mirror of https://gitlab.com/QEF/q-e.git
383 lines
15 KiB
Fortran
383 lines
15 KiB
Fortran
!
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! Copyright (C) 2001-2007 Quantum ESPRESSO group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!----------------------------------------------------------------------
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SUBROUTINE init_us_b0(ecutwfc,intra_bgrp_comm)
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!----------------------------------------------------------------------
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!! In this routine the beta_l(r) are smoothed.
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!
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USE upf_kinds, ONLY : DP
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USE upf_io, ONLY : stdout
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USE upf_const, ONLY : fpi
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USE atom, ONLY : rgrid
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USE uspp_data, ONLY : dq
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USE uspp_param, ONLY : nsp, upf, nbetam
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USE mp, ONLY : mp_sum
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!
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IMPLICIT NONE
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!
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REAL(DP), INTENT(IN) :: ecutwfc
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INTEGER, INTENT(IN) :: intra_bgrp_comm
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!
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! FILTER PARAMETERS: see REAL(DP) FUNCTION filter( x, a, n ) below for full definition and meaning.
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INTEGER :: nf ! Smoothing parameter, order of the polynomial in the inverse gaussian approximant.
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REAL(DP):: af ! Smoothing parameter, exponent of the gaussian decaying factor, to be chosen so that
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! the filter has a flex at x=2/3 => af = 1.125d0 * ( 2 * nf + 1) .
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!
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LOGICAL, PARAMETER :: tprint=.FALSE. ! Whether the beta_l(r) and its relatives are printed or not.
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REAL(DP) :: rcut, drcut ! beta function cutoff radius and its estimated increase due to the filtering
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REAL(DP), PARAMETER :: eps = 1.d-9 ! error tolerance for integrals, norms etc.
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!
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INTEGER :: nqx
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REAL(DP), ALLOCATABLE :: tab0(:,:), tab(:,:), beta(:,:), betas(:,:)
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REAL(DP), ALLOCATABLE :: power_r(:), power_q(:)
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!
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INTEGER :: nt, nb, l, ir, iq, startq, lastq, ndm
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! various counters
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REAL(DP), ALLOCATABLE :: aux(:), besr(:), ffrr(:)
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! various work space
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REAL(DP) :: qi, qmax, vqint
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! the modulus of g for each shell
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! q-point grid for interpolation
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! interpolated value
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INTEGER :: kktest
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REAL(DP) :: test, safe_test, error_estimate, missing_norm
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LOGICAL :: first
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!
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CALL start_clock( 'init_us_b0' )
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!
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! ... Initialization of variables
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!
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drcut = 3.D0 * ABS(LOG(eps)) / SQRT(ecutwfc)/ 2.D0 ! estimate (to be restricted later)
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qmax = 3.D0 * SQRT(ecutwfc) ! maximum q that avoids aliasing, higher Fourier components must be negligible
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nqx = INT( qmax / dq + 4) ! Think about what happens in a variable cell calculations
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!
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ALLOCATE( tab0(nqx,nbetam), tab(nqx,nbetam) )
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ALLOCATE( power_r(nbetam), power_q(nbetam) )
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!
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WRITE( stdout, '(/5X,"PSEUDOPOTENTIAL Beta Smoothing: ==============================================")' )
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IF (tprint) THEN
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WRITE( stdout,'(/5X,"table grid dimensions: NQX =",I7," NBETAM =", I4)') nqx, nbetam
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WRITE( stdout,'(11X,"initial rcut indices:",10i7)') upf(1:nsp)%kkbeta
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WRITE( stdout,'(19X,"rcut (ityp) :",10f7.3)') (rgrid(nt)%r(upf(nt)%kkbeta),nt=1,nsp)
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END IF
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!
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DO nt=1,nsp
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rcut = rgrid(nt)%r(upf(nt)%kkbeta)
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DO ir = upf(nt)%kkbeta, upf(nt)%mesh
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IF ( rgrid(nt)%r(ir) < rcut + drcut ) upf(nt)%kkbeta=ir
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ENDDO
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ENDDO
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!
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ndm = MAXVAL( upf(:)%kkbeta )
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ALLOCATE( beta(ndm,nbetam), betas(ndm,nbetam) )
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ALLOCATE( aux(ndm), besr(ndm), ffrr(ndm) )
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!
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WRITE(6,'(/5X,a)') 'Pseudopotential projectors are smoothed with filter( q / qmax, a, nn )'
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WRITE(6,'(5X,a,1p,e12.4)') 'target error: eps =', eps
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!
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! ... fill the interpolation table tab
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!
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CALL divide( intra_bgrp_comm, nqx, startq, lastq )
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!
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!- loop over pseudopotentials
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DO nt = 1, nsp
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! likely, there is no point in smoothing GTH PPs
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IF ( upf(nt)%is_gth ) CYCLE
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WRITE( stdout, '(/5X,a,i4)' ) 'Smoothing PSEUDO #', nt
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!
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!- compute original beta normalization in real space where grid is sufficient by definition
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DO nb = 1, upf(nt)%nbeta
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l = upf(nt)%lll (nb)
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kktest = upf(nt)%kkbeta
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aux(1:kktest) = upf(nt)%beta(1:kktest,nb) * upf(nt)%beta(1:kktest,nb)
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CALL simpson( kktest, aux, rgrid(nt)%rab, power_r(nb) )
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ENDDO
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IF (tprint) THEN
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WRITE( stdout, '(5X,a)' ) "BETA FUNCTIONS NORMS:"
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WRITE( stdout, '(5X,a,1p,10e12.4)') "norm2 R:", (power_r(nb), nb=1,upf(nt)%nbeta)
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!- write the radial beta_l(r) as defined in the pseudopotential
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CALL write_beta_r( 'br_', nt, upf(nt)%beta, upf(nt)%kkbeta, upf(nt)%nbeta )
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END IF
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!
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!- compute the fourier transform of the beta and their (truncated) back f.t. in real space
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tab0(:,:) = 0.d0 ; beta(:,:) = 0.d0
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DO nb = 1, upf(nt)%nbeta
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l = upf(nt)%lll (nb)
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DO iq = startq, lastq
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qi = (iq - 1) * dq
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CALL sph_bes (upf(nt)%kkbeta, rgrid(nt)%r, qi, l, besr)
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DO ir = 1, upf(nt)%kkbeta
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aux (ir) = upf(nt)%beta (ir, nb) * besr (ir) * rgrid(nt)%r(ir)
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ENDDO
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CALL simpson( upf(nt)%kkbeta, aux, rgrid(nt)%rab, vqint )
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!
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tab0(iq, nb) = vqint
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!
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DO ir = 1, upf(nt)%kkbeta
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beta (ir,nb) = beta (ir,nb) + qi*qi * dq * tab0(iq,nb) * besr (ir) * rgrid(nt)%r(ir)
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ENDDO
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ENDDO
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ENDDO
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CALL mp_sum( tab0, intra_bgrp_comm )
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beta = beta * 8.d0/fpi ; CALL mp_sum( beta , intra_bgrp_comm )
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!
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!- compute the beta normalization in q space to see how much of the original is lost
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DO nb = 1, upf(nt)%nbeta
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l = upf(nt)%lll (nb)
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power_q(nb) =0.d0
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DO iq = startq, lastq
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qi = (iq - 1) * dq
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power_q(nb) = power_q(nb) + qi*qi * dq * tab0(iq,nb) * tab0(iq,nb)
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ENDDO
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ENDDO
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power_q = power_q * 8.d0/fpi ; CALL mp_sum( power_q, intra_bgrp_comm )
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IF (tprint) THEN
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WRITE( stdout, '(5X,a,1p,10e12.4)') "norm2 Q:", (power_q(nb), nb=1,upf(nt)%nbeta)
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WRITE( stdout, '(5X,a,1p,10e12.4)') "1-ratio:", (1.D0-power_q(nb)/power_r(nb), nb=1,upf(nt)%nbeta)
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END IF
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!- fraction of beta normalizations that is lost due to Q space truncation
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missing_norm = MAXVAL(1.d0-power_q(1:upf(nt)%nbeta)/power_r(1:upf(nt)%nbeta))
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!
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!- determine the mildest filter that deliver the required accuracy in reciprocal space
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nf = 20 ; af = 1.125D0 * ( 2 * nf + 1) ; error_estimate= missing_norm * filter(1.d0,af,nf)**2
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do while ( error_estimate < eps .and. nf > 0)
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nf = nf - 1 ; af = 1.125D0 * ( 2 * nf + 1) ; error_estimate = missing_norm * filter(1.d0,af,nf)**2
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end do
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nf = min(nf+1,20) ; af = 1.125D0 * ( 2 * nf + 1); error_estimate = missing_norm * filter(1.d0,af,nf)**2
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WRITE ( stdout, '(5x,"Smoothing truncation error estimate in Q",1pe12.4," < eps")' ) error_estimate
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IF (error_estimate > eps ) CALL upf_error( 'init_us_b0','R and Q norms of beta are too different',nt)
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WRITE(6,'(5X,a,a,f6.2,a,i4,2(a,f11.8))') 'FILTER parameters :', &
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' a=',af,', nn=',nf,', filter(1.0/3)=', filter(1.d0/3,af,nf), ', filter(1.0)=', filter(1.d0,af,nf)
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!
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!- compute the fourier transform of the smoothed beta and their (truncated) back f.t. in real space
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tab(:,:) = 0.d0 ; betas(:,:) = 0.d0
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DO nb = 1, upf(nt)%nbeta
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l = upf(nt)%lll (nb)
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DO iq = startq, lastq
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qi = (iq - 1) * dq
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CALL sph_bes (upf(nt)%kkbeta, rgrid(nt)%r, qi, l, besr)
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!
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tab (iq, nb) = tab0(iq, nb) * filter( qi / qmax, af, nf )
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!
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DO ir = 1, upf(nt)%kkbeta
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betas(ir,nb) = betas(ir,nb) + qi*qi * dq * tab (iq,nb) * besr (ir) * rgrid(nt)%r(ir)
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ENDDO
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ENDDO
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ENDDO
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CALL mp_sum( tab , intra_bgrp_comm )
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betas= betas* 8.d0/fpi ; CALL mp_sum( betas, intra_bgrp_comm )
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upf(nt)%beta(1:upf(nt)%kkbeta,1:upf(nt)%nbeta) = betas(1:upf(nt)%kkbeta,1:upf(nt)%nbeta)
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!
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!-Fix the core cutoff radius kkbeta so that no more than eps of the integral is lost.
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! Parseval's identity is used to monitor the real space completeness of the integral of betas**2
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!
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!- Compute the integral in Fourier space of the smoothed projectors
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DO nb = 1, upf(nt)%nbeta
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l = upf(nt)%lll (nb)
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power_q(nb) =0.d0
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DO iq = startq, lastq
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qi = (iq - 1) * dq
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power_q(nb) = power_q(nb) + qi*qi * dq * tab(iq,nb) * tab(iq,nb)
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ENDDO
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ENDDO
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power_q = power_q * 8.d0/fpi ; CALL mp_sum( power_q, intra_bgrp_comm )
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!
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!- Compute norms in real space up to the current value of kkbeta and reduce it if close enough to power_q
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kktest = upf(nt)%kkbeta + 1 ; test = 0.d0 ; first =.TRUE. ! initialize mesh limit and test value
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DO WHILE ( test < eps )
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safe_test = test ; kktest = kktest - 1
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DO nb = 1, upf(nt)%nbeta
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l = upf(nt)%lll (nb)
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aux(1:kktest) = betas(1:kktest,nb) * betas(1:kktest,nb)
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CALL simpson( kktest, aux, rgrid(nt)%rab, power_r(nb) )
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ENDDO
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IF ( first ) THEN
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first = .FALSE.
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test = MAXVAL( 1.d0 - power_r(1:upf(nt)%nbeta)/power_q(1:upf(nt)%nbeta) )
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if (test>eps) WRITE (stdout,'(5X,"WARNING: R and Q norms disagree by",6X,1pe12.4," > eps !")') test
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power_q = power_r
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END IF
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test = MAXVAL( 1.d0 - power_r(1:upf(nt)%nbeta)/power_q(1:upf(nt)%nbeta) )
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! write( stdout, * ) kktest, rgrid(nt)%r(kktest), test
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ENDDO
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upf(nt)%kkbeta = kktest + 1 ! set the mesh limit to the last value fulfilling the test condition
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WRITE( stdout, '(5X,"kkbeta, r(kkbeta), error in R",i5,f7.3,1pe11.4," < eps")' ) &
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upf(nt)%kkbeta, rgrid(nt)%r(upf(nt)%kkbeta), safe_test
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!
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IF (tprint) THEN
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!- write the radial fourier transform of beta_l in reciprcal space up to qmax
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CALL write_beta_q( 'bq_', nt, tab0 )
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!- write the smoothed radial fourier transform of beta_l in reciprcal space up to qmax
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CALL write_beta_q( 'bqs', nt, tab )
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!- write the back radial fourier transform of beta_l in real space
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CALL write_beta_r( 'brq', nt, beta, ndm, nbetam )
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!- write the back radial fourier transform of the smoothed beta_l in real space
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CALL write_beta_r( 'brs', nt, betas, ndm, nbetam )
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!- write the filter in reciprocal space
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CALL write_filter_q( 'ffq', nt, af, nf )
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!- write the filter in real space
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CALL write_filter_r( 'ffr', nt, af, nf )
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ENDIF
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!
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ENDDO
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!- end of loop over pseudopotentials
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IF (tprint) THEN
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WRITE( stdout,'(/13X,"final rcut indices:",10i7)') upf(1:nsp)%kkbeta
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WRITE( stdout,'(19X,"rcut (ityp) :",10f7.3)') (rgrid(nt)%r(upf(nt)%kkbeta),nt=1,nsp)
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END IF
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WRITE( stdout, '(/5X,"PSEUDOPOTENTIAL end Beta Smoothing: ==========================================")' )
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!
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DEALLOCATE( power_r, power_q )
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DEALLOCATE( tab0, tab )
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DEALLOCATE( beta, betas )
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DEALLOCATE( besr, aux, ffrr )
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!
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CALL stop_clock( 'init_us_b0' )
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!
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RETURN
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!
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CONTAINS
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!
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REAL(DP) FUNCTION filter( x, a, n )
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!
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IMPLICIT NONE
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!
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REAL(DP), INTENT(IN) :: x, a
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INTEGER, INTENT(IN) :: n
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REAL(DP) :: axx, ff
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INTEGER :: k
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!
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axx = a * x * x
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!
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ff = 1.d0
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DO k = n, 1, -1
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ff = (1.d0+axx/REAL(k)*ff)
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ENDDO
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filter = ff * EXP(-axx)
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!
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RETURN
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!
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END FUNCTION filter
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!
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! I/O routines used when tprint = .TRUE.
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!
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SUBROUTINE write_beta_r( filename_, nt, beta_, ndm, nbetam )
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!
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IMPLICIT NONE
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!
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CHARACTER(LEN=3), INTENT(IN) :: filename_
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INTEGER, INTENT(IN) :: nt, ndm, nbetam
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REAL(DP), INTENT(IN) :: beta_(ndm, nbetam)
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!
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CHARACTER(LEN=4) :: filename
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INTEGER :: ir, nb
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filename(1:3) = filename_; WRITE(filename( 4:4 ),'(i1)') nt
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OPEN(4, FILE=filename, FORM='formatted', STATUS='unknown')
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if (filename(1:3)=='br_') WRITE(4,*) '# the radial beta_l(r) as defined in the pseudopotential'
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if (filename(1:3)=='brq') WRITE(4,*) '# the back radial fourier transform of beta_l in real space'
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WRITE(4,*) '# nbeta :', upf(nt)%nbeta,' kkbeta :',upf(nt)%kkbeta
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if ( upf(nt)%nbeta > nbetam ) CALL upf_error('init_us_b0','wrong nbetam in write_beta_r', nbetam )
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if ( upf(nt)%kkbeta > ndm ) CALL upf_error('init_us_b0','wrong ndm in write_beta_r', ndm )
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DO ir = 1, upf(nt)%kkbeta
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WRITE(4,'(12f16.10)') rgrid(nt)%r(ir), (beta_(ir,nb), nb=1,upf(nt)%nbeta)
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ENDDO
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CLOSE(4)
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!
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END SUBROUTINE write_beta_r
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SUBROUTINE write_beta_q( filename_, nt, tab_ )
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!
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IMPLICIT NONE
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!
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CHARACTER(LEN=3), INTENT(IN) :: filename_
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INTEGER, INTENT(IN) :: nt
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REAL(DP), INTENT(IN) :: tab_(nqx, nbetam)
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!
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CHARACTER(LEN=4) :: filename
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INTEGER :: iq, nb
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REAL(DP) :: qi
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!-
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filename(1:3) = filename_; WRITE(filename( 4:4 ),'(i1)') nt
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OPEN(4, FILE=filename, FORM='formatted', STATUS='unknown')
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if (filename(1:3)=='bq_') WRITE(4,*) &
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'# the radial fourier transform of beta_l in reciprcal space up to qmax'
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if (filename(1:3)=='bqs') WRITE(4,*) &
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'# the smoothed radial fourier transform of beta_l in reciprcal space up to qmax'
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WRITE(4,*) '# nbeta :', upf(nt)%nbeta,' nqx :',nqx, dq*nqx
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DO iq = 1, nqx
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qi = (iq - 1) * dq
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WRITE(4,'(12f16.10)') qi,(tab_(iq,nb), nb=1,upf(nt)%nbeta)
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ENDDO
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CLOSE(4)
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!
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END SUBROUTINE write_beta_q
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!
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SUBROUTINE write_filter_q( filename_, nt, af, nf )
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!
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IMPLICIT NONE
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!
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CHARACTER(LEN=3), INTENT(IN) :: filename_
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INTEGER, INTENT(IN) :: nt, nf
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REAL(DP), INTENT(IN) :: af
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!
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CHARACTER(LEN=4) :: filename
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INTEGER :: iq
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REAL(DP) :: qi
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filename(1:3) = filename_; WRITE(filename( 4:4 ),'(i1)') nt
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OPEN(4,FILE=filename, FORM='formatted', STATUS='unknown')
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WRITE(4, *) '# the filter in reciprocal space'
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WRITE(4, *) '# fillter : a=',af,', nn=', nf
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DO iq = 1, nqx
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qi = (iq - 1) * dq
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WRITE(4,'(12f16.10)') qi, filter( qi/qmax, af, nf)
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ENDDO
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CLOSE(4)
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!
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END SUBROUTINE write_filter_q
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SUBROUTINE write_filter_r( filename_, nt, af, nf )
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!
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IMPLICIT NONE
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!
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CHARACTER(LEN=3), INTENT(IN) :: filename_
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INTEGER, INTENT(IN) :: nt, nf
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REAL(DP), INTENT(IN) :: af
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!
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CHARACTER(LEN=4) :: filename
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INTEGER :: iq
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REAL(DP) :: qi
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!- compute the (spherical) fourier transform of the filter in real space
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ffrr(:) = 0.d0
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DO iq = startq, lastq
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qi = (iq - 1) * dq
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CALL sph_bes (upf(nt)%kkbeta, rgrid(nt)%r, qi, 0, besr)
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DO ir = 1, upf(nt)%kkbeta
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ffrr (ir) = ffrr (ir) + qi*qi * dq * filter( qi / qmax, af, nf) * besr (ir)
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ENDDO
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END DO
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CALL mp_sum( ffrr, intra_bgrp_comm )
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ffrr(:) = 8.D0 / fpi * ffrr(:)
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!- write it on file
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filename(1:3) = filename_; WRITE(filename( 4:4 ),'(i1)') nt
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OPEN(4,FILE=filename, FORM='formatted', STATUS='unknown')
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WRITE(4, *) '# the filter in real space'
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WRITE(4, *) '# fillter : a=',af,', nn=', nf
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DO ir = 1, upf(nt)%kkbeta
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WRITE(4,'(12f16.10)') rgrid(nt)%r(ir), ffrr(ir)
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ENDDO
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CLOSE(4)
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!
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END SUBROUTINE write_filter_r
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END SUBROUTINE init_us_b0
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