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!
! Copyright (C) 2006-2010 Quantum ESPRESSO group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!
!
!----------------------------------------------------------------------
! Module to compute finite differences gradients on dense real space grid
! Written by Oliviero Andreussi
!----------------------------------------------------------------------
!
!=----------------------------------------------------------------------=!
MODULE fd_gradient
!=----------------------------------------------------------------------=!
USE kinds, ONLY: DP
IMPLICIT NONE
CONTAINS
!=----------------------------------------------------------------------=!
SUBROUTINE calc_fd_gradient( nfdpoint, icfd, ncfd, nnr, f, grad )
!=----------------------------------------------------------------------=!
USE kinds, ONLY : DP
USE cell_base, ONLY : at, bg, alat
USE fft_base, ONLY : dfftp
USE fft_types, ONLY : fft_index_to_3d
USE scatter_mod, ONLY : scatter_grid
USE mp, ONLY : mp_sum
USE mp_bands, ONLY : me_bgrp, intra_bgrp_comm
IMPLICIT NONE
!
INTEGER, INTENT(IN) :: nfdpoint
INTEGER, INTENT(IN) :: ncfd
INTEGER, INTENT(IN) :: icfd(-nfdpoint:nfdpoint)
INTEGER, INTENT(IN) :: nnr
REAL( DP ), DIMENSION( nnr ), INTENT(IN) :: f
REAL( DP ), DIMENSION( 3, nnr ), INTENT(OUT) :: grad
INTEGER :: i, ir, ir_end, ipol, in
INTEGER :: ix(-nfdpoint:nfdpoint),iy(-nfdpoint:nfdpoint),iz(-nfdpoint:nfdpoint)
INTEGER :: ixc, iyc, izc, ixp, ixm, iyp, iym, izp, izm
REAL( DP ), DIMENSION( :, : ), ALLOCATABLE :: gradtmp, gradaux
LOGICAL :: offrange
!
grad = 0.D0
!
ALLOCATE( gradtmp( dfftp%nr1x*dfftp%nr2x*dfftp%nr3x, 3 ) )
gradtmp = 0.D0
!
#if defined (__MPI)
ir_end = MIN(nnr,dfftp%nr1x*dfftp%my_nr2p*dfftp%my_nr3p)
#else
ir_end = nnr
#endif
!
DO ir = 1, ir_end
!
CALL fft_index_to_3d (ir, dfftp, ix(0), iy(0), iz(0), offrange)
IF ( offrange ) CYCLE
!
DO in = 1, nfdpoint
ix(in) = ix(in-1) + 1
IF( ix(in) .GT. dfftp%nr1-1 ) ix(in) = 0
ix(-in) = ix(-in+1) - 1
IF( ix(-in) .LT. 0 ) ix(-in) = dfftp%nr1-1
iy(in) = iy(in-1) + 1
IF( iy(in) .GT. dfftp%nr2-1 ) iy(in) = 0
iy(-in) = iy(-in+1) - 1
IF( iy(-in) .LT. 0 ) iy(-in) = dfftp%nr2-1
iz(in) = iz(in-1) + 1
IF( iz(in) .GT. dfftp%nr3-1 ) iz(in) = 0
iz(-in) = iz(-in+1) - 1
IF( iz(-in) .LT. 0 ) iz(-in) = dfftp%nr3-1
ENDDO
!
DO in = -nfdpoint, nfdpoint
i = ix(in) + iy(0) * dfftp%nr1x + iz(0) * dfftp%nr1x * dfftp%nr2x + 1
gradtmp(i,1) = gradtmp(i,1) - icfd(in)*f(ir)*dfftp%nr1
i = ix(0) + iy(in) * dfftp%nr1x + iz(0) * dfftp%nr1x * dfftp%nr2x + 1
gradtmp(i,2) = gradtmp(i,2) - icfd(in)*f(ir)*dfftp%nr2
i = ix(0) + iy(0) * dfftp%nr1x + iz(in) * dfftp%nr1x * dfftp%nr2x + 1
gradtmp(i,3) = gradtmp(i,3) - icfd(in)*f(ir)*dfftp%nr3
ENDDO
!
ENDDO
!
ALLOCATE( gradaux(nnr,3) )
#if defined (__MPI)
DO ipol = 1, 3
CALL mp_sum( gradtmp(:,ipol), intra_bgrp_comm )
CALL scatter_grid ( dfftp, gradtmp(:,ipol), gradaux(:,ipol) )
ENDDO
#else
gradaux(1:nnr,:) = gradtmp(1:nnr,:)
#endif
!
DEALLOCATE( gradtmp )
!
DO ir = 1,nnr
grad(:,ir) = MATMUL( bg, gradaux(ir,:) )
ENDDO
DEALLOCATE( gradaux )
!
grad = grad / DBLE(ncfd) / alat
!
RETURN
END SUBROUTINE calc_fd_gradient
SUBROUTINE init_fd_gradient( ifdtype, nfdpoint, ncfd, icfd )
USE kinds, ONLY : DP
IMPLICIT NONE
!
INTEGER, INTENT(IN) :: ifdtype, nfdpoint
INTEGER, INTENT(OUT) :: ncfd
INTEGER, INTENT(OUT) :: icfd(-nfdpoint:nfdpoint)
!
INTEGER :: in
!
ncfd = 0
icfd = 0
!
SELECT CASE ( ifdtype )
!
CASE ( 1 )
! (2N+1)-point Central Differences
IF ( nfdpoint .EQ. 1 ) THEN
ncfd = 2
icfd( 1 ) = 1
ELSE IF ( nfdpoint .EQ. 2 ) THEN
ncfd = 12
icfd( 2 ) = -1
icfd( 1 ) = 8
ELSE IF ( nfdpoint .EQ. 3 ) THEN
ncfd = 60
icfd( 3 ) = 1
icfd( 2 ) = -9
icfd( 1 ) = 45
ELSE IF ( nfdpoint .EQ. 4 ) THEN
ncfd = 840
icfd( 4 ) = -3
icfd( 3 ) = 32
icfd( 2 ) =-168
icfd( 1 ) = 672
ELSE
WRITE(*,*)'ERROR: wrong number of points',nfdpoint,&
&' for finite difference type ',ifdtype
STOP
ENDIF
!
CASE ( 2 )
! Low-Noise Lanczos Differentiators ( M = 2 )
IF ( nfdpoint .GE. 2 ) THEN
ncfd = (nfdpoint)*(nfdpoint+1)*(2*nfdpoint+1)/3
DO in = 1,nfdpoint
icfd( in ) = in
ENDDO
ELSE
WRITE(*,*)'ERROR: wrong number of points',nfdpoint,&
&' for finite difference type ',ifdtype
STOP
END IF
!
CASE ( 3 )
! Super Lanczos Low-Noise Differentiators ( M = 4 )
IF ( nfdpoint .EQ. 3 ) THEN
ncfd = 252
icfd( 3 ) = -22
icfd( 2 ) = 67
icfd( 1 ) = 58
ELSE IF ( nfdpoint .EQ. 4 ) THEN
ncfd = 1188
icfd( 4 ) = -86
icfd( 3 ) = 142
icfd( 2 ) = 193
icfd( 1 ) = 126
ELSE IF ( nfdpoint .EQ. 5 ) THEN
ncfd = 5148
icfd( 5 ) =-300
icfd( 4 ) = 294
icfd( 3 ) = 532
icfd( 2 ) = 503
icfd( 1 ) = 296
ELSE
WRITE(*,*)'ERROR: wrong number of points',nfdpoint,&
&' for finite difference type ',ifdtype
STOP
ENDIF
!
CASE ( 4 )
! Smooth Noise-Robust Differentiators ( n = 2 )
IF ( nfdpoint .EQ. 2 ) THEN
ncfd = 8
icfd( 2 ) = 1
icfd( 1 ) = 2
ELSE IF ( nfdpoint .EQ. 3 ) THEN
ncfd = 32
icfd( 3 ) = 1
icfd( 2 ) = 4
icfd( 1 ) = 5
ELSE IF ( nfdpoint .EQ. 4 ) THEN
ncfd = 128
icfd( 4 ) = 1
icfd( 3 ) = 6
icfd( 2 ) = 14
icfd( 1 ) = 14
ELSE IF ( nfdpoint .EQ. 5 ) THEN
ncfd = 512
icfd( 5 ) = 1
icfd( 4 ) = 8
icfd( 3 ) = 27
icfd( 2 ) = 48
icfd( 1 ) = 42
ELSE
WRITE(*,*)'ERROR: wrong number of points',nfdpoint,&
&' for finite difference type ',ifdtype
STOP
ENDIF
!
CASE ( 5 )
! Smooth Noise-Robust Differentiators ( n = 4 )
IF ( nfdpoint .EQ. 3 ) THEN
ncfd = 96
icfd( 3 ) = -5
icfd( 2 ) = 12
icfd( 1 ) = 39
ELSE IF ( nfdpoint .EQ. 4 ) THEN
ncfd = 96
icfd( 4 ) = -2
icfd( 3 ) = -1
icfd( 2 ) = 16
icfd( 1 ) = 27
ELSE IF ( nfdpoint .EQ. 5 ) THEN
ncfd = 1536
icfd( 5 ) = -11
icfd( 4 ) = -32
icfd( 3 ) = 39
icfd( 2 ) = 256
icfd( 1 ) = 322
ELSE
WRITE(*,*)'ERROR: wrong number of points',nfdpoint,&
&' for finite difference type ',ifdtype
STOP
ENDIF
!
CASE DEFAULT
!
WRITE(*,*)'ERROR: finite difference type unknown, ifdtype=',ifdtype
STOP
!
END SELECT
!
DO in = 1,nfdpoint
icfd( -in ) = - icfd( in )
ENDDO
!
RETURN
!
END SUBROUTINE init_fd_gradient
!=----------------------------------------------------------------------=!
END MODULE fd_gradient
!=----------------------------------------------------------------------=!
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