      program pzndrv1 
c
c     Message Passing Layer: MPI
c
c     Example program to illustrate the idea of reverse communication
c     for a standard complex nonsymmetric eigenvalue problem. 
c
c     We implement example one of ex-complex.doc in DOCUMENTS directory
c
c\Example-1
c     ... Suppose we want to solve A*x = lambda*x in regular mode,
c         where A is obtained from the standard central difference
c         discretization of the convection-diffusion operator 
c                 (Laplacian u) + rho*(du / dx)
c         in the domain omega = (0,1)x(0,1), with 
c         u = 0 on the boundary of omega.
c
c     ... OP = A  and  B = I.
c     ... Assume "call av (comm, nloc, nx, mv_buf, x, y)" computes y = A*x
c     ... Use mode 1 of PZNAUPD.
c
c\BeginLib
c
c\Routines called
c     pznaupd  Parallel ARPACK reverse communication interface routine.
c     pzneupd  Parallel ARPACK routine that returns Ritz values and (optionally)
c              Ritz vectors.
c     pdznorm2 Parallel version of Level 1 BLAS that computes the norm of a complex vector.
c     zaxpy    Level 1 BLAS that computes y <- alpha*x+y.
c     av       Distributed matrix vector multiplication routine that computes A*x.
c     tv       Matrix vector multiplication routine that computes T*x,
c              where T is a tridiagonal matrix.  It is used in routine
c              av.
c
c\Author
c     Richard Lehoucq
c     Danny Sorensen
c     Chao Yang
c     Dept. of Computational &
c     Applied Mathematics
c     Rice University
c     Houston, Texas
c
c\Parallel Modifications
c     Kristi Maschhoff
c
c\Revision history:
c     Starting Point: Complex Code FILE: ndrv1.F   SID: 2.1
c
c\SCCS Information: 
c FILE: ndrv1.F   SID: 1.1   DATE OF SID: 8/13/96   RELEASE: 1
c
c\Remarks
c     1. None
c
c\EndLib
c---------------------------------------------------------------------------
c
      include 'mpif.h'
      include 'debug.h'
      include 'stat.h'
c 
c     %---------------%
c     | MPI INTERFACE |
c     %---------------%
 
      integer           comm, myid, nprocs, rc, nloc
c     %-----------------------------%
c     | Define maximum dimensions   |
c     | for all arrays.             |
c     | MAXN:   Maximum dimension   |
c     |         of the A allowed.   |
c     | MAXNEV: Maximum NEV allowed |
c     | MAXNCV: Maximum NCV allowed |
c     %-----------------------------%
c
      integer           maxn, maxnev, maxncv, ldv
      parameter         (maxn=256, maxnev=12, maxncv=30, ldv=maxn)
c
c     %--------------%
c     | Local Arrays |
c     %--------------%
c
      integer           iparam(11), ipntr(14)
      logical           select(maxncv)
      Complex*16
     &                  ax(maxn), d(maxncv), 
     &                  v(ldv,maxncv), workd(3*maxn), 
     &                  workev(3*maxncv), resid(maxn), 
     &                  workl(3*maxncv*maxncv+5*maxncv)
      Double precision 
     &                  rwork(maxncv), rd(maxncv,3)
c
c     %---------------%
c     | Local Scalars |
c     %---------------%
c
      character         bmat*1, which*2
      integer           ido, n, nx, nev, ncv, lworkl, info, j,
     &                  ierr, nconv, maxitr, ishfts, mode
      Complex*16
     &                  sigma
      Double precision
     &                  tol
      logical           rvec
c
c     %----------------------------------------------%
c     | Local Buffers needed for MPI communication |
c     %----------------------------------------------%
c
      Complex*16
     &                  mv_buf(maxn)
c
c     %-----------------------------%
c     | BLAS & LAPACK routines used |
c     %-----------------------------%
c
      Double precision
     &                  pdznorm2
      external          pdznorm2, zaxpy 
c
c     %-----------------------%
c     | Executable Statements |
c     %-----------------------%
c 
      call MPI_INIT( ierr )
      comm = MPI_COMM_WORLD
      call MPI_COMM_RANK( comm, myid, ierr )
      call MPI_COMM_SIZE( comm, nprocs, ierr )
c
      ndigit = -3
      logfil = 6
      mcaupd = 1
c
c     %--------------------------------------------------%
c     | The number NX is the number of interior points   |
c     | in the discretization of the 2-dimensional       |
c     | convection-diffusion operator on the unit        |
c     | square with zero Dirichlet boundary condition.   | 
c     | The number N(=NX*NX) is the dimension of the     |
c     | matrix.  A standard eigenvalue problem is        |
c     | solved (BMAT = 'I').  NEV is the number of       |
c     | eigenvalues to be approximated.  The user can    |
c     | modify NX, NEV, NCV, WHICH to solve problems of  |
c     | different sizes, and to get different parts of   |
c     | the spectrum.  However, The following            |
c     | conditions must be satisfied:                    |
c     |                   N <= MAXN                      |
c     |                 NEV <= MAXNEV                    |
c     |           NEV + 2 <= NCV <= MAXNCV               | 
c     %--------------------------------------------------% 
c
      nx    = 10 
      n     = nx*nx 
      nev   = 4
      ncv   = 20 
c
c     %--------------------------------------%
c     | Set up distribution of data to nodes |
c     %--------------------------------------%
c
      nloc = (nx / nprocs)*nx
      if ( mod(nx, nprocs) .gt. myid ) nloc = nloc + nx
c
      if ( nloc .gt. maxn ) then
         print *, ' ERROR with _NDRV1: NLOC is greater than MAXN '
         go to 9000
      else if ( nev .gt. maxnev ) then
         print *, ' ERROR with _NDRV1: NEV is greater than MAXNEV '
         go to 9000
      else if ( ncv .gt. maxncv ) then
         print *, ' ERROR with _NDRV1: NCV is greater than MAXNCV '
         go to 9000
      end if
      bmat  = 'I'
      which = 'LM'
c
c     %---------------------------------------------------%
c     | The work array WORKL is used in ZNAUPD as         | 
c     | workspace.  Its dimension LWORKL is set as        |
c     | illustrated below.  The parameter TOL determines  |
c     | the stopping criterion. If TOL<=0, machine        |
c     | precision is used.  The variable IDO is used for  |
c     | reverse communication, and is initially set to 0. |
c     | Setting INFO=0 indicates that a random vector is  |
c     | generated to start the ARNOLDI iteration.         | 
c     %---------------------------------------------------%
c
      lworkl  = 3*ncv**2+5*ncv 
      tol    = 0.0 
      ido    = 0
      info   = 0
c
c     %---------------------------------------------------%
c     | This program uses exact shift with respect to     |
c     | the current Hessenberg matrix (IPARAM(1) = 1).    |
c     | IPARAM(3) specifies the maximum number of Arnoldi |
c     | iterations allowed.  Mode 1 of ZNAUPD is used     |
c     | (IPARAM(7) = 1). All these options can be changed |
c     | by the user. For details see the documentation in |
c     | ZNAUPD.                                           |
c     %---------------------------------------------------%
c
      ishfts = 1
      maxitr = 300
      mode   = 1
c
      iparam(1) = ishfts
      iparam(3) = maxitr 
      iparam(7) = mode 
c
c     %-------------------------------------------%
c     | M A I N   L O O P (Reverse communication) | 
c     %-------------------------------------------%
c
 10   continue
c
c        %---------------------------------------------%
c        | Repeatedly call the routine ZNAUPD and take |
c        | actions indicated by parameter IDO until    |
c        | either convergence is indicated or maxitr   |
c        | has been exceeded.                          |
c        %---------------------------------------------%
c
         call pznaupd ( comm, ido, bmat, nloc, which, 
     &        nev, tol, resid, ncv, v, ldv, iparam, ipntr, 
     &        workd, workl, lworkl, rwork,info )
c
         if (ido .eq. -1 .or. ido .eq. 1) then
c
c           %-------------------------------------------%
c           | Perform matrix vector multiplication      |
c           |                y <--- OP*x                |
c           | The user should supply his/her own        |
c           | matrix vector multiplication routine here |
c           | that takes workd(ipntr(1)) as the input   |
c           | vector, and return the matrix vector      |
c           | product to workd(ipntr(2)).               | 
c           %-------------------------------------------%
c
            call av ( comm, nloc, nx, mv_buf,
     &                workd(ipntr(1)), workd(ipntr(2)))
c
c           %-----------------------------------------%
c           | L O O P   B A C K to call ZNAUPD again. |
c           %-----------------------------------------%
c
            go to 10
         end if
c 
c     %----------------------------------------%
c     | Either we have convergence or there is |
c     | an error.                              |
c     %----------------------------------------%
c
      if ( info .lt. 0 ) then
c
c        %--------------------------%
c        | Error message, check the |
c        | documentation in ZNAUPD  |
c        %--------------------------%
c
         if ( myid .eq. 0 ) then
            print *, ' '
            print *, ' Error with _naupd, info = ', info
            print *, ' Check the documentation of _naupd'
            print *, ' '
         endif
c
      else 
c
c        %-------------------------------------------%
c        | No fatal errors occurred.                 |
c        | Post-Process using ZNEUPD.                |
c        |                                           |
c        | Computed eigenvalues may be extracted.    |
c        |                                           |
c        | Eigenvectors may also be computed now if  |
c        | desired.  (indicated by rvec = .true.)    |
c        %-------------------------------------------%
c
         rvec = .true.
c
         call pzneupd (comm, rvec, 'A', select, d, v, ldv, sigma, 
     &        workev, bmat, nloc, which, nev, tol, resid, ncv, 
     &        v, ldv, iparam, ipntr, workd, workl, lworkl, 
     &        rwork, ierr)
c
c        %----------------------------------------------%
c        | Eigenvalues are returned in the one          |
c        | dimensional array D.  The corresponding      |
c        | eigenvectors are returned in the first NCONV |
c        | (=IPARAM(5)) columns of the two dimensional  | 
c        | array V if requested.  Otherwise, an         |
c        | orthogonal basis for the invariant subspace  |
c        | corresponding to the eigenvalues in D is     |
c        | returned in V.                               |
c        %----------------------------------------------%
c
         if ( ierr .ne. 0) then
c 
c           %------------------------------------%
c           | Error condition:                   |
c           | Check the documentation of ZNEUPD. |
c           %------------------------------------%
c
            if ( myid .eq. 0 ) then
                print *, ' '
                print *, ' Error with _neupd, info = ', ierr
                print *, ' Check the documentation of _neupd. '
                print *, ' '
            endif
c
         else
c
             nconv = iparam(5)
             do 20 j=1, nconv
c
c               %---------------------------%
c               | Compute the residual norm |
c               |                           |
c               |   ||  A*x - lambda*x ||   |
c               |                           |
c               | for the NCONV accurately  |
c               | computed eigenvalues and  |
c               | eigenvectors.  (iparam(5) |
c               | indicates how many are    |
c               | accurate to the requested |
c               | tolerance)                |
c               %---------------------------%
c
                call av(comm, nloc, nx, mv_buf, v(1,j), ax)
                call zaxpy(nloc, -d(j), v(1,j), 1, ax, 1)
                rd(j,1) = dble(d(j))
                rd(j,2) = dimag(d(j))
                rd(j,3) = pdznorm2(comm, nloc, ax, 1)
c
 20          continue
c
c            %-----------------------------%
c            | Display computed residuals. |
c            %-----------------------------%
c
             call pdmout(comm, 6, nconv, 3, rd, maxncv, -6,
     &            'Ritz values (Real, Imag) and direct residuals')
          end if
c
c        %-------------------------------------------%
c        | Print additional convergence information. |
c        %-------------------------------------------%
c
         if (myid .eq. 0)then
         if ( info .eq. 1) then
             print *, ' '
             print *, ' Maximum number of iterations reached.'
             print *, ' '
         else if ( info .eq. 3) then
             print *, ' ' 
             print *, ' No shifts could be applied during implicit
     &                  Arnoldi update, try increasing NCV.'
             print *, ' '
         end if      
c
         print *, ' '
         print *, '_NDRV1'
         print *, '====== '
         print *, ' '
         print *, ' Size of the matrix is ', n
         print *, ' The number of processors is ', nprocs
         print *, ' The number of Ritz values requested is ', nev
         print *, ' The number of Arnoldi vectors generated',
     &            ' (NCV) is ', ncv
         print *, ' What portion of the spectrum: ', which
         print *, ' The number of converged Ritz values is ', 
     &              nconv 
         print *, ' The number of Implicit Arnoldi update',
     &            ' iterations taken is ', iparam(3)
         print *, ' The number of OP*x is ', iparam(9)
         print *, ' The convergence criterion is ', tol
         print *, ' '
c
         endif
      end if
c
c     %----------------------------%
c     | Done with program pzndrv1. |
c     %----------------------------%
c
 9000 continue
c
c
c     %-------------------------%
c     | Release resources MPI |
c     %-------------------------%
c
      call MPI_FINALIZE(rc)
c
      end
c 
c==========================================================================
c
c     parallel matrix vector subroutine
c
c     The matrix used is the convection-diffusion operator
c     discretized using centered difference.
c
c     Computes w <--- OP*v, where OP is the nx*nx by nx*nx block 
c     tridiagonal matrix
c
c                  | T -I          | 
c                  |-I  T -I       |
c             OP = |   -I  T       |
c                  |        ...  -I|
c                  |           -I T|
c
c     derived from the standard central difference  discretization 
c     of the convection-diffusion operator (Laplacian u) + rho*(du/dx)
c     with zero boundary condition.
c
c     The subroutine TV is called to computed y<---T*x.
c
c----------------------------------------------------------------------------
      subroutine av (comm, nloc, nx, mv_buf, v, w )
c
c     .. MPI Declarations ...
      include           'mpif.h'
      integer           comm, nprocs, myid, ierr,
     &                  status(MPI_STATUS_SIZE)
c
      integer           nloc, nx, np, j, lo, next, prev
      Complex*16         
     &                  v(nloc), w(nloc), mv_buf(nx), one
      parameter         (one = (1.0, 0.0))
      external          zaxpy, tv
c
      call MPI_COMM_RANK( comm, myid, ierr )
      call MPI_COMM_SIZE( comm, nprocs, ierr )
c
      np = nloc/nx
      call tv(nx,v(1),w(1))
      call zaxpy(nx, -one, v(nx+1), 1, w(1), 1)
c
      do 10 j = 2, np-1
         lo = (j-1)*nx
         call tv(nx, v(lo+1), w(lo+1))
         call zaxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
         call zaxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1)
  10  continue 
c
      lo = (np-1)*nx
      call tv(nx, v(lo+1), w(lo+1))
      call zaxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1)
c
      next = myid + 1
      prev = myid - 1
      if ( myid .lt. nprocs-1 ) then
         call mpi_send( v((np-1)*nx+1), nx, MPI_DOUBLE_COMPLEX,
     &                  next, myid+1, comm, ierr )
      endif
      if ( myid .gt. 0 ) then
         call mpi_recv( mv_buf, nx, MPI_DOUBLE_COMPLEX, prev, myid,
     &                  comm, status, ierr )
         call zaxpy( nx, -one, mv_buf, 1, w(1), 1 )
      endif
c
      if ( myid .gt. 0 ) then
         call mpi_send( v(1), nx, MPI_DOUBLE_COMPLEX,
     &                  prev, myid-1, comm, ierr )
      endif
      if ( myid .lt. nprocs-1 ) then
         call mpi_recv( mv_buf, nx, MPI_DOUBLE_COMPLEX, next, myid,
     &                  comm, status, ierr )
         call zaxpy( nx, -one, mv_buf, 1, w(lo+1), 1 )
      endif
c
      return
      end
c=========================================================================
      subroutine tv (nx, x, y)
c
      integer           nx, j 
      Complex*16
     &                  x(nx), y(nx), h, dd, dl, du
c
      Complex*16
     &                  one, rho
      parameter         (one = (1.0, 0.0), rho = (100.0, 0.0))
c
c     Compute the matrix vector multiplication y<---T*x
c     where T is a nx by nx tridiagonal matrix with DD on the 
c     diagonal, DL on the subdiagonal, and DU on the superdiagonal
c     
      h   = one / dcmplx(nx+1)
      dd  = (4.0, 0.0)
      dl  = -one - (0.5, 0.0)*rho*h
      du  = -one + (0.5, 0.0)*rho*h
c 
      y(1) =  dd*x(1) + du*x(2)
      do 10 j = 2,nx-1
         y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 
 10   continue 
      y(nx) =  dl*x(nx-1) + dd*x(nx) 
      return
      end
