parallel-processingmpiscalapack

results of linear system using scalapack changing with processors number


I have used Jonathan's code and tried to solve A*X=B, but my results are changing based on the number of processors. Can anyone please help me in this regard.

! Use MPI-IO to read a diagonal matrix distributed block-cycliCALLy,
! use Scalapack to solve ax=b.
!
Program array
  USE mpi
  IMPLICIT NONE

  INTEGER, PARAMETER :: mk=SELECTED_REAL_KIND(15,307)
  INTEGER :: N,Nb    
  ! problem size and block size
  INTEGER :: myArows, myAcols, myBcols   
  ! size of local subset of global array
  REAL(mk), DIMENSION(:), ALLOCATABLE :: myA,myB
  INTEGER,  DIMENSION(:), ALLOCATABLE :: ipiv

  INTEGER, EXTERNAL :: numroc   
  ! blacs routine
  INTEGER :: me,nprocs,ictxt,prow,pcol,myrow,mycol  
  ! blacs data
  INTEGER :: info    
  ! scalapack return value
  INTEGER, DIMENSION(9) :: desca,descb 
  ! scalapack array desc
  INTEGER :: clock
  REAL(mk) :: calctime,iotime

  CHARACTER(LEN=128) :: matsize,fnamea,fnameb
  INTEGER :: myrank
  INTEGER :: ierr
  INTEGER, DIMENSION(2) :: pdims,dims,distribs,dargs
  INTEGER :: infile
  INTEGER, DIMENSION(MPI_STATUS_SIZE) :: mpistatus
  INTEGER :: darraya,darrayb
  !New data type (handle)
  INTEGER :: locsizea, nelementsa
  INTEGER :: locsizeb, nelementsb,nelementsw
  INTEGER(KIND=MPI_ADDRESS_KIND) :: lba,locextenta
  INTEGER(KIND=MPI_ADDRESS_KIND) :: lbb,locextentb
  !INTEGER(KIND=MPI_OFFSET_KIND) :: disp
  INTEGER :: nargs
  INTEGER :: m,IPACPY,ipa
  INTEGER :: mpik
  !MPI real kind precision

  CALL MPI_Init(ierr)
  CALL MPI_Comm_size(MPI_COMM_WORLD,nprocs,ierr)
  CALL MPI_Comm_rank(MPI_COMM_WORLD,myrank,ierr)
  ! Initialize MPI (for MPI-IO)

  pdims = 0
  CALL MPI_Dims_create(nprocs, 2, pdims, ierr)
  prow = pdims(1)
  pcol = pdims(2)
  !Get the process grid from MPI_Dims_create

  nargs = command_argument_count()
  IF  (nargs /= 3) THEN
      PRINT *,'Usage: mpirun -np np ./a.out  N filenamea filenameb'
      PRINT *,'       Where np is the number of processors'
      PRINT *,'       Where N is the size of Matrix A'
      PRINT *,'       Where filenamea = name of A matrix file data.'
      PRINT *,'       Where filenameb = name of B matrix file data.'
      CALL MPI_Abort(MPI_COMM_WORLD,1,ierr)
  ENDIF

  CALL get_command_argument(1, matsize)
  CALL get_command_argument(2, fnamea)
  CALL get_command_argument(3, fnameb)
  ! get filename

  READ(matsize(1:LEN_TRIM(matsize)),*) N
  !The size of the array we'll be using

  SELECT CASE (mk)
  CASE (SELECTED_REAL_KIND(6,37))
     mpik=MPI_REAL
  CASE (SELECTED_REAL_KIND(15,307))
     mpik=MPI_DOUBLE_PRECISION
  CASE DEFAULT
     PRINT*,"The input data type is not defined!"
     CALL MPI_Abort(MPI_COMM_WORLD,1,ierr)
  END SELECT

  Nb = 64 
  !Block size (for big matrix 32 or 64 are the suitable choice
  IF (Nb > (N/prow)) Nb = N/prow
  IF (Nb > (N/pcol)) Nb = N/pcol

  dims = [N,N]
  distribs = [MPI_DISTRIBUTE_CYCLIC, MPI_DISTRIBUTE_CYCLIC]
  dargs = [Nb,Nb]
  CALL MPI_Type_create_darray(nprocs,myrank,2,dims,distribs,dargs, &
  &    pdims,MPI_ORDER_FORTRAN,mpik,darraya,ierr)
  !Creates a distributed array datatype
  CALL MPI_Type_commit(darraya,ierr)
  CALL MPI_Type_size(darraya,locsizea,ierr)
  nelementsa = locsizea/mk
  CALL MPI_Type_get_extent(darraya,lba,locextenta,ierr)

  dims = [N,1]
  dargs = [Nb,1]
  CALL MPI_Type_create_darray(nprocs,myrank,2,dims,distribs,dargs, &
  &    pdims,MPI_ORDER_FORTRAN,mpik,darrayb,ierr)
  !Creates a distributed array datatype
  CALL MPI_Type_commit(darrayb,ierr)
  CALL MPI_Type_size(darrayb,locsizeb,ierr)
  nelementsb = locsizeb/mk
  CALL MPI_Type_get_extent(darrayb,lbb,locextentb,ierr)


  ALLOCATE(myA(nelementsa))
  ALLOCATE(myB(nelementsb))
  ! Initialize local arrays    

  CALL MPI_File_open(MPI_COMM_WORLD,TRIM(fnamea),MPI_MODE_RDONLY, &
  &    MPI_INFO_NULL,infile,ierr)
  CALL MPI_File_read_all(infile,myA,nelementsa,mpik,mpistatus,ierr)
  CALL MPI_File_close(infile,ierr)
  ! read in the data


  CALL MPI_File_open(MPI_COMM_WORLD,TRIM(fnameb),MPI_MODE_RDONLY, &
  &    MPI_INFO_NULL,infile,ierr)
  CALL MPI_File_read_all(infile,myB,nelementsb,mpik,mpistatus,ierr)
  CALL MPI_File_close(infile,ierr)
  ! read in the data

  iotime = tock(clock)
  IF (myrank == 0) THEN
     PRINT *,'I/O time      = ', iotime
  ENDIF

  ! Initialize blacs processor grid
  CALL tick(clock)
  CALL blacs_pinfo(me,nprocs)
  CALL blacs_get     (-1,0,ictxt)
  CALL blacs_gridinit(ictxt,'R',prow,pcol)
  CALL blacs_gridinfo(ictxt,prow,pcol,myrow,mycol)

  myArows = numroc(N,Nb,myrow,0,prow)
  myAcols = numroc(N,Nb,mycol,0,pcol)
  myBcols = numroc(1,Nb,mycol,0,pcol)
  !NUMROC computes the NUMber of Rows Or Columns of a distributed
  !matrix owned by the process indicated by the 3rd input.
  !the 4th input element is the coordinate of the process that possesses the
  !first row or column of the distributed matrix

  ! Construct local arrays
  ! Global structure:  matrix A of n rows and n columns
  CALL descinit(desca,N,N,Nb,Nb,0,0,ictxt,max(1,myArows),info)
  CALL descinit(descb,N,1,Nb, 1,0,0,ictxt,max(1,myArows),info)
  ! Prepare array descriptors for ScaLAPACK 


  nelementsw=descb(9)*myBcols
  ALLOCATE(ipiv(nelementsw))

  !CALL THE SCALAPACK ROUTINE
  !Solve the linear system A * X = B
  SELECT CASE (mk)
  CASE (SELECTED_REAL_KIND(6,37))
     CALL PSGESV(N,1,myA,1,1,desca,ipiv,myB,1,1,descb,info)
  CASE (SELECTED_REAL_KIND(15,307)) 
     CALL PDGESV(N,1,myA,1,1,desca,ipiv,myB,1,1,descb,info)
  END SELECT

  IF (info /= 0) THEN
      PRINT *, myrank,'Error -- info = ', info
      CALL MPI_Abort(MPI_COMM_WORLD,1,ierr)
  ENDIF 

  WRITE(fnameb,'(A)')'sol.dat'
  CALL PDLAWRITE(trim(fnameb),N,1,myB,1,1,DESCB,0,0,ipiv)
  !CALL MPI_File_open(MPI_COMM_WORLD,TRIM(fnameb),MPI_MODE_CREATE+ &
  !&    MPI_MODE_WRONLY,MPI_INFO_NULL,infile,ierr)
  !CALL MPI_File_write_all(infile,myB,nelementsb,mpik,mpistatus,ierr)
  !CALL MPI_File_close(infile,ierr)

  ! DEALLOCATE the local arrays
  DEALLOCATE(myA,ipiv,myB)

  ! End blacs for processors that are used
  CALL blacs_gridexit(ictxt)
  calctime = tock(clock)

  ! PRINT results
  IF (me == 0) THEN
    IF (info /= 0) THEN
         PRINT *, 'Error -- info = ', info
    ENDIF
    PRINT *,'Compute time = ', calctime
  ENDIF
  CALL MPI_Finalize(ierr)
CONTAINS
  SUBROUTINE tick(t)
      INTEGER, INTENT(  OUT) :: t
      CALL system_clock(t)
   END SUBROUTINE tick
  ! returns time in seconds from now to time described by t
  FUNCTION tock(t)
    INTEGER, INTENT(IN   ) :: t
    REAL(mk)               :: tock
    INTEGER :: now, clock_rate
    CALL system_clock(now,clock_rate)
    tock = REAL(now-t,mk)/REAL(clock_rate,mk)
  END FUNCTION tock
END PROGRAM array

The matrix A and B are the scalapack example ones. Just rewrited them in a binary format. So they can be used by the above program.

 19.0  3.0  1.0  12.0  1.0  16.0  1.0  3.0  11.0 
-19.0  3.0  1.0  12.0  1.0  16.0  1.0  3.0  11.0
-19.0 -3.0  1.0  12.0  1.0  16.0  1.0  3.0  11.0 
-19.0 -3.0 -1.0  12.0  1.0  16.0  1.0  3.0  11.0 
-19.0 -3.0 -1.0 -12.0  1.0  16.0  1.0  3.0  11.0 
-19.0 -3.0 -1.0 -12.0 -1.0  16.0  1.0  3.0  11.0 
-19.0 -3.0 -1.0 -12.0 -1.0 -16.0  1.0  3.0  11.0 
-19.0 -3.0 -1.0 -12.0 -1.0 -16.0 -1.0  3.0  11.0
-19.0 -3.0 -1.0 -12.0 -1.0 -16.0 -1.0 -3.0  11.0

and B

0.0
0.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0

For example for one processor:

mpirun -np 1 ./array 9 A.dat B.dat

           9           1
      0.000000000000000000D+00
     -0.166666666666666657D+00
      0.500000000000000000D+00
      0.000000000000000000D+00
      0.000000000000000000D+00
      0.000000000000000000D+00
      0.000000000000000000D+00
      0.000000000000000000D+00
      0.000000000000000000D+00

and for 2 processors

           9           1
     -0.432625129877109577D-01
     -0.000000000000000000D+00
     -0.677331518039483299D-01
     -0.250000000000000000D+00
      0.250000000000000056D+00
      0.769230769230769273D-01
      0.117743386633788305D+00
      0.122377622377622383D+00
      0.157721108027438911D+00

and for 6 processors I would receive an error

mpirun -np 6 ./a.out 9 A.dat B.dat

           0 Error -- info =            3
           1 Error -- info =            3
           2 Error -- info =            3
           3 Error -- info =            3
           4 Error -- info =            3
           5 Error -- info =            3

which does not occur using the scalapack example.


Solution

  • The problem solved.

    First, I fixed the process’s view of data in file after opening the file

    CALL MPI_File_set_view(infile,0_MPI_OFFSET_KIND,mpik,darraya,"native",MPI_INFO_NULL,ierr)
    

    Secondly, I fixed my mistake in preparing array descriptors for ScaLAPACK by changing

    CALL descinit(descb,N,1,Nb, 1,0,0,ictxt,max(1,myArows),info)
    

    to

    CALL descinit(descb,N,1,Nb,Nb,0,0,ictxt,max(1,myArows),info)
    

    These changes were the pieces of the problem which I was missing.