pclaevswp.f

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*
*
      SUBROUTINE pclaevswp( N, ZIN, LDZI, Z, IZ, JZ, DESCZ, NVS, KEY,
     $                      RWORK, LRWORK )
*
*  -- ScaLAPACK routine (version 1.7) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     April 15, 1997
*
*     .. Scalar Arguments ..
      INTEGER            IZ, JZ, LDZI, LRWORK, N
*     ..
*     .. Array Arguments ..
      INTEGER            DESCZ( * ), KEY( * ), NVS( * )
      REAL               RWORK( * ), ZIN( LDZI, * )
      COMPLEX            Z( * )
*     ..
*
*  Purpose
*  =======
*
*  PCLAEVSWP moves the eigenvectors (potentially unsorted) from
*  where they are computed, to a ScaLAPACK standard block cyclic
*  array, sorted so that the corresponding eigenvalues are sorted.
*
*  Notes
*  =====
*
*
*  Each global data object is described by an associated description
*  vector.  This vector stores the information required to establish
*  the mapping between an object element and its corresponding process
*  and memory location.
*
*  Let A be a generic term for any 2D block cyclicly distributed array.
*  Such a global array has an associated description vector DESCA.
*  In the following comments, the character _ should be read as
*  "of the global array".
*
*  NOTATION        STORED IN      EXPLANATION
*  --------------- -------------- --------------------------------------
*  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
*                                 DTYPE_A = 1.
*  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
*                                 the BLACS process grid A is distribu-
*                                 ted over. The context itself is glo-
*                                 bal, but the handle (the integer
*                                 value) may vary.
*  M_A    (global) DESCA( M_ )    The number of rows in the global
*                                 array A.
*  N_A    (global) DESCA( N_ )    The number of columns in the global
*                                 array A.
*  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
*                                 the rows of the array.
*  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
*                                 the columns of the array.
*  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
*                                 row of the array A is distributed.
*  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
*                                 first column of the array A is
*                                 distributed.
*  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
*                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
*
*  Let K be the number of rows or columns of a distributed matrix,
*  and assume that its process grid has dimension p x q.
*  LOCr( K ) denotes the number of elements of K that a process
*  would receive if K were distributed over the p processes of its
*  process column.
*  Similarly, LOCc( K ) denotes the number of elements of K that a
*  process would receive if K were distributed over the q processes of
*  its process row.
*  The values of LOCr() and LOCc() may be determined via a call to the
*  ScaLAPACK tool function, NUMROC:
*          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
*          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
*  An upper bound for these quantities may be computed by:
*          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
*          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
*
*  Arguments
*  =========
*
*     NP = the number of rows local to a given process.
*     NQ = the number of columns local to a given process.
*
*  N       (global input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  ZIN     (local input) REAL array,
*          dimension ( LDZI, NVS(iam) )
*          The eigenvectors on input.  Each eigenvector resides entirely
*          in one process.  Each process holds a contiguous set of
*          NVS(iam) eigenvectors.  The first eigenvector which the
*          process holds is:  sum for i=[0,iam-1) of NVS(i)
*
*  LDZI    (locl input) INTEGER
*          leading dimension of the ZIN array
*
*  Z       (local output) COMPLEX array
*          global dimension (N, N), local dimension (DESCZ(DLEN_), NQ)
*          The eigenvectors on output.  The eigenvectors are distributed
*          in a block cyclic manner in both dimensions, with a
*          block size of NB.
*
*  IZ      (global input) INTEGER
*          Z's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*
*  JZ      (global input) INTEGER
*          Z's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*
*  DESCZ   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix Z.
*
*  NVS     (global input) INTEGER array, dimension( nprocs+1 )
*          nvs(i) = number of processes
*          number of eigenvectors held by processes [0,i-1)
*          nvs(1) = number of eigen vectors held by [0,1-1) == 0
*          nvs(nprocs+1) = number of eigen vectors held by [0,nprocs) ==
*            total number of eigenvectors
*
*  KEY     (global input) INTEGER array, dimension( N )
*          Indicates the actual index (after sorting) for each of the
*          eigenvectors.
*
*  RWORK    (local workspace) REAL array, dimension (LRWORK)
*
*  LRWORK   (local input) INTEGER dimension of RWORK
*     .. Parameters ..
      INTEGER            BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
     $                   mb_, nb_, rsrc_, csrc_, lld_
      parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
     $                   ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
     $                   rsrc_ = 7, csrc_ = 8, lld_ = 9 )
*     ..
*     .. Local Scalars ..
      INTEGER            CYCLIC_I, CYCLIC_J, DIST, I, IAM, II, INCII, J,
     $                   maxi, maxii, mini, minii, mycol, myrow, nb,
     $                   nbufsize, npcol, nprocs, nprow, pcol, recvcol,
     $                   recvfrom, recvrow, sendcol, sendrow, sendto
*     ..
*     .. External Functions ..
      INTEGER            INDXG2L, INDXG2P
      EXTERNAL           indxg2l, indxg2p
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, sgerv2d, sgesd2d
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          cmplx, max, min, mod
*     ..
*     .. Executable Statements ..
*       This is just to keep ftnchek happy
      IF( block_cyclic_2d*csrc_*ctxt_*dlen_*dtype_*lld_*mb_*m_*nb_*n_*
     $    rsrc_.LT.0 )RETURN
      CALL blacs_gridinfo( descz( ctxt_ ), nprow, npcol, myrow, mycol )
      iam = myrow + mycol*nprow
      iam = myrow*npcol + mycol
*
      nb = descz( mb_ )
*
      nprocs = nprow*npcol
*
*     If PxSTEIN operates on a sub-matrix of a global matrix, the
*     key [] that contains the indicies of the eigenvectors is refe-
*     renced to the dimensions of the sub-matrix and not the global
*     distrubited matrix. Because of this, PxLAEVSWP will incorrectly
*     map the eigenvectors to the global eigenvector matrix, Z, unless
*     the key[] elements are shifted as below.
*
      DO 10 j = descz( n_ ), 1, -1
         key( j ) = key( j-jz+1 ) + ( jz-1 )
   10 CONTINUE
*
      DO 110 dist = 0, nprocs - 1
*
         sendto = mod( iam+dist, nprocs )
         recvfrom = mod( nprocs+iam-dist, nprocs )
*
         sendrow = mod( sendto, nprow )
         sendcol = sendto / nprow
         recvrow = mod( recvfrom, nprow )
         recvcol = recvfrom / nprow
*
         sendrow = sendto / npcol
         sendcol = mod( sendto, npcol )
         recvrow = recvfrom / npcol
         recvcol = mod( recvfrom, npcol )
*
*        Figure out what I have that process "sendto" wants
*
         nbufsize = 0
*
*        We are looping through the eigenvectors that I presently own.
*
         DO 40 j = nvs( 1+iam ) + jz, nvs( 1+iam+1 ) + jz - 1
            pcol = indxg2p( key( j ), descz( nb_ ), -1, descz( csrc_ ),
     $             npcol )
            IF( sendcol.EQ.pcol ) THEN
               minii = mod( sendrow+descz( rsrc_ ), nprow )*
     $                 descz( mb_ ) + 1
               maxii = descz( m_ )
               incii = descz( mb_ )*nprow
               DO 30 ii = minii, maxii, incii
                  mini = max( ii, iz )
                  maxi = min( ii+descz( mb_ )-1, n+iz-1 )
                  DO 20 i = mini, maxi, 1
                     nbufsize = nbufsize + 1
                     rwork( nbufsize ) = zin( i+1-iz,
     $                                   j-nvs( 1+iam )+1-jz )
   20             CONTINUE
   30          CONTINUE
            END IF
   40    CONTINUE
*
*
         IF( myrow.NE.sendrow .OR. mycol.NE.sendcol )
     $      CALL sgesd2d( descz( ctxt_ ), nbufsize, 1, rwork, nbufsize,
     $                    sendrow, sendcol )
*
*
*        Figure out what process "recvfrom" has that I want
*
         nbufsize = 0
         DO 70 j = nvs( 1+recvfrom ) + jz,
     $           nvs( 1+recvfrom+1 ) + jz - 1, 1
            pcol = indxg2p( key( j ), descz( nb_ ), -1, descz( csrc_ ),
     $             npcol )
            IF( mycol.EQ.pcol ) THEN
               minii = mod( myrow+descz( rsrc_ ), nprow )*descz( mb_ ) +
     $                 1
               maxii = descz( m_ )
               incii = descz( mb_ )*nprow
               DO 60 ii = minii, maxii, incii
                  mini = max( ii, iz )
                  maxi = min( ii+nb-1, n+iz-1 )
                  DO 50 i = mini, maxi, 1
                     nbufsize = nbufsize + 1
   50             CONTINUE
   60          CONTINUE
            END IF
   70    CONTINUE
*
*
*
         IF( myrow.NE.recvrow .OR. mycol.NE.recvcol )
     $      CALL sgerv2d( descz( ctxt_ ), 1, nbufsize, rwork, 1,
     $                    recvrow, recvcol )
*
         nbufsize = 0
         DO 100 j = nvs( 1+recvfrom ) + jz,
     $           nvs( 1+recvfrom+1 ) + jz - 1, 1
            pcol = indxg2p( key( j ), descz( nb_ ), -1, descz( csrc_ ),
     $             npcol )
            IF( mycol.EQ.pcol ) THEN
               cyclic_j = indxg2l( key( j ), descz( mb_ ), -1, -1,
     $                    npcol )
               cyclic_i = 1
               minii = mod( myrow+descz( rsrc_ ), nprow )*descz( mb_ ) +
     $                 1
               maxii = descz( m_ )
               incii = descz( mb_ )*nprow
               DO 90 ii = minii, maxii, incii
                  mini = max( ii, iz )
                  cyclic_i = indxg2l( mini, descz( mb_ ), -1, -1,
     $                       nprow )
                  maxi = min( ii+nb-1, n+iz-1 )
                  DO 80 i = mini, maxi, 1
                     nbufsize = nbufsize + 1
                     z( cyclic_i+( cyclic_j-1 )*descz( lld_ ) )
     $                  = cmplx( rwork( nbufsize ) )
                     cyclic_i = cyclic_i + 1
   80             CONTINUE
   90          CONTINUE
            END IF
  100    CONTINUE
*
  110 CONTINUE
      RETURN
*
*     End of PCLAEVSWP
*
      SUBROUTINE pclaevswp( N, ZIN, LDZI, Z, IZ, JZ, DESCZ, NVS, KEY, …
      END