pssyevr.f

Go to the documentation of this file.

      SUBROUTINE pssyevr( JOBZ, RANGE, UPLO, N, A, IA, JA, 
     $                    DESCA, VL, VU, IL, IU, M, NZ, W, Z, IZ,
     $                    JZ, DESCZ, WORK, LWORK, IWORK, LIWORK,
     $                    INFO )
 
      IMPLICIT NONE
*
*  -- ScaLAPACK routine (version 2.0.2) --
*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
*     May 1 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE, UPLO
      INTEGER            IA, IL, INFO, IU, IZ, JA, JZ, LIWORK, LWORK, M,
     $                   N, NZ
      REAL             VL, VU
*     ..
*     .. Array Arguments ..
      INTEGER            DESCA( * ), DESCZ( * ), IWORK( * )
      REAL               A( * ), W( * ), WORK( * ), Z( * )
*     ..
*
*  Purpose
*  =======
*
*  PSSYEVR computes selected eigenvalues and, optionally, eigenvectors
*  of a real symmetric matrix A distributed in 2D blockcyclic format
*  by calling the recommended sequence of ScaLAPACK routines.  
*
*  First, the matrix A is reduced to real symmetric tridiagonal form.
*  Then, the eigenproblem is solved using the parallel MRRR algorithm.
*  Last, if eigenvectors have been computed, a backtransformation is done.
*
*  Upon successful completion, each processor stores a copy of all computed
*  eigenvalues in W. The eigenvector matrix Z is stored in 
*  2D blockcyclic format distributed over all processors.
*
*  Note that subsets of eigenvalues/vectors can be selected by
*  specifying a range of values or a range of indices for the desired
*  eigenvalues.
*
*  For constructive feedback and comments, please contact cvoemel@lbl.gov
*  C. Voemel
*
*  Arguments
*  =========
*
*  JOBZ    (global input) CHARACTER*1
*          Specifies whether or not to compute the eigenvectors:
*          = 'N':  Compute eigenvalues only.
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  RANGE   (global input) CHARACTER*1
*          = 'A': all eigenvalues will be found.
*          = 'V': all eigenvalues in the interval [VL,VU] will be found.
*          = 'I': the IL-th through IU-th eigenvalues will be found.
*
*  UPLO    (global input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (global input) INTEGER
*          The number of rows and columns of the matrix A.  N >= 0
*
*  A       (local input/workspace) 2D block cyclic REAL array,
*          global dimension (N, N),
*          local dimension ( LLD_A, LOCc(JA+N-1) ),
*          (see Notes below for more detailed explanation of 2d arrays)  
*
*          On entry, the symmetric matrix A.  If UPLO = 'U', only the
*          upper triangular part of A is used to define the elements of
*          the symmetric matrix.  If UPLO = 'L', only the lower
*          triangular part of A is used to define the elements of the
*          symmetric matrix.
*
*          On exit, the lower triangle (if UPLO='L') or the upper
*          triangle (if UPLO='U') of A, including the diagonal, is
*          destroyed.
*
*  IA      (global input) INTEGER
*          A's global row index, which points to the beginning of the
*          submatrix which is to be operated on. 
*          It should be set to 1 when operating on a full matrix.
*
*  JA      (global input) INTEGER
*          A's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*          It should be set to 1 when operating on a full matrix.
*
*  DESCA   (global and local input) INTEGER array of dimension DLEN=9.
*          The array descriptor for the distributed matrix A.
*          The descriptor stores details about the 2D block-cyclic 
*          storage, see the notes below.
*          If DESCA is incorrect, PSSYEVR cannot guarantee
*          correct error reporting.
*          Also note the array alignment requirements specified below.
*
*  VL      (global input) REAL 
*          If RANGE='V', the lower bound of the interval to be searched
*          for eigenvalues.  Not referenced if RANGE = 'A' or 'I'.
*
*  VU      (global input) REAL 
*          If RANGE='V', the upper bound of the interval to be searched
*          for eigenvalues.  Not referenced if RANGE = 'A' or 'I'.
*
*  IL      (global input) INTEGER
*          If RANGE='I', the index (from smallest to largest) of the
*          smallest eigenvalue to be returned.  IL >= 1.
*          Not referenced if RANGE = 'A'.
*
*  IU      (global input) INTEGER
*          If RANGE='I', the index (from smallest to largest) of the
*          largest eigenvalue to be returned.  min(IL,N) <= IU <= N.
*          Not referenced if RANGE = 'A'.
*
*  M       (global output) INTEGER
*          Total number of eigenvalues found.  0 <= M <= N.
*
*  NZ      (global output) INTEGER
*          Total number of eigenvectors computed.  0 <= NZ <= M.
*          The number of columns of Z that are filled.
*          If JOBZ .NE. 'V', NZ is not referenced.
*          If JOBZ .EQ. 'V', NZ = M 
*
*  W       (global output) REAL array, dimension (N)
*          Upon successful exit, the first M entries contain the selected
*          eigenvalues in ascending order.
*
*  Z       (local output) REAL array,
*          global dimension (N, N),
*          local dimension ( LLD_Z, LOCc(JZ+N-1) )
*          (see Notes below for more detailed explanation of 2d arrays)  
*          If JOBZ = 'V', then on normal exit the first M columns of Z
*          contain the orthonormal eigenvectors of the matrix
*          corresponding to the selected eigenvalues.
*          If JOBZ = 'N', then Z is not referenced.
*
*  IZ      (global input) INTEGER
*          Z's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*          It should be set to 1 when operating on a full matrix.
*
*  JZ      (global input) INTEGER
*          Z's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*          It should be set to 1 when operating on a full matrix.
*
*  DESCZ   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix Z.
*          The context DESCZ( CTXT_ ) must equal DESCA( CTXT_ ).
*          Also note the array alignment requirements specified below.
*
*  WORK    (local workspace/output) REAL  array,
*          dimension (LWORK)
*          On return, WORK(1) contains the optimal amount of
*          workspace required for efficient execution.
*          if JOBZ='N' WORK(1) = optimal amount of workspace
*             required to compute the eigenvalues.
*          if JOBZ='V' WORK(1) = optimal amount of workspace
*             required to compute eigenvalues and eigenvectors.
*
*  LWORK   (local input) INTEGER
*          Size of WORK, must be at least 3.
*          See below for definitions of variables used to define LWORK.
*          If no eigenvectors are requested (JOBZ = 'N') then
*             LWORK >= 2 + 5*N + MAX( 12 * NN, NB * ( NP0 + 1 ) )
*          If eigenvectors are requested (JOBZ = 'V' ) then
*             the amount of workspace required is:
*             LWORK >= 2 + 5*N + MAX( 18*NN, NP0 * MQ0 + 2 * NB * NB ) +
*               (2 + ICEIL( NEIG, NPROW*NPCOL))*NN
*
*          Variable definitions:
*             NEIG = number of eigenvectors requested
*             NB = DESCA( MB_ ) = DESCA( NB_ ) =
*                  DESCZ( MB_ ) = DESCZ( NB_ )
*             NN = MAX( N, NB, 2 )
*             DESCA( RSRC_ ) = DESCA( NB_ ) = DESCZ( RSRC_ ) =
*                              DESCZ( CSRC_ ) = 0
*             NP0 = NUMROC( NN, NB, 0, 0, NPROW )
*             MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL )
*             ICEIL( X, Y ) is a ScaLAPACK function returning
*             ceiling(X/Y)
*
*          If LWORK = -1, then LWORK is global input and a workspace
*          query is assumed; the routine only calculates the size
*          required for optimal performance for all work arrays. Each of
*          these values is returned in the first entry of the
*          corresponding work arrays, and no error message is issued by
*          PXERBLA.
*          Note that in a workspace query, for performance the optimal 
*          workspace LWOPT is returned rather than the minimum necessary 
*          WORKSPACE LWMIN. For very small matrices, LWOPT >> LWMIN.
*
*  IWORK   (local workspace) INTEGER array
*          On return, IWORK(1) contains the amount of integer workspace
*          required.
*
*  LIWORK  (local input) INTEGER
*          size of IWORK
*
*          Let  NNP = MAX( N, NPROW*NPCOL + 1, 4 ). Then:
*          LIWORK >= 12*NNP + 2*N when the eigenvectors are desired
*          LIWORK >= 10*NNP + 2*N when only the eigenvalues have to be computed
*          
*          If LIWORK = -1, then LIWORK is global input and a workspace
*          query is assumed; the routine only calculates the minimum
*          and optimal size for all work arrays. Each of these
*          values is returned in the first entry of the corresponding
*          work array, and no error message is issued by PXERBLA.
*
*  INFO    (global output) INTEGER
*          = 0:  successful exit
*          < 0:  If the i-th argument is an array and the j-entry had
*                an illegal value, then INFO = -(i*100+j), if the i-th
*                argument is a scalar and had an illegal value, then
*                INFO = -i.
*
*  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, 
*  or DESCZ for the descriptor of Z, etc. 
*  The length of a ScaLAPACK descriptor is nine.
*  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
*
*  PSSYEVR assumes IEEE 754 standard compliant arithmetic. 
*
*  Alignment requirements
*  ======================
*
*  The distributed submatrices A(IA:*, JA:*) and Z(IZ:IZ+M-1,JZ:JZ+N-1)
*  must satisfy the following alignment properties:
*
*  1.Identical (quadratic) dimension: 
*    DESCA(M_) = DESCZ(M_) = DESCA(N_) = DESCZ(N_)
*  2.Quadratic conformal blocking: 
*    DESCA(MB_) = DESCA(NB_) = DESCZ(MB_) = DESCZ(NB_)
*    DESCA(RSRC_) = DESCZ(RSRC_)
*  3.MOD( IA-1, MB_A ) = MOD( IZ-1, MB_Z ) = 0
*  4.IAROW = IZROW
*
*
*     .. Parameters ..
      INTEGER            CTXT_, M_, N_,
     $                   MB_, NB_, RSRC_, CSRC_
      PARAMETER          ( CTXT_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
     $                   rsrc_ = 7, csrc_ = 8 )
      REAL               ZERO
      parameter( zero = 0.0e0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ALLEIG, COLBRT, DOBCST, FINISH, FIRST, INDEIG,
     $                   LOWER, LQUERY, VALEIG, VSTART, WANTZ
      INTEGER            ANB, DOL, DOU, DSTCOL, DSTROW, EIGCNT, FRSTCL,
     $                   i, iarow, ictxt, iil, iinderr, iindwlc, iinfo,
     $                   iiu, im, indd, indd2, inde, inde2, inderr,
     $                   indilu, indrw, indtau, indwlc, indwork, ipil,
     $                   ipiu, iproc, izrow, lastcl, lengthi, lengthi2,
     $                   liwmin, llwork, lwmin, lwopt, maxcls, mq00,
     $                   mycol, myil, myiu, myproc, myrow, mz, nb,
     $                   ndepth, needil, neediu, nnp, np00, npcol,
     $                   nprocs, nprow, nps, nsplit, nsytrd_lwopt,
     $                   offset, parity, rlengthi, rlengthi2, rstarti,
     $                   size1, size2, sqnpc, srccol, srcrow, starti,
     $                   zoffset
 
      REAL                        PIVMIN, SAFMIN, SCALE, VLL, VUU, WL,
     $                            WU
*
*     .. Local Arrays ..
      INTEGER            IDUM1( 4 ), IDUM2( 4 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ICEIL, INDXG2P, NUMROC, PJLAENV
      REAL               PSLAMCH
      EXTERNAL            iceil, indxg2p, lsame, numroc, pjlaenv,
     $                    pslamch
*     ..
*     .. External Subroutines ..
      EXTERNAL            blacs_gridinfo, chk1mat, igebr2d, igebs2d,
     $                    igerv2d, igesd2d, igsum2d, pchk1mat, pchk2mat,
     $                    pselget, pslaevswp, pslared1d, psormtr,
     $                    pssyntrd, pxerbla, scopy, sgebr2d, sgebs2d,
     $                    sgerv2d, sgesd2d, slarrc, slasrt2,
     $                    sstegr2a, sstegr2b, sstegr2
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, real, ichar, int, max, min, mod, sqrt
*     ..
*     .. Executable Statements ..
*
 
 
      info = 0
***********************************************************************
*
*     Decode character arguments to find out what the code should do
*
***********************************************************************
      wantz = lsame( jobz, 'V' )
      lower = lsame( uplo, 'L' )
      alleig = lsame( range, 'A' )
      valeig = lsame( range, 'V' )
      indeig = lsame( range, 'I' )
      lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
 
***********************************************************************
*
*     GET MACHINE PARAMETERS
*
***********************************************************************
      ictxt = desca( ctxt_ )
      safmin = pslamch( ictxt, 'Safe minimum' )
 
***********************************************************************
*
*     Set up pointers into the WORK array
*     
***********************************************************************
      indtau = 1
      indd = indtau + n
      inde = indd + n + 1
      indd2 = inde + n + 1
      inde2 = indd2 + n
      indwork = inde2 + n
      llwork = lwork - indwork + 1
 
***********************************************************************
*
*     BLACS PROCESSOR GRID SETUP
*
***********************************************************************
      CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
 
 
      nprocs = nprow * npcol
      myproc = myrow * npcol + mycol
      IF( nprow.EQ.-1 ) THEN
         info = -( 800+ctxt_ )
      ELSE IF( wantz ) THEN
         IF( ictxt.NE.descz( ctxt_ ) ) THEN
            info = -( 2100+ctxt_ )
         END IF
      END IF
 
***********************************************************************
*
*     COMPUTE REAL WORKSPACE
*
***********************************************************************
      IF ( alleig ) THEN
         mz = n
      ELSE IF ( indeig ) THEN
         mz = iu - il + 1
      ELSE
*        Take upper bound for VALEIG case
         mz = n
      END IF
*     
      nb =  desca( nb_ )
      IF ( wantz ) THEN
         np00 = numroc( n, nb, 0, 0, nprow )
         mq00 = numroc( mz, nb, 0, 0, npcol )            
         indrw = indwork + max(18*n, np00*mq00 + 2*nb*nb)
         lwmin = indrw - 1 + (iceil(mz, nprocs) + 2)*n
      ELSE
         indrw = indwork + 12*n
         lwmin = indrw - 1
      END IF
*     The code that validates the input requires 3 workspace entries
      lwmin = max(3, lwmin)
      lwopt = lwmin
      anb = pjlaenv( ictxt, 3, 'PSSYTTRD', 'L', 0, 0, 0, 0 )
      sqnpc = int( sqrt( real( nprocs ) ) )
      nps = max( numroc( n, 1, 0, 0, sqnpc ), 2*anb )
      nsytrd_lwopt = 2*( anb+1 )*( 4*nps+2 ) + ( nps+4 )*nps
      lwopt = max( lwopt, 5*n+nsytrd_lwopt )
*
      size1 = indrw - indwork
 
***********************************************************************
*
*     COMPUTE INTEGER WORKSPACE
*
***********************************************************************
      nnp = max( n, nprocs+1, 4 )
      IF ( wantz ) THEN
        liwmin = 12*nnp + 2*n 
      ELSE
        liwmin = 10*nnp + 2*n
      END IF
 
***********************************************************************
*
*     Set up pointers into the IWORK array
*     
***********************************************************************
*     Pointer to eigenpair distribution over processors
      indilu = liwmin - 2*nprocs + 1            
      size2 = indilu - 2*n 
        
 
***********************************************************************
*
*     Test the input arguments.
*
***********************************************************************
      IF( info.EQ.0 ) THEN
         CALL chk1mat( n, 4, n, 4, ia, ja, desca, 8, info )
         IF( wantz )
     $      CALL chk1mat( n, 4, n, 4, iz, jz, descz, 21, info )
*
         IF( info.EQ.0 ) THEN
            IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
               info = -1
            ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
               info = -2
            ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
               info = -3
            ELSE IF( mod( ia-1, desca( mb_ ) ).NE.0 ) THEN
               info = -6
            ELSE IF( valeig .AND. n.GT.0 .AND. vu.LE.vl ) THEN
               info = -10
            ELSE IF( indeig .AND. ( il.LT.1 .OR. il.GT.max( 1, n ) ) )
     $                THEN
               info = -11
            ELSE IF( indeig .AND. ( iu.LT.min( n, il ) .OR. iu.GT.n ) )
     $                THEN
               info = -12
            ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
               info = -21
            ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
               info = -23
            ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
               info = -( 800+nb_ )
            END IF
            IF( wantz ) THEN
               iarow = indxg2p( 1, desca( nb_ ), myrow, 
     $                       desca( rsrc_ ), nprow )
               izrow = indxg2p( 1, desca( nb_ ), myrow, 
     $                          descz( rsrc_ ), nprow )
               IF( iarow.NE.izrow ) THEN
                  info = -19
               ELSE IF( mod( ia-1, desca( mb_ ) ).NE.
     $             mod( iz-1, descz( mb_ ) ) ) THEN
                  info = -19
               ELSE IF( desca( m_ ).NE.descz( m_ ) ) THEN
                  info = -( 2100+m_ )
               ELSE IF( desca( n_ ).NE.descz( n_ ) ) THEN
                  info = -( 2100+n_ )
               ELSE IF( desca( mb_ ).NE.descz( mb_ ) ) THEN
                  info = -( 2100+mb_ )
               ELSE IF( desca( nb_ ).NE.descz( nb_ ) ) THEN
                  info = -( 2100+nb_ )
               ELSE IF( desca( rsrc_ ).NE.descz( rsrc_ ) ) THEN
                  info = -( 2100+rsrc_ )
               ELSE IF( desca( csrc_ ).NE.descz( csrc_ ) ) THEN
                  info = -( 2100+csrc_ )
               ELSE IF( ictxt.NE.descz( ctxt_ ) ) THEN
                  info = -( 2100+ctxt_ )
               END IF
            END IF
         END IF
         idum2( 1 ) = 1
         IF( lower ) THEN
            idum1( 2 ) = ichar( 'L' )
         ELSE
            idum1( 2 ) = ichar( 'U' )
         END IF
         idum2( 2 ) = 2
         IF( alleig ) THEN
            idum1( 3 ) = ichar( 'A' )
         ELSE IF( indeig ) THEN
            idum1( 3 ) = ichar( 'I' )
         ELSE
            idum1( 3 ) = ichar( 'V' )
         END IF
         idum2( 3 ) = 3
         IF( lquery ) THEN
            idum1( 4 ) = -1
         ELSE
            idum1( 4 ) = 1
         END IF
         idum2( 4 ) = 4
         IF( wantz ) THEN
            idum1( 1 ) = ichar( 'V' )
            CALL pchk2mat( n, 4, n, 4, ia, ja, desca, 8, n, 4, n, 4, iz,
     $                     jz, descz, 21, 4, idum1, idum2, info )
         ELSE
            idum1( 1 ) = ichar( 'N' )
            CALL pchk1mat( n, 4, n, 4, ia, ja, desca, 8, 4, idum1,
     $                     idum2, info )
         END IF
         work( 1 ) = real( lwopt )
         iwork( 1 ) = liwmin
      END IF
*
      IF( info.NE.0 ) THEN
         CALL pxerbla( ictxt, 'PSSYEVR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
 
***********************************************************************
*
*     Quick return if possible
*
***********************************************************************
      IF( n.EQ.0 ) THEN
         IF( wantz ) THEN
            nz = 0
         END IF
         m = 0
         work( 1 ) = real( lwopt )
         iwork( 1 ) = liwmin
         RETURN
      END IF
 
      IF( valeig ) THEN
         vll = vl
         vuu = vu
      ELSE
         vll = zero
         vuu = zero
      END IF
*
*     No scaling done here, leave this to MRRR kernel.
*     Scale tridiagonal rather than full matrix.
*
***********************************************************************
*
*     REDUCE SYMMETRIC MATRIX TO TRIDIAGONAL FORM.
*
***********************************************************************
 
 
      CALL pssyntrd( uplo, n, a, ia, ja, desca, work( indd ),
     $               work( inde ), work( indtau ), work( indwork ),
     $               llwork, iinfo )
 
 
      IF (iinfo .NE. 0) THEN
         CALL pxerbla( ictxt, 'PSSYNTRD', -iinfo )
         RETURN
      END IF
 
***********************************************************************
*
*     DISTRIBUTE TRIDIAGONAL TO ALL PROCESSORS
*
***********************************************************************
      offset = 0
      IF( ia.EQ.1 .AND. ja.EQ.1 .AND. 
     $    desca( rsrc_ ).EQ.0 .AND. desca( csrc_ ).EQ.0 )
     $   THEN
         CALL pslared1d( n, ia, ja, desca, work( indd ), work( indd2 ),
     $                   work( indwork ), llwork )
*
         CALL pslared1d( n, ia, ja, desca, work( inde ), work( inde2 ),
     $                   work( indwork ), llwork )
         IF( .NOT.lower )
     $      offset = 1
      ELSE
         DO 10 i = 1, n
            CALL pselget( 'A', ' ', work( indd2+i-1 ), a, i+ia-1,
     $                    i+ja-1, desca )
   10    CONTINUE
         IF( lsame( uplo, 'U' ) ) THEN
            DO 20 i = 1, n - 1
               CALL pselget( 'A', ' ', work( inde2+i-1 ), a, i+ia-1,
     $                       i+ja, desca )
   20       CONTINUE
         ELSE
            DO 30 i = 1, n - 1
               CALL pselget( 'A', ' ', work( inde2+i-1 ), a, i+ia,
     $                       i+ja-1, desca )
   30       CONTINUE
         END IF
      END IF
 
 
 
 
***********************************************************************
*
*     SET IIL, IIU
*
***********************************************************************
      IF ( alleig ) THEN 
         iil = 1
         iiu = n
      ELSE IF ( indeig ) THEN
         iil = il
         iiu = iu
      ELSE IF ( valeig ) THEN
         CALL slarrc('T', n, vll, vuu, work( indd2 ), 
     $    work( inde2 + offset ), safmin, eigcnt, iil, iiu, info)
*        Refine upper bound N that was taken 
         mz = eigcnt
         iil = iil + 1
      ENDIF
 
      IF(mz.EQ.0) THEN
         m = 0
         IF( wantz ) THEN
            nz = 0
         END IF
         work( 1 ) = real( lwopt )
         iwork( 1 ) = liwmin
         RETURN
      END IF
 
      myil = 0
      myiu = 0
      m = 0
      im = 0
 
***********************************************************************
*
*     COMPUTE WORK ASSIGNMENTS
*
***********************************************************************
*
*     Each processor computes the work assignments for all processors
*
      CALL pmpim2( iil, iiu, nprocs,
     $             iwork(indilu), iwork(indilu+nprocs) )
*
*     Find local work assignment
*
      myil = iwork(indilu+myproc)
      myiu = iwork(indilu+nprocs+myproc)
 
 
      zoffset = max(0, myil - iil - 1) 
      first = ( myil .EQ. iil )
 
 
***********************************************************************
*
*     CALLS TO MRRR KERNEL
*
***********************************************************************
      IF(.NOT.wantz) THEN
*
*        Compute eigenvalues only.
*
         iinfo = 0
         IF ( myil.GT.0 ) THEN
            dol = 1
            dou = myiu - myil + 1
            CALL sstegr2( jobz, 'I', n,  work( indd2 ),
     $                  work( inde2+offset ), vll, vuu, myil, myiu,
     $                  im, w( 1 ), work( indrw ), n, 
     $                  myiu - myil + 1,
     $                  iwork( 1 ), work( indwork ), size1, 
     $                  iwork( 2*n+1 ), size2, 
     $                  dol, dou, zoffset, iinfo )
*           SSTEGR2 zeroes out the entire W array, so we can't just give
*           it the part of W we need.  So here we copy the W entries into
*           their correct location
            DO 49 i = 1, im
              w( myil-iil+i ) = w( i )
 49         CONTINUE
*           W( MYIL ) is at W( MYIL - IIL + 1 )
*           W( X ) is at W(X - IIL + 1 )
         END IF
         IF (iinfo .NE. 0) THEN
            CALL pxerbla( ictxt, 'SSTEGR2', -iinfo )
            RETURN
         END IF
      ELSEIF ( wantz .AND. nprocs.EQ.1 ) THEN
*
*        Compute eigenvalues and -vectors, but only on one processor
*
         iinfo = 0
         IF ( myil.GT.0 ) THEN
            dol = myil - iil + 1
            dou = myiu - iil + 1
            CALL sstegr2( jobz, 'I', n,  work( indd2 ),
     $                  work( inde2+offset ), vll, vuu, iil, iiu,
     $                  im, w( 1 ), work( indrw ), n, 
     $                  n,
     $                  iwork( 1 ), work( indwork ), size1, 
     $                  iwork( 2*n+1 ), size2, dol, dou,
     $                  zoffset, iinfo )
         ENDIF
         IF (iinfo .NE. 0) THEN
            CALL pxerbla( ictxt, 'SSTEGR2', -iinfo )
            RETURN
         END IF
      ELSEIF ( wantz ) THEN
*
*        Compute representations in parallel.
*        Share eigenvalue computation for root between all processors
*        Then compute the eigenvectors. 
*
         iinfo = 0
*        Part 1. compute root representations and root eigenvalues
         IF ( myil.GT.0 ) THEN
            dol = myil - iil + 1
            dou = myiu - iil + 1
            CALL sstegr2a( jobz, 'I', n,  work( indd2 ),
     $                  work( inde2+offset ), vll, vuu, iil, iiu,
     $                  im, w( 1 ), work( indrw ), n, 
     $                  n, work( indwork ), size1, 
     $                  iwork( 2*n+1 ), size2, dol, 
     $                  dou, needil, neediu,
     $                  inderr, nsplit, pivmin, scale, wl, wu,
     $                  iinfo )
         ENDIF
         IF (iinfo .NE. 0) THEN
            CALL pxerbla( ictxt, 'SSTEGR2A', -iinfo )
            RETURN
         END IF
*
*        The second part of parallel MRRR, the representation tree
*        construction begins. Upon successful completion, the 
*        eigenvectors have been computed. This is indicated by
*        the flag FINISH.
*
         vstart = .true.
         finish = (myil.LE.0)
C        Part 2. Share eigenvalues and uncertainties between all processors
         iinderr = indwork + inderr - 1
 
*
*
*        There are currently two ways to communicate eigenvalue information
*        using the BLACS.
*        1.) BROADCAST 
*        2.) POINT2POINT between collaborators (those processors working
*            jointly on a cluster.
*        For efficiency, BROADCAST has been disabled.
*        At a later stage, other more efficient communication algorithms 
*        might be implemented, e. g. group or tree-based communication.
*
         dobcst = .false.
         IF(dobcst) THEN
*           First gather everything on the first processor.
*           Then use BROADCAST-based communication 
            DO 45 i = 2, nprocs
               IF (myproc .EQ. (i - 1)) THEN
                  dstrow = 0
                  dstcol = 0
                  starti = dol
                  iwork(1) = starti
                  IF(myil.GT.0) THEN
                     lengthi = myiu - myil + 1
                  ELSE
                     lengthi = 0
                  ENDIF
                  iwork(2) = lengthi
                  CALL igesd2d( ictxt, 2, 1, iwork, 2, 
     $                    dstrow, dstcol )
                  IF (( starti.GE.1 ) .AND. ( lengthi.GE.1 )) THEN
                     lengthi2 = 2*lengthi
*                    Copy eigenvalues into communication buffer
                     CALL scopy(lengthi,w( starti ),1,
     $                          work( indd ), 1)                    
*                    Copy uncertainties into communication buffer
                     CALL scopy(lengthi,work( iinderr+starti-1 ),1,
     $                          work( indd+lengthi ), 1)                    
*                    send buffer
                     CALL sgesd2d( ictxt, lengthi2, 
     $                    1, work( indd ), lengthi2,
     $                    dstrow, dstcol )
                  END IF
               ELSE IF (myproc .EQ. 0) THEN
                  srcrow = (i-1) / npcol
                  srccol = mod(i-1, npcol)
                  CALL igerv2d( ictxt, 2, 1, iwork, 2, 
     $                    srcrow, srccol )
                  starti = iwork(1)
                  lengthi = iwork(2)
                  IF (( starti.GE.1 ) .AND. ( lengthi.GE.1 )) THEN
                     lengthi2 = 2*lengthi
*                    receive buffer
                     CALL sgerv2d( ictxt, lengthi2, 1,
     $                 work(indd), lengthi2, srcrow, srccol )
*                    copy eigenvalues from communication buffer
                     CALL scopy( lengthi, work(indd), 1,
     $                          w( starti ), 1)                    
*                    copy uncertainties (errors) from communication buffer
                     CALL scopy(lengthi,work(indd+lengthi),1,
     $                          work( iinderr+starti-1 ), 1)     
                  END IF
               END IF
  45        CONTINUE
            lengthi = iiu - iil + 1
            lengthi2 = lengthi * 2
            IF (myproc .EQ. 0) THEN
*              Broadcast eigenvalues and errors to all processors
               CALL scopy(lengthi,w ,1, work( indd ), 1)                 
               CALL scopy(lengthi,work( iinderr ),1,
     $                          work( indd+lengthi ), 1)                    
               CALL sgebs2d( ictxt, 'A', ' ', lengthi2, 1, 
     $              work(indd), lengthi2 )
            ELSE
               srcrow = 0
               srccol = 0
               CALL sgebr2d( ictxt, 'A', ' ', lengthi2, 1,
     $             work(indd), lengthi2, srcrow, srccol )
               CALL scopy( lengthi, work(indd), 1, w, 1)
               CALL scopy(lengthi,work(indd+lengthi),1,
     $                          work( iinderr ), 1)                   
            END IF
         ELSE
*
*           Enable point2point communication between collaborators
*
*           Find collaborators of MYPROC            
            IF( (nprocs.GT.1).AND.(myil.GT.0) ) THEN
               CALL pmpcol( myproc, nprocs, iil, needil, neediu, 
     $                   iwork(indilu), iwork(indilu+nprocs),
     $                   colbrt, frstcl, lastcl )
            ELSE
               colbrt = .false.
            ENDIF
 
            IF(colbrt) THEN
*              If the processor collaborates with others,
*              communicate information. 
               DO 47 iproc = frstcl, lastcl
                  IF (myproc .EQ. iproc) THEN
                     starti = dol
                     iwork(1) = starti
                     lengthi = myiu - myil + 1
                     iwork(2) = lengthi
                     
                     IF ((starti.GE.1) .AND. (lengthi.GE.1)) THEN
*                       Copy eigenvalues into communication buffer
                        CALL scopy(lengthi,w( starti ),1,
     $                              work(indd), 1)                    
*                       Copy uncertainties into communication buffer
                        CALL scopy(lengthi,
     $                          work( iinderr+starti-1 ),1,
     $                          work(indd+lengthi), 1)                    
                     ENDIF
 
                     DO 46 i = frstcl, lastcl                      
                        IF(i.EQ.myproc) GOTO 46
                        dstrow = i/ npcol
                        dstcol = mod(i, npcol)
                        CALL igesd2d( ictxt, 2, 1, iwork, 2, 
     $                             dstrow, dstcol )
                        IF ((starti.GE.1) .AND. (lengthi.GE.1)) THEN
                           lengthi2 = 2*lengthi
*                          send buffer
                           CALL sgesd2d( ictxt, lengthi2, 
     $                          1, work(indd), lengthi2,
     $                          dstrow, dstcol )
                        END IF
  46                 CONTINUE
                  ELSE
                     srcrow = iproc / npcol
                     srccol = mod(iproc, npcol)
                     CALL igerv2d( ictxt, 2, 1, iwork, 2, 
     $                             srcrow, srccol )
                     rstarti = iwork(1)
                     rlengthi = iwork(2)
                     IF ((rstarti.GE.1 ) .AND. (rlengthi.GE.1 )) THEN
                        rlengthi2 = 2*rlengthi
                        CALL sgerv2d( ictxt, rlengthi2, 1,
     $                      work(inde), rlengthi2,
     $                      srcrow, srccol )
*                       copy eigenvalues from communication buffer
                        CALL scopy( rlengthi, work(inde), 1,
     $                          w( rstarti ), 1)                    
*                       copy uncertainties (errors) from communication buffer
                        CALL scopy(rlengthi,work(inde+rlengthi),1,
     $                          work( iinderr+rstarti-1 ), 1)                    
                     END IF
                  END IF
  47           CONTINUE
            ENDIF
         ENDIF
 
*
*        Part 3. Compute representation tree and eigenvectors.
*                What follows is a loop in which the tree
*                is constructed in parallel from top to bottom,
*                on level at a time, until all eigenvectors
*                have been computed.
*      
 100     CONTINUE
         IF ( myil.GT.0 ) THEN
            CALL sstegr2b( jobz, n,  work( indd2 ),
     $                  work( inde2+offset ), 
     $                  im, w( 1 ), work( indrw ), n, n,
     $                  iwork( 1 ), work( indwork ), size1, 
     $                  iwork( 2*n+1 ), size2, dol, 
     $                  dou, needil, neediu, indwlc,
     $                  pivmin, scale, wl, wu,
     $                  vstart, finish, 
     $                  maxcls, ndepth, parity, zoffset, iinfo )
            iindwlc = indwork + indwlc - 1
            IF(.NOT.finish) THEN
               IF((needil.LT.dol).OR.(neediu.GT.dou)) THEN
                  CALL pmpcol( myproc, nprocs, iil, needil, neediu,
     $                 iwork(indilu), iwork(indilu+nprocs),
     $                   colbrt, frstcl, lastcl )
               ELSE
                  colbrt = .false.
                  frstcl = myproc
                  lastcl = myproc
               ENDIF
*
*              Check if this processor collaborates, i.e. 
*              communication is needed.
*
               IF(colbrt) THEN
                  DO 147 iproc = frstcl, lastcl
                     IF (myproc .EQ. iproc) THEN
                        starti = dol
                        iwork(1) = starti
                        IF(myil.GT.0) THEN
                           lengthi = myiu - myil + 1
                        ELSE
                           lengthi = 0
                        ENDIF
                        iwork(2) = lengthi
                        IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
*                          Copy eigenvalues into communication buffer
                           CALL scopy(lengthi,
     $                          work( iindwlc+starti-1 ),1,
     $                          work(indd), 1)                    
*                          Copy uncertainties into communication buffer
                           CALL scopy(lengthi,
     $                          work( iinderr+starti-1 ),1,
     $                          work(indd+lengthi), 1)                    
                        ENDIF
                     
                        DO 146 i = frstcl, lastcl                      
                           IF(i.EQ.myproc) GOTO 146
                           dstrow = i/ npcol
                           dstcol = mod(i, npcol)
                           CALL igesd2d( ictxt, 2, 1, iwork, 2, 
     $                             dstrow, dstcol )
                           IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
                              lengthi2 = 2*lengthi
*                             send buffer
                              CALL sgesd2d( ictxt, lengthi2, 
     $                             1, work(indd), lengthi2,
     $                             dstrow, dstcol )
                           END IF
 146                    CONTINUE
                     ELSE
                        srcrow = iproc / npcol
                        srccol = mod(iproc, npcol)
                        CALL igerv2d( ictxt, 2, 1, iwork, 2, 
     $                             srcrow, srccol )
                        rstarti = iwork(1)
                        rlengthi = iwork(2)
                        IF ((rstarti.GE.1).AND.(rlengthi.GE.1)) THEN
                           rlengthi2 = 2*rlengthi
                           CALL sgerv2d( ictxt,rlengthi2, 1,
     $                         work(inde),rlengthi2,
     $                         srcrow, srccol )
*                          copy eigenvalues from communication buffer
                           CALL scopy(rlengthi, work(inde), 1,
     $                          work( iindwlc+rstarti-1 ), 1)        
*                          copy uncertainties (errors) from communication buffer
                           CALL scopy(rlengthi,work(inde+rlengthi),1,
     $                          work( iinderr+rstarti-1 ), 1)            
                        END IF
                     END IF
 147              CONTINUE
               ENDIF
               GOTO 100         
            ENDIF
         ENDIF
         IF (iinfo .NE. 0) THEN
            CALL pxerbla( ictxt, 'SSTEGR2B', -iinfo )
            RETURN
         END IF
*
      ENDIF
 
*
***********************************************************************
*
*     MAIN PART ENDS HERE
*
***********************************************************************
*
***********************************************************************
*
*     ALLGATHER: EACH PROCESSOR SENDS ITS EIGENVALUES TO THE FIRST ONE,
*                THEN THE FIRST PROCESSOR BROADCASTS ALL EIGENVALUES
*
***********************************************************************
*
      DO 50 i = 2, nprocs
         IF (myproc .EQ. (i - 1)) THEN
            dstrow = 0
            dstcol = 0
            starti = myil - iil + 1
            iwork(1) = starti
            IF(myil.GT.0) THEN
               lengthi = myiu - myil + 1
            ELSE
               lengthi = 0
            ENDIF
            iwork(2) = lengthi
            CALL igesd2d( ictxt, 2, 1, iwork, 2, 
     $                    dstrow, dstcol )
            IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
               CALL sgesd2d( ictxt, lengthi, 
     $              1, w( starti ), lengthi,
     $              dstrow, dstcol )
            ENDIF
         ELSE IF (myproc .EQ. 0) THEN
            srcrow = (i-1) / npcol
            srccol = mod(i-1, npcol)
            CALL igerv2d( ictxt, 2, 1, iwork, 2, 
     $                    srcrow, srccol )
            starti = iwork(1)
            lengthi = iwork(2)
            IF ((starti.GE.1).AND.(lengthi.GE.1)) THEN
               CALL sgerv2d( ictxt, lengthi, 1,
     $                 w( starti ), lengthi, srcrow, srccol )
            ENDIF
         ENDIF
   50 CONTINUE
 
*     Accumulate M from all processors
      m = im
      CALL igsum2d( ictxt, 'A', ' ', 1, 1, m, 1, -1, -1 )
 
*     Broadcast eigenvalues to all processors
      IF (myproc .EQ. 0) THEN
*        Send eigenvalues
         CALL sgebs2d( ictxt, 'A', ' ', m, 1, w, m )
      ELSE
         srcrow = 0
         srccol = 0
         CALL sgebr2d( ictxt, 'A', ' ', m, 1,
     $           w, m, srcrow, srccol )
      END IF
*
*     Sort the eigenvalues and keep permutation in IWORK to
*     sort the eigenvectors accordingly
*
      DO 160 i = 1, m
         iwork( nprocs+1+i ) = i
  160 CONTINUE
      CALL slasrt2( 'I', m, w, iwork( nprocs+2 ), iinfo )
      IF (iinfo.NE.0) THEN
         CALL pxerbla( ictxt, 'SLASRT2', -iinfo )
         RETURN
      END IF
 
***********************************************************************
*
*     TRANSFORM Z FROM 1D WORKSPACE INTO 2D BLOCKCYCLIC STORAGE     
*
***********************************************************************
      IF ( wantz ) THEN
         DO 170 i = 1, m
            iwork( m+nprocs+1+iwork( nprocs+1+i ) ) = i
  170    CONTINUE
*        Store NVS in IWORK(1:NPROCS+1) for PSLAEVSWP
         iwork( 1 ) = 0
         DO 180 i = 1, nprocs
*           Find IL and IU for processor i-1
*           Has already been computed by PMPIM2 and stored
            ipil = iwork(indilu+i-1)
            ipiu = iwork(indilu+nprocs+i-1)
            IF (ipil .EQ. 0) THEN
               iwork( i + 1 ) = iwork( i )
            ELSE
               iwork( i + 1 ) = iwork( i ) + ipiu - ipil + 1
            ENDIF
  180    CONTINUE
 
         IF ( first ) THEN
            CALL pslaevswp(n, work( indrw ), n, z, iz, jz, 
     $       descz, iwork( 1 ), iwork( nprocs+m+2 ), work( indwork ), 
     $       indrw - indwork )
         ELSE
            CALL pslaevswp(n, work( indrw + n ), n, z, iz, jz, 
     $       descz, iwork( 1 ), iwork( nprocs+m+2 ), work( indwork ), 
     $       indrw - indwork )
         END IF
*
         nz = m
*
 
***********************************************************************
*
*       Compute eigenvectors of A from eigenvectors of T
*
***********************************************************************
         IF( nz.GT.0 ) THEN
           CALL psormtr( 'L', uplo, 'N', n, nz, a, ia, ja, desca,
     $                    work( indtau ), z, iz, jz, descz,
     $                    work( indwork ), size1, iinfo )
         END IF
         IF (iinfo.NE.0) THEN
            CALL pxerbla( ictxt, 'PSORMTR', -iinfo )
            RETURN
         END IF
*
 
      END IF
*
      work( 1 ) = real( lwopt )
      iwork( 1 ) = liwmin
 
      RETURN
*
*     End of PSSYEVR
*
      END