test_complex.F90 14.7 KB
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!    This file is part of ELPA.
!
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!    The ELPA library was originally created by the ELPA consortium,
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!    consisting of the following organizations:
!
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!    - Rechenzentrum Garching der Max-Planck-Gesellschaft (RZG),
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!    - Bergische Universität Wuppertal, Lehrstuhl für angewandte
!      Informatik,
!    - Technische Universität München, Lehrstuhl für Informatik mit
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!      Schwerpunkt Wissenschaftliches Rechnen ,
!    - Fritz-Haber-Institut, Berlin, Abt. Theorie,
!    - Max-Plack-Institut für Mathematik in den Naturwissenschaftrn,
!      Leipzig, Abt. Komplexe Strukutren in Biologie und Kognition,
!      and
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!    - IBM Deutschland GmbH
!
!
!    More information can be found here:
!    http://elpa.rzg.mpg.de/
!
!    ELPA is free software: you can redistribute it and/or modify
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!    it under the terms of the version 3 of the license of the
!    GNU Lesser General Public License as published by the Free
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!    Software Foundation.
!
!    ELPA 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 ELPA.  If not, see <http://www.gnu.org/licenses/>
!
!    ELPA reflects a substantial effort on the part of the original
!    ELPA consortium, and we ask you to respect the spirit of the
!    license that we chose: i.e., please contribute any changes you
!    may have back to the original ELPA library distribution, and keep
!    any derivatives of ELPA under the same license that we chose for
!    the original distribution, the GNU Lesser General Public License.
!
!
#include "config-f90.h"
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!>
!> Fortran test programm to demonstrates the use of
!> ELPA 1 complex case library.
!> If "HAVE_REDIRECT" was defined at build time
!> the stdout and stderr output of each MPI task
!> can be redirected to files if the environment
!> variable "REDIRECT_ELPA_TEST_OUTPUT" is set
!> to "true".
!>
!> By calling executable [arg1] [arg2] [arg3] [arg4]
!> one can define the size (arg1), the number of
!> Eigenvectors to compute (arg2), and the blocking (arg3).
!> If these values are not set default values (4000, 1500, 16)
!> are choosen.
!> If these values are set the 4th argument can be
!> "output", which specifies that the EV's are written to
!> an ascii file.
!>
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program test_complex

!-------------------------------------------------------------------------------
! Standard eigenvalue problem - COMPLEX version
!
! This program demonstrates the use of the ELPA module
! together with standard scalapack routines
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!
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! Copyright of the original code rests with the authors inside the ELPA
! consortium. The copyright of any additional modifications shall rest
! with their original authors, but shall adhere to the licensing terms
! distributed along with the original code in the file "COPYING".
!-------------------------------------------------------------------------------

   use ELPA1
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#ifdef WITH_OPENMP
   use test_util
#endif
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#ifdef HAVE_ISO_FORTRAN_ENV
   use iso_fortran_env, only : error_unit
#endif
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#ifdef HAVE_REDIRECT
   use redirect
#endif
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#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
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   implicit none
   include 'mpif.h'

   !-------------------------------------------------------------------------------
   ! Please set system size parameters below!
   ! na:   System size
   ! nev:  Number of eigenvectors to be calculated
   ! nblk: Blocking factor in block cyclic distribution
   !-------------------------------------------------------------------------------

   integer :: nblk
   integer na, nev

   !-------------------------------------------------------------------------------
   !  Local Variables

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   integer                 :: np_rows, np_cols, na_rows, na_cols
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   integer                 :: myid, nprocs, my_prow, my_pcol, mpi_comm_rows, mpi_comm_cols
   integer                 :: i, mpierr, my_blacs_ctxt, sc_desc(9), info, nprow, npcol
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   integer, external       :: numroc
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   real*8                  :: err, errmax
   real*8, allocatable     :: ev(:), xr(:,:)
   complex*16              :: xc
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   complex*16, allocatable :: a(:,:), z(:,:), tmp1(:,:), tmp2(:,:), as(:,:)

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   complex*16, parameter   :: CZERO = (0.d0,0.d0), CONE = (1.d0,0.d0)
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   integer                 :: iseed(4096) ! Random seed, size should be sufficient for every generator
   integer                 :: STATUS
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#ifdef WITH_OPENMP
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   integer                 :: omp_get_max_threads,  required_mpi_thread_level, provided_mpi_thread_level
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#endif
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   logical                 :: write_to_file
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   !-------------------------------------------------------------------------------
   !  Parse command line argumnents, if given
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   character*16            :: arg1
   character*16            :: arg2
   character*16            :: arg3
   character*16            :: arg4
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#ifndef HAVE_ISO_FORTRAN_ENV
  integer, parameter       :: error_unit = 6
#endif
  logical                  :: success
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  success = .true.
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  write_to_file = .false.
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   nblk = 16
   na = 4000
   nev = 1500

   if (COMMAND_ARGUMENT_COUNT() == 3) then
      call GET_COMMAND_ARGUMENT(1, arg1)
      call GET_COMMAND_ARGUMENT(2, arg2)
      call GET_COMMAND_ARGUMENT(3, arg3)

      read(arg1, *) na
      read(arg2, *) nev
      read(arg3, *) nblk
   endif

   if (COMMAND_ARGUMENT_COUNT() == 4) then
      call GET_COMMAND_ARGUMENT(1, arg1)
      call GET_COMMAND_ARGUMENT(2, arg2)
      call GET_COMMAND_ARGUMENT(3, arg3)
      call GET_COMMAND_ARGUMENT(4, arg4)
      read(arg1, *) na
      read(arg2, *) nev
      read(arg3, *) nblk
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   endif

   !-------------------------------------------------------------------------------
   !  MPI Initialization
#ifndef WITH_OPENMP
   call mpi_init(mpierr)
#else
   required_mpi_thread_level = MPI_THREAD_MULTIPLE
   call mpi_init_thread(required_mpi_thread_level,     &
                        provided_mpi_thread_level, mpierr)

   if (required_mpi_thread_level .ne. provided_mpi_thread_level) then
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      write(error_unit,*) "MPI ERROR: MPI_THREAD_MULTIPLE is not provided on this system"
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      write(error_unit,*) "           only ", mpi_thread_level_name(provided_mpi_thread_level), " is available"
      call exit(77)
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   endif
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#endif
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   call mpi_comm_rank(mpi_comm_world,myid,mpierr)
   call mpi_comm_size(mpi_comm_world,nprocs,mpierr)
   STATUS = 0
#ifdef WITH_OPENMP
   if (myid .eq. 0) then
      print *,"Threaded version of test program"
      print *,"Using ",omp_get_max_threads()," threads"
      print *," "
   endif
#endif
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#ifdef HAVE_REDIRECT
   if (check_redirect_environment_variable()) then
     if (myid .eq. 0) then
       print *," "
       print *,"Redirection of mpi processes is used"
       print *," "
       if (create_directories() .ne. 1) then
         write(error_unit,*) "Unable to create directory for stdout and stderr!"
         stop
       endif
     endif
     call MPI_BARRIER(MPI_COMM_WORLD, mpierr)
     call redirect_stdout(myid)
   endif
#endif
   if (arg4 .eq. "output") then
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      write_to_file = .true.
      if (myid .eq. 0) print *,"Writing output files"
   endif

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#ifdef HAVE_DETAILED_TIMINGS

   ! initialise the timing functionality

#ifdef HAVE_LIBPAPI
   call timer%measure_flops(.true.)
#endif

   call timer%measure_allocated_memory(.true.)
   call timer%measure_virtual_memory(.true.)
   call timer%measure_max_allocated_memory(.true.)

   call timer%set_print_options(&
#ifdef HAVE_LIBPAPI
                print_flop_count=.true., &
                print_flop_rate=.true., &
#endif
                print_allocated_memory = .true. , &
                print_virtual_memory=.true., &
                print_max_allocated_memory=.true.)


  call timer%enable()

  call timer%start("program")
#endif

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   !-------------------------------------------------------------------------------
   ! Selection of number of processor rows/columns
   ! We try to set up the grid square-like, i.e. start the search for possible
   ! divisors of nprocs with a number next to the square root of nprocs
   ! and decrement it until a divisor is found.

   do np_cols = NINT(SQRT(REAL(nprocs))),2,-1
      if(mod(nprocs,np_cols) == 0 ) exit
   enddo
   ! at the end of the above loop, nprocs is always divisible by np_cols

   np_rows = nprocs/np_cols

   if(myid==0) then
      print *
      print '(a)','Standard eigenvalue problem - COMPLEX version'
      print *
      print '(3(a,i0))','Matrix size=',na,', Number of eigenvectors=',nev,', Block size=',nblk
      print '(3(a,i0))','Number of processor rows=',np_rows,', cols=',np_cols,', total=',nprocs
      print *
   endif

   !-------------------------------------------------------------------------------
   ! Set up BLACS context and MPI communicators
   !
   ! The BLACS context is only necessary for using Scalapack.
   !
   ! For ELPA, the MPI communicators along rows/cols are sufficient,
   ! and the grid setup may be done in an arbitrary way as long as it is
   ! consistent (i.e. 0<=my_prow<np_rows, 0<=my_pcol<np_cols and every
   ! process has a unique (my_prow,my_pcol) pair).

   my_blacs_ctxt = mpi_comm_world
   call BLACS_Gridinit( my_blacs_ctxt, 'C', np_rows, np_cols )
   call BLACS_Gridinfo( my_blacs_ctxt, nprow, npcol, my_prow, my_pcol )

   if (myid==0) then
     print '(a)','| Past BLACS_Gridinfo.'
   end if

   ! All ELPA routines need MPI communicators for communicating within
   ! rows or columns of processes, these are set in get_elpa_row_col_comms.

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   mpierr = get_elpa_row_col_comms(mpi_comm_world, my_prow, my_pcol, &
                                   mpi_comm_rows, mpi_comm_cols)
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   if (myid==0) then
     print '(a)','| Past split communicator setup for rows and columns.'
   end if

   ! Determine the necessary size of the distributed matrices,
   ! we use the Scalapack tools routine NUMROC for that.

   na_rows = numroc(na, nblk, my_prow, 0, np_rows)
   na_cols = numroc(na, nblk, my_pcol, 0, np_cols)

   ! Set up a scalapack descriptor for the checks below.
   ! For ELPA the following restrictions hold:
   ! - block sizes in both directions must be identical (args 4+5)
   ! - first row and column of the distributed matrix must be on row/col 0/0 (args 6+7)

   call descinit( sc_desc, na, na, nblk, nblk, 0, 0, my_blacs_ctxt, na_rows, info )

   if (myid==0) then
     print '(a)','| Past scalapack descriptor setup.'
   end if

   !-------------------------------------------------------------------------------
   ! Allocate matrices and set up a test matrix for the eigenvalue problem

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#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("set up matrix")
#endif
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   allocate(a (na_rows,na_cols))
   allocate(z (na_rows,na_cols))
   allocate(as(na_rows,na_cols))

   allocate(ev(na))

   ! For getting a hermitian test matrix A we get a random matrix Z
   ! and calculate A = Z + Z**H

   ! We want different random numbers on every process
   ! (otherways A might get rank deficient):

   iseed(:) = myid
   call RANDOM_SEED(put=iseed)

   allocate(xr(na_rows,na_cols))
   call RANDOM_NUMBER(xr)
   z(:,:) = xr(:,:)
   call RANDOM_NUMBER(xr)
   z(:,:) = z(:,:) + (0.d0,1.d0)*xr(:,:)
   deallocate(xr)

   a(:,:) = z(:,:)

   if (myid==0) then
     print '(a)','| Random matrix block has been set up. (only processor 0 confirms this step)'
   end if

   call pztranc(na, na, CONE, z, 1, 1, sc_desc, CONE, a, 1, 1, sc_desc) ! A = A + Z**H

   if (myid==0) then
     print '(a)','| Random matrix has been symmetrized.'
   end if

   ! Save original matrix A for later accuracy checks

   as = a

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#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("set up matrix")
#endif
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   !-------------------------------------------------------------------------------
   ! Calculate eigenvalues/eigenvectors

   if (myid==0) then
     print '(a)','| Entering one-step ELPA solver ... '
     print *
   end if

   call mpi_barrier(mpi_comm_world, mpierr) ! for correct timings only
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   success = solve_evp_complex(na, nev, a, na_rows, ev, z, na_rows, nblk, &
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                          mpi_comm_rows, mpi_comm_cols)

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   if (.not.(success)) then
      write(error_unit,*) "solve_evp_complex produced an error! Aborting..."
      call MPI_ABORT(mpi_comm_world, mpierr)
   endif

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   if (myid==0) then
     print '(a)','| One-step ELPA solver complete.'
     print *
   end if

   if(myid == 0) print *,'Time tridiag_complex  :',time_evp_fwd
   if(myid == 0) print *,'Time solve_tridi      :',time_evp_solve
   if(myid == 0) print *,'Time trans_ev_complex :',time_evp_back
   if(myid == 0) print *,'Total time (sum above):',time_evp_back+time_evp_solve+time_evp_fwd

   if(write_to_file) then
      if (myid == 0) then
         open(17,file="EVs_complex_out.txt",form='formatted',status='new')
         do i=1,na
            write(17,*) i,ev(i)
         enddo
         close(17)
      endif
   endif
   !-------------------------------------------------------------------------------
   ! Test correctness of result (using plain scalapack routines)

   ! 1. Residual (maximum of || A*Zi - Zi*EVi ||)

   deallocate(a)
   allocate(tmp1(na_rows,na_cols))

   ! tmp1 =  A * Z
   call pzgemm('N','N',na,nev,na,CONE,as,1,1,sc_desc, &
               z,1,1,sc_desc,CZERO,tmp1,1,1,sc_desc)

   deallocate(as)
   allocate(tmp2(na_rows,na_cols))

   ! tmp2 = Zi*EVi
   tmp2(:,:) = z(:,:)
   do i=1,nev
      xc = ev(i)
      call pzscal(na,xc,tmp2,1,i,sc_desc,1)
   enddo

   !  tmp1 = A*Zi - Zi*EVi
   tmp1(:,:) =  tmp1(:,:) - tmp2(:,:)

   ! Get maximum norm of columns of tmp1
   errmax = 0
   do i=1,nev
      xc = 0
      call pzdotc(na,xc,tmp1,1,i,sc_desc,1,tmp1,1,i,sc_desc,1)
      errmax = max(errmax, sqrt(real(xc,8)))
   enddo

   ! Get maximum error norm over all processors
   err = errmax
   call mpi_allreduce(err,errmax,1,MPI_REAL8,MPI_MAX,MPI_COMM_WORLD,mpierr)
   if(myid==0) print *
   if(myid==0) print *,'Error Residual     :',errmax

   if (errmax .gt. 5e-12) then
      status = 1
   endif
   ! 2. Eigenvector orthogonality

   ! tmp1 = Z**T * Z
   tmp1 = 0
   call pzgemm('C','N',nev,nev,na,CONE,z,1,1,sc_desc, &
               z,1,1,sc_desc,CZERO,tmp1,1,1,sc_desc)
   ! Initialize tmp2 to unit matrix
   tmp2 = 0
   call pzlaset('A',nev,nev,CZERO,CONE,tmp2,1,1,sc_desc)

   ! tmp1 = Z**T * Z - Unit Matrix
   tmp1(:,:) =  tmp1(:,:) - tmp2(:,:)

   ! Get maximum error (max abs value in tmp1)
   err = maxval(abs(tmp1))
   call mpi_allreduce(err,errmax,1,MPI_REAL8,MPI_MAX,MPI_COMM_WORLD,mpierr)
   if(myid==0) print *,'Error Orthogonality:',errmax
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   if (errmax .gt. 5e-12) then
      status = 1
   endif
   deallocate(z)
   deallocate(tmp1)
   deallocate(tmp2)
   deallocate(ev)
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#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("program")
   print *," "
   print *,"Timings program:"
   call timer%print("program")
   print *," "
   print *,"End timings program"
#endif
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   call blacs_gridexit(my_blacs_ctxt)
   call mpi_finalize(mpierr)
   call EXIT(STATUS)
end

!-------------------------------------------------------------------------------