Line data    Source code

       1             : !--------------------------------------------------------------------------------------------------!
       2             : !   CP2K: A general program to perform molecular dynamics simulations                              !
       3             : !   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
       4             : !                                                                                                  !
       5             : !   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
       6             : !--------------------------------------------------------------------------------------------------!
       7             : 
       8             : ! **************************************************************************************************
       9             : !> \brief Optimizers used by pao_main.F
      10             : !> \author Ole Schuett
      11             : ! **************************************************************************************************
      12             : MODULE pao_optimizer
      13             :    USE arnoldi_api,                     ONLY: arnoldi_extremal
      14             :    USE dbcsr_api,                       ONLY: &
      15             :         dbcsr_add, dbcsr_add_on_diag, dbcsr_copy, dbcsr_create, dbcsr_dot, dbcsr_frobenius_norm, &
      16             :         dbcsr_get_info, dbcsr_multiply, dbcsr_release, dbcsr_reserve_diag_blocks, dbcsr_scale, &
      17             :         dbcsr_set, dbcsr_type
      18             :    USE kinds,                           ONLY: dp
      19             :    USE pao_input,                       ONLY: pao_opt_bfgs,&
      20             :                                               pao_opt_cg
      21             :    USE pao_types,                       ONLY: pao_env_type
      22             : #include "./base/base_uses.f90"
      23             : 
      24             :    IMPLICIT NONE
      25             : 
      26             :    PRIVATE
      27             : 
      28             :    PUBLIC :: pao_opt_init, pao_opt_finalize, pao_opt_new_dir
      29             : 
      30             : CONTAINS
      31             : 
      32             : ! **************************************************************************************************
      33             : !> \brief Initialize the optimizer
      34             : !> \param pao ...
      35             : ! **************************************************************************************************
      36         246 :    SUBROUTINE pao_opt_init(pao)
      37             :       TYPE(pao_env_type), POINTER                        :: pao
      38             : 
      39         246 :       CALL dbcsr_copy(pao%matrix_D, pao%matrix_G)
      40         246 :       CALL dbcsr_set(pao%matrix_D, 0.0_dp)
      41             : 
      42         246 :       CALL dbcsr_copy(pao%matrix_G_prev, pao%matrix_D)
      43             : 
      44         246 :       IF (pao%precondition) THEN
      45          82 :          CALL dbcsr_copy(pao%matrix_D_preconed, pao%matrix_D)
      46             :       END IF
      47             : 
      48         246 :       IF (pao%optimizer == pao_opt_bfgs) &
      49          12 :          CALL pao_opt_init_bfgs(pao)
      50             : 
      51         246 :    END SUBROUTINE pao_opt_init
      52             : 
      53             : ! **************************************************************************************************
      54             : !> \brief Initialize the BFGS optimizer
      55             : !> \param pao ...
      56             : ! **************************************************************************************************
      57          12 :    SUBROUTINE pao_opt_init_bfgs(pao)
      58             :       TYPE(pao_env_type), POINTER                        :: pao
      59             : 
      60          12 :       INTEGER, DIMENSION(:), POINTER                     :: nparams
      61             : 
      62          12 :       CALL dbcsr_get_info(pao%matrix_X, row_blk_size=nparams)
      63             : 
      64             :       CALL dbcsr_create(pao%matrix_BFGS, &
      65             :                         template=pao%matrix_X, &
      66             :                         row_blk_size=nparams, &
      67             :                         col_blk_size=nparams, &
      68          12 :                         name="PAO matrix_BFGS")
      69             : 
      70          12 :       CALL dbcsr_reserve_diag_blocks(pao%matrix_BFGS)
      71          12 :       CALL dbcsr_set(pao%matrix_BFGS, 0.0_dp)
      72          12 :       CALL dbcsr_add_on_diag(pao%matrix_BFGS, 1.0_dp)
      73             : 
      74          12 :    END SUBROUTINE pao_opt_init_bfgs
      75             : 
      76             : ! **************************************************************************************************
      77             : !> \brief Finalize the optimizer
      78             : !> \param pao ...
      79             : ! **************************************************************************************************
      80         246 :    SUBROUTINE pao_opt_finalize(pao)
      81             :       TYPE(pao_env_type), POINTER                        :: pao
      82             : 
      83         246 :       CALL dbcsr_release(pao%matrix_D)
      84         246 :       CALL dbcsr_release(pao%matrix_G_prev)
      85         246 :       IF (pao%precondition) &
      86          82 :          CALL dbcsr_release(pao%matrix_D_preconed)
      87             : 
      88         246 :       IF (pao%optimizer == pao_opt_bfgs) &
      89          12 :          CALL dbcsr_release(pao%matrix_BFGS)
      90             : 
      91         246 :    END SUBROUTINE pao_opt_finalize
      92             : 
      93             : ! **************************************************************************************************
      94             : !> \brief Calculates the new search direction.
      95             : !> \param pao ...
      96             : !> \param icycle ...
      97             : ! **************************************************************************************************
      98        2622 :    SUBROUTINE pao_opt_new_dir(pao, icycle)
      99             :       TYPE(pao_env_type), POINTER                        :: pao
     100             :       INTEGER, INTENT(IN)                                :: icycle
     101             : 
     102             :       CHARACTER(len=*), PARAMETER                        :: routineN = 'pao_opt_new_dir'
     103             : 
     104             :       INTEGER                                            :: handle
     105             :       TYPE(dbcsr_type)                                   :: matrix_G_preconed
     106             : 
     107        2622 :       CALL timeset(routineN, handle)
     108             : 
     109        2622 :       IF (pao%precondition) THEN
     110             :          ! We can't convert matrix_D for and back every time, the numeric noise would disturb the CG,
     111             :          ! hence we keep matrix_D_preconed around.
     112        1290 :          CALL dbcsr_copy(matrix_G_preconed, pao%matrix_G)
     113             :          CALL dbcsr_multiply("N", "N", 1.0_dp, pao%matrix_precon, pao%matrix_G, &
     114        1290 :                              0.0_dp, matrix_G_preconed, retain_sparsity=.TRUE.)
     115        1290 :          CALL pao_opt_new_dir_low(pao, icycle, matrix_G_preconed, pao%matrix_G_prev, pao%matrix_D_preconed)
     116             :          CALL dbcsr_multiply("N", "N", 1.0_dp, pao%matrix_precon, pao%matrix_D_preconed, &
     117        1290 :                              0.0_dp, pao%matrix_D, retain_sparsity=.TRUE.)
     118             : 
     119             :          ! store preconditioned gradient for next iteration
     120        1290 :          CALL dbcsr_copy(pao%matrix_G_prev, matrix_G_preconed)
     121             : 
     122        1290 :          pao%norm_G = dbcsr_frobenius_norm(matrix_G_preconed)
     123        1290 :          IF (pao%iw > 0) WRITE (pao%iw, *) "PAO| norm of preconditioned gradient:", pao%norm_G
     124        1290 :          CALL dbcsr_release(matrix_G_preconed)
     125             : 
     126             :       ELSE
     127        1332 :          CALL pao_opt_new_dir_low(pao, icycle, pao%matrix_G, pao%matrix_G_prev, pao%matrix_D)
     128        1332 :          CALL dbcsr_copy(pao%matrix_G_prev, pao%matrix_G) ! store gradient for next iteration
     129        1332 :          pao%norm_G = dbcsr_frobenius_norm(pao%matrix_G)
     130        1332 :          IF (pao%iw > 0) WRITE (pao%iw, *) "PAO| norm of gradient:", pao%norm_G
     131             :       END IF
     132             : 
     133        2622 :       CALL timestop(handle)
     134             : 
     135        2622 :    END SUBROUTINE pao_opt_new_dir
     136             : 
     137             : ! **************************************************************************************************
     138             : !> \brief Calculates the new search direction.
     139             : !> \param pao ...
     140             : !> \param icycle ...
     141             : !> \param matrix_G ...
     142             : !> \param matrix_G_prev ...
     143             : !> \param matrix_D ...
     144             : ! **************************************************************************************************
     145        2622 :    SUBROUTINE pao_opt_new_dir_low(pao, icycle, matrix_G, matrix_G_prev, matrix_D)
     146             :       TYPE(pao_env_type), POINTER                        :: pao
     147             :       INTEGER, INTENT(IN)                                :: icycle
     148             :       TYPE(dbcsr_type)                                   :: matrix_G, matrix_G_prev, matrix_D
     149             : 
     150        4956 :       SELECT CASE (pao%optimizer)
     151             :       CASE (pao_opt_cg)
     152        2334 :          CALL pao_opt_newdir_cg(pao, icycle, matrix_G, matrix_G_prev, matrix_D)
     153             :       CASE (pao_opt_bfgs)
     154         288 :          CALL pao_opt_newdir_bfgs(pao, icycle, matrix_G, matrix_G_prev, matrix_D)
     155             :       CASE DEFAULT
     156        2622 :          CPABORT("PAO: unknown optimizer")
     157             :       END SELECT
     158             : 
     159        2622 :    END SUBROUTINE pao_opt_new_dir_low
     160             : 
     161             : ! **************************************************************************************************
     162             : !> \brief Conjugate Gradient algorithm
     163             : !> \param pao ...
     164             : !> \param icycle ...
     165             : !> \param matrix_G ...
     166             : !> \param matrix_G_prev ...
     167             : !> \param matrix_D ...
     168             : ! **************************************************************************************************
     169        2334 :    SUBROUTINE pao_opt_newdir_cg(pao, icycle, matrix_G, matrix_G_prev, matrix_D)
     170             :       TYPE(pao_env_type), POINTER                        :: pao
     171             :       INTEGER, INTENT(IN)                                :: icycle
     172             :       TYPE(dbcsr_type)                                   :: matrix_G, matrix_G_prev, matrix_D
     173             : 
     174             :       REAL(KIND=dp)                                      :: beta, change, trace_D, trace_D_Gnew, &
     175             :                                                             trace_G_mix, trace_G_new, trace_G_prev
     176             : 
     177             :       ! determine CG mixing factor
     178        2334 :       IF (icycle <= pao%cg_init_steps) THEN
     179         444 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| warming up with steepest descent"
     180         444 :          beta = 0.0_dp
     181             :       ELSE
     182        1890 :          CALL dbcsr_dot(matrix_G, matrix_G, trace_G_new)
     183        1890 :          CALL dbcsr_dot(matrix_G_prev, matrix_G_prev, trace_G_prev)
     184        1890 :          CALL dbcsr_dot(matrix_G, matrix_G_prev, trace_G_mix)
     185        1890 :          CALL dbcsr_dot(matrix_D, matrix_G, trace_D_Gnew)
     186        1890 :          CALL dbcsr_dot(matrix_D, matrix_D, trace_D)
     187        1890 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| trace_G_new ", trace_G_new
     188        1890 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| trace_G_prev ", trace_G_prev
     189        1890 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| trace_G_mix ", trace_G_mix
     190        1890 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| trace_D ", trace_D
     191        1890 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| trace_D_Gnew", trace_D_Gnew
     192             : 
     193        1890 :          IF (trace_G_prev /= 0.0_dp) THEN
     194        1890 :             beta = (trace_G_new - trace_G_mix)/trace_G_prev !Polak-Ribiere
     195             :          END IF
     196             : 
     197        1890 :          IF (beta < 0.0_dp) THEN
     198          78 :             IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| resetting because beta < 0"
     199          78 :             beta = 0.0_dp
     200             :          END IF
     201             : 
     202        1890 :          change = trace_D_Gnew**2/trace_D*trace_G_new
     203        1890 :          IF (change > pao%cg_reset_limit) THEN
     204           0 :             IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| resetting because change > CG_RESET_LIMIT"
     205           0 :             beta = 0.0_dp
     206             :          END IF
     207             : 
     208             :       END IF
     209             : 
     210        2334 :       IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|CG| beta: ", beta
     211             : 
     212             :       ! calculate new CG direction matrix_D
     213        2334 :       CALL dbcsr_add(matrix_D, matrix_G, beta, -1.0_dp)
     214             : 
     215        2334 :    END SUBROUTINE pao_opt_newdir_cg
     216             : 
     217             : ! **************************************************************************************************
     218             : !> \brief Broyden-Fletcher-Goldfarb-Shanno algorithm
     219             : !> \param pao ...
     220             : !> \param icycle ...
     221             : !> \param matrix_G ...
     222             : !> \param matrix_G_prev ...
     223             : !> \param matrix_D ...
     224             : ! **************************************************************************************************
     225         288 :    SUBROUTINE pao_opt_newdir_bfgs(pao, icycle, matrix_G, matrix_G_prev, matrix_D)
     226             :       TYPE(pao_env_type), POINTER                        :: pao
     227             :       INTEGER, INTENT(IN)                                :: icycle
     228             :       TYPE(dbcsr_type)                                   :: matrix_G, matrix_G_prev, matrix_D
     229             : 
     230             :       CHARACTER(len=*), PARAMETER :: routineN = 'pao_opt_newdir_bfgs'
     231             : 
     232             :       INTEGER                                            :: handle
     233             :       LOGICAL                                            :: arnoldi_converged
     234             :       REAL(dp)                                           :: eval_max, eval_min, theta, trace_ry, &
     235             :                                                             trace_sy, trace_yHy, trace_yy
     236             :       TYPE(dbcsr_type)                                   :: matrix_Hy, matrix_Hyr, matrix_r, &
     237             :                                                             matrix_rr, matrix_ryH, matrix_ryHyr, &
     238             :                                                             matrix_s, matrix_y, matrix_yr
     239             : 
     240         288 :       CALL timeset(routineN, handle)
     241             : 
     242             :       !TODO add filtering?
     243             : 
     244             :       ! Notation according to the book from Nocedal and Wright, see chapter 6.
     245         288 :       IF (icycle > 1) THEN
     246             :          ! y = G - G_prev
     247         276 :          CALL dbcsr_copy(matrix_y, matrix_G)
     248         276 :          CALL dbcsr_add(matrix_y, matrix_G_prev, 1.0_dp, -1.0_dp) ! dG
     249             : 
     250             :          ! s = X - X_prev
     251         276 :          CALL dbcsr_copy(matrix_s, matrix_D)
     252         276 :          CALL dbcsr_scale(matrix_s, pao%linesearch%step_size) ! dX
     253             : 
     254             :          ! sy = MATMUL(TRANPOSE(s), y)
     255         276 :          CALL dbcsr_dot(matrix_s, matrix_y, trace_sy)
     256             : 
     257             :          ! heuristic initialization
     258         276 :          IF (icycle == 2) THEN
     259          10 :             CALL dbcsr_dot(matrix_Y, matrix_Y, trace_yy)
     260          10 :             CALL dbcsr_scale(pao%matrix_BFGS, trace_sy/trace_yy)
     261          10 :             IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|BFGS| Initializing with:", trace_sy/trace_yy
     262             :          END IF
     263             : 
     264             :          ! Hy = MATMUL(H, y)
     265         276 :          CALL dbcsr_create(matrix_Hy, template=matrix_G, matrix_type="N")
     266         276 :          CALL dbcsr_multiply("N", "N", 1.0_dp, pao%matrix_BFGS, matrix_y, 0.0_dp, matrix_Hy)
     267             : 
     268             :          ! yHy = MATMUL(TRANPOSE(y), Hy)
     269         276 :          CALL dbcsr_dot(matrix_y, matrix_Hy, trace_yHy)
     270             : 
     271             :          ! Use damped BFGS algorithm to ensure H remains positive definite.
     272             :          ! See chapter 18 in Nocedal and Wright's book for details.
     273             :          ! The formulas were adopted to inverse Hessian algorithm.
     274         276 :          IF (trace_sy < 0.2_dp*trace_yHy) THEN
     275           0 :             theta = 0.8_dp*trace_yHy/(trace_yHy - trace_sy)
     276           0 :             IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|BFGS| Dampening theta:", theta
     277             :          ELSE
     278         276 :             theta = 1.0
     279             :          END IF
     280             : 
     281             :          ! r = theta*s + (1-theta)*Hy
     282         276 :          CALL dbcsr_copy(matrix_r, matrix_s)
     283         276 :          CALL dbcsr_add(matrix_r, matrix_Hy, theta, (1.0_dp - theta))
     284             : 
     285             :          ! use t instead of y to update B matrix
     286         276 :          CALL dbcsr_dot(matrix_r, matrix_y, trace_ry)
     287         276 :          CPASSERT(trace_RY > 0.0_dp)
     288             : 
     289             :          ! yr = MATMUL(y, TRANSPOSE(r))
     290         276 :          CALL dbcsr_create(matrix_yr, template=pao%matrix_BFGS, matrix_type="N")
     291         276 :          CALL dbcsr_multiply("N", "T", 1.0_dp, matrix_y, matrix_r, 0.0_dp, matrix_yr)
     292             : 
     293             :          ! Hyr = MATMUL(H, yr)
     294         276 :          CALL dbcsr_create(matrix_Hyr, template=pao%matrix_BFGS, matrix_type="N")
     295         276 :          CALL dbcsr_multiply("N", "N", 1.0_dp, pao%matrix_BFGS, matrix_yr, 0.0_dp, matrix_Hyr)
     296             : 
     297             :          ! ryH = MATMUL(TRANSPOSE(yr), H)
     298         276 :          CALL dbcsr_create(matrix_ryH, template=pao%matrix_BFGS, matrix_type="N")
     299         276 :          CALL dbcsr_multiply("T", "N", 1.0_dp, matrix_yr, pao%matrix_BFGS, 0.0_dp, matrix_ryH)
     300             : 
     301             :          ! ryHry = MATMUL(ryH,yr)
     302         276 :          CALL dbcsr_create(matrix_ryHyr, template=pao%matrix_BFGS, matrix_type="N")
     303         276 :          CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_ryH, matrix_yr, 0.0_dp, matrix_ryHyr)
     304             : 
     305             :          ! rr = MATMUL(r,TRANSPOSE(r))
     306         276 :          CALL dbcsr_create(matrix_rr, template=pao%matrix_BFGS, matrix_type="N")
     307         276 :          CALL dbcsr_multiply("N", "T", 1.0_dp, matrix_r, matrix_r, 0.0_dp, matrix_rr)
     308             : 
     309             :          ! H = H - Hyr/ry - ryH/ry + ryHyr/(ry**2) + rr/ry
     310         276 :          CALL dbcsr_add(pao%matrix_BFGS, matrix_HYR, 1.0_dp, -1.0_dp/trace_ry)
     311         276 :          CALL dbcsr_add(pao%matrix_BFGS, matrix_ryH, 1.0_dp, -1.0_dp/trace_ry)
     312         276 :          CALL dbcsr_add(pao%matrix_BFGS, matrix_ryHyr, 1.0_dp, +1.0_dp/(trace_ry**2))
     313         276 :          CALL dbcsr_add(pao%matrix_BFGS, matrix_rr, 1.0_dp, +1.0_dp/trace_ry)
     314             : 
     315             :          ! clean up
     316         276 :          CALL dbcsr_release(matrix_y)
     317         276 :          CALL dbcsr_release(matrix_s)
     318         276 :          CALL dbcsr_release(matrix_r)
     319         276 :          CALL dbcsr_release(matrix_Hy)
     320         276 :          CALL dbcsr_release(matrix_yr)
     321         276 :          CALL dbcsr_release(matrix_Hyr)
     322         276 :          CALL dbcsr_release(matrix_ryH)
     323         276 :          CALL dbcsr_release(matrix_ryHyr)
     324         276 :          CALL dbcsr_release(matrix_rr)
     325             :       END IF
     326             : 
     327             :       ! approximate condition of Hessian
     328             :       !TODO: good setting for arnoldi?
     329             :       CALL arnoldi_extremal(pao%matrix_BFGS, eval_max, eval_min, max_iter=100, &
     330         288 :                             threshold=1e-2_dp, converged=arnoldi_converged)
     331         288 :       IF (arnoldi_converged) THEN
     332         432 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|BFGS| evals of inv. Hessian: min, max, max/min", &
     333         288 :             eval_min, eval_max, eval_max/eval_min
     334             :       ELSE
     335           0 :          IF (pao%iw_opt > 0) WRITE (pao%iw_opt, *) "PAO|BFGS| arnoldi of inv. Hessian did not converged."
     336             :       END IF
     337             : 
     338             :       ! calculate new direction
     339             :       ! d = MATMUL(H, -g)
     340             :       CALL dbcsr_multiply("N", "N", -1.0_dp, pao%matrix_BFGS, matrix_G, &
     341         288 :                           0.0_dp, matrix_D, retain_sparsity=.TRUE.)
     342             : 
     343         288 :       CALL timestop(handle)
     344         288 :    END SUBROUTINE pao_opt_newdir_bfgs
     345             : 
     346             : END MODULE pao_optimizer