_filter)
CALL dbcsr_copy(pp, oo)
CALL dbcsr_multiply("N", "N", 1.0_dp, p_index_up, pq, 0.0_dp, on, &
filter_eps=eps_filter)
CALL dbcsr_copy(pq, on)
CALL dbcsr_release(no)
CALL dbcsr_release(oo)
CASE (tensor_orthogonal)
CALL dbcsr_create(oo, template=pp, &
matrix_type=dbcsr_type_no_symmetry)
! both indeces up in the pp block
CALL dbcsr_multiply("N", "N", 1.0_dp, p_index_up, pp, 0.0_dp, oo, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, oo, p_index_up, 0.0_dp, pp, &
filter_eps=eps_filter)
CALL dbcsr_release(oo)
END SELECT
CALL dbcsr_release(sp)
CALL dbcsr_release(spf)
END IF
CALL timestop(handle)
END SUBROUTINE assemble_ks_qp_blocks
! **************************************************************************************************
!> \brief Solves the generalized Riccati or Sylvester eqation
!> using the preconditioned conjugate gradient algorithm
!> qp + qq.x.oo - vv.x.pp - vv.x.pq.x.oo = 0 [oo and vv are optional]
!> qp + qq.x - x.pp - x.pq.x = 0
!> \param pp ...
!> \param qq ...
!> \param qp ...
!> \param pq ...
!> \param oo ...
!> \param vv ...
!> \param x ...
!> \param res ...
!> \param neglect_quadratic_term ...
!> \param conjugator ...
!> \param max_iter ...
!> \param eps_convergence ...
!> \param eps_filter ...
!> \param converged ...
!> \par History
!> 2011.06 created [Rustam Z Khaliullin]
!> 2011.11 generalized [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
RECURSIVE SUBROUTINE solve_riccati_equation(pp, qq, qp, pq, oo, vv, x, res, &
neglect_quadratic_term, &
conjugator, max_iter, eps_convergence, eps_filter, &
converged)
TYPE(dbcsr_type), INTENT(IN) :: pp, qq
TYPE(dbcsr_type), INTENT(INOUT) :: qp
TYPE(dbcsr_type), INTENT(IN) :: pq
TYPE(dbcsr_type), INTENT(IN), OPTIONAL :: oo, vv
TYPE(dbcsr_type), INTENT(INOUT) :: x
TYPE(dbcsr_type), INTENT(OUT) :: res
LOGICAL, INTENT(IN) :: neglect_quadratic_term
INTEGER, INTENT(IN) :: conjugator, max_iter
REAL(KIND=dp), INTENT(IN) :: eps_convergence, eps_filter
LOGICAL, INTENT(OUT) :: converged
CHARACTER(len=*), PARAMETER :: routineN = 'solve_riccati_equation'
INTEGER :: handle, istep, iteration, nsteps, &
unit_nr, update_prec_freq
LOGICAL :: prepare_to_exit, present_oo, present_vv, &
quadratic_term, restart_conjugator
REAL(KIND=dp) :: best_norm, best_step_size, beta, c0, c1, &
c2, c3, denom, kappa, numer, &
obj_function, t1, t2, tau
REAL(KIND=dp), DIMENSION(3) :: step_size
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_type) :: aux1, aux2, grad, m, n, oo1, oo2, prec, &
res_trial, step, step_oo, vv_step
!TYPE(dbcsr_type) :: qqqq, pppp, zero_pq, zero_qp
CALL timeset(routineN, handle)
logger => cp_get_default_logger()
IF (logger%para_env%is_source()) THEN
unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
ELSE
unit_nr = -1
END IF
t1 = m_walltime()
!IF (level.gt.5) THEN
! CPErrorMessage(cp_failure_level,routineP,"recursion level is too high")
! CPPrecondition(.FALSE.,cp_failure_level,routineP,failure)
!ENDIF
!IF (unit_nr>0) THEN
! WRITE(unit_nr,*) &
! "========== LEVEL ",level,"=========="
!ENDIF
!CALL dbcsr_print(qq)
!CALL dbcsr_print(pp)
!CALL dbcsr_print(qp)
!!CALL dbcsr_print(pq)
!IF (unit_nr>0) THEN
! WRITE(unit_nr,*) &
! "====== END LEVEL ",level,"=========="
!ENDIF
quadratic_term = .NOT. neglect_quadratic_term
present_oo = PRESENT(oo)
present_vv = PRESENT(vv)
! create aux1 matrix and init
CALL dbcsr_create(aux1, template=pp)
CALL dbcsr_copy(aux1, pp)
CALL dbcsr_scale(aux1, -1.0_dp)
! create aux2 matrix and init
CALL dbcsr_create(aux2, template=qq)
CALL dbcsr_copy(aux2, qq)
! create the gradient matrix and init
CALL dbcsr_create(grad, template=x)
CALL dbcsr_set(grad, 0.0_dp)
! create a preconditioner
! RZK-warning how to apply it to up_down tensor?
CALL dbcsr_create(prec, template=x)
!CALL create_preconditioner(prec,aux1,aux2,qp,res,tensor_type,eps_filter)
!CALL dbcsr_set(prec,1.0_dp)
! create the step matrix and init
CALL dbcsr_create(step, template=x)
!CALL dbcsr_hadamard_product(prec,grad,step)
!CALL dbcsr_scale(step,-1.0_dp)
CALL dbcsr_create(n, template=x)
CALL dbcsr_create(m, template=x)
CALL dbcsr_create(oo1, template=pp)
CALL dbcsr_create(oo2, template=pp)
CALL dbcsr_create(res_trial, template=res)
CALL dbcsr_create(vv_step, template=res)
CALL dbcsr_create(step_oo, template=res)
! start conjugate gradient iterations
iteration = 0
converged = .FALSE.
prepare_to_exit = .FALSE.
beta = 0.0_dp
best_step_size = 0.0_dp
best_norm = 1.0E+100_dp
!ecorr=0.0_dp
!change_ecorr=0.0_dp
restart_conjugator = .FALSE.
update_prec_freq = 20
DO
! (re)-compute the residuals
IF (iteration .EQ. 0) THEN
CALL dbcsr_copy(res, qp)
IF (present_oo) THEN
CALL dbcsr_multiply("N", "N", +1.0_dp, qq, x, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", +1.0_dp, res_trial, oo, 1.0_dp, res, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", +1.0_dp, qq, x, 1.0_dp, res, &
filter_eps=eps_filter)
END IF
IF (present_vv) THEN
CALL dbcsr_multiply("N", "N", -1.0_dp, x, pp, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", +1.0_dp, vv, res_trial, 1.0_dp, res, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", -1.0_dp, x, pp, 1.0_dp, res, &
filter_eps=eps_filter)
END IF
IF (quadratic_term) THEN
IF (present_oo) THEN
CALL dbcsr_multiply("N", "N", +1.0_dp, pq, x, 0.0_dp, oo1, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", +1.0_dp, oo1, oo, 0.0_dp, oo2, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", +1.0_dp, pq, x, 0.0_dp, oo2, &
filter_eps=eps_filter)
END IF
IF (present_vv) THEN
CALL dbcsr_multiply("N", "N", -1.0_dp, x, oo2, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", +1.0_dp, vv, res_trial, 1.0_dp, res, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", -1.0_dp, x, oo2, 1.0_dp, res, &
filter_eps=eps_filter)
END IF
END IF
CALL dbcsr_norm(res, dbcsr_norm_maxabsnorm, norm_scalar=best_norm)
ELSE
CALL dbcsr_add(res, m, 1.0_dp, best_step_size)
CALL dbcsr_add(res, n, 1.0_dp, -best_step_size*best_step_size)
CALL dbcsr_filter(res, eps_filter)
END IF
! check convergence and other exit criteria
converged = (best_norm .LT. eps_convergence)
IF (converged .OR. (iteration .GE. max_iter)) THEN
prepare_to_exit = .TRUE.
END IF
IF (.NOT. prepare_to_exit) THEN
! update aux1=-pp-pq.x.oo and aux2=qq-vv.x.pq
IF (quadratic_term) THEN
IF (iteration .EQ. 0) THEN
IF (present_oo) THEN
CALL dbcsr_multiply("N", "N", -1.0_dp, pq, x, 0.0_dp, oo1, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", +1.0_dp, oo1, oo, 1.0_dp, aux1, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", -1.0_dp, pq, x, 1.0_dp, aux1, &
filter_eps=eps_filter)
END IF
IF (present_vv) THEN
CALL dbcsr_multiply("N", "N", -1.0_dp, vv, x, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", +1.0_dp, res_trial, pq, 1.0_dp, aux2, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", -1.0_dp, x, pq, 1.0_dp, aux2, &
filter_eps=eps_filter)
END IF
ELSE
IF (present_oo) THEN
CALL dbcsr_multiply("N", "N", -best_step_size, pq, step_oo, 1.0_dp, aux1, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", -best_step_size, pq, step, 1.0_dp, aux1, &
filter_eps=eps_filter)
END IF
IF (present_vv) THEN
CALL dbcsr_multiply("N", "N", -best_step_size, vv_step, pq, 1.0_dp, aux2, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", -best_step_size, step, pq, 1.0_dp, aux2, &
filter_eps=eps_filter)
END IF
END IF
END IF
! recompute the gradient, do not update it yet
! use m matrix as a temporary storage
! grad=t(vv).res.t(aux1)+t(aux2).res.t(oo)
IF (present_vv) THEN
CALL dbcsr_multiply("N", "T", 1.0_dp, res, aux1, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("T", "N", 1.0_dp, vv, res_trial, 0.0_dp, m, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "T", 1.0_dp, res, aux1, 0.0_dp, m, &
filter_eps=eps_filter)
END IF
IF (present_oo) THEN
CALL dbcsr_multiply("T", "N", 1.0_dp, aux1, res, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "T", 1.0_dp, res_trial, oo, 1.0_dp, m, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("T", "N", 1.0_dp, aux2, res, 1.0_dp, m, &
filter_eps=eps_filter)
END IF
! compute preconditioner
!IF (iteration.eq.0.OR.(mod(iteration,update_prec_freq).eq.0)) THEN
IF (iteration .EQ. 0) THEN
CALL create_preconditioner(prec, aux1, aux2, eps_filter)
!restart_conjugator=.TRUE.
!CALL dbcsr_set(prec,1.0_dp)
!CALL dbcsr_print(prec)
END IF
! compute the conjugation coefficient - beta
IF ((iteration .EQ. 0) .OR. restart_conjugator) THEN
beta = 0.0_dp
ELSE
restart_conjugator = .FALSE.
SELECT CASE (conjugator)
CASE (cg_hestenes_stiefel)
CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
CALL dbcsr_hadamard_product(prec, grad, n)
CALL dbcsr_dot(n, m, numer)
CALL dbcsr_dot(grad, step, denom)
beta = numer/denom
CASE (cg_fletcher_reeves)
CALL dbcsr_hadamard_product(prec, grad, n)
CALL dbcsr_dot(grad, n, denom)
CALL dbcsr_hadamard_product(prec, m, n)
CALL dbcsr_dot(m, n, numer)
beta = numer/denom
CASE (cg_polak_ribiere)
CALL dbcsr_hadamard_product(prec, grad, n)
CALL dbcsr_dot(grad, n, denom)
CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
CALL dbcsr_hadamard_product(prec, grad, n)
CALL dbcsr_dot(n, m, numer)
beta = numer/denom
CASE (cg_fletcher)
CALL dbcsr_hadamard_product(prec, m, n)
CALL dbcsr_dot(m, n, numer)
CALL dbcsr_dot(grad, step, denom)
beta = -1.0_dp*numer/denom
CASE (cg_liu_storey)
CALL dbcsr_dot(grad, step, denom)
CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
CALL dbcsr_hadamard_product(prec, grad, n)
CALL dbcsr_dot(n, m, numer)
beta = -1.0_dp*numer/denom
CASE (cg_dai_yuan)
CALL dbcsr_hadamard_product(prec, m, n)
CALL dbcsr_dot(m, n, numer)
CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
CALL dbcsr_dot(grad, step, denom)
beta = numer/denom
CASE (cg_hager_zhang)
CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
CALL dbcsr_dot(grad, step, denom)
CALL dbcsr_hadamard_product(prec, grad, n)
CALL dbcsr_dot(n, grad, numer)
kappa = 2.0_dp*numer/denom
CALL dbcsr_dot(n, m, numer)
tau = numer/denom
CALL dbcsr_dot(step, m, numer)
beta = tau - kappa*numer/denom
CASE (cg_zero)
beta = 0.0_dp
CASE DEFAULT
CPABORT("illegal conjugator")
END SELECT
END IF ! iteration.eq.0
! move the current gradient to its storage
CALL dbcsr_copy(grad, m)
! precondition new gradient (use m as tmp storage)
CALL dbcsr_hadamard_product(prec, grad, m)
CALL dbcsr_filter(m, eps_filter)
! recompute the step direction
CALL dbcsr_add(step, m, beta, -1.0_dp)
CALL dbcsr_filter(step, eps_filter)
!! ALTERNATIVE METHOD TO OBTAIN THE STEP FROM THE GRADIENT
!CALL dbcsr_init(qqqq)
!CALL dbcsr_create(qqqq,template=qq)
!CALL dbcsr_init(pppp)
!CALL dbcsr_create(pppp,template=pp)
!CALL dbcsr_init(zero_pq)
!CALL dbcsr_create(zero_pq,template=pq)
!CALL dbcsr_init(zero_qp)
!CALL dbcsr_create(zero_qp,template=qp)
!CALL dbcsr_multiply("T","N",1.0_dp,aux2,aux2,0.0_dp,qqqq,&
! filter_eps=eps_filter)
!CALL dbcsr_multiply("N","T",-1.0_dp,aux1,aux1,0.0_dp,pppp,&
! filter_eps=eps_filter)
!CALL dbcsr_set(zero_qp,0.0_dp)
!CALL dbcsr_set(zero_pq,0.0_dp)
!CALL solve_riccati_equation(pppp,qqqq,grad,zero_pq,zero_qp,zero_qp,&
! .TRUE.,tensor_type,&
! conjugator,max_iter,eps_convergence,eps_filter,&
! converged,level+1)
!CALL dbcsr_release(qqqq)
!CALL dbcsr_release(pppp)
!CALL dbcsr_release(zero_qp)
!CALL dbcsr_release(zero_pq)
! calculate the optimal step size
! m=step.aux1+aux2.step
IF (present_vv) THEN
CALL dbcsr_multiply("N", "N", 1.0_dp, vv, step, 0.0_dp, vv_step, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, vv_step, aux1, 0.0_dp, m, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", 1.0_dp, step, aux1, 0.0_dp, m, &
filter_eps=eps_filter)
END IF
IF (present_oo) THEN
CALL dbcsr_multiply("N", "N", 1.0_dp, step, oo, 0.0_dp, step_oo, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, aux2, step_oo, 1.0_dp, m, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", 1.0_dp, aux2, step, 1.0_dp, m, &
filter_eps=eps_filter)
END IF
IF (quadratic_term) THEN
! n=step.pq.step
IF (present_oo) THEN
CALL dbcsr_multiply("N", "N", 1.0_dp, pq, step, 0.0_dp, oo1, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, oo1, oo, 0.0_dp, oo2, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", 1.0_dp, pq, step, 0.0_dp, oo2, &
filter_eps=eps_filter)
END IF
IF (present_vv) THEN
CALL dbcsr_multiply("N", "N", 1.0_dp, step, oo2, 0.0_dp, res_trial, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, vv, res_trial, 0.0_dp, n, &
filter_eps=eps_filter)
ELSE
CALL dbcsr_multiply("N", "N", 1.0_dp, step, oo2, 0.0_dp, n, &
filter_eps=eps_filter)
END IF
ELSE
CALL dbcsr_set(n, 0.0_dp)
END IF
! calculate coefficients of the cubic eq for alpha - step size
c0 = 2.0_dp*(dbcsr_frobenius_norm(n))**2
CALL dbcsr_dot(m, n, c1)
c1 = -3.0_dp*c1
CALL dbcsr_dot(res, n, c2)
c2 = -2.0_dp*c2 + (dbcsr_frobenius_norm(m))**2
CALL dbcsr_dot(res, m, c3)
! find step size
CALL analytic_line_search(c0, c1, c2, c3, step_size, nsteps)
IF (nsteps .EQ. 0) THEN
CPABORT("no step sizes!")
END IF
! if we have several possible step sizes
! choose one with the lowest objective function
best_norm = 1.0E+100_dp
best_step_size = 0.0_dp
DO istep = 1, nsteps
! recompute the residues
CALL dbcsr_copy(res_trial, res)
CALL dbcsr_add(res_trial, m, 1.0_dp, step_size(istep))
CALL dbcsr_add(res_trial, n, 1.0_dp, -step_size(istep)*step_size(istep))
CALL dbcsr_filter(res_trial, eps_filter)
! RZK-warning objective function might be different in the case of
! tensor_up_down
!obj_function=0.5_dp*(dbcsr_frobenius_norm(res_trial))**2
CALL dbcsr_norm(res_trial, dbcsr_norm_maxabsnorm, norm_scalar=obj_function)
IF (obj_function .LT. best_norm) THEN
best_norm = obj_function
best_step_size = step_size(istep)
END IF
END DO
END IF
! update X along the line
CALL dbcsr_add(x, step, 1.0_dp, best_step_size)
CALL dbcsr_filter(x, eps_filter)
! evaluate current energy correction
!change_ecorr=ecorr
!CALL dbcsr_dot(qp,x,ecorr,"T","N")
!change_ecorr=ecorr-change_ecorr
! check convergence and other exit criteria
converged = (best_norm .LT. eps_convergence)
IF (converged .OR. (iteration .GE. max_iter)) THEN
prepare_to_exit = .TRUE.
END IF
t2 = m_walltime()
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T6,A,1X,I4,1X,E12.3,F8.3)') &
"RICCATI iter ", iteration, best_norm, t2 - t1
!WRITE(unit_nr,'(T6,A,1X,I4,1X,F15.9,F15.9,E12.3,F8.3)') &
! "RICCATI iter ",iteration,ecorr,change_ecorr,best_norm,t2-t1
END IF
t1 = m_walltime()
iteration = iteration + 1
IF (prepare_to_exit) EXIT
END DO
CALL dbcsr_release(aux1)
CALL dbcsr_release(aux2)
CALL dbcsr_release(grad)
CALL dbcsr_release(step)
CALL dbcsr_release(n)
CALL dbcsr_release(m)
CALL dbcsr_release(oo1)
CALL dbcsr_release(oo2)
CALL dbcsr_release(res_trial)
CALL dbcsr_release(vv_step)
CALL dbcsr_release(step_oo)
CALL timestop(handle)
END SUBROUTINE solve_riccati_equation
! **************************************************************************************************
!> \brief Computes a preconditioner from diagonal elements of ~f_oo, ~f_vv
!> The preconditioner is approximately equal to
!> prec_ai ~ (e_a - e_i)^(-2)
!> However, the real expression is more complex
!> \param prec ...
!> \param pp ...
!> \param qq ...
!> \param eps_filter ...
!> \par History
!> 2011.07 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE create_preconditioner(prec, pp, qq, eps_filter)
TYPE(dbcsr_type), INTENT(OUT) :: prec
TYPE(dbcsr_type), INTENT(IN) :: pp, qq
REAL(KIND=dp), INTENT(IN) :: eps_filter
CHARACTER(len=*), PARAMETER :: routineN = 'create_preconditioner'
INTEGER :: col, handle, hold, iblock_col, &
iblock_row, mynode, nblkcols_tot, &
nblkrows_tot, p_nrows, q_nrows, row
LOGICAL :: tr
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: p_diagonal, q_diagonal
REAL(KIND=dp), DIMENSION(:, :), POINTER :: p_new_block
TYPE(dbcsr_distribution_type) :: dist
TYPE(dbcsr_type) :: pp_diag, qq_diag, t1, t2, tmp
!LOGICAL, INTENT(IN) :: use_virt_orbs
CALL timeset(routineN, handle)
! ! copy diagonal elements
! CALL dbcsr_get_info(pp,nfullrows_total=nrows)
! CALL dbcsr_init(pp_diag)
! CALL dbcsr_create(pp_diag,template=pp)
! ALLOCATE(diagonal(nrows))
! CALL dbcsr_get_diag(pp,diagonal)
! CALL dbcsr_add_on_diag(pp_diag,1.0_dp)
! CALL dbcsr_set_diag(pp_diag,diagonal)
! DEALLOCATE(diagonal)
!
! initialize a matrix to 1.0
CALL dbcsr_create(tmp, template=prec)
! use an ugly hack to set all elements of tmp to 1
! because dbcsr_set does not do it (despite its name)
!CALL dbcsr_set(tmp,1.0_dp)
CALL dbcsr_get_info(tmp, distribution=dist)
CALL dbcsr_distribution_get(dist, mynode=mynode)
CALL dbcsr_work_create(tmp, work_mutable=.TRUE.)
nblkrows_tot = dbcsr_nblkrows_total(tmp)
nblkcols_tot = dbcsr_nblkcols_total(tmp)
DO row = 1, nblkrows_tot
DO col = 1, nblkcols_tot
tr = .FALSE.
iblock_row = row
iblock_col = col
CALL dbcsr_get_stored_coordinates(tmp, iblock_row, iblock_col, hold)
IF (hold .EQ. mynode) THEN
NULLIFY (p_new_block)
CALL dbcsr_reserve_block2d(tmp, iblock_row, iblock_col, p_new_block)
CPASSERT(ASSOCIATED(p_new_block))
p_new_block(:, :) = 1.0_dp
END IF ! mynode
END DO
END DO
CALL dbcsr_finalize(tmp)
! copy diagonal elements of pp into cols of a matrix
CALL dbcsr_get_info(pp, nfullrows_total=p_nrows)
CALL dbcsr_create(pp_diag, template=pp)
ALLOCATE (p_diagonal(p_nrows))
CALL dbcsr_get_diag(pp, p_diagonal)
CALL dbcsr_add_on_diag(pp_diag, 1.0_dp)
CALL dbcsr_set_diag(pp_diag, p_diagonal)
! RZK-warning is it possible to use dbcsr_scale_by_vector?
! or even insert elements directly in the prev cycles
CALL dbcsr_create(t2, template=prec)
CALL dbcsr_multiply("N", "N", 1.0_dp, tmp, pp_diag, &
0.0_dp, t2, filter_eps=eps_filter)
! copy diagonal elements qq into rows of a matrix
CALL dbcsr_get_info(qq, nfullrows_total=q_nrows)
CALL dbcsr_create(qq_diag, template=qq)
ALLOCATE (q_diagonal(q_nrows))
CALL dbcsr_get_diag(qq, q_diagonal)
CALL dbcsr_add_on_diag(qq_diag, 1.0_dp)
CALL dbcsr_set_diag(qq_diag, q_diagonal)
CALL dbcsr_set(tmp, 1.0_dp)
CALL dbcsr_create(t1, template=prec)
CALL dbcsr_multiply("N", "N", 1.0_dp, qq_diag, tmp, &
0.0_dp, t1, filter_eps=eps_filter)
CALL dbcsr_hadamard_product(t1, t2, prec)
CALL dbcsr_release(t1)
CALL dbcsr_scale(prec, 2.0_dp)
! Get the diagonal of tr(qq).qq
CALL dbcsr_multiply("T", "N", 1.0_dp, qq, qq, &
0.0_dp, qq_diag, retain_sparsity=.TRUE., &
filter_eps=eps_filter)
CALL dbcsr_get_diag(qq_diag, q_diagonal)
CALL dbcsr_set(qq_diag, 0.0_dp)
CALL dbcsr_add_on_diag(qq_diag, 1.0_dp)
CALL dbcsr_set_diag(qq_diag, q_diagonal)
DEALLOCATE (q_diagonal)
CALL dbcsr_set(tmp, 1.0_dp)
CALL dbcsr_multiply("N", "N", 1.0_dp, qq_diag, tmp, &
0.0_dp, t2, filter_eps=eps_filter)
CALL dbcsr_release(qq_diag)
CALL dbcsr_add(prec, t2, 1.0_dp, 1.0_dp)
! Get the diagonal of pp.tr(pp)
CALL dbcsr_multiply("N", "T", 1.0_dp, pp, pp, &
0.0_dp, pp_diag, retain_sparsity=.TRUE., &
filter_eps=eps_filter)
CALL dbcsr_get_diag(pp_diag, p_diagonal)
CALL dbcsr_set(pp_diag, 0.0_dp)
CALL dbcsr_add_on_diag(pp_diag, 1.0_dp)
CALL dbcsr_set_diag(pp_diag, p_diagonal)
DEALLOCATE (p_diagonal)
CALL dbcsr_set(tmp, 1.0_dp)
CALL dbcsr_multiply("N", "N", 1.0_dp, tmp, pp_diag, &
0.0_dp, t2, filter_eps=eps_filter)
CALL dbcsr_release(tmp)
CALL dbcsr_release(pp_diag)
CALL dbcsr_add(prec, t2, 1.0_dp, 1.0_dp)
! now add the residual component
!CALL dbcsr_hadamard_product(res,qp,t2)
!CALL dbcsr_add(prec,t2,1.0_dp,-2.0_dp)
CALL dbcsr_release(t2)
CALL dbcsr_function_of_elements(prec, func=dbcsr_func_inverse)
CALL dbcsr_filter(prec, eps_filter)
CALL timestop(handle)
END SUBROUTINE create_preconditioner
! **************************************************************************************************
!> \brief Finds real roots of a cubic equation
!> > a*x**3 + b*x**2 + c*x + d = 0
!> and returns only those roots for which the derivative is positive
!>
!> Step 0: Check the true order of the equation. Cubic, quadratic, linear?
!> Step 1: Calculate p and q
!> p = ( 3*c/a - (b/a)**2 ) / 3
!> q = ( 2*(b/a)**3 - 9*b*c/a/a + 27*d/a ) / 27
!> Step 2: Calculate discriminant D
!> D = (p/3)**3 + (q/2)**2
!> Step 3: Depending on the sign of D, we follow different strategy.
!> If D<0, three distinct real roots.
!> If D=0, three real roots of which at least two are equal.
!> If D>0, one real and two complex roots.
!> Step 3a: For D>0 and D=0,
!> Calculate u and v
!> u = cubic_root(-q/2 + sqrt(D))
!> v = cubic_root(-q/2 - sqrt(D))
!> Find the three transformed roots
!> y1 = u + v
!> y2 = -(u+v)/2 + i (u-v)*sqrt(3)/2
!> y3 = -(u+v)/2 - i (u-v)*sqrt(3)/2
!> Step 3b Alternately, for D<0, a trigonometric formulation is more convenient
!> y1 = 2 * sqrt(|p|/3) * cos(phi/3)
!> y2 = -2 * sqrt(|p|/3) * cos((phi+pi)/3)
!> y3 = -2 * sqrt(|p|/3) * cos((phi-pi)/3)
!> where phi = acos(-q/2/sqrt(|p|**3/27))
!> pi = 3.141592654...
!> Step 4 Find the real roots
!> x = y - b/a/3
!> Step 5 Check the derivative and return only those real roots
!> for which the derivative is positive
!>
!> \param a ...
!> \param b ...
!> \param c ...
!> \param d ...
!> \param minima ...
!> \param nmins ...
!> \par History
!> 2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE analytic_line_search(a, b, c, d, minima, nmins)
REAL(KIND=dp), INTENT(IN) :: a, b, c, d
REAL(KIND=dp), DIMENSION(3), INTENT(OUT) :: minima
INTEGER, INTENT(OUT) :: nmins
INTEGER :: i, nroots
REAL(KIND=dp) :: DD, der, p, phi, pi, q, temp1, temp2, u, &
v, y1, y2, y2i, y2r, y3
REAL(KIND=dp), DIMENSION(3) :: x
! CALL timeset(routineN,handle)
pi = ACOS(-1.0_dp)
! Step 0: Check coefficients and find the true order of the eq
IF (a .EQ. 0.0_dp) THEN
IF (b .EQ. 0.0_dp) THEN
IF (c .EQ. 0.0_dp) THEN
! Non-equation, no valid solutions
nroots = 0
ELSE
! Linear equation with one root.
nroots = 1
x(1) = -d/c
END IF
ELSE
! Quadratic equation with max two roots.
DD = c*c - 4.0_dp*b*d
IF (DD .GT. 0.0_dp) THEN
nroots = 2
x(1) = (-c + SQRT(DD))/2.0_dp/b
x(2) = (-c - SQRT(DD))/2.0_dp/b
ELSE IF (DD .LT. 0.0_dp) THEN
nroots = 0
ELSE
nroots = 1
x(1) = -c/2.0_dp/b
END IF
END IF
ELSE
! Cubic equation with max three roots
! Calculate p and q
p = c/a - b*b/a/a/3.0_dp
q = (2.0_dp*b*b*b/a/a/a - 9.0_dp*b*c/a/a + 27.0_dp*d/a)/27.0_dp
! Calculate DD
DD = p*p*p/27.0_dp + q*q/4.0_dp
IF (DD .LT. 0.0_dp) THEN
! three real unequal roots -- use the trigonometric formulation
phi = ACOS(-q/2.0_dp/SQRT(ABS(p*p*p)/27.0_dp))
temp1 = 2.0_dp*SQRT(ABS(p)/3.0_dp)
y1 = temp1*COS(phi/3.0_dp)
y2 = -temp1*COS((phi + pi)/3.0_dp)
y3 = -temp1*COS((phi - pi)/3.0_dp)
ELSE
! 1 real & 2 conjugate complex roots OR 3 real roots (some are equal)
temp1 = -q/2.0_dp + SQRT(DD)
temp2 = -q/2.0_dp - SQRT(DD)
u = ABS(temp1)**(1.0_dp/3.0_dp)
v = ABS(temp2)**(1.0_dp/3.0_dp)
IF (temp1 .LT. 0.0_dp) u = -u
IF (temp2 .LT. 0.0_dp) v = -v
y1 = u + v
y2r = -(u + v)/2.0_dp
y2i = (u - v)*SQRT(3.0_dp)/2.0_dp
END IF
! Final transformation
temp1 = b/a/3.0_dp
y1 = y1 - temp1
y2 = y2 - temp1
y3 = y3 - temp1
y2r = y2r - temp1
! Assign answers
IF (DD .LT. 0.0_dp) THEN
nroots = 3
x(1) = y1
x(2) = y2
x(3) = y3
ELSE IF (DD .EQ. 0.0_dp) THEN
nroots = 2
x(1) = y1
x(2) = y2r
!x(3) = cmplx(y2r, 0.)
ELSE
nroots = 1
x(1) = y1
!x(2) = cmplx(y2r, y2i)
!x(3) = cmplx(y2r,-y2i)
END IF
END IF
!write(*,'(i2,a)') nroots, ' real root(s)'
nmins = 0
DO i = 1, nroots
! maximum or minimum? use the derivative
! 3*a*x**2+2*b*x+c
der = 3.0_dp*a*x(i)*x(i) + 2.0_dp*b*x(i) + c
IF (der .GT. 0.0_dp) THEN
nmins = nmins + 1
minima(nmins) = x(i)
!write(*,'(a,i2,a,f10.5)') 'Minimum ', i, ', value: ', x(i)
END IF
END DO
! CALL timestop(handle)
END SUBROUTINE analytic_line_search
! **************************************************************************************************
!> \brief Diagonalizes diagonal blocks of a symmetric dbcsr matrix
!> and returs its eigenvectors
!> \param matrix ...
!> \param c ...
!> \param e ...
!> \par History
!> 2011.07 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE diagonalize_diagonal_blocks(matrix, c, e)
TYPE(dbcsr_type), INTENT(IN) :: matrix
TYPE(dbcsr_type), INTENT(OUT) :: c
TYPE(dbcsr_type), INTENT(OUT), OPTIONAL :: e
CHARACTER(len=*), PARAMETER :: routineN = 'diagonalize_diagonal_blocks'
INTEGER :: handle, iblock_col, iblock_row, &
iblock_size, info, lwork, orbital
LOGICAL :: block_needed, do_eigenvalues
REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: eigenvalues, work
REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: data_copy
REAL(kind=dp), DIMENSION(:, :), POINTER :: data_p, p_new_block
TYPE(dbcsr_iterator_type) :: iter
CALL timeset(routineN, handle)
IF (PRESENT(e)) THEN
do_eigenvalues = .TRUE.
ELSE
do_eigenvalues = .FALSE.
END IF
! create a matrix for eigenvectors
CALL dbcsr_work_create(c, work_mutable=.TRUE.)
IF (do_eigenvalues) &
CALL dbcsr_work_create(e, work_mutable=.TRUE.)
CALL dbcsr_iterator_start(iter, matrix)
DO WHILE (dbcsr_iterator_blocks_left(iter))
CALL dbcsr_iterator_next_block(iter, iblock_row, iblock_col, data_p, row_size=iblock_size)
block_needed = .FALSE.
IF (iblock_row == iblock_col) block_needed = .TRUE.
IF (block_needed) THEN
! Prepare data
ALLOCATE (eigenvalues(iblock_size))
ALLOCATE (data_copy(iblock_size, iblock_size))
data_copy(:, :) = data_p(:, :)
! Query the optimal workspace for dsyev
LWORK = -1
ALLOCATE (WORK(MAX(1, LWORK)))
CALL DSYEV('V', 'L', iblock_size, data_copy, iblock_size, eigenvalues, WORK, LWORK, INFO)
LWORK = INT(WORK(1))
DEALLOCATE (WORK)
! Allocate the workspace and solve the eigenproblem
ALLOCATE (WORK(MAX(1, LWORK)))
CALL DSYEV('V', 'L', iblock_size, data_copy, iblock_size, eigenvalues, WORK, LWORK, INFO)
IF (INFO .NE. 0) THEN
CPABORT("DSYEV failed")
END IF
! copy eigenvectors into a cp_dbcsr matrix
NULLIFY (p_new_block)
CALL dbcsr_reserve_block2d(c, iblock_row, iblock_col, p_new_block)
CPASSERT(ASSOCIATED(p_new_block))
p_new_block(:, :) = data_copy(:, :)
! if requested copy eigenvalues into a cp_dbcsr matrix
IF (do_eigenvalues) THEN
NULLIFY (p_new_block)
CALL dbcsr_reserve_block2d(e, iblock_row, iblock_col, p_new_block)
CPASSERT(ASSOCIATED(p_new_block))
p_new_block(:, :) = 0.0_dp
DO orbital = 1, iblock_size
p_new_block(orbital, orbital) = eigenvalues(orbital)
END DO
END IF
DEALLOCATE (WORK)
DEALLOCATE (data_copy)
DEALLOCATE (eigenvalues)
END IF
END DO
CALL dbcsr_iterator_stop(iter)
CALL dbcsr_finalize(c)
IF (do_eigenvalues) CALL dbcsr_finalize(e)
CALL timestop(handle)
END SUBROUTINE diagonalize_diagonal_blocks
! **************************************************************************************************
!> \brief Transforms a matrix M_out = tr(U1) * M_in * U2
!> \param matrix ...
!> \param u1 ...
!> \param u2 ...
!> \param eps_filter ...
!> \par History
!> 2011.10 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE matrix_forward_transform(matrix, u1, u2, eps_filter)
TYPE(dbcsr_type), INTENT(INOUT) :: matrix
TYPE(dbcsr_type), INTENT(IN) :: u1, u2
REAL(KIND=dp), INTENT(IN) :: eps_filter
CHARACTER(len=*), PARAMETER :: routineN = 'matrix_forward_transform'
INTEGER :: handle
TYPE(dbcsr_type) :: tmp
CALL timeset(routineN, handle)
CALL dbcsr_create(tmp, template=matrix, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix, u2, 0.0_dp, tmp, &
filter_eps=eps_filter)
CALL dbcsr_multiply("T", "N", 1.0_dp, u1, tmp, 0.0_dp, matrix, &
filter_eps=eps_filter)
CALL dbcsr_release(tmp)
CALL timestop(handle)
END SUBROUTINE matrix_forward_transform
! **************************************************************************************************
!> \brief Transforms a matrix M_out = U1 * M_in * tr(U2)
!> \param matrix ...
!> \param u1 ...
!> \param u2 ...
!> \param eps_filter ...
!> \par History
!> 2011.10 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
SUBROUTINE matrix_backward_transform(matrix, u1, u2, eps_filter)
TYPE(dbcsr_type), INTENT(INOUT) :: matrix
TYPE(dbcsr_type), INTENT(IN) :: u1, u2
REAL(KIND=dp), INTENT(IN) :: eps_filter
CHARACTER(len=*), PARAMETER :: routineN = 'matrix_backward_transform'
INTEGER :: handle
TYPE(dbcsr_type) :: tmp
CALL timeset(routineN, handle)
CALL dbcsr_create(tmp, template=matrix, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "T", 1.0_dp, matrix, u2, 0.0_dp, tmp, &
filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, u1, tmp, 0.0_dp, matrix, &
filter_eps=eps_filter)
CALL dbcsr_release(tmp)
CALL timestop(handle)
END SUBROUTINE matrix_backward_transform
!! **************************************************************************************************
!!> \brief Transforms to a representation in which diagonal blocks
!!> of qq and pp matrices are diagonal. This can improve convergence
!!> of PCG
!!> \par History
!!> 2011.07 created [Rustam Z Khaliullin]
!!> \author Rustam Z Khaliullin
!! **************************************************************************************************
! SUBROUTINE transform_matrices_to_blk_diag(matrix_pp,matrix_qq,matrix_qp,&
! matrix_pq,eps_filter)
!
! TYPE(dbcsr_type), INTENT(INOUT) :: matrix_pp, matrix_qq,&
! matrix_qp, matrix_pq
! REAL(KIND=dp), INTENT(IN) :: eps_filter
!
! CHARACTER(len=*), PARAMETER :: routineN = 'transform_matrices_to_blk_diag',&
! routineP = moduleN//':'//routineN
!
! TYPE(dbcsr_type) :: tmp_pp, tmp_qq,&
! tmp_qp, tmp_pq,&
! blk, blk2
! INTEGER :: handle
!
! CALL timeset(routineN,handle)
!
! ! find a better basis by diagonalizing diagonal blocks
! ! first pp
! CALL dbcsr_init(blk)
! CALL dbcsr_create(blk,template=matrix_pp)
! CALL diagonalize_diagonal_blocks(matrix_pp,blk)
!
! ! convert matrices to the new basis
! CALL dbcsr_init(tmp_pp)
! CALL dbcsr_create(tmp_pp,template=matrix_pp)
! CALL dbcsr_multiply("N","N",1.0_dp,matrix_pp,blk,0.0_dp,tmp_pp,&
! filter_eps=eps_filter)
! CALL dbcsr_multiply("T","N",1.0_dp,blk,tmp_pp,0.0_dp,matrix_pp,&
! filter_eps=eps_filter)
! CALL dbcsr_release(tmp_pp)
!
! ! now qq
! CALL dbcsr_init(blk2)
! CALL dbcsr_create(blk2,template=matrix_qq)
! CALL diagonalize_diagonal_blocks(matrix_qq,blk2)
!
! CALL dbcsr_init(tmp_qq)
! CALL dbcsr_create(tmp_qq,template=matrix_qq)
! CALL dbcsr_multiply("N","N",1.0_dp,matrix_qq,blk2,0.0_dp,tmp_qq,&
! filter_eps=eps_filter)
! CALL dbcsr_multiply("T","N",1.0_dp,blk2,tmp_qq,0.0_dp,matrix_qq,&
! filter_eps=eps_filter)
! CALL dbcsr_release(tmp_qq)
!
! ! transform pq
! CALL dbcsr_init(tmp_pq)
! CALL dbcsr_create(tmp_pq,template=matrix_pq)
! CALL dbcsr_multiply("T","N",1.0_dp,blk,matrix_pq,0.0_dp,tmp_pq,&
! filter_eps=eps_filter)
! CALL dbcsr_multiply("N","N",1.0_dp,tmp_pq,blk2,0.0_dp,matrix_pq,&
! filter_eps=eps_filter)
! CALL dbcsr_release(tmp_pq)
!
! ! transform qp
! CALL dbcsr_init(tmp_qp)
! CALL dbcsr_create(tmp_qp,template=matrix_qp)
! CALL dbcsr_multiply("N","N",1.0_dp,matrix_qp,blk,0.0_dp,tmp_qp,&
! filter_eps=eps_filter)
! CALL dbcsr_multiply("T","N",1.0_dp,blk2,tmp_qp,0.0_dp,matrix_qp,&
! filter_eps=eps_filter)
! CALL dbcsr_release(tmp_qp)
!
! CALL dbcsr_release(blk2)
! CALL dbcsr_release(blk)
!
! CALL timestop(handle)
!
! END SUBROUTINE transform_matrices_to_blk_diag
! **************************************************************************************************
!> \brief computes oo, ov, vo, and vv blocks of the ks matrix
!> \par History
!> 2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
! SUBROUTINE ct_step_env_execute(env)
!
! TYPE(ct_step_env_type) :: env
!
! CHARACTER(len=*), PARAMETER :: routineN = 'ct_step_env_execute', &
! routineP = moduleN//':'//routineN
!
! INTEGER :: handle
!
! CALL timeset(routineN,handle)
!
!
! CALL timestop(handle)
!
! END SUBROUTINE ct_step_env_execute
END MODULE ct_methods
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