2006-04-03 18:33:22 +08:00
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!
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! Copyright (C) 2001-2004 PWSCF 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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#define ZERO ( 0.D0, 0.D0 )
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#define ONE ( 1.D0, 0.D0 )
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!
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!
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!----------------------------------------------------------------------------
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2006-12-12 19:02:09 +08:00
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SUBROUTINE cegterg_vdw( ndim, ndmx, nvec, nvecx, evc, &
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2006-04-03 18:33:22 +08:00
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ethr, overlap, e, btype, notcnv, iter )
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!----------------------------------------------------------------------------
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!
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! ... iterative solution of the eigenvalue problem:
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!
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! ... ( H - e S ) * evc = 0
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!
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! ... where H is an hermitean operator, e is a real scalar,
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! ... S is an overlap matrix, evc is a complex vector
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!
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USE io_global, ONLY : stdout
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USE kinds, ONLY : DP
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2008-04-13 00:12:49 +08:00
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USE mp_global, ONLY : intra_pool_comm
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USE mp, ONLY : mp_sum
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2006-04-03 18:33:22 +08:00
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!
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IMPLICIT NONE
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!
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! ... on INPUT
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!
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INTEGER :: ndim, ndmx, nvec, nvecx
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! dimension of the matrix to be diagonalized
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! leading dimension of matrix evc, as declared in the calling pgm unit
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! integer number of searched low-lying roots
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! maximum dimension of the reduced basis set
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! (the basis set is refreshed when its dimension would exceed nvecx)
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COMPLEX (KIND=DP) :: evc(ndmx,nvec)
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! evc contains the refined estimates of the eigenvectors
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REAL (KIND=DP) :: ethr
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! energy threshold for convergence
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! root improvement is stopped, when two consecutive estimates of the root
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! differ by less than ethr.
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LOGICAL :: overlap
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! if .FALSE. : do not calculate S|psi>
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INTEGER, INTENT(IN) :: btype(nvec)
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! band type ( 1 = occupied, 0 = empty )
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!
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! ... on OUTPUT
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!
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REAL(KIND=DP) :: e(nvec)
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! contains the estimated roots.
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INTEGER :: iter, notcnv
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! integer number of iterations performed
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! number of unconverged roots
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!
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! ... LOCAL variables
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!
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INTEGER, PARAMETER :: maxter = 20
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! maximum number of iterations
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!
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INTEGER :: kter, nbase, np, n, m
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! counter on iterations
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! dimension of the reduced basis
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! counter on the reduced basis vectors
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! do-loop counters
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COMPLEX (KIND=DP), ALLOCATABLE :: hc(:,:), sc(:,:), vc(:,:)
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! Hamiltonian on the reduced basis
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! S matrix on the reduced basis
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! the eigenvectors of the Hamiltonian
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COMPLEX(KIND=DP), ALLOCATABLE :: psi(:,:), hpsi(:,:), spsi(:,:)
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! work space, contains psi
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! the product of H and psi
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! the product of S and psi
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2009-08-03 16:15:09 +08:00
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COMPLEX(KIND=DP), EXTERNAL :: zdotc
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! auxiliary complex variable
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REAL(KIND=DP), ALLOCATABLE :: ew(:)
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! eigenvalues of the reduced hamiltonian
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LOGICAL, ALLOCATABLE :: conv(:)
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! true if the root is converged
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REAL (KIND=DP) :: empty_ethr
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! threshold for empty bands
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!
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! ... Called routines:
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!
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EXTERNAL h_psi, s_psi, g_psi
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! h_psi(ndmx,ndim,nvec,psi,hpsi)
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! calculates H|psi>
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! s_psi(ndmx,ndim,nvec,spsi)
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! calculates S|psi> (if needed)
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! Vectors psi,hpsi,spsi are dimensioned (ndmx,nvec)
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2007-02-02 21:55:32 +08:00
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! g_psi(ndmx,ndim,notcnv,npol,psi,e)
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! calculates (diag(h)-e)^-1 * psi, diagonal approx. to (h-e)^-1*psi
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! the first nvec columns contain the trial eigenvectors
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!
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!
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CALL start_clock( 'cegterg' )
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!
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! ... allocate the work arrays
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!
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ALLOCATE( psi( ndmx, nvecx ) )
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ALLOCATE( hpsi( ndmx, nvecx ) )
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IF ( overlap ) ALLOCATE( spsi( ndmx, nvecx ) )
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ALLOCATE( sc( nvecx, nvecx ) )
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ALLOCATE( hc( nvecx, nvecx ) )
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ALLOCATE( vc( nvecx, nvecx ) )
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ALLOCATE( ew( nvecx ) )
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ALLOCATE( conv( nvec ) )
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!
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IF ( nvec > nvecx / 2 ) CALL errore( 'cegter', 'nvecx is too small', 1 )
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!
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! ... threshold for empty bands
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!
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empty_ethr = MAX( ( ethr * 5.D0 ), 1.D-5 )
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!
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! ... prepare the hamiltonian for the first iteration
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!
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notcnv = nvec
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nbase = nvec
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conv = .FALSE.
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!
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IF ( overlap ) spsi = ZERO
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psi = ZERO
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hpsi = ZERO
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psi(:,1:nvec) = evc(:,1:nvec)
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!
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! ... hpsi contains h times the basis vectors
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!
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CALL h_psi( ndmx, ndim, nvec, psi, hpsi )
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!
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IF ( overlap ) CALL s_psi( ndmx, ndim, nvec, psi, spsi )
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!
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! ... hc contains the projection of the hamiltonian onto the reduced space
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! ... vc contains the eigenvectors of hc
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!
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hc(:,:) = ZERO
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sc(:,:) = ZERO
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vc(:,:) = ZERO
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'C', 'N', nbase, nbase, ndim, ONE, &
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2006-04-03 18:33:22 +08:00
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psi, ndmx, hpsi, ndmx, ZERO, hc, nvecx )
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!
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2008-04-13 00:12:49 +08:00
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CALL mp_sum( hc, intra_pool_comm )
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!
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IF ( overlap ) THEN
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!
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CALL zgemm( 'C', 'N', nbase, nbase, ndim, ONE, &
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2006-04-03 18:33:22 +08:00
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psi, ndmx, spsi, ndmx, ZERO, sc, nvecx )
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!
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ELSE
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!
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CALL zgemm( 'C', 'N', nbase, nbase, ndim, ONE, &
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2006-04-03 18:33:22 +08:00
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psi, ndmx, psi, ndmx, ZERO, sc, nvecx )
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!
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END IF
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!
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2008-04-13 00:12:49 +08:00
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CALL mp_sum( sc, intra_pool_comm )
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!
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FORALL( n = 1 : nbase )
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!
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e(n) = hc(n,n)
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!
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vc(n,n) = ONE
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!
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END FORALL
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!
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! ... iterate
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!
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iterate: DO kter = 1, maxter
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!
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iter = kter
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!
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CALL start_clock( 'update' )
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!
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np = 0
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!
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DO n = 1, nvec
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!
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IF ( .NOT. conv(n) ) THEN
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!
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! ... this root not yet converged ...
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!
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np = np + 1
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!
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! ... reorder eigenvectors so that coefficients for unconverged
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! ... roots come first. This allows to use quick matrix-matrix
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! ... multiplications to set a new basis vector (see below)
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!
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IF ( np /= n ) vc(:,np) = vc(:,n)
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!
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! ... for use in g_psi
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!
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ew(nbase+np) = e(n)
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!
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END IF
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!
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END DO
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!
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! ... expand the basis set with new basis vectors ( H - e*S )|psi> ...
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!
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IF ( overlap ) THEN
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'N', 'N', ndim, notcnv, nbase, ONE, spsi, &
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2006-04-03 18:33:22 +08:00
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ndmx, vc, nvecx, ZERO, psi(1,nbase+1), ndmx )
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!
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ELSE
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'N', 'N', ndim, notcnv, nbase, ONE, psi, &
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2006-04-03 18:33:22 +08:00
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ndmx, vc, nvecx, ZERO, psi(1,nbase+1), ndmx )
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!
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END IF
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!
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FORALL( np = 1: notcnv ) &
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psi(:,nbase+np) = - ew(nbase+np) * psi(:,nbase+np)
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'N', 'N', ndim, notcnv, nbase, ONE, hpsi, &
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2006-04-03 18:33:22 +08:00
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ndmx, vc, nvecx, ONE, psi(1,nbase+1), ndmx )
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!
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CALL stop_clock( 'update' )
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!
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! ... approximate inverse iteration
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!
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2007-02-02 21:55:32 +08:00
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CALL g_psi( ndmx, ndim, notcnv, 1, psi(1,nbase+1), ew(nbase+1) )
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2006-04-03 18:33:22 +08:00
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!
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! ... "normalize" correction vectors psi(:,nbase+1:nbase+notcnv) in order
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! ... to improve numerical stability of subspace diagonalization cdiaghg
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! ... ew is used as work array : ew = <psi_i|psi_i>, i=nbase+1,nbase+notcnv
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!
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DO n = 1, notcnv
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!
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ew(n) = zdotc( ndim, psi(1,nbase+n), 1, psi (1,nbase+n), 1 )
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!
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END DO
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!
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2008-04-13 00:12:49 +08:00
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CALL mp_sum( ew, intra_pool_comm )
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2006-04-03 18:33:22 +08:00
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!
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FORALL( n = 1 : notcnv )
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!
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psi(:,nbase+n) = psi(:,nbase+n) / SQRT( ew(n) )
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!
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END FORALL
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!
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! ... here compute the hpsi and spsi of the new functions
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!
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CALL h_psi( ndmx, ndim, notcnv, psi(1,nbase+1), hpsi(1,nbase+1) )
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!
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IF ( overlap ) &
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CALL s_psi( ndmx, ndim, notcnv, psi(1,nbase+1), spsi(1,nbase+1) )
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!
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! ... update the reduced hamiltonian
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!
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CALL start_clock( 'overlap' )
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'C', 'N', nbase+notcnv, notcnv, ndim, ONE, psi, ndmx, &
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2006-04-03 18:33:22 +08:00
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hpsi(1,nbase+1), ndmx, ZERO, hc(1,nbase+1), nvecx )
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!
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2008-04-13 00:12:49 +08:00
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CALL mp_sum( hc(:,nbase+1:nbase+notcnv), intra_pool_comm )
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2006-04-03 18:33:22 +08:00
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!
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IF ( overlap ) THEN
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'C', 'N', nbase+notcnv, notcnv, ndim, ONE, psi, ndmx, &
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2006-04-03 18:33:22 +08:00
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spsi(1,nbase+1), ndmx, ZERO, sc(1,nbase+1), nvecx )
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!
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ELSE
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'C', 'N', nbase+notcnv, notcnv, ndim, ONE, psi, ndmx, &
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2006-04-03 18:33:22 +08:00
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psi(1,nbase+1), ndmx, ZERO, sc(1,nbase+1), nvecx )
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!
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END IF
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!
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2008-04-13 00:12:49 +08:00
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CALL mp_sum( sc(:,nbase+1:nbase+notcnv), intra_pool_comm )
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2006-04-03 18:33:22 +08:00
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!
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CALL stop_clock( 'overlap' )
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!
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nbase = nbase + notcnv
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!
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! ifort 8.1 has some weird problem with forall
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!
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! FORALL( n = 1 : nbase )
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DO n = 1, nbase
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!
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! ... the diagonal of hc and sc must be strictly real
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!
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2009-08-03 16:15:09 +08:00
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hc(n,n) = CMPLX( REAL( hc(n,n) ), 0.D0 ,kind=DP)
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sc(n,n) = CMPLX( REAL( sc(n,n) ), 0.D0 ,kind=DP)
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2006-04-03 18:33:22 +08:00
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!
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! FORALL( m = n + 1 : nbase )
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DO m = n + 1, nbase
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!
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hc(m,n) = CONJG( hc(n,m) )
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sc(m,n) = CONJG( sc(n,m) )
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!
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END DO ! FORALL
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!
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END DO ! FORALL
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!
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! ... diagonalize the reduced hamiltonian
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!
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CALL cdiaghg( nbase, nvec, hc, sc, nvecx, ew, vc )
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!
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! ... test for convergence
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!
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WHERE( btype(:) == 1 )
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!
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conv(:) = ( ( ABS( ew(:) - e(:) ) < ethr ) )
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!
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ELSEWHERE
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!
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conv(:) = ( ( ABS( ew(:) - e(:) ) < empty_ethr ) )
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!
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END WHERE
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!
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notcnv = COUNT( .NOT. conv(:) )
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!
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e(1:nvec) = ew(1:nvec)
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!
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! ... if overall convergence has been achieved, OR
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! ... the dimension of the reduced basis set is becoming too large, OR
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! ... in any case if we are at the last iteration
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! ... refresh the basis set. i.e. replace the first nvec elements
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! ... with the current estimate of the eigenvectors;
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! ... set the basis dimension to nvec.
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!
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IF ( notcnv == 0 .OR. nbase+notcnv > nvecx .OR. iter == maxter ) THEN
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!
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|
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CALL start_clock( 'last' )
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|
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!
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2009-08-03 16:15:09 +08:00
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CALL zgemm( 'N', 'N', ndim, nvec, nbase, ONE, psi, &
|
2006-04-03 18:33:22 +08:00
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ndmx, vc, nvecx, ZERO, evc, ndmx )
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!
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|
|
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IF ( notcnv == 0 ) THEN
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!
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! ... all roots converged: return
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!
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CALL stop_clock( 'last' )
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!
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|
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EXIT iterate
|
|
|
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!
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|
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ELSE IF ( iter == maxter ) THEN
|
|
|
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!
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|
|
|
! ... last iteration, some roots not converged: return
|
|
|
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!
|
|
|
|
WRITE( UNIT = stdout, &
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|
|
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FMT = '(" WARNING: ",i5," eigenvalues not converged")' ) &
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|
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notcnv
|
|
|
|
!
|
|
|
|
CALL stop_clock( 'last' )
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|
|
!
|
|
|
|
EXIT iterate
|
|
|
|
!
|
|
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END IF
|
|
|
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!
|
|
|
|
! ... refresh psi, H*psi and S*psi
|
|
|
|
!
|
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|
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psi(:,1:nvec) = evc(:,1:nvec)
|
|
|
|
!
|
|
|
|
IF ( overlap ) THEN
|
|
|
|
!
|
2009-08-03 16:15:09 +08:00
|
|
|
CALL zgemm( 'N', 'N', ndim, nvec, nbase, ONE, spsi, &
|
2006-04-03 18:33:22 +08:00
|
|
|
ndmx, vc, nvecx, ZERO, psi(1,nvec+1), ndmx )
|
|
|
|
!
|
|
|
|
spsi(:,1:nvec) = psi(:,nvec+1:2*nvec)
|
|
|
|
!
|
|
|
|
END IF
|
|
|
|
!
|
2009-08-03 16:15:09 +08:00
|
|
|
CALL zgemm( 'N', 'N', ndim, nvec, nbase, ONE, hpsi, &
|
2006-04-03 18:33:22 +08:00
|
|
|
ndmx, vc, nvecx, ZERO, psi(1,nvec+1), ndmx )
|
|
|
|
!
|
|
|
|
hpsi(:,1:nvec) = psi(:,nvec+1:2*nvec)
|
|
|
|
!
|
|
|
|
! ... refresh the reduced hamiltonian
|
|
|
|
!
|
|
|
|
nbase = nvec
|
|
|
|
!
|
|
|
|
hc(:,1:nbase) = ZERO
|
|
|
|
sc(:,1:nbase) = ZERO
|
|
|
|
vc(:,1:nbase) = ZERO
|
|
|
|
!
|
|
|
|
FORALL( n = 1 : nbase )
|
|
|
|
!
|
|
|
|
hc(n,n) = e(n)
|
|
|
|
sc(n,n) = ONE
|
|
|
|
vc(n,n) = ONE
|
|
|
|
!
|
|
|
|
END FORALL
|
|
|
|
!
|
|
|
|
CALL stop_clock( 'last' )
|
|
|
|
!
|
|
|
|
END IF
|
|
|
|
!
|
|
|
|
END DO iterate
|
|
|
|
!
|
|
|
|
DEALLOCATE( conv )
|
|
|
|
DEALLOCATE( ew )
|
|
|
|
DEALLOCATE( vc )
|
|
|
|
DEALLOCATE( hc )
|
|
|
|
DEALLOCATE( sc )
|
|
|
|
IF ( overlap ) DEALLOCATE( spsi )
|
|
|
|
DEALLOCATE( hpsi )
|
|
|
|
DEALLOCATE( psi )
|
|
|
|
!
|
|
|
|
CALL stop_clock( 'cegterg' )
|
|
|
|
!
|
|
|
|
RETURN
|
|
|
|
!
|
2006-12-12 19:02:09 +08:00
|
|
|
END SUBROUTINE cegterg_vdw
|