quantum-espresso/PHonon/Gamma/cgsolve.f90

155 lines
4.7 KiB
Fortran

!
! Copyright (C) 2003 PWSCF 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 .
!
!
!-----------------------------------------------------------------------
SUBROUTINE cgsolve (operator,npw,evc,npwx,nbnd,overlap, &
& nbndx,orthonormal,precondition,diagonal, &
& startwith0,e,b,u,h,Ah,pu,niter,eps,iter,x)
!-----------------------------------------------------------------------
!
! conjugate-gradient solution of a system of constrained linear equations
! "operator" is the linear operator - diagonal preconditioning allowed
! x = solution, u = gradient, h = conjugate gradient, Ah = operator*h
!
USE io_global, ONLY : stdout
USE kinds, ONLY : DP
USE becmod, ONLY : calbec
IMPLICIT NONE
INTEGER npw, npwx, nbnd, nbndx, niter, iter
real(DP) :: diagonal(npw), e(nbnd), overlap(nbndx,nbnd)
COMPLEX(DP) :: x(npwx,nbnd), b(npwx,nbnd), u(npwx,nbnd), &
h(npwx,nbnd),Ah(npwx,nbnd),evc(npwx,nbnd), pu(npwx,nbnd)
LOGICAL :: orthonormal, precondition,startwith0
!
INTEGER :: ibnd, jbnd, i, info
real(DP) :: lagrange(nbnd,nbnd)
real(DP) :: lambda, u_u, uu0, u_A_h, alfa, eps, uu(nbnd), ddot
EXTERNAL ddot, operator
!
CALL start_clock('cgsolve')
!
! starting gradient |u> = (A|x>-|b>)-lambda|psi> (lambda=<Ax-b|psi_i>)
!
IF (.not.startwith0) THEN
CALL operator(npw,e,x,u)
ELSE
u (:,:) = (0.d0, 0.d0)
! note that we assume x=0 on input
ENDIF
!
CALL daxpy(2*npwx*nbnd,-1.d0,b,1,u,1)
IF (precondition) THEN
CALL zvscal(npw,npwx,nbnd,diagonal,u,pu)
CALL calbec ( npw, evc, pu, lagrange )
ELSE
CALL calbec ( npw, evc, u, lagrange )
ENDIF
IF (.not. orthonormal) &
CALL DPOTRS('U',nbnd,nbnd,overlap,nbndx,lagrange,nbnd,info)
IF (info/=0) CALL errore('cgsolve','error in potrs',info)
!
CALL dgemm ('N', 'N', 2*npw, nbnd, nbnd, -1.d0, evc, &
2*npwx, lagrange, nbndx, 1.d0, u, 2*npwx)
!
! starting conjugate gradient |h> = |u>
IF (precondition) THEN
CALL zvscal(npw,npwx,nbnd,diagonal,u,h)
ELSE
CALL zcopy(npwx,nbnd,u,1,h,1)
ENDIF
! uu = <u|h>
CALL pw_dot('Y',npw,nbnd,u,npwx,h,npwx,uu)
u_u = 0.0d0
DO ibnd=1,nbnd
u_u = u_u + uu(ibnd)
ENDDO
!
! print '(" iter # ",i3," u_u = ",e10.4)', 0, u_u
!
! main iteration loop
!
DO iter = 1, niter
!
! calculate A|h>
!
CALL operator(npw,e,h,Ah)
!
! u_A_h = <u|A|h> (NB: must be equal to <h|A|h>)
IF (precondition) THEN
CALL zvscal(npw,npwx,nbnd,diagonal,u,pu)
! uu = <u|PA|h>
CALL pw_dot('Y',npw,nbnd,pu,npwx,Ah,npwx,uu)
ELSE
! uu = <u|A|h>
CALL pw_dot('Y',npw,nbnd, u,npwx,Ah,npwx,uu)
ENDIF
u_A_h = 0.0d0
DO ibnd=1,nbnd
u_A_h = u_A_h + uu(ibnd)
ENDDO
!
lambda = - u_u / u_A_h
! update the gradient and the trial solution
uu0 = u_u
u_u = 0.0d0
CALL daxpy(2*npwx*nbnd,lambda, h,1,x,1)
CALL daxpy(2*npwx*nbnd,lambda,Ah,1,u,1)
! lagrange multipliers ensure orthogonality of the solution
IF (precondition) THEN
CALL zvscal(npw,npwx,nbnd,diagonal,u,pu)
CALL calbec ( npw, evc, pu, lagrange )
ELSE
CALL calbec ( npw, evc, u, lagrange )
ENDIF
IF (.not. orthonormal) &
CALL DPOTRS('U',nbnd,nbnd,overlap,nbndx,lagrange,nbnd,info)
IF (info/=0) CALL errore('cgsolve','error in potrs',info)
CALL dgemm ('N', 'N', 2*npw, nbnd, nbnd,-1.d0, evc, &
2*npwx, lagrange, nbndx, 1.d0, u, 2*npwx)
IF (precondition) THEN
CALL zvscal(npw,npwx,nbnd,diagonal,u,pu)
! uu = <u|A|u>
CALL pw_dot('Y',npw,nbnd, u,npwx,pu,npwx,uu)
ELSE
! uu = <u|u>
CALL pw_dot('Y',npw,nbnd, u,npwx, u,npwx,uu)
ENDIF
u_u = 0.0d0
DO ibnd=1,nbnd
u_u = u_u + uu(ibnd)
ENDDO
! print '(" iter # ",i3," u_u = ",e10.4)', iter, u_u
!
IF( u_u <= eps) GOTO 10
IF (iter==niter) THEN
WRITE( stdout,'(" *** Conjugate Gradient minimization", &
& " not converged after ",i3," iterations"/ &
& " residual norm |Ax-b|^2 : ",e10.4)') iter,u_u
GOTO 10
ENDIF
! update the conjugate gradient
alfa = u_u / uu0
DO ibnd = 1,nbnd
IF (precondition) THEN
DO i=1,npw
h(i,ibnd) = alfa*h(i,ibnd) + u(i,ibnd)*diagonal(i)
ENDDO
ELSE
DO i=1,npw
h(i,ibnd) = alfa*h(i,ibnd) + u(i,ibnd)
ENDDO
ENDIF
ENDDO
ENDDO
!
10 CONTINUE
CALL stop_clock('cgsolve')
!
RETURN
END SUBROUTINE cgsolve