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dm_ls_scf_curvy.F
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dm_ls_scf_curvy.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 density matrix optimization using exponential transformations
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
MODULE dm_ls_scf_curvy
USE bibliography, ONLY: Shao2003,&
cite_reference
USE cp_dbcsr_api, ONLY: &
dbcsr_add, dbcsr_copy, dbcsr_create, dbcsr_dot, dbcsr_filter, dbcsr_frobenius_norm, &
dbcsr_multiply, dbcsr_norm, dbcsr_release, dbcsr_scale, dbcsr_set, dbcsr_transposed, &
dbcsr_type, dbcsr_type_no_symmetry
USE cp_log_handling, ONLY: cp_get_default_logger,&
cp_logger_get_default_unit_nr,&
cp_logger_type
USE dm_ls_scf_types, ONLY: ls_scf_curvy_type,&
ls_scf_env_type
USE input_constants, ONLY: ls_scf_line_search_3point,&
ls_scf_line_search_3point_2d
USE iterate_matrix, ONLY: purify_mcweeny
USE kinds, ONLY: dp
USE machine, ONLY: m_flush
USE mathconstants, ONLY: ifac
USE mathlib, ONLY: invmat
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'dm_ls_scf_curvy'
PUBLIC :: dm_ls_curvy_optimization, deallocate_curvy_data
CONTAINS
! **************************************************************************************************
!> \brief driver routine for Head-Gordon curvy step approach
!> \param ls_scf_env ...
!> \param energy ...
!> \param check_conv ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE dm_ls_curvy_optimization(ls_scf_env, energy, check_conv)
TYPE(ls_scf_env_type) :: ls_scf_env
REAL(KIND=dp) :: energy
LOGICAL :: check_conv
CHARACTER(LEN=*), PARAMETER :: routineN = 'dm_ls_curvy_optimization'
INTEGER :: handle, i, lsstep
CALL timeset(routineN, handle)
CALL cite_reference(Shao2003)
! Upon first call initialize all matrices needed curing optimization
! In addition transform P into orthonormal basis. Will be scaled by 0.5 in closed shell case
! Only to be done once as it will be stored and reused afterwards
! TRS4 might yield a non-idempotent P therefore McWeeny purification is applied on initial P
IF (.NOT. ALLOCATED(ls_scf_env%curvy_data%matrix_dp)) THEN
CALL init_curvy(ls_scf_env%curvy_data, ls_scf_env%matrix_s, ls_scf_env%nspins)
ls_scf_env%curvy_data%line_search_step = 1
IF (ls_scf_env%curvy_data%line_search_type == ls_scf_line_search_3point_2d) THEN
DO i = 1, ls_scf_env%nspins
CALL dbcsr_copy(ls_scf_env%curvy_data%matrix_psave(i, 1), &
ls_scf_env%matrix_p(i))
END DO
END IF
IF (ls_scf_env%nspins == 1) CALL dbcsr_scale(ls_scf_env%matrix_p(1), 0.5_dp)
CALL transform_matrix_orth(ls_scf_env%matrix_p, ls_scf_env%matrix_s_sqrt, &
ls_scf_env%eps_filter)
CALL purify_mcweeny(ls_scf_env%matrix_p, ls_scf_env%eps_filter, 3)
DO i = 1, ls_scf_env%nspins
CALL dbcsr_copy(ls_scf_env%curvy_data%matrix_p(i), ls_scf_env%matrix_p(i))
END DO
END IF
lsstep = ls_scf_env%curvy_data%line_search_step
! If new search direction has to be computed transform H into the orthnormal basis
IF (ls_scf_env%curvy_data%line_search_step == 1) &
CALL transform_matrix_orth(ls_scf_env%matrix_ks, ls_scf_env%matrix_s_sqrt_inv, &
ls_scf_env%eps_filter)
! Set the energies for the line search and make sure to give the correct energy back to scf_main
ls_scf_env%curvy_data%energies(lsstep) = energy
IF (lsstep .NE. 1) energy = ls_scf_env%curvy_data%energies(1)
! start the optimization by calling the driver routine or simply combine saved P(2D line search)
IF (lsstep .LE. 2) THEN
CALL optimization_step(ls_scf_env%curvy_data, ls_scf_env)
ELSE IF (lsstep == ls_scf_env%curvy_data%line_search_type) THEN
! line_search type has the value appropriate to the number of energy calculations needed
CALL optimization_step(ls_scf_env%curvy_data, ls_scf_env)
ELSE
CALL new_p_from_save(ls_scf_env%matrix_p, ls_scf_env%curvy_data%matrix_psave, lsstep, &
ls_scf_env%curvy_data%double_step_size)
ls_scf_env%curvy_data%line_search_step = ls_scf_env%curvy_data%line_search_step + 1
CALL timestop(handle)
RETURN
END IF
lsstep = ls_scf_env%curvy_data%line_search_step
! transform new density matrix back into nonorthonormal basis (again scaling might apply)
CALL transform_matrix_orth(ls_scf_env%matrix_p, ls_scf_env%matrix_s_sqrt_inv, &
ls_scf_env%eps_filter)
IF (ls_scf_env%nspins == 1) CALL dbcsr_scale(ls_scf_env%matrix_p(1), 2.0_dp)
! P-matrices only need to be stored in case of 2D line search
IF (lsstep .LE. 3 .AND. ls_scf_env%curvy_data%line_search_type == ls_scf_line_search_3point_2d) THEN
DO i = 1, ls_scf_env%nspins
CALL dbcsr_copy(ls_scf_env%curvy_data%matrix_psave(i, lsstep), &
ls_scf_env%matrix_p(i))
END DO
END IF
check_conv = lsstep == 1
CALL timestop(handle)
END SUBROUTINE dm_ls_curvy_optimization
! **************************************************************************************************
!> \brief low level routine for Head-Gordons curvy step approach
!> computes gradients, performs a cg and line search,
!> and evaluates the BCH series to obtain the new P matrix
!> \param curvy_data ...
!> \param ls_scf_env ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE optimization_step(curvy_data, ls_scf_env)
TYPE(ls_scf_curvy_type) :: curvy_data
TYPE(ls_scf_env_type) :: ls_scf_env
CHARACTER(LEN=*), PARAMETER :: routineN = 'optimization_step'
INTEGER :: handle, ispin
REAL(KIND=dp) :: filter, step_size(2)
! Upon first line search step compute new search direction and apply CG if required
CALL timeset(routineN, handle)
IF (curvy_data%line_search_step == 1) THEN
curvy_data%step_size = MAXVAL(curvy_data%step_size)
curvy_data%step_size = MIN(MAX(0.10_dp, 0.5_dp*ABS(curvy_data%step_size(1))), 0.5_dp)
! Dynamic eps_filter for newton steps
filter = MAX(ls_scf_env%eps_filter*curvy_data%min_filter, &
ls_scf_env%eps_filter*curvy_data%filter_factor)
CALL compute_direction_newton(curvy_data%matrix_p, ls_scf_env%matrix_ks, &
curvy_data%matrix_dp, filter, curvy_data%fix_shift, curvy_data%shift, &
curvy_data%cg_numer, curvy_data%cg_denom, curvy_data%min_shift)
curvy_data%filter_factor = curvy_data%scale_filter*curvy_data%filter_factor
step_size = curvy_data%step_size
curvy_data%BCH_saved = 0
ELSE IF (curvy_data%line_search_step == 2) THEN
step_size = curvy_data%step_size
IF (curvy_data%energies(1) - curvy_data%energies(2) .GT. 0.0_dp) THEN
curvy_data%step_size = curvy_data%step_size*2.0_dp
curvy_data%double_step_size = .TRUE.
ELSE
curvy_data%step_size = curvy_data%step_size*0.5_dp
curvy_data%double_step_size = .FALSE.
END IF
step_size = curvy_data%step_size
ELSE IF (curvy_data%line_search_step == ls_scf_line_search_3point_2d) THEN
CALL line_search_2d(curvy_data%energies, curvy_data%step_size)
step_size = curvy_data%step_size
ELSE IF (curvy_data%line_search_step == ls_scf_line_search_3point) THEN
CALL line_search_3pnt(curvy_data%energies, curvy_data%step_size)
step_size = curvy_data%step_size
END IF
CALL update_p_exp(curvy_data%matrix_p, ls_scf_env%matrix_p, curvy_data%matrix_dp, &
curvy_data%matrix_BCH, ls_scf_env%eps_filter, step_size, curvy_data%BCH_saved, &
curvy_data%n_bch_hist)
! line_search type has the value appropriate to the numeber of energy calculations needed
curvy_data%line_search_step = MOD(curvy_data%line_search_step, curvy_data%line_search_type) + 1
IF (curvy_data%line_search_step == 1) THEN
DO ispin = 1, SIZE(curvy_data%matrix_p)
CALL dbcsr_copy(curvy_data%matrix_p(ispin), ls_scf_env%matrix_p(ispin))
END DO
END IF
CALL timestop(handle)
END SUBROUTINE optimization_step
! **************************************************************************************************
!> \brief Perform a 6pnt-2D line search for spin polarized calculations.
!> Fit a 2D parabolic function to 6 points
!> \param energies ...
!> \param step_size ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE line_search_2d(energies, step_size)
REAL(KIND=dp) :: energies(6), step_size(2)
INTEGER :: info, unit_nr
REAL(KIND=dp) :: e_pred, param(6), s1, s1sq, s2, s2sq, &
sys_lin_eq(6, 6), tmp_e, v1, v2
TYPE(cp_logger_type), POINTER :: logger
logger => cp_get_default_logger()
IF (energies(1) - energies(2) .LT. 0._dp) THEN
tmp_e = energies(2); energies(2) = energies(3); energies(3) = tmp_e
step_size = step_size*2.0_dp
END IF
IF (logger%para_env%is_source()) THEN
unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
ELSE
unit_nr = -1
END IF
s1 = 0.5_dp*step_size(1); s2 = step_size(1); s1sq = s1**2; s2sq = s2**2
sys_lin_eq = 0.0_dp; sys_lin_eq(:, 6) = 1.0_dp
sys_lin_eq(2, 1) = s1sq; sys_lin_eq(2, 2) = s1sq; sys_lin_eq(2, 3) = s1sq; sys_lin_eq(2, 4) = s1; sys_lin_eq(2, 5) = s1
sys_lin_eq(3, 1) = s2sq; sys_lin_eq(3, 2) = s2sq; sys_lin_eq(3, 3) = s2sq; sys_lin_eq(3, 4) = s2; sys_lin_eq(3, 5) = s2
sys_lin_eq(4, 3) = s1sq; sys_lin_eq(4, 5) = s1
sys_lin_eq(5, 1) = s1sq; sys_lin_eq(5, 4) = s1
sys_lin_eq(6, 3) = s2sq; sys_lin_eq(6, 5) = s2
CALL invmat(sys_lin_eq, info)
param = MATMUL(sys_lin_eq, energies)
v1 = (param(2)*param(4))/(2.0_dp*param(1)) - param(5)
v2 = -(param(2)**2)/(2.0_dp*param(1)) + 2.0_dp*param(3)
step_size(2) = v1/v2
step_size(1) = (-param(2)*step_size(2) - param(4))/(2.0_dp*param(1))
IF (step_size(1) .LT. 0.0_dp) step_size(1) = 1.0_dp
IF (step_size(2) .LT. 0.0_dp) step_size(2) = 1.0_dp
! step_size(1)=MIN(step_size(1),2.0_dp)
! step_size(2)=MIN(step_size(2),2.0_dp)
e_pred = param(1)*step_size(1)**2 + param(2)*step_size(1)*step_size(2) + &
param(3)*step_size(2)**2 + param(4)*step_size(1) + param(5)*step_size(2) + param(6)
IF (unit_nr .GT. 0) WRITE (unit_nr, "(t3,a,F10.5,F10.5,A,F20.9)") &
" Line Search: Step Size", step_size, " Predicted energy", e_pred
e_pred = param(1)*s1**2 + param(2)*s2*s1*0.0_dp + &
param(3)*s1**2*0.0_dp + param(4)*s1 + param(5)*s1*0.0_dp + param(6)
END SUBROUTINE line_search_2d
! **************************************************************************************************
!> \brief Perform a 3pnt line search
!> \param energies ...
!> \param step_size ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE line_search_3pnt(energies, step_size)
REAL(KIND=dp) :: energies(3), step_size(2)
INTEGER :: unit_nr
REAL(KIND=dp) :: a, b, c, e_pred, min_val, step1, tmp, &
tmp_e
TYPE(cp_logger_type), POINTER :: logger
logger => cp_get_default_logger()
IF (energies(1) - energies(2) .LT. 0._dp) THEN
tmp_e = energies(2); energies(2) = energies(3); energies(3) = tmp_e
step_size = step_size*2.0_dp
END IF
IF (logger%para_env%is_source()) THEN
unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
ELSE
unit_nr = -1
END IF
step1 = 0.5_dp*step_size(1)
c = energies(1)
a = (energies(3) + c - 2.0_dp*energies(2))/(2.0_dp*step1**2)
b = (energies(2) - c - a*step1**2)/step1
IF (a .LT. 1.0E-12_dp) a = -1.0E-12_dp
min_val = -b/(2.0_dp*a)
e_pred = a*min_val**2 + b*min_val + c
tmp = step_size(1)
IF (e_pred .LT. energies(1) .AND. e_pred .LT. energies(2)) THEN
step_size = MAX(-1.0_dp, &
MIN(min_val, 10_dp*step_size))
ELSE
step_size = 1.0_dp
END IF
e_pred = a*(step_size(1))**2 + b*(step_size(1)) + c
IF (unit_nr .GT. 0) THEN
WRITE (unit_nr, "(t3,a,f16.8,a,F20.9)") "Line Search: Step Size", step_size(1), " Predicted energy", e_pred
CALL m_flush(unit_nr)
END IF
END SUBROUTINE line_search_3pnt
! **************************************************************************************************
!> \brief Get a new search direction. Iterate to obtain a Newton like step
!> Refine with a CG update of the search direction
!> \param matrix_p ...
!> \param matrix_ks ...
!> \param matrix_dp ...
!> \param eps_filter ...
!> \param fix_shift ...
!> \param curvy_shift ...
!> \param cg_numer ...
!> \param cg_denom ...
!> \param min_shift ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE compute_direction_newton(matrix_p, matrix_ks, matrix_dp, eps_filter, fix_shift, &
curvy_shift, cg_numer, cg_denom, min_shift)
TYPE(dbcsr_type), DIMENSION(:) :: matrix_p, matrix_ks, matrix_dp
REAL(KIND=dp) :: eps_filter
LOGICAL :: fix_shift(2)
REAL(KIND=dp) :: curvy_shift(2), cg_numer(2), &
cg_denom(2), min_shift
CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_direction_newton'
INTEGER :: handle, i, ispin, ncyc, nspin, unit_nr
LOGICAL :: at_limit
REAL(KIND=dp) :: beta, conv_val, maxel, old_conv, shift
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_type) :: matrix_Ax, matrix_b, matrix_cg, &
matrix_dp_old, matrix_PKs, matrix_res, &
matrix_tmp, matrix_tmp1
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
CALL timeset(routineN, handle)
nspin = SIZE(matrix_p)
CALL dbcsr_create(matrix_PKs, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_Ax, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_tmp, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_tmp1, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_res, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_cg, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_b, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_dp_old, template=matrix_dp(1), matrix_type=dbcsr_type_no_symmetry)
DO ispin = 1, nspin
CALL dbcsr_copy(matrix_dp_old, matrix_dp(ispin))
! Precompute some matrices to save work during iterations
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_p(ispin), matrix_ks(ispin), &
0.0_dp, matrix_PKs, filter_eps=eps_filter)
CALL dbcsr_transposed(matrix_b, matrix_PKs)
CALL dbcsr_copy(matrix_cg, matrix_b)
! Starting CG with guess 0-matrix gives -2*gradient=[Ks*P-(Ks*P)T] for cg_matrix in second step
CALL dbcsr_add(matrix_cg, matrix_PKs, 2.0_dp, -2.0_dp)
! Residual matrix in first step=cg matrix. Keep Pks for later use in CG!
CALL dbcsr_copy(matrix_res, matrix_cg)
! Precompute -FP-[FP]T which will be used throughout the CG iterations
CALL dbcsr_add(matrix_b, matrix_PKs, -1.0_dp, -1.0_dp)
! Setup some values to check convergence and safety checks for eigenvalue shifting
CALL dbcsr_norm(matrix_res, which_norm=2, norm_scalar=old_conv)
old_conv = dbcsr_frobenius_norm(matrix_res)
shift = MIN(10.0_dp, MAX(min_shift, 0.05_dp*old_conv))
conv_val = MAX(0.010_dp*old_conv, 100.0_dp*eps_filter)
old_conv = 100.0_dp
IF (fix_shift(ispin)) THEN
shift = MAX(min_shift, MIN(10.0_dp, MAX(shift, curvy_shift(ispin) - 0.5_dp*curvy_shift(ispin))))
curvy_shift(ispin) = shift
END IF
! Begin the real optimization loop
CALL dbcsr_set(matrix_dp(ispin), 0.0_dp)
ncyc = 10
DO i = 1, ncyc
! One step to compute: -FPD-DPF-DFP-PFD (not obvious but symmetry allows for some tricks)
CALL commutator_symm(matrix_b, matrix_cg, matrix_Ax, eps_filter, 1.0_dp)
! Compute the missing bits 2*(FDP+PDF) (again use symmetry to compute as a commutator)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_cg, matrix_p(ispin), &
0.0_dp, matrix_tmp, filter_eps=eps_filter)
CALL commutator_symm(matrix_ks(ispin), matrix_tmp, matrix_tmp1, eps_filter, 2.0_dp)
CALL dbcsr_add(matrix_Ax, matrix_tmp1, 1.0_dp, 1.0_dp)
! Apply the shift and hope it's enough to stabilize the CG iterations
CALL dbcsr_add(matrix_Ax, matrix_cg, 1.0_dp, shift)
CALL compute_cg_matrices(matrix_Ax, matrix_res, matrix_cg, matrix_dp(ispin), &
matrix_tmp, eps_filter, at_limit)
CALL dbcsr_filter(matrix_cg, eps_filter)
! check for convergence of the newton step
maxel = dbcsr_frobenius_norm(matrix_res)
IF (unit_nr .GT. 0) THEN
WRITE (unit_nr, "(T3,A,F12.6)") "Convergence of Newton iteration ", maxel
CALL m_flush(unit_nr)
END IF
at_limit = at_limit .OR. (old_conv/maxel .LT. 1.01_dp)
old_conv = maxel
IF (i == ncyc .AND. maxel/conv_val .GT. 5.0_dp) THEN
fix_shift(ispin) = .TRUE.
curvy_shift(ispin) = 4.0_dp*shift
END IF
IF (maxel .LT. conv_val .OR. at_limit) EXIT
END DO
! Refine the Newton like search direction with a preconditioned cg update
CALL dbcsr_transposed(matrix_b, matrix_PKs)
!compute b= -2*KsP+2*PKs=-(2*gradient)
CALL dbcsr_copy(matrix_cg, matrix_b)
CALL dbcsr_add(matrix_cg, matrix_PKs, 1.0_dp, -1.0_dp)
cg_denom(ispin) = cg_numer(ispin)
CALL dbcsr_dot(matrix_cg, matrix_dp(ispin), cg_numer(ispin))
beta = cg_numer(ispin)/MAX(cg_denom(ispin), 1.0E-6_dp)
IF (beta .LT. 1.0_dp) THEN
beta = MAX(0.0_dp, beta)
CALL dbcsr_add(matrix_dp(ispin), matrix_dp_old, 1.0_dp, beta)
END IF
IF (unit_nr .GT. 0) WRITE (unit_nr, "(A)") " "
END DO
CALL dbcsr_release(matrix_PKs)
CALL dbcsr_release(matrix_dp_old)
CALL dbcsr_release(matrix_b)
CALL dbcsr_release(matrix_Ax)
CALL dbcsr_release(matrix_tmp)
CALL dbcsr_release(matrix_tmp1)
CALL dbcsr_release(matrix_b)
CALL dbcsr_release(matrix_res)
CALL dbcsr_release(matrix_cg)
IF (unit_nr .GT. 0) CALL m_flush(unit_nr)
CALL timestop(handle)
END SUBROUTINE compute_direction_newton
! **************************************************************************************************
!> \brief compute the optimal step size of the current cycle and update the
!> matrices needed to solve the system of linear equations
!> \param Ax ...
!> \param res ...
!> \param cg ...
!> \param deltp ...
!> \param tmp ...
!> \param eps_filter ...
!> \param at_limit ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE compute_cg_matrices(Ax, res, cg, deltp, tmp, eps_filter, at_limit)
TYPE(dbcsr_type) :: Ax, res, cg, deltp, tmp
REAL(KIND=dp) :: eps_filter
LOGICAL :: at_limit
INTEGER :: i, info
REAL(KIND=dp) :: alpha, beta, devi(3), fac, fac1, &
lin_eq(3, 3), new_norm, norm_cA, &
norm_rr, vec(3)
at_limit = .FALSE.
CALL dbcsr_dot(res, res, norm_rr)
CALL dbcsr_dot(cg, Ax, norm_cA)
lin_eq = 0.0_dp
fac = norm_rr/norm_cA
fac1 = fac
! Use a 3point line search and a fit to a quadratic function to determine optimal step size
DO i = 1, 3
CALL dbcsr_copy(tmp, res)
CALL dbcsr_add(tmp, Ax, 1.0_dp, -fac)
devi(i) = dbcsr_frobenius_norm(tmp)
lin_eq(i, :) = (/fac**2, fac, 1.0_dp/)
fac = fac1 + fac1*((-1)**i)*0.5_dp
END DO
CALL invmat(lin_eq, info)
vec = MATMUL(lin_eq, devi)
alpha = -vec(2)/(2.0_dp*vec(1))
fac = SQRT(norm_rr/(norm_cA*alpha))
!scale the previous matrices to match the step size
CALL dbcsr_scale(Ax, fac)
CALL dbcsr_scale(cg, fac)
norm_cA = norm_cA*fac**2
! USe CG to get the new matrices
alpha = norm_rr/norm_cA
CALL dbcsr_add(res, Ax, 1.0_dp, -alpha)
CALL dbcsr_dot(res, res, new_norm)
IF (norm_rr .LT. eps_filter*0.001_dp .OR. new_norm .LT. eps_filter*0.001_dp) THEN
beta = 0.0_dp
at_limit = .TRUE.
ELSE
beta = new_norm/norm_rr
CALL dbcsr_add(deltp, cg, 1.0_dp, alpha)
END IF
beta = new_norm/norm_rr
CALL dbcsr_add(cg, res, beta, 1.0_dp)
END SUBROUTINE compute_cg_matrices
! **************************************************************************************************
!> \brief Only for 2D line search. Use saved P-components to construct new
!> test density matrix. Takes care as well, whether step_size
!> increased or decreased during 2nd step and combines matrices accordingly
!> \param matrix_p ...
!> \param matrix_psave ...
!> \param lsstep ...
!> \param DOUBLE ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE new_p_from_save(matrix_p, matrix_psave, lsstep, DOUBLE)
TYPE(dbcsr_type), DIMENSION(:) :: matrix_p
TYPE(dbcsr_type), DIMENSION(:, :) :: matrix_psave
INTEGER :: lsstep
LOGICAL :: DOUBLE
SELECT CASE (lsstep)
CASE (3)
CALL dbcsr_copy(matrix_p(1), matrix_psave(1, 1))
IF (DOUBLE) THEN
CALL dbcsr_copy(matrix_p(2), matrix_psave(2, 2))
ELSE
CALL dbcsr_copy(matrix_p(2), matrix_psave(2, 3))
END IF
CASE (4)
IF (DOUBLE) THEN
CALL dbcsr_copy(matrix_p(1), matrix_psave(1, 2))
ELSE
CALL dbcsr_copy(matrix_p(1), matrix_psave(1, 3))
END IF
CALL dbcsr_copy(matrix_p(2), matrix_psave(2, 1))
CASE (5)
CALL dbcsr_copy(matrix_p(1), matrix_psave(1, 1))
IF (DOUBLE) THEN
CALL dbcsr_copy(matrix_p(2), matrix_psave(2, 3))
ELSE
CALL dbcsr_copy(matrix_p(2), matrix_psave(2, 2))
END IF
END SELECT
END SUBROUTINE new_p_from_save
! **************************************************************************************************
!> \brief computes a commutator exploiting symmetry RES=k*[A,B]=k*[AB-(AB)T]
!> \param a ...
!> \param b ...
!> \param res ...
!> \param eps_filter filtering threshold for sparse matrices
!> \param prefac prefactor k in above equation
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE commutator_symm(a, b, res, eps_filter, prefac)
TYPE(dbcsr_type) :: a, b, res
REAL(KIND=dp) :: eps_filter, prefac
CHARACTER(LEN=*), PARAMETER :: routineN = 'commutator_symm'
INTEGER :: handle
TYPE(dbcsr_type) :: work
CALL timeset(routineN, handle)
CALL dbcsr_create(work, template=a, matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_multiply("N", "N", prefac, a, b, 0.0_dp, res, filter_eps=eps_filter)
CALL dbcsr_transposed(work, res)
CALL dbcsr_add(res, work, 1.0_dp, -1.0_dp)
CALL dbcsr_release(work)
CALL timestop(handle)
END SUBROUTINE commutator_symm
! **************************************************************************************************
!> \brief Use the BCH update to get the new idempotent P
!> Numerics don't allow for perfect idempotency, therefore a mc weeny
!> step is used to make sure we stay close to the idempotent surface
!> \param matrix_p_in ...
!> \param matrix_p_out ...
!> \param matrix_dp ...
!> \param matrix_BCH ...
!> \param threshold ...
!> \param step_size ...
!> \param BCH_saved ...
!> \param n_bch_hist ...
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE update_p_exp(matrix_p_in, matrix_p_out, matrix_dp, matrix_BCH, threshold, step_size, &
BCH_saved, n_bch_hist)
TYPE(dbcsr_type), DIMENSION(:) :: matrix_p_in, matrix_p_out, matrix_dp
TYPE(dbcsr_type), DIMENSION(:, :) :: matrix_BCH
REAL(KIND=dp) :: threshold, step_size(2)
INTEGER :: BCH_saved(2), n_bch_hist
CHARACTER(LEN=*), PARAMETER :: routineN = 'update_p_exp'
INTEGER :: handle, i, ispin, nsave, nspin, unit_nr
LOGICAL :: save_BCH
REAL(KIND=dp) :: frob_norm, step_fac
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_type) :: matrix, matrix_tmp
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
CALL dbcsr_create(matrix, template=matrix_p_in(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_tmp, template=matrix_p_in(1), matrix_type=dbcsr_type_no_symmetry)
nspin = SIZE(matrix_p_in)
DO ispin = 1, nspin
step_fac = 1.0_dp
frob_norm = 1.0_dp
nsave = 0
CALL dbcsr_copy(matrix_tmp, matrix_p_in(ispin))
CALL dbcsr_copy(matrix_p_out(ispin), matrix_p_in(ispin))
! If a BCH history is used make good use of it and do a few steps as a copy and scale update of P
! else BCH_saved will be 0 and loop is skipped
DO i = 1, BCH_saved(ispin)
step_fac = step_fac*step_size(ispin)
CALL dbcsr_copy(matrix_tmp, matrix_p_out(ispin))
CALL dbcsr_add(matrix_p_out(ispin), matrix_BCH(ispin, i), 1.0_dp, ifac(i)*step_fac)
CALL dbcsr_add(matrix_tmp, matrix_p_out(ispin), 1.0_dp, -1.0_dp)
frob_norm = dbcsr_frobenius_norm(matrix_tmp)
IF (unit_nr .GT. 0) WRITE (unit_nr, "(t3,a,i3,a,f16.8)") "BCH: step", i, " Norm of P_old-Pnew:", frob_norm
IF (frob_norm .LT. threshold) EXIT
END DO
IF (frob_norm .LT. threshold) CYCLE
! If the copy and scale isn't enough compute a few more BCH steps. 20 seems high but except of the first step it will never be close
save_BCH = BCH_saved(ispin) == 0 .AND. n_bch_hist .GT. 0
DO i = BCH_saved(ispin) + 1, 20
step_fac = step_fac*step_size(ispin)
!allow for a bit of matrix magic here by exploiting matrix and matrix_tmp
!matrix_tmp is alway the previous order of the BCH series
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp, matrix_dp(ispin), &
0.0_dp, matrix, filter_eps=threshold)
!(anti)symmetry allows to sum the transposed instead of the full commutator, matrix becomes the latest result
CALL dbcsr_transposed(matrix_tmp, matrix)
CALL dbcsr_add(matrix, matrix_tmp, 1.0_dp, 1.0_dp)
!Finally, add the new BCH order to P, but store the previous one for a convergence check
CALL dbcsr_copy(matrix_tmp, matrix_p_out(ispin))
CALL dbcsr_add(matrix_p_out(ispin), matrix, 1.0_dp, ifac(i)*step_fac)
IF (save_BCH .AND. i .LE. n_bch_hist) THEN
CALL dbcsr_copy(matrix_BCH(ispin, i), matrix)
nsave = i
END IF
CALL dbcsr_add(matrix_tmp, matrix_p_out(ispin), 1.0_dp, -1.0_dp)
!Stop the BCH-series if two successive P's differ by less the threshold
frob_norm = dbcsr_frobenius_norm(matrix_tmp)
IF (unit_nr .GT. 0) WRITE (unit_nr, "(t3,a,i3,a,f16.8)") "BCH: step", i, " Norm of P_old-Pnew:", frob_norm
IF (frob_norm .LT. threshold) EXIT
!Copy the latest BCH-matrix on matrix tmp, so we can cycle with all matrices in place
CALL dbcsr_copy(matrix_tmp, matrix)
CALL dbcsr_filter(matrix_tmp, threshold)
END DO
BCH_saved(ispin) = nsave
IF (unit_nr .GT. 0) WRITE (unit_nr, "(A)") " "
END DO
CALL purify_mcweeny(matrix_p_out, threshold, 1)
IF (unit_nr .GT. 0) CALL m_flush(unit_nr)
CALL dbcsr_release(matrix_tmp)
CALL dbcsr_release(matrix)
CALL timestop(handle)
END SUBROUTINE update_p_exp
! **************************************************************************************************
!> \brief performs a transformation of a matrix back to/into orthonormal basis
!> in case of P a scaling of 0.5 has to be applied for closed shell case
!> \param matrix matrix to be transformed
!> \param matrix_trafo transformation matrix
!> \param eps_filter filtering threshold for sparse matrices
!> \par History
!> 2012.05 created [Florian Schiffmann]
!> \author Florian Schiffmann
! **************************************************************************************************
SUBROUTINE transform_matrix_orth(matrix, matrix_trafo, eps_filter)
TYPE(dbcsr_type), DIMENSION(:) :: matrix
TYPE(dbcsr_type) :: matrix_trafo
REAL(KIND=dp) :: eps_filter
CHARACTER(LEN=*), PARAMETER :: routineN = 'transform_matrix_orth'
INTEGER :: handle, ispin
TYPE(dbcsr_type) :: matrix_tmp, matrix_work
CALL timeset(routineN, handle)
CALL dbcsr_create(matrix_work, template=matrix(1), matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_create(matrix_tmp, template=matrix(1), matrix_type=dbcsr_type_no_symmetry)
DO ispin = 1, SIZE(matrix)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix(ispin), matrix_trafo, &
0.0_dp, matrix_work, filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_trafo, matrix_work, &
0.0_dp, matrix_tmp, filter_eps=eps_filter)
! symmetrize results (this is again needed to make sure everything is stable)
CALL dbcsr_transposed(matrix_work, matrix_tmp)
CALL dbcsr_add(matrix_tmp, matrix_work, 0.5_dp, 0.5_dp)
CALL dbcsr_copy(matrix(ispin), matrix_tmp)
END DO
CALL dbcsr_release(matrix_tmp)
CALL dbcsr_release(matrix_work)
CALL timestop(handle)
END SUBROUTINE
! **************************************************************************************************
!> \brief ...
!> \param curvy_data ...
! **************************************************************************************************
SUBROUTINE deallocate_curvy_data(curvy_data)
TYPE(ls_scf_curvy_type) :: curvy_data
INTEGER :: i, j
CALL release_dbcsr_array(curvy_data%matrix_dp)
CALL release_dbcsr_array(curvy_data%matrix_p)
IF (ALLOCATED(curvy_data%matrix_psave)) THEN
DO i = 1, SIZE(curvy_data%matrix_psave, 1)
DO j = 1, 3
CALL dbcsr_release(curvy_data%matrix_psave(i, j))
END DO
END DO
DEALLOCATE (curvy_data%matrix_psave)
END IF
IF (ALLOCATED(curvy_data%matrix_BCH)) THEN
DO i = 1, SIZE(curvy_data%matrix_BCH, 1)
DO j = 1, 7
CALL dbcsr_release(curvy_data%matrix_BCH(i, j))
END DO
END DO
DEALLOCATE (curvy_data%matrix_BCH)
END IF
END SUBROUTINE deallocate_curvy_data
! **************************************************************************************************
!> \brief ...
!> \param matrix ...
! **************************************************************************************************
SUBROUTINE release_dbcsr_array(matrix)
TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:) :: matrix
INTEGER :: i
IF (ALLOCATED(matrix)) THEN
DO i = 1, SIZE(matrix)
CALL dbcsr_release(matrix(i))
END DO
DEALLOCATE (matrix)
END IF
END SUBROUTINE release_dbcsr_array
! **************************************************************************************************
!> \brief ...
!> \param curvy_data ...
!> \param matrix_s ...
!> \param nspins ...
! **************************************************************************************************
SUBROUTINE init_curvy(curvy_data, matrix_s, nspins)
TYPE(ls_scf_curvy_type) :: curvy_data
TYPE(dbcsr_type) :: matrix_s
INTEGER :: nspins
INTEGER :: ispin, j
ALLOCATE (curvy_data%matrix_dp(nspins))
ALLOCATE (curvy_data%matrix_p(nspins))
DO ispin = 1, nspins
CALL dbcsr_create(curvy_data%matrix_dp(ispin), template=matrix_s, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_set(curvy_data%matrix_dp(ispin), 0.0_dp)
CALL dbcsr_create(curvy_data%matrix_p(ispin), template=matrix_s, &
matrix_type=dbcsr_type_no_symmetry)
curvy_data%fix_shift = .FALSE.
curvy_data%double_step_size = .TRUE.
curvy_data%shift = 1.0_dp
curvy_data%BCH_saved = 0
curvy_data%step_size = 0.60_dp
curvy_data%cg_numer = 0.00_dp
curvy_data%cg_denom = 0.00_dp
END DO
IF (curvy_data%line_search_type == ls_scf_line_search_3point_2d) THEN
ALLOCATE (curvy_data%matrix_psave(nspins, 3))
DO ispin = 1, nspins
DO j = 1, 3
CALL dbcsr_create(curvy_data%matrix_psave(ispin, j), template=matrix_s, &
matrix_type=dbcsr_type_no_symmetry)
END DO
END DO
END IF
IF (curvy_data%n_bch_hist .GT. 0) THEN
ALLOCATE (curvy_data%matrix_BCH(nspins, curvy_data%n_bch_hist))
DO ispin = 1, nspins
DO j = 1, curvy_data%n_bch_hist
CALL dbcsr_create(curvy_data%matrix_BCH(ispin, j), template=matrix_s, &
matrix_type=dbcsr_type_no_symmetry)
END DO
END DO
END IF
END SUBROUTINE init_curvy
END MODULE dm_ls_scf_curvy