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MODULE m_closure

use m_juDFT

!- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!     Contains 3 subroutines that more or less check the closure:
!     closure :    checks whether the space group operations close
!     close_pt:    checks that the point group of the bravais 
!                  lattice closes
!     check_close: additionally calculate the multiplication table,
!                  inverse operations and also determines the type 
!                  of every operation                    mw99,gs00
!- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

CONTAINS

SUBROUTINE closure(mops,mrot,tau,nops,index_op,lclose)

   IMPLICIT NONE

   INTEGER, INTENT (IN)  :: mops           ! number of operations of the bravais lattice
   INTEGER, INTENT (IN)  :: nops           ! number of operations in space group
   INTEGER, INTENT (IN)  :: mrot(3,3,mops) ! refer to the operations of the 
   REAL,    INTENT (IN)  :: tau(3,mops)    ! bravais lattice
   INTEGER, INTENT (IN)  :: index_op(nops) ! mapping function between space group 
                                              ! op's and those of the bravais lattice
   LOGICAL, INTENT (OUT) :: lclose

   REAL    ttau(3),eps7
   INTEGER i,ii,j,jj,k,kk,mp(3,3),map(nops)

   eps7 = 1.0e-7

   ! loop over all operations
   DO jj = 1, nops
      j = index_op(jj)

      map(1:nops) = 0

      ! multiply {R_j|t_j}{R_i|t_i}
      DO ii = 1, nops
         i = index_op(ii)
         mp = matmul( mrot(:,:,j) , mrot(:,:,i) )
         ttau = tau(:,j) + matmul( mrot(:,:,j) , tau(:,i) )
         ttau = ttau - anint( ttau - eps7 )

         ! determine which operation this is
         DO kk=1,nops
            k = index_op(kk)
            IF ( all( mp(:,:) == mrot(:,:,k) ) .AND. all( abs( ttau(:)-tau(:,k) ) < eps7 ) ) THEN
               IF ( map(ii) .eq. 0 ) THEN
                  map(ii) = kk
               ELSE
                  write(6,*)'ERROR Closure: Multiplying ', jj,' with ',kk, ' and with ',map(ii)
                  write(6,*) 'yields the same matrix'
                  lclose = .false.
                  RETURN
               END IF
            END IF
         END DO

         IF (map(ii).eq.0) THEN
            write(6,*)'ERROR Closure:',ii,' times',jj,' leaves group'
            lclose = .false.
            RETURN
         END IF
      END DO
   END DO

   lclose = .true.

END SUBROUTINE closure

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

SUBROUTINE close_pt(nops,mrot,mtable)

   IMPLICIT NONE

   INTEGER, INTENT (IN)  :: nops,mrot(3,3,nops)
   INTEGER, INTENT (OUT) :: mtable(nops,nops)   ! table(i,j) = {R_i|0}{R_j|0}

   INTEGER              :: i,j,k,mp(3,3),map(nops)

   ! loop over all operations
   DO j = 1, nops

      map(1:nops) = 0

      ! multiply {R_j|0}{R_i|0}
      DO i = 1, nops
         mp = matmul( mrot(:,:,j) , mrot(:,:,i) )

         ! determine which operation this is
         DO k = 1, nops
            IF ( all( mp(:,:)==mrot(:,:,k) ) ) THEN
               IF ( map(i) .eq. 0 ) THEN
                  map(i) = k
               ELSE
                  WRITE (6,'(" Symmetry error : multiple ops")')
                  CALL juDFT_error("close_pt: Multiple ops (Bravais)",calledby ="closure")
               END IF
            END IF
         END DO

         IF (map(i).eq.0) THEN
            WRITE(6,*) 'Symmetry operations:'
            DO k = 1, nops
               WRITE(6,*) 'Matrix ', k, ':'
               WRITE(6,'(3i7)') mrot(:,1,k)
               WRITE(6,'(3i7)') mrot(:,2,k)
               WRITE(6,'(3i7)') mrot(:,3,k)
               WRITE(6,*) ''
            END DO
            WRITE (6,'(" Group not closed (Bravais lattice)")')
            WRITE (6,'(" operation j=",i2,"  map=",12i4,:/,(21x,12i4))')  j, map(1:nops)
            WRITE(6,*) ''
            WRITE(6,*) 'Expected product of operations ', j, ' and ', i, ':'
            WRITE(6,'(3i7)') mp(:,1)
            WRITE(6,'(3i7)') mp(:,2)
            WRITE(6,'(3i7)') mp(:,3)
            WRITE(6,*) ''
            CALL juDFT_error("close_pt:Not closed",calledby="closure")
         END IF
      END DO
      mtable(j,1:nops) = map(1:nops)
   END DO

END SUBROUTINE close_pt

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

SUBROUTINE check_close(nops,mrot,tau,multtab,inv_op,optype)

   IMPLICIT NONE

   INTEGER, INTENT (IN)  :: nops
   INTEGER, INTENT (IN)  :: mrot(3,3,nops)
   REAL,    INTENT (IN)  :: tau(3,nops)
   INTEGER, INTENT (OUT) :: inv_op(nops)
   INTEGER, INTENT (OUT) :: multtab(nops,nops)
   INTEGER, INTENT (OUT) :: optype(nops)

   REAL    ttau(3)
   INTEGER i,j,n,k,mp(3,3),mdet,mtr

   REAL,    PARAMETER :: eps=1.0e-7
   INTEGER, PARAMETER :: cops(-1:3)=(/ 2, 3, 4, 6, 1 /)

   inv_op(1:nops) = 0

   multtab = 0

   ! loop over all operations
   DO j = 1, nops

      ! multiply {R_j|t_j}{R_i|t_i}
      DO i = 1, nops
         mp = matmul( mrot(:,:,j) , mrot(:,:,i) )
         ttau = tau(:,j) + matmul( mrot(:,:,j) , tau(:,i) )
         ttau = ttau - anint( ttau - eps )

         ! determine which operation this is
         DO k=1,nops
            IF ( all( mp(:,:) == mrot(:,:,k) ) .and. all( abs( ttau(:)-tau(:,k) ) < eps ) ) THEN
               IF ( multtab(j,i) .eq. 0 ) THEN
                  multtab(j,i) = k
                  IF (k .eq. 1) inv_op(j)=i
               ELSE
                  WRITE(6,'(" Symmetry error: multiple ops")')
                  CALL juDFT_error("check_close: Multiple ops",calledby ="closure")
               END IF
            END IF
         END DO

         IF (multtab(j,i).eq.0) THEN
            WRITE (6,'(" Group not closed")')
            WRITE (6,'("  j , i =",2i4)') j,i
            CALL juDFT_error("check_close: Not closed",calledby="closure")
         END IF
      END DO
   END DO

   ! determine the type of each operation
   DO n = 1, nops
      mtr = mrot(1,1,n) + mrot(2,2,n) + mrot(3,3,n)
      mdet = mrot(1,1,n)*(mrot(2,2,n)*mrot(3,3,n)-mrot(3,2,n)*mrot(2,3,n)) +&
             mrot(1,2,n)*(mrot(3,1,n)*mrot(2,3,n)-mrot(2,1,n)*mrot(3,3,n)) +&
             mrot(1,3,n)*(mrot(2,1,n)*mrot(3,2,n)-mrot(3,1,n)*mrot(2,2,n))

      optype(n) = mdet*cops(mdet*mtr)

   END DO

END SUBROUTINE check_close

END MODULE m_closure