Chimie Théorique » Opt'n Path

     ! Geom = input parameter vector (Geometry), Grad = input gradient vector.

     ! HEAT is Energy(Geom)

      SUBROUTINE Step_GEDIIS(Geom_new,Geom,Grad,HEAT,Hess,NCoord,FRST)

! This routine was adapted from the public domain mopac6 diis.f

!  source file (c) 2009, Stewart Computational Chemistry.

!  <http://www.openmopac.net/Downloads/Downloads.html>

!

!----------------------------------------------------------------------

!  Copyright 2003-2014 Ecole Normale Supérieure de Lyon,

!  Centre National de la Recherche Scientifique,

!  Université Claude Bernard Lyon 1. All rights reserved.

!

!  This work is registered with the Agency for the Protection of Programs

!  as IDDN.FR.001.100009.000.S.P.2014.000.30625

!

!  Authors: P. Fleurat-Lessard, P. Dayal

!  Contact: optnpath@gmail.com

!

! This file is part of "Opt'n Path".

!

!  "Opt'n Path" is free software: you can redistribute it and/or modify

!  it under the terms of the GNU Affero General Public License as

!  published by the Free Software Foundation, either version 3 of the License,

!  or (at your option) any later version.

!

!  "Opt'n Path" is distributed in the hope that it will be useful,

!  but WITHOUT ANY WARRANTY; without even the implied warranty of

!

!  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

!  GNU Affero General Public License for more details.

!

!  You should have received a copy of the GNU Affero General Public License

!  along with "Opt'n Path". If not, see <http://www.gnu.org/licenses/>.

!

! Contact The Office of Technology Licensing, valorisation@ens-lyon.fr,

! for commercial licensing opportunities.

!----------------------------------------------------------------------

    use Io_module

      IMPLICIT NONE

      INTEGER(KINT) :: NCoord

      REAL(KREAL) :: Geom_new(NCoord), Grad(NCoord), Hess(NCoord*NCoord)

    REAL(KREAL), INTENT(IN) :: Geom(NCoord)

    REAL(KREAL) :: HEAT ! HEAT= Energy

      LOGICAL :: FRST

      ! MRESET = maximum number of iterations.

      INTEGER(KINT), PARAMETER :: MRESET=15, M2=(MRESET+1)*(MRESET+1) !M2 = 256

      REAL(KREAL), ALLOCATABLE, SAVE :: GeomSet(:), GradSet(:) ! MRESET*NCoord

      REAL(KREAL), ALLOCATABLE, SAVE :: DX(:), GSAVE(:) !NCoord

    REAL(KREAL), SAVE :: ESET(MRESET)

    REAL(KREAL) :: ESET_tmp(MRESET), B(M2),BS(M2),BST(M2), B_tmp(M2) ! M2=256

      LOGICAL DEBUG, PRINT, ci_lt_zero

      INTEGER(KINT), SAVE :: MSET ! mth Iteration

    REAL(KREAL) :: ci(MRESET), ci_tmp(MRESET) ! MRESET = maximum number of iterations.

      INTEGER(KINT) :: NGEDIIS, MPLUS, INV, ITERA, MM, cis_zero

      INTEGER(KINT) :: I, J, K, JJ, JNV, II, IONE, IJ, IX, JX, KX

    INTEGER(KINT) :: current_size_B_mat, MyPointer

      REAL(KREAL) :: XMax, XNorm, DET, THRES, tmp, ER_star, ER_star_tmp

      DEBUG=.TRUE.

      PRINT=.FALSE.

      IF (PRINT)  WRITE(*,'(/,''      BEGIN GEDIIS   '')')

      ! Initialization

      IF (FRST) THEN

      ! FRST will be set to False in SPACE_GEDIIS, so no need to modify it here

         IF (ALLOCATED(GeomSet)) THEN

            IF (PRINT)  WRITE(*,'(/,''    In FRST, GEDIIS Dealloc  '')')

            DEALLOCATE(GeomSet,GradSet,DX,GSave)

            RETURN

         ELSE

            IF (PRINT)  WRITE(*,'(/,''     In FRST,  GEDIIS Alloc  '')')

            ALLOCATE(GeomSet(MRESET*NCoord),GradSet(MRESET*NCoord),DX(NCoord),GSAVE(NCoord))

         END IF

      END IF ! IF (FRST) THEN

      ! SPACE_GEDIIS SIMPLY LOADS THE CURRENT VALUES OF Geom AND Grad INTO THE ARRAYS GeomSet

      ! AND GradSet, MSET is set to zero and then 1 in SPACE_GEDIIS at first iteration.

      CALL SPACE_GEDIIS(MRESET,MSET,Geom,Grad,HEAT,NCoord,GeomSet,GradSet,ESET,FRST)

      IF (PRINT)  WRITE(*,'(/,''       GEDIIS after SPACE_GEDIIS  '')')

      ! INITIALIZE SOME VARIABLES AND CONSTANTS:

      NGEDIIS = MSET !MSET=mth iteration

      MPLUS = MSET + 1

      MM = MPLUS * MPLUS

      ! CONSTRUCT THE GEDIIS MATRIX:

      ! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>

      JJ=0

      INV=-NCoord

      DO I=1,MSET

         INV=INV+NCoord

         JNV=-NCoord

         DO J=1,MSET

            JNV=JNV+NCoord

            JJ = JJ + 1

            B(JJ)=0.D0

      DO K=1, NCoord

         B(JJ) = B(JJ) + (((GradSet(INV+K)-GradSet(JNV+K))*(GeomSet(INV+K)-GeomSet(JNV+K)))/2.D0)

      END DO

         END DO

      END DO

     ! The following shifting is required to correct indices of B_ij elements in the GEDIIS matrix.

   ! The correction is needed because the last coloumn of the matrix contains all 1 and one zero.

      DO I=MSET-1,1,-1

         DO J=MSET,1,-1

            B(I*MSET+J+I) = B(I*MSET+J)

         END DO

    END DO

      ! for last row and last column of GEDIIS matrix

      DO I=1,MPLUS

         B(MPLUS*I) = 1.D0

         B(MPLUS*MSET+I) = 1.D0

      END DO

      B(MM) = 0.D0

    DO I=1, MPLUS

       !WRITE(*,'(10(1X,F20.4))') B((I-1)*MPLUS+1:I*(MPLUS))

    END DO

      ! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM:

   80 CONTINUE

      DO I=1,MM !MM = (MSET+1) * (MSET+1)

         BS(I) = B(I) !just a copy of the original B (GEDIIS) matrix

      END DO

      IF (NGEDIIS .NE. MSET) THEN

        DO II=1,MSET-NGEDIIS

           XMAX = -1.D10

           ITERA = 0

           DO I=1,MSET

              XNORM = 0.D0

              INV = (I-1) * MPLUS

              DO J=1,MSET

                 XNORM = XNORM + ABS(B(INV + J))

              END DO

              IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN

                 XMAX = XNORM

                 ITERA = I

                 IONE = INV + I

              ENDIF

           END DO

           DO I=1,MPLUS

              INV = (I-1) * MPLUS

              DO J=1,MPLUS

                 JNV = (J-1) * MPLUS

                 IF (J.EQ.ITERA) B(INV + J) = 0.D0

                 B(JNV + I) = B(INV + J)

              END DO

       END DO

           B(IONE) = 1.0D0

        END DO

    END IF ! matches IF (NGEDIIS .NE. MSET) THEN

      ! SCALE GEDIIS MATRIX BEFORE INVERSION:

      DO I=1,MPLUS

         II = MPLUS * (I-1) + I ! B(II)=diagonal elements of B matrix

         GSAVE(I) = 1.D0 / DSQRT(1.D-20+DABS(B(II)))

     !Print *, 'GSAVE(',I,')=', GSAVE(I)

      END DO

      GSAVE(MPLUS) = 1.D0

      DO I=1,MPLUS

         DO J=1,MPLUS

            IJ = MPLUS * (I-1) + J

            B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J)

         END DO

      END DO

     ! INVERT THE GEDIIS MATRIX B:

    DO I=1, MPLUS

       !WRITE(*,'(10(1X,F20.4))') B((I-1)*MPLUS+1:I*(MPLUS))

    END DO

      CALL MINV(B,MPLUS,DET) ! matrix inversion.

    DO I=1, MPLUS

       !WRITE(*,'(10(1X,F20.16))') B((I-1)*MPLUS+1:I*(MPLUS))

    END DO

      DO I=1,MPLUS

         DO J=1,MPLUS

            IJ = MPLUS * (I-1) + J

            B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J)

         END DO

      END DO

      ! COMPUTE THE NEW INTERPOLATED PARAMETER VECTOR (Geometry):

    ci=0.d0

    ci_tmp=0.d0

    ci_lt_zero= .FALSE.

    DO I=1, MSET

     DO J=1, MSET ! B matrix is read column-wise

        ci(I)=ci(I)+B((J-1)*(MPLUS)+I)*ESET(J) !ESET is energy set, yet to be fixed.

     END DO

     ci(I)=ci(I)+B((MPLUS-1)*(MPLUS)+I)

     !Print *, 'NO ci < 0 yet, c(',I,')=', ci(I)

     IF((ci(I) .LT. 0.0D0) .OR. (ci(I) .GT. 1.0D0)) THEN

       ci_lt_zero=.TRUE.

       EXIT

     END IF

      END DO !matches DO I=1, MSET

    IF (ci_lt_zero) Then

       cis_zero = 0

         ER_star = 0.D0

     ER_star_tmp = 1e32

     ! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>, Full B matrix created first and then rows and columns are removed.

         JJ=0

         INV=-NCoord

         DO IX=1,MSET

            INV=INV+NCoord

            JNV=-NCoord

            DO JX=1,MSET

               JNV=JNV+NCoord

               JJ = JJ + 1

               BST(JJ)=0.D0

           DO KX=1, NCoord

              BST(JJ) = BST(JJ) + (((GradSet(INV+KX)-GradSet(JNV+KX))*(GeomSet(INV+KX)-GeomSet(JNV+KX)))/2.D0)

           END DO

            END DO

       END DO

     DO I=1, (2**MSET)-2 ! all (2**MSET)-2 combinations of cis, except the one where all cis are .GT. 0 and .LT. 1

         ci(:)=1.D0

         ! find out which cis are zero in I:

       DO IX=1, MSET

          JJ=IAND(I, 2**(IX-1))

        IF(JJ .EQ. 0) Then

          ci(IX)=0.D0

          END IF

       END DO

       ci_lt_zero = .FALSE.

       ! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>, Full B matrix created first and then rows and columns are removed.

       DO IX=1, MSET*MSET

                B(IX) = BST(IX) !just a copy of the original B (GEDIIS) matrix

             END DO

             ! Removal of KXth row and KXth column in order to accomodate cI to be zero:

       current_size_B_mat=MSET

       cis_zero = 0

       ! The bits of I (index of the upper loop 'DO I=1, (2**MSET)-2'), gives which cis are zero.

       DO KX=1, MSET ! searching for each bit of I (index of the upper loop 'DO I=1, (2**MSET)-2')

          IF (ci(KX) .EQ. 0.D0) Then !remove KXth row and KXth column

           cis_zero = cis_zero + 1

             ! First row removal: (B matrix is read column-wise)

             JJ=0

                   DO IX=1,current_size_B_mat ! columns reading

                      DO JX=1,current_size_B_mat ! rows reading

                 IF (JX .NE. KX) Then

                     JJ = JJ + 1

                     B_tmp(JJ) = B((IX-1)*current_size_B_mat+JX)

                 END IF

              END DO

             END DO

             DO IX=1,current_size_B_mat*(current_size_B_mat-1)

                B(IX) = B_tmp(IX)

             END DO

             ! Now column removal:

             JJ=0

                   DO IX=1,KX-1 ! columns reading

                      DO JX=1,current_size_B_mat-1 ! rows reading

                 JJ = JJ + 1

                 B_tmp(JJ) = B(JJ)

              END DO

             END DO

                   DO IX=KX+1,current_size_B_mat

                      DO JX=1,current_size_B_mat-1

                 JJ = JJ + 1

                    B_tmp(JJ) = B(JJ+current_size_B_mat-1)

              END DO

             END DO

             DO IX=1,(current_size_B_mat-1)*(current_size_B_mat-1)

                B(IX) = B_tmp(IX)

             END DO

           current_size_B_mat = current_size_B_mat - 1

        END IF ! matches IF (ci(KX) .EQ. 0.D0) Then !remove

           END DO ! matches DO KX=1, MSET

       ! The following shifting is required to correct indices of B_ij elements in the GEDIIS matrix.

       ! The correction is needed because the last coloumn and row of the matrix contains all 1 and one zero.

       DO IX=MSET-cis_zero-1,1,-1

        DO JX=MSET-cis_zero,1,-1

           B(IX*(MSET-cis_zero)+JX+IX) = B(IX*(MSET-cis_zero)+JX)

        END DO

       END DO

       ! for last row and last column of GEDIIS matrix

       DO IX=1,MPLUS-cis_zero

        B((MPLUS-cis_zero)*IX) = 1.D0

        B((MPLUS-cis_zero)*(MSET-cis_zero)+IX) = 1.D0

       END DO

       B((MPLUS-cis_zero) * (MPLUS-cis_zero)) = 0.D0

           DO IX=1, MPLUS

              !WRITE(*,'(10(1X,F20.4))') B((IX-1)*MPLUS+1:IX*(MPLUS))

           END DO

       ! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM:

             IF (NGEDIIS .NE. MSET) THEN

          JX = min(MSET-NGEDIIS,MSET-cis_zero-1)

                DO II=1,JX

                   XMAX = -1.D10

                   ITERA = 0

                   DO IX=1,MSET-cis_zero

                      XNORM = 0.D0

                      INV = (IX-1) * (MPLUS-cis_zero)

                      DO J=1,MSET-cis_zero

                         XNORM = XNORM + ABS(B(INV + J))

                      END DO

                      IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN

                         XMAX = XNORM

                         ITERA = IX

                         IONE = INV + IX

                      ENDIF

           END DO

                   DO IX=1,MPLUS-cis_zero

                      INV = (IX-1) * (MPLUS-cis_zero)

                      DO J=1,MPLUS-cis_zero

                         JNV = (J-1) * (MPLUS-cis_zero)

                         IF (J.EQ.ITERA) B(INV + J) = 0.D0

                         B(JNV + IX) = B(INV + J)

            END DO

               END DO

                   B(IONE) = 1.0D0

          END DO

           END IF ! matches IF (NGEDIIS .NE. MSET) THEN

       ! SCALE GEDIIS MATRIX BEFORE INVERSION:

       DO IX=1,MPLUS-cis_zero

        II = (MPLUS-cis_zero) * (IX-1) + IX ! B(II)=diagonal elements of B matrix

        GSAVE(IX) = 1.D0 / DSQRT(1.D-20+DABS(B(II)))

       END DO

       GSAVE(MPLUS-cis_zero) = 1.D0

       DO IX=1,MPLUS-cis_zero

        DO JX=1,MPLUS-cis_zero

           IJ = (MPLUS-cis_zero) * (IX-1) + JX

           B(IJ) = B(IJ) * GSAVE(IX) * GSAVE(JX)

        END DO

       END DO

       ! INVERT THE GEDIIS MATRIX B:

       CALL MINV(B,MPLUS-cis_zero,DET) ! matrix inversion.

       DO IX=1,MPLUS-cis_zero

        DO JX=1,MPLUS-cis_zero

           IJ = (MPLUS-cis_zero) * (IX-1) + JX

           B(IJ) = B(IJ) * GSAVE(IX) * GSAVE(JX)

        END DO

       END DO

           DO IX=1, MPLUS

              !WRITE(*,'(10(1X,F20.4))') B((IX-1)*MPLUS+1:IX*(MPLUS))

           END DO

             ! ESET is rearranged to handle zero cis and stored in ESET_tmp:

       JJ=0

       DO IX=1, MSET

        IF (ci(IX) .NE. 0) Then

           JJ=JJ+1

           ESET_tmp(JJ) = ESET(IX)

        END IF

       END DO

       ! DETERMINATION OF nonzero cis:

       MyPointer=1

            DO IX=1, MSET-cis_zero

          tmp = 0.D0

            DO J=1, MSET-cis_zero ! B matrix is read column-wise

           tmp=tmp+B((J-1)*(MPLUS-cis_zero)+IX)*ESET_tmp(J)

        END DO

            tmp=tmp+B((MPLUS-cis_zero-1)*(MPLUS-cis_zero)+IX)

            IF((tmp .LT. 0.0D0) .OR. (tmp .GT. 1.0D0)) THEN

               ci_lt_zero=.TRUE.

               EXIT

        ELSE

           DO JX=MyPointer,MSET

              IF (ci(JX) .NE. 0) Then

                 ci(JX) = tmp

               MyPointer=JX+1

               EXIT

            END IF

           END DO

            END IF

             END DO !matches DO I=1, MSET-cis_zero

           !Print *, 'Local set of cis, first 10:, MSET=', MSET, ', I of (2**MSET)-2=', I

       !WRITE(*,'(10(1X,F20.4))') ci(1:MSET)

           !Print *, 'Local set of cis ends:****************************************'

             ! new set of cis determined based on the lower energy (ER_star):

       IF (.NOT. ci_lt_zero) Then

                Call Energy_GEDIIS(MRESET,MSET,ci,GeomSet,GradSet,ESET,NCoord,ER_star)

        IF (ER_star .LT. ER_star_tmp) Then

           ci_tmp=ci

           ER_star_tmp = ER_star

        END IF

             END IF ! matches IF (.NOT. ci_lt_zero) Then

          END DO !matches DO I=1, (2**K)-2 ! all (2**K)-2 combinations of cis, except the one where all cis are .GT. 0 and .LT. 1

      ci = ci_tmp

    END IF! matches IF (ci_lt_zero) Then

    Print *, 'Final set of cis, first 10:***********************************'

    WRITE(*,'(10(1X,F20.4))') ci(1:MSET)

    Print *, 'Final set of cis ends:****************************************'

    Geom_new(:) = 0.D0

    DO I=1, MSET

         Geom_new(:) = Geom_new(:) + (ci(I)*GeomSet((I-1)*NCoord+1:I*NCoord)) !MPLUS=MSET+1

     ! R_(N+1)=R*+DeltaR:

     DO J=1, NCoord

      tmp=0.D0

      DO K=1,NCoord

         !tmp=tmp+Hess((J-1)*NCoord+K)*GradSet((I-1)*NCoord+K) ! If Hinv=.False., then we need to invert Hess

      END DO

      Geom_new(J) = Geom_new(J) - (ci(I)*tmp)

     END DO

    END DO

    DX(:) = Geom(:) - Geom_new(:)

      XNORM = SQRT(DOT_PRODUCT(DX,DX))

      IF (PRINT) THEN

         WRITE (6,'(/10X,''DEVIATION IN X '',F10.4,8X,''DETERMINANT '',G9.3)') XNORM, DET

         !WRITE(*,'(10X,''GEDIIS COEFFICIENTS'')')

         !WRITE(*,'(10X,5F12.5)') (B(MPLUS*MSET+I),I=1,MSET)

      ENDIF

      ! THE FOLLOWING TOLERENCES FOR XNORM AND DET ARE SOMEWHAT ARBITRARY!

      THRES = MAX(10.D0**(-NCoord), 1.D-25)

      IF (XNORM.GT.2.D0 .OR. DABS(DET) .LT. THRES) THEN

         IF (PRINT)THEN

            WRITE(*,*) "THE GEDIIS MATRIX IS ILL CONDITIONED"

            WRITE(*,*) " - PROBABLY, VECTORS ARE LINEARLY DEPENDENT - "

            WRITE(*,*) "THE GEDIIS STEP WILL BE REPEATED WITH A SMALLER SPACE"

         END IF

         DO K=1,MM

      B(K) = BS(K) ! why this is reverted? Because "IF (NGEDIIS .GT. 0) GO TO 80", see below

         END DO

         NGEDIIS = NGEDIIS - 1

         IF (NGEDIIS .GT. 0) GO TO 80

         IF (PRINT) WRITE(*,'(10X,''NEWTON-RAPHSON STEP TAKEN'')')

         Geom_new(:) = Geom(:) ! Geom_new is set to original Geom, thus DX = Geom(:) - Geom_new(:)=zero

      END IF ! matches IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN

   !*******************************************************************************************************************

    Geom_new(:) = 0.D0

    DO I=1, MSET

         Geom_new(:) = Geom_new(:) + (ci(I)*GeomSet((I-1)*NCoord+1:I*NCoord)) !MPLUS=MSET+1

     ! R_(N+1)=R*+DeltaR:

     DO J=1, NCoord

      tmp=0.D0

      DO K=1,NCoord

         tmp=tmp+Hess((J-1)*NCoord+K)*GradSet((I-1)*NCoord+K) ! If Hinv=.False., then we need to invert Hess

      END DO

      Geom_new(J) = Geom_new(J) - (ci(I)*tmp)

     END DO

    END DO

   !*******************************************************************************************************************

      IF (PRINT)  WRITE(*,'(/,''       END GEDIIS  '',/)')

      END SUBROUTINE Step_GEDIIS