huti_cgs.F90

module huti_cgs
  use huti_aux
  implicit none
  !
  ! *
  ! *  Elmer, A Finite Element Software for Multiphysical Problems
  ! *
  ! *  Copyright 1st April 1995 - , CSC - IT Center for Science Ltd., Finland
  ! * 
  ! * This library is free software; you can redistribute it and/or
  ! * modify it under the terms of the GNU Lesser General Public
  ! * License as published by the Free Software Foundation; either
  ! * version 2.1 of the License, or (at your option) any later version.
  ! *
  ! * This library is distributed in the hope that it will be useful,
  ! * but WITHOUT ANY WARRANTY; without even the implied warranty of
  ! * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  ! * Lesser General Public License for more details.
  ! * 
  ! * You should have received a copy of the GNU Lesser General Public
  ! * License along with this library (in file ../LGPL-2.1); if not, write 
  ! * to the Free Software Foundation, Inc., 51 Franklin Street, 
  ! * Fifth Floor, Boston, MA  02110-1301  USA
  ! *
  ! *****************************************************************************/

  !
  ! Subroutines to implement Conjugate Gradient Squared iteration

#include  "huti_fdefs.h" 

  !*************************************************************************
  !*************************************************************************
  !
  ! This subroutine is based on a book by Barret et al.:
  ! "Templates for the Solution of Linear Systems: Building Blocks for
  !  Iterative Methods", 1993.
  !
  ! All matrix-vector operations are done externally, so we do not need
  ! to know about the matrix structure (sparse or dense). Memory allocation
  ! for the working arrays has also been done externally.

  !*************************************************************************
  ! Work array is used in the following order:
  ! work(:,1) = r tilde (zero)
  ! work(:,2) = p
  ! work(:,3) = q
  ! work(:,4) = u
  ! work(:,5) = t1v (temporary)
  ! work(:,6) = t2v (temporary)
  ! work(:,7) = r
  !
  !*************************************************************************
  ! Definitions to make the code more understandable and to make it look
  ! like the pseudo code
  !

#define  X  xvec 
#define  B  rhsvec 

#define  RTLD  work(:,1) 
#define  RTLD_ind  1 
#define  P  work(:,2) 
#define  P_ind  2 
#define  Q  work(:,3) 
#define  Q_ind  3 
#define  U  work(:,4) 
#define  U_ind  4 
#define  T1V  work(:,5) 
#define  T1V_ind  5 
#define  T2V  work(:,6) 
#define  T2V_ind  6 
#define  R  work(:,7) 
#define  R_ind  7 

contains


  !*************************************************************************
  !*************************************************************************
  ! Single precision version
  !*************************************************************************
  !*************************************************************************

  subroutine  huti_scgssolv  ( ndim, wrkdim, xvec, rhsvec, ipar,&
       dpar, work, matvecsubr, pcondlsubr, pcondrsubr, &
       dotprodfun, normfun, stopcfun )

    use huti_interfaces
    implicit none

    procedure( mv_iface_s ), pointer :: matvecsubr
    procedure( pc_iface_s ), pointer :: pcondlsubr
    procedure( pc_iface_s ), pointer :: pcondrsubr
    procedure( dotp_iface_s ), pointer :: dotprodfun
    procedure( norm_iface_s ), pointer :: normfun
    procedure( stopc_iface_s ), pointer :: stopcfun

    ! Parameters

    integer :: ndim, wrkdim
    real, dimension(ndim) :: xvec, rhsvec
    integer, dimension(HUTI_IPAR_DFLTSIZE) :: ipar
    double precision, dimension(HUTI_DPAR_DFLTSIZE) :: dpar
    real, dimension(ndim,wrkdim) :: work

    ! Local variables

    real :: rho, oldrho, alpha, beta
    integer :: iter_count

    real :: residual, rhsnorm, precrhsnorm

    !
    ! End of variable declarations
    !*********************************************************************

    !*********************************************************************
    ! The actual CGS begins here (look the pseudo code in the
    ! "Templates..."-book, page 26)
    !
    ! First the initialization part
    !

    iter_count = 1

    ! The following applies for all matrix operations in this solver

    HUTI_EXTOP_MATTYPE = HUTI_MAT_NOTTRPSED

    ! Norms of right-hand side vector are used in convergence tests

    if ( HUTI_STOPC .eq. HUTI_TRESID_SCALED_BYB .or. & 
         HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYB ) then
       rhsnorm = normfun( HUTI_NDIM, B, 1 )
    end if
    if ( HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYPRECB ) then
       call pcondlsubr( P, B, ipar )
       precrhsnorm = normfun( HUTI_NDIM, P, 1 )
    end if

    ! Generate vector X if needed

    if ( HUTI_INITIALX .eq. HUTI_RANDOMX ) then
       call  huti_srandvec   ( X, ipar )
    else if ( HUTI_INITIALX .ne. HUTI_USERSUPPLIEDX ) then
       X = 1
    end if

    call matvecsubr( X, R, ipar )
    R = B - R
    RTLD = R

    !
    ! This is where the loop starts (that is we continue from here after
    ! the first iteration)
    !

300 continue

    rho = dotprodfun( HUTI_NDIM, RTLD, 1, R, 1 )
    if ( rho .eq. 0 ) then
       HUTI_INFO = HUTI_CGS_RHO
       go to 1000
    end if

    if ( iter_count .eq. 1 ) then
       U = R
       P = U
    else
       beta = rho / oldrho
       U = R + beta * Q
       P = U + beta * Q + beta * beta * P
    end if

    call pcondlsubr( T2V, P, ipar )
    call pcondrsubr( T1V, T2V, ipar )

    call matvecsubr( T1V, T2V, ipar )

    alpha = rho / dotprodfun( HUTI_NDIM, RTLD, 1, T2V, 1 )
    Q = U - alpha * T2V

    T2V = U + Q

    call pcondlsubr( U, T2V, ipar )
    call pcondrsubr( T1V, U, ipar )
    X = X + alpha * T1V

    call matvecsubr( T1V, T2V, ipar )
    R = R - alpha * T2V

    !
    ! Check the convergence against selected stopping criterion
    !

    select case (HUTI_STOPC)
    case (HUTI_TRUERESIDUAL)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_TRESID_SCALED_BYB)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 ) / rhsnorm
    case (HUTI_PSEUDORESIDUAL)
       residual = normfun( HUTI_NDIM, R, 1 )
    case (HUTI_PRESID_SCALED_BYB)
       residual = normfun( HUTI_NDIM, R, 1 ) / rhsnorm
    case (HUTI_PRESID_SCALED_BYPRECB)
       residual = normfun( HUTI_NDIM, R, 1 ) / precrhsnorm
    case (HUTI_XDIFF_NORM)
       T1V = alpha * T1V
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_USUPPLIED_STOPC)
       residual = stopcfun( X, B, R, ipar, dpar )
    case default
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    end select

    !
    ! Print debugging output if desired
    !

    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       if ( mod(iter_count, HUTI_DBUGLVL) .eq. 0 ) then
          write (*, '(I8, E11.4)') iter_count, residual
       end if
    end if

    if ( residual .lt. HUTI_TOLERANCE ) then
       HUTI_INFO = HUTI_CONVERGENCE
       go to 1000
    end if

    IF( residual /= residual .OR. residual > HUTI_MAXTOLERANCE ) THEN
      HUTI_INFO = HUTI_DIVERGENCE
      GOTO 1000
    END IF

    oldrho = rho

    !
    ! Return next time back to the iteration loop (without initialization)
    !

    iter_count = iter_count + 1
    if ( iter_count .gt. HUTI_MAXIT ) then
       HUTI_INFO = HUTI_MAXITER
       go to 1000
    end if

    go to 300

    !
    ! This is where we exit last time (after enough iterations or breakdown)
    !

1000 continue
    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       write (*, '(I8, E11.4)') iter_count, residual
    end if

    HUTI_ITERS = iter_count
    return

    ! End of execution
    !*********************************************************************

  end subroutine  huti_scgssolv

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


  !*************************************************************************
  !*************************************************************************
  ! Double precision version
  !*************************************************************************
  !*************************************************************************

  subroutine  huti_dcgssolv  ( ndim, wrkdim, xvec, rhsvec, ipar,&
       dpar, work, matvecsubr, pcondlsubr, pcondrsubr, &
       dotprodfun, normfun, stopcfun )

    use huti_interfaces
    implicit none

    procedure( mv_iface_d ), pointer :: matvecsubr
    procedure( pc_iface_d ), pointer :: pcondlsubr
    procedure( pc_iface_d ), pointer :: pcondrsubr
    procedure( dotp_iface_d ), pointer :: dotprodfun
    procedure( norm_iface_d ), pointer :: normfun
    procedure( stopc_iface_d ), pointer :: stopcfun

    ! Parameters

    integer :: ndim, wrkdim
    double precision, dimension(ndim) :: xvec, rhsvec
    integer, dimension(HUTI_IPAR_DFLTSIZE) :: ipar
    double precision, dimension(HUTI_DPAR_DFLTSIZE) :: dpar
    double precision, dimension(ndim,wrkdim) :: work

    ! Local variables

    double precision :: rho, oldrho, alpha, beta
    integer :: iter_count

    double precision :: residual, rhsnorm, precrhsnorm

    !
    ! End of variable declarations
    !*********************************************************************

    !*********************************************************************
    ! The actual CGS begins here (look the pseudo code in the
    ! "Templates..."-book, page 26)
    !
    ! First the initialization part
    !

    iter_count = 1

    ! The following applies for all matrix operations in this solver

    HUTI_EXTOP_MATTYPE = HUTI_MAT_NOTTRPSED

    ! Norms of right-hand side vector are used in convergence tests

    if ( HUTI_STOPC .eq. HUTI_TRESID_SCALED_BYB .or. & 
         HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYB ) then
       rhsnorm = normfun( HUTI_NDIM, B, 1 )
    end if
    if ( HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYPRECB ) then
       call pcondlsubr( P, B, ipar )
       precrhsnorm = normfun( HUTI_NDIM, P, 1 )
    end if

    ! Generate vector X if needed

    if ( HUTI_INITIALX .eq. HUTI_RANDOMX ) then
       call  huti_drandvec   ( X, ipar )
    else if ( HUTI_INITIALX .ne. HUTI_USERSUPPLIEDX ) then
       X = 1
    end if

    call matvecsubr( X, R, ipar )
    R = B - R
    RTLD = R

    !
    ! This is where the loop starts (that is we continue from here after
    ! the first iteration)
    !

300 continue

    rho = dotprodfun( HUTI_NDIM, RTLD, 1, R, 1 )
    if ( rho .eq. 0 ) then
       HUTI_INFO = HUTI_CGS_RHO
       go to 1000
    end if

    if ( iter_count .eq. 1 ) then
       U = R
       P = U
    else
       beta = rho / oldrho
       U = R + beta * Q
       P = U + beta * Q + beta * beta * P
    end if

    call pcondlsubr( T2V, P, ipar )
    call pcondrsubr( T1V, T2V, ipar )

    call matvecsubr( T1V, T2V, ipar )

    alpha = rho / dotprodfun( HUTI_NDIM, RTLD, 1, T2V, 1 )
    Q = U - alpha * T2V

    T2V = U + Q

    call pcondlsubr( U, T2V, ipar )
    call pcondrsubr( T1V, U, ipar )
    X = X + alpha * T1V

    call matvecsubr( T1V, T2V, ipar )
    R = R - alpha * T2V

    !
    ! Check the convergence against selected stopping criterion
    !

    select case (HUTI_STOPC)
    case (HUTI_TRUERESIDUAL)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_TRESID_SCALED_BYB)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 ) / rhsnorm
    case (HUTI_PSEUDORESIDUAL)
       residual = normfun( HUTI_NDIM, R, 1 )
    case (HUTI_PRESID_SCALED_BYB)
       residual = normfun( HUTI_NDIM, R, 1 ) / rhsnorm
    case (HUTI_PRESID_SCALED_BYPRECB)
       residual = normfun( HUTI_NDIM, R, 1 ) / precrhsnorm
    case (HUTI_XDIFF_NORM)
       T1V = alpha * T1V
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_USUPPLIED_STOPC)
       residual = stopcfun( X, B, R, ipar, dpar )
    case default
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    end select

    !
    ! Print debugging output if desired
    !

    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       if ( mod(iter_count, HUTI_DBUGLVL) .eq. 0 ) then
          write (*, '(I8, E11.4)') iter_count, residual
       end if
    end if

    if ( residual .lt. HUTI_TOLERANCE ) then
       HUTI_INFO = HUTI_CONVERGENCE
       go to 1000
    end if

    IF( residual /= residual .OR. residual > HUTI_MAXTOLERANCE ) THEN
      HUTI_INFO = HUTI_DIVERGENCE
      GOTO 1000
    END IF
    
    oldrho = rho

    !
    ! Return next time back to the iteration loop (without initialization)
    !

    iter_count = iter_count + 1
    if ( iter_count .gt. HUTI_MAXIT ) then
       HUTI_INFO = HUTI_MAXITER
       go to 1000
    end if

    go to 300

    !
    ! This is where we exit last time (after enough iterations or breakdown)
    !

1000 continue
    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       write (*, '(I8, E11.4)') iter_count, residual
    end if

    HUTI_ITERS = iter_count
    return

    ! End of execution
    !*********************************************************************

  end subroutine  huti_dcgssolv

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


  !*************************************************************************
  !*************************************************************************
  ! Complex version
  !*************************************************************************
  !*************************************************************************

  subroutine  huti_ccgssolv  ( ndim, wrkdim, xvec, rhsvec, ipar,&
       dpar, work, matvecsubr, pcondlsubr, pcondrsubr, &
       dotprodfun, normfun, stopcfun )

    use huti_interfaces
    implicit none

    procedure( mv_iface_c ), pointer :: matvecsubr
    procedure( pc_iface_c ), pointer :: pcondlsubr
    procedure( pc_iface_c ), pointer :: pcondrsubr
    procedure( dotp_iface_c ), pointer :: dotprodfun
    procedure( norm_iface_c ), pointer :: normfun
    procedure( stopc_iface_c ), pointer :: stopcfun

    ! Parameters

    integer :: ndim, wrkdim
    complex, dimension(ndim) :: xvec, rhsvec
    integer, dimension(HUTI_IPAR_DFLTSIZE) :: ipar
    double precision, dimension(HUTI_DPAR_DFLTSIZE) :: dpar
    complex, dimension(ndim,wrkdim) :: work

    ! Local variables

    complex :: rho, oldrho, alpha, beta
    integer :: iter_count

    real :: residual, rhsnorm, precrhsnorm

    !
    ! End of variable declarations
    !*********************************************************************

    !*********************************************************************
    ! The actual CGS begins here (look the pseudo code in the
    ! "Templates..."-book, page 26)
    !
    ! First the initialization part
    !

    iter_count = 1

    ! The following applies for all matrix operations in this solver

    HUTI_EXTOP_MATTYPE = HUTI_MAT_NOTTRPSED

    ! Norms of right-hand side vector are used in convergence tests

    if ( HUTI_STOPC .eq. HUTI_TRESID_SCALED_BYB .or. & 
         HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYB ) then
       rhsnorm = normfun( HUTI_NDIM, B, 1 )
    end if
    if ( HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYPRECB ) then
       call pcondlsubr( P, B, ipar )
       precrhsnorm = normfun( HUTI_NDIM, P, 1 )
    end if

    ! Generate vector X if needed

    if ( HUTI_INITIALX .eq. HUTI_RANDOMX ) then
       call  huti_crandvec   ( X, ipar )
    else if ( HUTI_INITIALX .ne. HUTI_USERSUPPLIEDX ) then
       X = 1
    end if

    call matvecsubr( X, R, ipar )
    R = B - R
    RTLD = R

    !
    ! This is where the loop starts (that is we continue from here after
    ! the first iteration)
    !

300 continue

    rho = dotprodfun( HUTI_NDIM, RTLD, 1, R, 1 )
    if ( rho .eq. 0 ) then
       HUTI_INFO = HUTI_CGS_RHO
       go to 1000
    end if

    if ( iter_count .eq. 1 ) then
       U = R
       P = U
    else
       beta = rho / oldrho
       U = R + beta * Q
       P = U + beta * Q + beta * beta * P
    end if

    call pcondlsubr( T2V, P, ipar )
    call pcondrsubr( T1V, T2V, ipar )

    call matvecsubr( T1V, T2V, ipar )

    alpha = rho / dotprodfun( HUTI_NDIM, RTLD, 1, T2V, 1 )
    Q = U - alpha * T2V

    T2V = U + Q

    call pcondlsubr( U, T2V, ipar )
    call pcondrsubr( T1V, U, ipar )
    X = X + alpha * T1V

    call matvecsubr( T1V, T2V, ipar )
    R = R - alpha * T2V

    !
    ! Check the convergence against selected stopping criterion
    !

    select case (HUTI_STOPC)
    case (HUTI_TRUERESIDUAL)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_TRESID_SCALED_BYB)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 ) / rhsnorm
    case (HUTI_PSEUDORESIDUAL)
       residual = normfun( HUTI_NDIM, R, 1 )
    case (HUTI_PRESID_SCALED_BYB)
       residual = normfun( HUTI_NDIM, R, 1 ) / rhsnorm
    case (HUTI_PRESID_SCALED_BYPRECB)
       residual = normfun( HUTI_NDIM, R, 1 ) / precrhsnorm
    case (HUTI_XDIFF_NORM)
       T1V = alpha * T1V
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_USUPPLIED_STOPC)
       residual = stopcfun( X, B, R, ipar, dpar )
    case default
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    end select

    !
    ! Print debugging output if desired
    !

    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       if ( mod(iter_count, HUTI_DBUGLVL) .eq. 0 ) then
          write (*, '(I8, E11.4)') iter_count, residual
       end if
    end if

    if ( residual .lt. HUTI_TOLERANCE ) then
       HUTI_INFO = HUTI_CONVERGENCE
       go to 1000
    end if

    IF( residual /= residual .OR. residual > HUTI_MAXTOLERANCE ) THEN
      HUTI_INFO = HUTI_DIVERGENCE
      GOTO 1000
    END IF

    oldrho = rho

    !
    ! Return next time back to the iteration loop (without initialization)
    !

    iter_count = iter_count + 1
    if ( iter_count .gt. HUTI_MAXIT ) then
       HUTI_INFO = HUTI_MAXITER
       go to 1000
    end if

    go to 300

    !
    ! This is where we exit last time (after enough iterations or breakdown)
    !

1000 continue
    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       write (*, '(I8, E11.4)') iter_count, residual
    end if

    HUTI_ITERS = iter_count
    return

    ! End of execution
    !*********************************************************************

  end subroutine  huti_ccgssolv

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


  !*************************************************************************
  !*************************************************************************
  ! Double complex version
  !*************************************************************************
  !*************************************************************************

  subroutine  huti_zcgssolv  ( ndim, wrkdim, xvec, rhsvec, ipar,&
       dpar, work, matvecsubr, pcondlsubr, pcondrsubr, &
       dotprodfun, normfun, stopcfun )

    use huti_interfaces
    implicit none

    procedure( mv_iface_z ), pointer :: matvecsubr
    procedure( pc_iface_z ), pointer :: pcondlsubr
    procedure( pc_iface_z ), pointer :: pcondrsubr
    procedure( dotp_iface_z ), pointer :: dotprodfun
    procedure( norm_iface_z ), pointer :: normfun
    procedure( stopc_iface_z ), pointer :: stopcfun

    ! Parameters

    integer :: ndim, wrkdim
    double complex, dimension(ndim) :: xvec, rhsvec
    integer, dimension(HUTI_IPAR_DFLTSIZE) :: ipar
    double precision, dimension(HUTI_DPAR_DFLTSIZE) :: dpar
    double complex, dimension(ndim,wrkdim) :: work

    ! Local variables

    double complex :: rho, oldrho, alpha, beta
    integer :: iter_count

    double precision :: residual, rhsnorm, precrhsnorm

    !
    ! End of variable declarations
    !*********************************************************************

    !*********************************************************************
    ! The actual CGS begins here (look the pseudo code in the
    ! "Templates..."-book, page 26)
    !
    ! First the initialization part
    !

    iter_count = 1

    ! The following applies for all matrix operations in this solver

    HUTI_EXTOP_MATTYPE = HUTI_MAT_NOTTRPSED

    ! Norms of right-hand side vector are used in convergence tests

    if ( HUTI_STOPC .eq. HUTI_TRESID_SCALED_BYB .or. & 
         HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYB ) then
       rhsnorm = normfun( HUTI_NDIM, B, 1 )
    end if
    if ( HUTI_STOPC .eq. HUTI_PRESID_SCALED_BYPRECB ) then
       call pcondlsubr( P, B, ipar )
       precrhsnorm = normfun( HUTI_NDIM, P, 1 )
    end if

    ! Generate vector X if needed

    if ( HUTI_INITIALX .eq. HUTI_RANDOMX ) then
       call  huti_zrandvec   ( X, ipar )
    else if ( HUTI_INITIALX .ne. HUTI_USERSUPPLIEDX ) then
       X = 1
    end if

    call matvecsubr( X, R, ipar )
    R = B - R
    RTLD = R

    !
    ! This is where the loop starts (that is we continue from here after
    ! the first iteration)
    !

300 continue

    rho = dotprodfun( HUTI_NDIM, RTLD, 1, R, 1 )
    if ( rho .eq. 0 ) then
       HUTI_INFO = HUTI_CGS_RHO
       go to 1000
    end if

    if ( iter_count .eq. 1 ) then
       U = R
       P = U
    else
       beta = rho / oldrho
       U = R + beta * Q
       P = U + beta * Q + beta * beta * P
    end if

    call pcondlsubr( T2V, P, ipar )
    call pcondrsubr( T1V, T2V, ipar )

    call matvecsubr( T1V, T2V, ipar )

    alpha = rho / dotprodfun( HUTI_NDIM, RTLD, 1, T2V, 1 )
    Q = U - alpha * T2V

    T2V = U + Q

    call pcondlsubr( U, T2V, ipar )
    call pcondrsubr( T1V, U, ipar )
    X = X + alpha * T1V

    call matvecsubr( T1V, T2V, ipar )
    R = R - alpha * T2V

    !
    ! Check the convergence against selected stopping criterion
    !

    select case (HUTI_STOPC)
    case (HUTI_TRUERESIDUAL)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_TRESID_SCALED_BYB)
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 ) / rhsnorm
    case (HUTI_PSEUDORESIDUAL)
       residual = normfun( HUTI_NDIM, R, 1 )
    case (HUTI_PRESID_SCALED_BYB)
       residual = normfun( HUTI_NDIM, R, 1 ) / rhsnorm
    case (HUTI_PRESID_SCALED_BYPRECB)
       residual = normfun( HUTI_NDIM, R, 1 ) / precrhsnorm
    case (HUTI_XDIFF_NORM)
       T1V = alpha * T1V
       residual = normfun( HUTI_NDIM, T1V, 1 )
    case (HUTI_USUPPLIED_STOPC)
       residual = stopcfun( X, B, R, ipar, dpar )
    case default
       call matvecsubr( X, T1V, ipar )
       T1V = T1V - B
       residual = normfun( HUTI_NDIM, T1V, 1 )
    end select

    !
    ! Print debugging output if desired
    !

    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       if ( mod(iter_count, HUTI_DBUGLVL) .eq. 0 ) then
          write (*, '(I8, E11.4)') iter_count, residual
       end if
    end if

    if ( residual .lt. HUTI_TOLERANCE ) then
       HUTI_INFO = HUTI_CONVERGENCE
       go to 1000
    end if

    IF( residual /= residual .OR. residual > HUTI_MAXTOLERANCE ) THEN
      HUTI_INFO = HUTI_DIVERGENCE
      GOTO 1000
    END IF

    oldrho = rho

    !
    ! Return next time back to the iteration loop (without initialization)
    !

    iter_count = iter_count + 1
    if ( iter_count .gt. HUTI_MAXIT ) then
       HUTI_INFO = HUTI_MAXITER
       go to 1000
    end if

    go to 300

    !
    ! This is where we exit last time (after enough iterations or breakdown)
    !

1000 continue
    if ( HUTI_DBUGLVL .ne. HUTI_NO_DEBUG ) then
       write (*, '(I8, E11.4)') iter_count, residual
    end if

    HUTI_ITERS = iter_count
    return

    ! End of execution
    !*********************************************************************

  end subroutine  huti_zcgssolv

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


end module huti_cgs