Simple test case for elpa_solve_tridi

Makefile.am

@@ -195,6 +195,7 @@ dist_files_DATA = \
   test/fortran_test_programs/test_real2_choose_kernel_with_api.F90 \
   test/fortran_test_programs/test_real.F90 \
   test/fortran_test_programs/test_real_with_c.F90 \
+  test/fortran_test_programs/test_real_toeplitz_matrix.F90 \
   src/elpa2_print_kernels.F90
 
 dist_doc_DATA = README.md USERS_GUIDE.md INSTALL.md CONTRIBUTING.md LICENSE Changelog COPYING/COPYING COPYING/gpl.txt COPYING/lgpl.txt
@@ -217,6 +218,7 @@ noinst_PROGRAMS = \
   elpa2_test_complex_default_kernel@SUFFIX@ \
   elpa2_test_real_choose_kernel_with_api@SUFFIX@ \
   elpa2_test_complex_choose_kernel_with_api@SUFFIX@ \
+  elpa1_test_real_toeplitz_matrix@SUFFIX@ \
   elpa1_test_real_with_c@SUFFIX@
 if !WITH_OPENMP
 noinst_PROGRAMS += \
@@ -279,6 +281,11 @@ elpa1_test_real@SUFFIX@_LDADD = $(build_lib)
 elpa1_test_real@SUFFIX@_FCFLAGS = $(AM_FCFLAGS) @FC_MODOUT@private_modules @FC_MODINC@private_modules
 EXTRA_elpa1_test_real@SUFFIX@_DEPENDENCIES = test/fortran_test_programs/elpa_test_programs_print_headers.X90
 
+elpa1_test_real_toeplitz_matrix@SUFFIX@_SOURCES = test/fortran_test_programs/test_real_toeplitz_matrix.F90
+elpa1_test_real_toeplitz_matrix@SUFFIX@_LDADD = $(build_lib)
+elpa1_test_real_toeplitz_matrix@SUFFIX@_FCFLAGS = $(AM_FCFLAGS) @FC_MODOUT@private_modules @FC_MODINC@private_modules
+EXTRA_elpa1_test_real_toeplitz_matrix@SUFFIX@_DEPENDENCIES = test/fortran_test_programs/elpa_test_programs_print_headers.X90
+
 elpa1_test_real_with_c@SUFFIX@_SOURCES = test/fortran_test_programs/test_real_with_c.F90
 elpa1_test_real_with_c@SUFFIX@_LDADD = $(build_lib)
 elpa1_test_real_with_c@SUFFIX@_FCFLAGS = $(AM_FCFLAGS) @FC_MODOUT@private_modules @FC_MODINC@private_modules
@@ -340,9 +347,11 @@ check_SCRIPTS = \
   elpa2_test_real_default_kernel@SUFFIX@.sh \
   elpa1_test_complex@SUFFIX@.sh \
   elpa2_test_complex@SUFFIX@.sh \
+  elpa2_test_real_default_kernel_qr_decomposition@SUFFIX@.sh \
   elpa2_test_complex_default_kernel@SUFFIX@.sh \
   elpa2_test_real_choose_kernel_with_api@SUFFIX@.sh \
   elpa2_test_complex_choose_kernel_with_api@SUFFIX@.sh \
+  elpa1_test_real_toeplitz_matrix@SUFFIX@.sh \
   elpa2_print_kernels@SUFFIX@
 
 

src/elpa_utilities.F90

@@ -60,6 +60,7 @@ module ELPA_utilities
   private ! By default, all routines contained are private
 
   public :: debug_messages_via_environment_variable, pcol, prow, error_unit
+  public :: map_global_array_index_to_local_index
 #ifndef HAVE_ISO_FORTRAN_ENV
   integer(kind=ik), parameter :: error_unit = 0
 #endif
@@ -123,4 +124,43 @@ module ELPA_utilities
 
 !-------------------------------------------------------------------------------
 
+ function map_global_array_index_to_local_index(iGLobal, jGlobal, iLocal, jLocal , nblk, np_rows, np_cols, my_prow, my_pcol) &
+   result(possible)
+   use precision
+
+   implicit none
+
+   integer(kind=ik)              :: pi, pj, li, lj, xi, xj
+   integer(kind=ik), intent(in)  :: iGlobal, jGlobal, nblk, np_rows, np_cols, my_prow, my_pcol
+   integer(kind=ik), intent(out) :: iLocal, jLocal
+   logical                       :: possible
+
+   possible = .true.
+   iLocal = 0
+   jLocal = 0
+
+   pi = prow(iGlobal, nblk, np_rows)
+
+   if (my_prow .ne. pi) then
+     possible = .false.
+     return
+   endif
+
+   pj = pcol(jGlobal, nblk, np_cols)
+
+   if (my_pcol .ne. pj) then
+     possible = .false.
+     return
+   endif
+   li = (iGlobal-1)/(np_rows*nblk) ! block number for rows
+   lj = (jGlobal-1)/(np_cols*nblk) ! block number for columns
+
+   xi = mod( (iGlobal-1),nblk)+1   ! offset in block li
+   xj = mod( (jGlobal-1),nblk)+1   ! offset in block lj
+
+   iLocal = li * nblk + xi
+   jLocal = lj * nblk + xj
+
+ end function
+
 end module ELPA_utilities

test/fortran_test_programs/test_real_toeplitz_matrix.F90

+!    This file is part of ELPA.
+!
+!    The ELPA library was originally created by the ELPA consortium,
+!    consisting of the following organizations:
+!
+!    - Max Planck Computing and Data Facility (MPCDF), formerly known as
+!      Rechenzentrum Garching der Max-Planck-Gesellschaft (RZG),
+!    - Bergische Universität Wuppertal, Lehrstuhl für angewandte
+!      Informatik,
+!    - Technische Universität München, Lehrstuhl für Informatik mit
+!      Schwerpunkt Wissenschaftliches Rechnen ,
+!    - Fritz-Haber-Institut, Berlin, Abt. Theorie,
+!    - Max-Plack-Institut für Mathematik in den Naturwissenschaften,
+!      Leipzig, Abt. Komplexe Strukutren in Biologie und Kognition,
+!      and
+!    - IBM Deutschland GmbH
+!
+!
+!    More information can be found here:
+!    http://elpa.mpcdf.mpg.de/
+!
+!    ELPA is free software: you can redistribute it and/or modify
+!    it under the terms of the version 3 of the license of the
+!    GNU Lesser General Public License as published by the Free
+!    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"
+!>
+!> Fortran test programm to demonstrates the use of
+!> the elpa_solve_tridi library function
+!>
+program test_solve_tridi
+
+!
+! 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 precision
+   use ELPA1
+   use elpa_utilities
+#ifdef WITH_OPENMP
+   use test_util
+#endif
+
+   use mod_read_input_parameters
+   use mod_check_correctness
+   use mod_setup_mpi
+   use mod_blacs_infrastructure
+   use mod_prepare_matrix
+
+   use elpa_mpi
+#ifdef HAVE_REDIRECT
+   use redirect
+#endif
+#ifdef HAVE_DETAILED_TIMINGS
+  use timings
+#endif
+  use output_types
+
+   implicit none
+
+   !-------------------------------------------------------------------------------
+   ! Please set system size parameters below!
+   ! na:   System size
+   ! nev:  Number of eigenvectors to be calculated
+   ! nblk: Blocking factor in block cyclic distribution
+   !-------------------------------------------------------------------------------
+   integer(kind=ik)           :: nblk
+   integer(kind=ik)           :: na, nev
+
+   integer(kind=ik)           :: np_rows, np_cols, na_rows, na_cols
+
+   integer(kind=ik)           :: myid, nprocs, my_prow, my_pcol, mpi_comm_rows, mpi_comm_cols
+   integer(kind=ik)           :: i, mpierr, my_blacs_ctxt, sc_desc(9), info, nprow, npcol
+
+   integer, external          :: numroc
+
+   real(kind=rk), allocatable :: a(:,:), d(:), e(:), ev_analytic(:), ev(:)
+   real(kind=rk)              :: diagonalELement, subdiagonalElement
+
+   real(kind=rk), allocatable :: tmp1(:,:), tmp2(:,:), as(:,:)
+   real(kind=rk)              :: tmp
+   integer(kind=ik)           :: loctmp ,rowLocal, colLocal
+
+
+   real(kind=rk)              :: maxerr
+
+   logical                    :: wantDebug
+
+   real(kind=rk), parameter   :: pi = 3.141592653589793238462643383279_rk
+
+   integer(kind=ik)           :: iseed(4096) ! Random seed, size should be sufficient for every generator
+
+   integer(kind=ik)           :: STATUS
+#ifdef WITH_OPENMP
+   integer(kind=ik)           :: omp_get_max_threads,  required_mpi_thread_level, &
+                                 provided_mpi_thread_level
+#endif
+   type(output_t)             :: write_to_file
+   logical                    :: success
+   character(len=8)           :: task_suffix
+   integer(kind=ik)           :: j
+   !-------------------------------------------------------------------------------
+
+   success = .true.
+
+   call read_input_parameters(na, nev, nblk, write_to_file)
+
+   !-------------------------------------------------------------------------------
+   !  MPI Initialization
+   call setup_mpi(myid, nprocs)
+
+   STATUS = 0
+
+!#define DATATYPE REAL
+!#define ELPA1
+!#include "elpa_test_programs_print_headers.X90"
+
+#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
+
+   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)','Test program for elpa_solve_tridi with a Toeplitz matrix'
+      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).
+
+   call set_up_blacsgrid(mpi_comm_world, my_blacs_ctxt, np_rows, np_cols, &
+                         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_communicators.
+
+   mpierr = get_elpa_communicators(mpi_comm_world, my_prow, my_pcol, &
+                                   mpi_comm_rows, mpi_comm_cols)
+
+   if (myid==0) then
+     print '(a)','| Past split communicator setup for rows and columns.'
+   end if
+
+   call set_up_blacs_descriptor(na ,nblk, my_prow, my_pcol, np_rows, np_cols, &
+                                na_rows, na_cols, sc_desc, my_blacs_ctxt, info)
+
+   if (myid==0) then
+     print '(a)','| Past scalapack descriptor setup.'
+   end if
+
+   !-------------------------------------------------------------------------------
+   ! Allocate matrices and set up a test toeplitz matrix for solve_tridi
+
+#ifdef HAVE_DETAILED_TIMINGS
+   call timer%start("set up matrix")
+#endif
+   allocate(a (na_rows,na_cols))
+   allocate(as(na_rows,na_cols))
+
+   allocate(d (na))
+   allocate(e (na))
+   allocate(ev_analytic(na))
+   allocate(ev(na))
+
+   a(:,:) = 0.0_rk
+
+
+   ! changeable numbers here would be nice
+   diagonalElement = 0.45_rk
+   subdiagonalElement =  0.78_rk
+
+   d(:) = diagonalElement
+   e(:) = subdiagonalElement
+
+
+   ! set up the diagonal and subdiagonals (for general solver test)
+   do i=1, na ! for diagonal elements
+     if (map_global_array_index_to_local_index(i, i, rowLocal, colLocal, nblk, np_rows, np_cols, my_prow, my_pcol)) then
+       a(rowLocal,colLocal) = diagonalElement
+     endif
+   enddo
+
+   do i=1, na-1
+     if (map_global_array_index_to_local_index(i, i+1, rowLocal, colLocal, nblk, np_rows, np_cols, my_prow, my_pcol)) then
+       a(rowLocal,colLocal) = subdiagonalElement
+     endif
+   enddo
+
+   do i=2, na
+     if (map_global_array_index_to_local_index(i, i-1, rowLocal, colLocal, nblk, np_rows, np_cols, my_prow, my_pcol)) then
+       a(rowLocal,colLocal) = subdiagonalElement
+     endif
+   enddo
+
+   as = a
+
+#ifdef HAVE_DETAILED_TIMINGS
+   call timer%stop("set up matrix")
+#endif
+
+
+   !-------------------------------------------------------------------------------
+   ! Calculate eigenvalues/eigenvectors
+
+   if (myid==0) then
+     print '(a)','| Entering elpa_solve_tridi ... '
+     print *
+   end if
+
+#ifdef WITH_MPI
+   call mpi_barrier(mpi_comm_world, mpierr) ! for correct timings only
+#endif
+
+   success = elpa_solve_tridi(na, nev, d, e, a, na_rows, nblk, na_cols, mpi_comm_rows, &
+                              mpi_comm_cols, wantDebug)
+
+   if (.not.(success)) then
+      write(error_unit,*) "elpa_solve_tridi produced an error! Aborting..."
+#ifdef WITH_MPI
+      call MPI_ABORT(mpi_comm_world, 1, mpierr)
+#endif
+   endif
+
+   if (myid==0) then
+     print '(a)','| elpa_solve_tridi complete.'
+     print *
+   end if
+
+
+   ev = d
+
+!
+!   if(myid == 0) print *,'Time tridiag_real     :',time_evp_fwd
+!   if(myid == 0) print *,'Time solve_tridi      :',time_evp_solve
+!   if(myid == 0) print *,'Time trans_ev_real    :',time_evp_back
+!   if(myid == 0) print *,'Total time (sum above):',time_evp_back+time_evp_solve+time_evp_fwd
+!
+!   if(write_to_file%eigenvectors) then
+!     write(unit = task_suffix, fmt = '(i8.8)') myid
+!     open(17,file="EVs_real_out_task_"//task_suffix(1:8)//".txt",form='formatted',status='new')
+!     write(17,*) "Part of eigenvectors: na_rows=",na_rows,"of na=",na," na_cols=",na_cols," of na=",na
+!
+!     do i=1,na_rows
+!       do j=1,na_cols
+!         write(17,*) "row=",i," col=",j," element of eigenvector=",z(i,j)
+!       enddo
+!     enddo
+!     close(17)
+!   endif
+!
+!   if(write_to_file%eigenvalues) then
+!      if (myid == 0) then
+!         open(17,file="Eigenvalues_real_out.txt",form='formatted',status='new')
+!         do i=1,na
+!            write(17,*) i,ev(i)
+!         enddo
+!         close(17)
+!      endif
+!   endif
+!
+!
+   !-------------------------------------------------------------------------------
+
+   ! analytic solution
+   do i=1, na
+     ev_analytic(i) = diagonalElement + 2.0_rk * subdiagonalElement *cos( pi*real(i,kind=rk)/ real(na+1,kind=rk) )
+   enddo
+
+   ! sort analytic solution:
+
+   ! this hack is neihter elegant, nor optimized: for huge matrixes it might be expensive
+   ! a proper sorting algorithmus might be implemented here
+
+   tmp    = minval(ev_analytic)
+   loctmp = minloc(ev_analytic, 1)
+
+   ev_analytic(loctmp) = ev_analytic(1)
+   ev_analytic(1) = tmp
+
+   do i=2, na
+     tmp = ev_analytic(i)
+     do j= i, na
+       if (ev_analytic(j) .lt. tmp) then
+         tmp    = ev_analytic(j)
+         loctmp = j
+       endif
+     enddo
+     ev_analytic(loctmp) = ev_analytic(i)
+     ev_analytic(i) = tmp
+   enddo
+
+   ! compute a simple error max of eigenvalues
+   maxerr = 0.0_rk
+   maxerr = maxval( (d(:) - ev_analytic(:))/ev_analytic(:) , 1)
+
+   if (maxerr .gt. 8.e-13) then
+     if (myid .eq. 0) then
+       print *,"Eigenvalues differ from analytic solution: maxerr = ",maxerr
+     endif
+
+   status = 1
+
+   endif
+
+   ! Test correctness of result (using plain scalapack routines)
+   allocate(tmp1(na_rows,na_cols))
+   allocate(tmp2(na_rows,na_cols))
+
+   status = check_correctness(na, nev, as, a, ev, sc_desc, myid, tmp1, tmp2)
+
+   deallocate(a)
+
+   deallocate(as)
+   deallocate(d)
+
+   deallocate(tmp1)
+   deallocate(tmp2)
+   deallocate(e)
+   deallocate(ev)
+   deallocate(ev_analytic)
+
+#ifdef HAVE_DETAILED_TIMINGS
+   call timer%stop("program")
+   print *," "
+   print *,"Timings program:"
+   print *," "
+   call timer%print("program")
+   print *," "
+   print *,"End timings program"
+   print *," "
+#endif
+
+#ifdef WITH_MPI
+   call blacs_gridexit(my_blacs_ctxt)
+   call mpi_finalize(mpierr)
+#endif
+
+   call EXIT(STATUS)
+
+
+end
+
+!-------------------------------------------------------------------------------