File: pslaqr5.f

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file content (2275 lines) | stat: -rw-r--r-- 103,522 bytes parent folder | download | duplicates (3)
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      SUBROUTINE PSLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
     $                    SR, SI, H, DESCH, ILOZ, IHIZ, Z, DESCZ, WORK,
     $                    LWORK, IWORK, LIWORK )
*
*     Contribution from the Department of Computing Science and HPC2N,
*     Umea University, Sweden
*
*  -- ScaLAPACK auxiliary routine (version 2.0.2) --
*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
*     May 1 2012
*
      IMPLICIT NONE
*
*     .. Scalar Arguments ..
      INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, N, NSHFTS,
     $                   LWORK, LIWORK
      LOGICAL            WANTT, WANTZ
*     ..
*     .. Array Arguments ..
      INTEGER            DESCH( * ), DESCZ( * ), IWORK( * )
      REAL               H( * ), SI( * ), SR( * ), Z( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  This auxiliary subroutine called by PSLAQR0 performs a
*  single small-bulge multi-shift QR sweep by chasing separated
*  groups of bulges along the main block diagonal of H.
*
*   WANTT  (global input) logical scalar
*          WANTT = .TRUE. if the quasi-triangular Schur factor
*          is being computed.  WANTT is set to .FALSE. otherwise.
*
*   WANTZ  (global input) logical scalar
*          WANTZ = .TRUE. if the orthogonal Schur factor is being
*          computed.  WANTZ is set to .FALSE. otherwise.
*
*   KACC22 (global input) integer with value 0, 1, or 2.
*          Specifies the computation mode of far-from-diagonal
*          orthogonal updates.
*     = 1: PSLAQR5 accumulates reflections and uses matrix-matrix
*          multiply to update the far-from-diagonal matrix entries.
*     = 2: PSLAQR5 accumulates reflections, uses matrix-matrix
*          multiply to update the far-from-diagonal matrix entries,
*          and takes advantage of 2-by-2 block structure during
*          matrix multiplies.
*
*   N      (global input) integer scalar
*          N is the order of the Hessenberg matrix H upon which this
*          subroutine operates.
*
*   KTOP   (global input) integer scalar
*   KBOT   (global input) integer scalar
*          These are the first and last rows and columns of an
*          isolated diagonal block upon which the QR sweep is to be
*          applied. It is assumed without a check that
*                    either KTOP = 1  or   H(KTOP,KTOP-1) = 0
*          and
*                    either KBOT = N  or   H(KBOT+1,KBOT) = 0.
*
*   NSHFTS (global input) integer scalar
*          NSHFTS gives the number of simultaneous shifts.  NSHFTS
*          must be positive and even.
*
*   SR     (global input) REAL             array of size (NSHFTS)
*   SI     (global input) REAL             array of size (NSHFTS)
*          SR contains the real parts and SI contains the imaginary
*          parts of the NSHFTS shifts of origin that define the
*          multi-shift QR sweep.
*
*   H      (local input/output) REAL             array of size 
*          (DESCH(LLD_),*)
*          On input H contains a Hessenberg matrix.  On output a
*          multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
*          to the isolated diagonal block in rows and columns KTOP
*          through KBOT.
*
*   DESCH  (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix H.
*
*   ILOZ   (global input) INTEGER
*   IHIZ   (global input) INTEGER
*          Specify the rows of Z to which transformations must be
*          applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
*
*   Z      (local input/output) REAL             array of size
*          (DESCZ(LLD_),*)
*          If WANTZ = .TRUE., then the QR Sweep orthogonal
*          similarity transformation is accumulated into
*          Z(ILOZ:IHIZ,ILO:IHI) from the right.
*          If WANTZ = .FALSE., then Z is unreferenced.
*
*   DESCZ  (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix Z.
*
*   WORK   (local workspace) REAL             array, dimension(DWORK)
*
*   LWORK  (local input) INTEGER
*          The length of the workspace array WORK.
*
*   IWORK  (local workspace) INTEGER array, dimension (LIWORK)
*
*   LIWORK (local input) INTEGER
*          The length of the workspace array IWORK.
*
*     ================================================================
*     Based on contributions by
*        Robert Granat, Department of Computing Science and HPC2N,
*        University of Umea, Sweden.
*
*     ============================================================
*     References:
*       K. Braman, R. Byers, and R. Mathias,
*       The Multi-Shift QR Algorithm Part I: Maintaining Well Focused
*       Shifts, and Level 3 Performance.
*       SIAM J. Matrix Anal. Appl., 23(4):929--947, 2002.
*
*       R. Granat, B. Kagstrom, and D. Kressner,
*       A Novel Parallel QR Algorithm for Hybrid Distributed Momory HPC
*       Systems.
*       SIAM J. Sci. Comput., 32(4):2345--2378, 2010.
*
*     ============================================================
*     .. Parameters ..
      INTEGER            BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
     $                   LLD_, MB_, M_, NB_, N_, RSRC_
      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 )
      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0e0, ONE = 1.0e0 )
      INTEGER            NTINY
      PARAMETER          ( NTINY = 11 )
*     ..
*     .. Local Scalars ..
      REAL               ALPHA, BETA, H11, H12, H21, H22, REFSUM,
     $                   SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2,
     $                   ULP, TAU, ELEM, STAMP, DDUM, ORTH
      INTEGER            I, I2, I4, INCOL, J, J2, J4, JBOT, JCOL, JLEN,
     $                   JROW, JTOP, K, K1, KDU, KMS, KNZ, KRCOL, KZS,
     $                   M, M22, MBOT, MEND, MSTART, MTOP, NBMPS, NDCOL,
     $                   NS, NU, LLDH, LLDZ, LLDU, LLDV, LLDW, LLDWH,
     $                   INFO, ICTXT, NPROW, NPCOL, NB, IROFFH, ITOP,
     $                   NWIN, MYROW, MYCOL, LNS, NUMWIN, LKACC22,
     $                   LCHAIN, WIN, IDONEJOB, IPNEXT, ANMWIN, LENRBUF,
     $                   LENCBUF, ICHOFF, LRSRC, LCSRC, LKTOP, LKBOT,
     $                   II, JJ, SWIN, EWIN, LNWIN, DIM, LLKTOP, LLKBOT,
     $                   IPV, IPU, IPH, IPW, KU, KWH, KWV, NVE, LKS,
     $                   IDUM, NHO, DIR, WINID, INDX, ILOC, JLOC, RSRC1,
     $                   CSRC1, RSRC2, CSRC2, RSRC3, CSRC3, RSRC4, IPUU,
     $                   CSRC4, LROWS, LCOLS, INDXS, KS, JLOC1, ILOC1,
     $                   LKTOP1, LKTOP2, WCHUNK, NUMCHUNK, ODDEVEN,
     $                   CHUNKNUM, DIM1, DIM4, IPW3, HROWS, ZROWS,
     $                   HCOLS, IPW1, IPW2, RSRC, EAST, JLOC4, ILOC4,
     $                   WEST, CSRC, SOUTH, NORHT, INDXE, NORTH,
     $                   IHH, IPIW, LKBOT1, NPROCS, LIROFFH,
     $                   WINFIN, RWS3, CLS3, INDX2, HROWS2,
     $                   ZROWS2, HCOLS2, MNRBUF,
     $                   MXRBUF, MNCBUF, MXCBUF, LWKOPT
      LOGICAL            BLK22, BMP22, INTRO, DONEJOB, ODDNPROW,
     $                   ODDNPCOL, LQUERY, BCDONE
      CHARACTER          JBCMPZ*2, JOB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            PILAENVX, ICEIL, INDXG2P, INDXG2L, NUMROC
      REAL               SLAMCH, SLANGE
      EXTERNAL           SLAMCH, PILAENVX, ICEIL, INDXG2P, INDXG2L,
     $                   NUMROC, LSAME, SLANGE
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, FLOAT, MAX, MIN, MOD
*     ..
*     .. Local Arrays ..
      REAL               VT( 3 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           SGEMM, SLABAD, SLAMOV, SLAQR1, SLARFG, SLASET,
     $                   STRMM, SLAQR6
*     ..
*     .. Executable Statements ..
*
      INFO = 0
      ICTXT = DESCH( CTXT_ )
      CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
      NPROCS = NPROW*NPCOL
      LLDH = DESCH( LLD_ )
      LLDZ = DESCZ( LLD_ )
      NB = DESCH( MB_ )
      IROFFH = MOD( KTOP - 1, NB )
      LQUERY = LWORK.EQ.-1 .OR. LIWORK.EQ.-1
*
*     If there are no shifts, then there is nothing to do.
*
      IF( .NOT. LQUERY .AND. NSHFTS.LT.2 )
     $   RETURN
*
*     If the active block is empty or 1-by-1, then there
*     is nothing to do.
*
      IF( .NOT. LQUERY .AND. KTOP.GE.KBOT )
     $   RETURN
*
*     Shuffle shifts into pairs of real shifts and pairs of
*     complex conjugate shifts assuming complex conjugate
*     shifts are already adjacent to one another.
*
      IF( .NOT. LQUERY ) THEN
         DO 10 I = 1, NSHFTS - 2, 2
            IF( SI( I ).NE.-SI( I+1 ) ) THEN
*
               SWAP = SR( I )
               SR( I ) = SR( I+1 )
               SR( I+1 ) = SR( I+2 )
               SR( I+2 ) = SWAP
*
               SWAP = SI( I )
               SI( I ) = SI( I+1 )
               SI( I+1 ) = SI( I+2 )
               SI( I+2 ) = SWAP
            END IF
   10    CONTINUE
      END IF
*
*     NSHFTS is supposed to be even, but if is odd,
*     then simply reduce it by one.  The shuffle above
*     ensures that the dropped shift is real and that
*     the remaining shifts are paired.
*
      NS = NSHFTS - MOD( NSHFTS, 2 )
*
*     Extract the size of the computational window.
*
      NWIN = PILAENVX( ICTXT, 19, 'PSLAQR5', JBCMPZ, N, NB, NB, NB )
      NWIN = MIN( NWIN, KBOT-KTOP+1 )
*
*     Adjust number of simultaneous shifts if it exceeds the limit
*     set by the number of diagonal blocks in the active submatrix
*     H(KTOP:KBOT,KTOP:KBOT).
*
      NS = MAX( 2, MIN( NS, ICEIL( KBOT-KTOP+1, NB )*NWIN/3 ) )
      NS = NS - MOD( NS, 2 )

*
*     Decide the number of simultaneous computational windows
*     from the number of shifts - each window should contain up to
*     (NWIN / 3) shifts. Also compute the number of shifts per
*     window and make sure that number is even.
*
      LNS = MIN( MAX( 2, NWIN / 3 ), MAX( 2, NS / MIN(NPROW,NPCOL) ) )
      LNS = LNS - MOD( LNS, 2 )
      NUMWIN = MAX( 1, MIN( ICEIL( NS, LNS ),
     $     ICEIL( KBOT-KTOP+1, NB ) - 1 ) )
      IF( NPROW.NE.NPCOL ) THEN
         NUMWIN = MIN( NUMWIN, MIN(NPROW,NPCOL) )
         LNS = MIN( LNS, MAX( 2, NS / MIN(NPROW,NPCOL) ) )
         LNS = LNS - MOD( LNS, 2 )
      END IF
*
*     Machine constants for deflation.
*
      SAFMIN = SLAMCH( 'SAFE MINIMUM' )
      SAFMAX = ONE / SAFMIN
      CALL SLABAD( SAFMIN, SAFMAX )
      ULP = SLAMCH( 'PRECISION' )
      SMLNUM = SAFMIN*( FLOAT( N ) / ULP )
*
*     Use accumulated reflections to update far-from-diagonal
*     entries on a local level?
*
      IF( LNS.LT.14 ) THEN
         LKACC22 = 1
      ELSE
         LKACC22 = 2
      END IF
*
*     If so, exploit the 2-by-2 block structure?
*     ( Usually it is not efficient to exploit the 2-by-2 structure
*       because the block size is too small. )
*
      BLK22 = ( LNS.GT.2 ) .AND. ( KACC22.EQ.2 )
*
*     Clear trash.
*
      IF( .NOT. LQUERY .AND. KTOP+2.LE.KBOT )
     $   CALL PSELSET( H, KTOP+2, KTOP, DESCH, ZERO )
*
*     NBMPS = number of 2-shift bulges in each chain
*
      NBMPS = LNS / 2
*
*     KDU = width of slab
*
      KDU = 6*NBMPS - 3
*
*     LCHAIN = length of each chain
*
      LCHAIN = 3 * NBMPS + 1
*
*     Check if workspace query.
*
      IF( LQUERY ) THEN
         HROWS = NUMROC( N, NB, MYROW, DESCH(RSRC_), NPROW )
         HCOLS = NUMROC( N, NB, MYCOL, DESCH(CSRC_), NPCOL )
         LWKOPT = (5+2*NUMWIN)*NB**2 + 2*HROWS*NB + HCOLS*NB +
     $        MAX( HROWS*NB, HCOLS*NB )
         WORK(1)  = FLOAT(LWKOPT)
         IWORK(1) = 5*NUMWIN
         RETURN
      END IF
*
*     Check if KTOP and KBOT are valid.
*
      IF( KTOP.LT.1 .OR. KBOT.GT.N ) RETURN
*
*     Create and chase NUMWIN chains of NBMPS bulges.
*
*     Set up window introduction.
*
      ANMWIN = 0
      INTRO = .TRUE.
      IPIW = 1
*
*     Main loop:
*     While-loop over the computational windows which is
*     terminated when all windows have been introduced,
*     chased down to the bottom of the considered submatrix
*     and chased off.
*
 20   CONTINUE
*
*     Set up next window as long as we have less than the prescribed
*     number of windows. Each window is described an integer quadruple:
*     1. Local value of KTOP (below denoted by LKTOP)
*     2. Local value of KBOT (below denoted by LKBOT)
*     3-4. Processor indices (LRSRC,LCSRC) associated with the window.
*     (5. Mark that decides if a window is fully processed or not)
*
*     Notice - the next window is only introduced if the first block
*     in the active submatrix does not contain any other windows.
*
      IF( ANMWIN.GT.0 ) THEN
         LKTOP = IWORK( 1+(ANMWIN-1)*5 )
      ELSE
         LKTOP = KTOP
      END IF
      IF( INTRO .AND. (ANMWIN.EQ.0 .OR. LKTOP.GT.ICEIL(KTOP,NB)*NB) )
     $     THEN
         ANMWIN = ANMWIN + 1
*
*        Structure of IWORK:
*        IWORK( 1+(WIN-1)*5 ): start position
*        IWORK( 2+(WIN-1)*5 ): stop position
*        IWORK( 3+(WIN-1)*5 ): processor row id
*        IWORK( 4+(WIN-1)*5 ): processor col id
*        IWORK( 5+(WIN-1)*5 ): window status (0, 1, or 2)
*
         IWORK( 1+(ANMWIN-1)*5 ) = KTOP
         IWORK( 2+(ANMWIN-1)*5 ) = KTOP +
     $                             MIN( NWIN,NB-IROFFH,KBOT-KTOP+1 ) - 1
         IWORK( 3+(ANMWIN-1)*5 ) = INDXG2P( IWORK(1+(ANMWIN-1)*5), NB,
     $                             MYROW, DESCH(RSRC_), NPROW )
         IWORK( 4+(ANMWIN-1)*5 ) = INDXG2P( IWORK(2+(ANMWIN-1)*5), NB,
     $                             MYCOL, DESCH(CSRC_), NPCOL )
         IWORK( 5+(ANMWIN-1)*5 ) = 0
         IPIW = 6+(ANMWIN-1)*5
         IF( ANMWIN.EQ.NUMWIN ) INTRO = .FALSE.
      END IF
*
*     Do-loop over the number of windows.
*
      IPNEXT = 1
      DONEJOB = .FALSE.
      IDONEJOB = 0
      LENRBUF = 0
      LENCBUF = 0
      ICHOFF = 0
      DO 40 WIN = 1, ANMWIN
*
*        Extract window information to simplify the rest.
*
         LRSRC = IWORK( 3+(WIN-1)*5 )
         LCSRC = IWORK( 4+(WIN-1)*5 )
         LKTOP = IWORK( 1+(WIN-1)*5 )
         LKBOT = IWORK( 2+(WIN-1)*5 )
         LNWIN = LKBOT - LKTOP + 1
*
*        Check if anything to do for current window, i.e., if the local
*        chain of bulges has reached the next block border etc.
*
         IF( IWORK(5+(WIN-1)*5).LT.2 .AND. LNWIN.GT.1 .AND.
     $        (LNWIN.GT.LCHAIN .OR. LKBOT.EQ.KBOT ) ) THEN
            LIROFFH = MOD(LKTOP-1,NB)
            SWIN = LKTOP-LIROFFH
            EWIN = MIN(KBOT,LKTOP-LIROFFH+NB-1)
            DIM = EWIN-SWIN+1
            IF( DIM.LE.NTINY .AND. .NOT.LKBOT.EQ.KBOT ) THEN
               IWORK( 5+(WIN-1)*5 ) = 2
               GO TO 45
            END IF
            IDONEJOB = 1
            IF( IWORK(5+(WIN-1)*5).EQ.0 ) THEN
               IWORK(5+(WIN-1)*5) = 1
            END IF
*
*           Let the process that owns the corresponding window do the
*           local bulge chase.
*
            IF( MYROW.EQ.LRSRC .AND. MYCOL.EQ.LCSRC ) THEN
*
*              Set the kind of job to do in SLAQR6:
*              1. JOB = 'I': Introduce and chase bulges in window WIN
*              2. JOB = 'C': Chase bulges from top to bottom of window WIN
*              3. JOB = 'O': Chase bulges off window WIN
*              4. JOB = 'A': All of 1-3 above is done - this will for
*                            example happen for very small active
*                            submatrices (like 2-by-2)
*
               LLKBOT = LLKTOP + LNWIN - 1
               IF( LKTOP.EQ.KTOP .AND. LKBOT.EQ.KBOT ) THEN
                  JOB = 'All steps'
                  ICHOFF = 1
               ELSEIF( LKTOP.EQ.KTOP ) THEN
                  JOB = 'Introduce and chase'
               ELSEIF( LKBOT.EQ.KBOT ) THEN
                  JOB = 'Off-chase bulges'
                  ICHOFF = 1
               ELSE
                  JOB = 'Chase bulges'
               END IF
*
*              Copy submatrix of H corresponding to window WIN into
*              workspace and set out additional workspace for storing
*              orthogonal transformations. This submatrix must be at
*              least (NTINY+1)-by-(NTINY+1) to fit into SLAQR6 - if not,
*              abort and go for cross border bulge chasing with this
*              particular window.
*
               II = INDXG2L( SWIN, NB, MYROW, DESCH(RSRC_), NPROW )
               JJ = INDXG2L( SWIN, NB, MYCOL, DESCH(CSRC_), NPCOL )
               LLKTOP = 1 + LIROFFH
               LLKBOT = LLKTOP + LNWIN - 1
*
               IPU = IPNEXT
               IPH = IPU + LNWIN**2
               IPUU = IPH + MAX(NTINY+1,DIM)**2
               IPV = IPUU + MAX(NTINY+1,DIM)**2
               IPNEXT = IPH
*
               IF( LSAME( JOB, 'A' ) .OR. LSAME( JOB, 'O' ) .AND.
     $              DIM.LT.NTINY+1 ) THEN
                  CALL SLASET( 'All', NTINY+1, NTINY+1, ZERO, ONE,
     $                 WORK(IPH), NTINY+1 )
               END IF
               CALL SLAMOV( 'Upper', DIM, DIM, H(II+(JJ-1)*LLDH), LLDH,
     $              WORK(IPH), MAX(NTINY+1,DIM) )
               CALL SCOPY(  DIM-1, H(II+(JJ-1)*LLDH+1), LLDH+1,
     $              WORK(IPH+1), MAX(NTINY+1,DIM)+1 )
               IF( LSAME( JOB, 'C' ) .OR. LSAME( JOB, 'O') ) THEN
                  CALL SCOPY(  DIM-2, H(II+(JJ-1)*LLDH+2), LLDH+1,
     $                 WORK(IPH+2), MAX(NTINY+1,DIM)+1 )
                  CALL SCOPY(  DIM-3, H(II+(JJ-1)*LLDH+3), LLDH+1,
     $                 WORK(IPH+3), MAX(NTINY+1,DIM)+1 )
                  CALL SLASET( 'Lower', DIM-4, DIM-4, ZERO,
     $                 ZERO, WORK(IPH+4), MAX(NTINY+1,DIM) )
               ELSE
                  CALL SLASET( 'Lower', DIM-2, DIM-2, ZERO,
     $                 ZERO, WORK(IPH+2), MAX(NTINY+1,DIM) )
               END IF
*
               KU = MAX(NTINY+1,DIM) - KDU + 1
               KWH = KDU + 1
               NHO = ( MAX(NTINY+1,DIM)-KDU+1-4 ) - ( KDU+1 ) + 1
               KWV = KDU + 4
               NVE = MAX(NTINY+1,DIM) - KDU - KWV + 1
               CALL SLASET( 'All', MAX(NTINY+1,DIM),
     $              MAX(NTINY+1,DIM), ZERO, ONE, WORK(IPUU),
     $              MAX(NTINY+1,DIM) )
*
*              Small-bulge multi-shift QR sweep.
*
               LKS = MAX( 1, NS - WIN*LNS + 1 )
               CALL SLAQR6( JOB, WANTT, .TRUE., LKACC22,
     $              MAX(NTINY+1,DIM), LLKTOP, LLKBOT, LNS, SR( LKS ),
     $              SI( LKS ), WORK(IPH), MAX(NTINY+1,DIM), LLKTOP,
     $              LLKBOT, WORK(IPUU), MAX(NTINY+1,DIM), WORK(IPU),
     $              3, WORK( IPH+KU-1 ),
     $              MAX(NTINY+1,DIM), NVE, WORK( IPH+KWV-1 ),
     $              MAX(NTINY+1,DIM), NHO, WORK( IPH-1+KU+(KWH-1)*
     $              MAX(NTINY+1,DIM) ), MAX(NTINY+1,DIM) )
*
*              Copy submatrix of H back.
*
               CALL SLAMOV( 'Upper', DIM, DIM, WORK(IPH),
     $              MAX(NTINY+1,DIM), H(II+(JJ-1)*LLDH), LLDH )
               CALL SCOPY( DIM-1, WORK(IPH+1), MAX(NTINY+1,DIM)+1,
     $              H(II+(JJ-1)*LLDH+1), LLDH+1 )
               IF( LSAME( JOB, 'I' ) .OR. LSAME( JOB, 'C' ) ) THEN
                  CALL SCOPY( DIM-2, WORK(IPH+2), DIM+1,
     $                 H(II+(JJ-1)*LLDH+2), LLDH+1 )
                  CALL SCOPY( DIM-3, WORK(IPH+3), DIM+1,
     $                 H(II+(JJ-1)*LLDH+3), LLDH+1 )
               ELSE
                  CALL SLASET( 'Lower', DIM-2, DIM-2, ZERO,
     $                 ZERO, H(II+(JJ-1)*LLDH+2), LLDH )
               END IF
*
*              Copy actual submatrix of U to the correct place
*              of the buffer.
*
               CALL SLAMOV( 'All', LNWIN, LNWIN,
     $              WORK(IPUU+(MAX(NTINY+1,DIM)*LIROFFH)+LIROFFH),
     $              MAX(NTINY+1,DIM), WORK(IPU), LNWIN )
            END IF
*
*           In case the local submatrix was smaller than
*           (NTINY+1)-by-(NTINY+1) we go here and proceed.
*
 45         CONTINUE
         ELSE
            IWORK( 5+(WIN-1)*5 ) = 2
         END IF
*
*        Increment counter for buffers of orthogonal transformations.
*
         IF( MYROW.EQ.LRSRC .OR. MYCOL.EQ.LCSRC ) THEN
            IF( IDONEJOB.EQ.1 .AND. IWORK(5+(WIN-1)*5).LT.2 ) THEN
               IF( MYROW.EQ.LRSRC ) LENRBUF = LENRBUF + LNWIN*LNWIN
               IF( MYCOL.EQ.LCSRC ) LENCBUF = LENCBUF + LNWIN*LNWIN
            END IF
         END IF
 40   CONTINUE
*
*     Did some work in the above do-loop?
*
      CALL IGSUM2D( ICTXT, 'All', '1-Tree', 1, 1, IDONEJOB, 1, -1, -1 )
      DONEJOB = IDONEJOB.GT.0
*
*     Chased off bulges from first window?
*
      IF( NPROCS.GT.1 )
     $   CALL IGAMX2D( ICTXT, 'All', '1-Tree', 1, 1, ICHOFF, 1, -1,
     $        -1, -1, -1, -1 )
*
*     If work was done in the do-loop over local windows, perform
*     updates, otherwise go for cross border bulge chasing and updates.
*
      IF( DONEJOB ) THEN
*
*        Broadcast orthogonal transformations.
*
 49      CONTINUE
         IF( LENRBUF.GT.0 .OR. LENCBUF.GT.0 ) THEN
            DO 50 DIR = 1, 2
               BCDONE = .FALSE.
               DO 60 WIN = 1, ANMWIN
                  IF( ( LENRBUF.EQ.0 .AND. LENCBUF.EQ.0 ) .OR.
     $                 BCDONE ) GO TO 62
                  LRSRC = IWORK( 3+(WIN-1)*5 )
                  LCSRC = IWORK( 4+(WIN-1)*5 )
                  IF( MYROW.EQ.LRSRC .AND. MYCOL.EQ.LCSRC ) THEN
                     IF( DIR.EQ.1 .AND. LENRBUF.GT.0 .AND.
     $                    NPCOL.GT.1 ) THEN
                        CALL SGEBS2D( ICTXT, 'Row', '1-Tree', LENRBUF,
     $                       1, WORK, LENRBUF )
                     ELSEIF( DIR.EQ.2 .AND. LENCBUF.GT.0 .AND.
     $                    NPROW.GT.1 ) THEN
                        CALL SGEBS2D( ICTXT, 'Col', '1-Tree', LENCBUF,
     $                       1, WORK, LENCBUF )
                     END IF
                     IF( LENRBUF.GT.0 )
     $                  CALL SLAMOV( 'All', LENRBUF, 1, WORK, LENRBUF,
     $                       WORK(1+LENRBUF), LENCBUF )
                     BCDONE = .TRUE.
                  ELSEIF( MYROW.EQ.LRSRC .AND. DIR.EQ.1 ) THEN
                     IF( LENRBUF.GT.0 .AND. NPCOL.GT.1 ) THEN
                        CALL SGEBR2D( ICTXT, 'Row', '1-Tree', LENRBUF,
     $                       1, WORK, LENRBUF, LRSRC, LCSRC )
                        BCDONE = .TRUE.
                     END IF
                  ELSEIF( MYCOL.EQ.LCSRC .AND. DIR.EQ.2 ) THEN
                     IF( LENCBUF.GT.0 .AND. NPROW.GT.1 ) THEN
                        CALL SGEBR2D( ICTXT, 'Col', '1-Tree', LENCBUF,
     $                       1, WORK(1+LENRBUF), LENCBUF, LRSRC, LCSRC )
                        BCDONE = .TRUE.
                     END IF
                  END IF
 62               CONTINUE
 60            CONTINUE
 50         CONTINUE
         END IF
*
*        Compute updates - make sure to skip windows that was skipped
*        regarding local bulge chasing.
*
         DO 65 DIR = 1, 2
            WINID = 0
            IF( DIR.EQ.1 ) THEN
               IPNEXT = 1
            ELSE
               IPNEXT = 1 + LENRBUF
            END IF
            DO 70 WIN = 1, ANMWIN
               IF( IWORK( 5+(WIN-1)*5 ).EQ.2 ) GO TO 75
               LRSRC = IWORK( 3+(WIN-1)*5 )
               LCSRC = IWORK( 4+(WIN-1)*5 )
               LKTOP = IWORK( 1+(WIN-1)*5 )
               LKBOT = IWORK( 2+(WIN-1)*5 )
               LNWIN = LKBOT - LKTOP + 1
               IF( (MYROW.EQ.LRSRC.AND.LENRBUF.GT.0.AND.DIR.EQ.1) .OR.
     $              (MYCOL.EQ.LCSRC.AND.LENCBUF.GT.0.AND.DIR.EQ.2 ) )
     $              THEN
*
*                 Set up workspaces.
*
                  IPU = IPNEXT
                  IPNEXT = IPU + LNWIN*LNWIN
                  IPW = 1 + LENRBUF + LENCBUF
                  LIROFFH = MOD(LKTOP-1,NB)
                  WINID = WINID + 1
*
*                 Recompute JOB to see if block structure of U could
*                 possibly be exploited or not.
*
                  IF( LKTOP.EQ.KTOP .AND. LKBOT.EQ.KBOT ) THEN
                     JOB = 'All steps'
                  ELSEIF( LKTOP.EQ.KTOP ) THEN
                     JOB = 'Introduce and chase'
                  ELSEIF( LKBOT.EQ.KBOT ) THEN
                     JOB = 'Off-chase bulges'
                  ELSE
                     JOB = 'Chase bulges'
                  END IF
               END IF
*
*              Use U to update far-from-diagonal entries in H.
*              If required, use U to update Z as well.
*
               IF( .NOT. BLK22 .OR. .NOT. LSAME(JOB,'C')
     $              .OR. LNS.LE.2 ) THEN
*
                  IF( DIR.EQ.2 .AND. LENCBUF.GT.0 .AND.
     $                 MYCOL.EQ.LCSRC ) THEN
                     IF( WANTT ) THEN
                        DO 80 INDX = 1, LKTOP-LIROFFH-1, NB
                           CALL INFOG2L( INDX, LKTOP, DESCH, NPROW,
     $                          NPCOL, MYROW, MYCOL, ILOC, JLOC, RSRC1,
     $                          CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
                              LROWS = MIN( NB, LKTOP-INDX )
                              CALL SGEMM('No transpose', 'No transpose',
     $                             LROWS, LNWIN, LNWIN, ONE,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             WORK( IPU ), LNWIN, ZERO,
     $                             WORK(IPW),
     $                             LROWS )
                              CALL SLAMOV( 'All', LROWS, LNWIN,
     $                             WORK(IPW), LROWS,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
 80                     CONTINUE
                     END IF
                     IF( WANTZ ) THEN
                        DO 90 INDX = 1, N, NB
                           CALL INFOG2L( INDX, LKTOP, DESCZ, NPROW,
     $                          NPCOL, MYROW, MYCOL, ILOC, JLOC, RSRC1,
     $                          CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
                              LROWS = MIN(NB,N-INDX+1)
                              CALL SGEMM( 'No transpose',
     $                             'No transpose', LROWS, LNWIN, LNWIN,
     $                             ONE, Z((JLOC-1)*LLDZ+ILOC), LLDZ,
     $                             WORK( IPU ), LNWIN, ZERO,
     $                             WORK(IPW), LROWS )
                              CALL SLAMOV( 'All', LROWS, LNWIN,
     $                             WORK(IPW), LROWS,
     $                             Z((JLOC-1)*LLDZ+ILOC), LLDZ )
                           END IF
 90                     CONTINUE
                     END IF
                  END IF
*
*                 Update the rows of H affected by the bulge-chase.
*
                  IF( DIR.EQ.1 .AND. LENRBUF.GT.0 .AND.
     $                 MYROW.EQ.LRSRC ) THEN
                     IF( WANTT ) THEN
                        IF( ICEIL(LKBOT,NB).EQ.ICEIL(KBOT,NB) ) THEN
                           LCOLS = MIN(ICEIL(KBOT,NB)*NB,N) - KBOT
                        ELSE
                           LCOLS = 0
                        END IF
                        IF( LCOLS.GT.0 ) THEN
                           INDX = KBOT + 1
                           CALL INFOG2L( LKTOP, INDX, DESCH, NPROW,
     $                          NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                          RSRC1, CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
                              CALL SGEMM( 'Transpose', 'No Transpose',
     $                             LNWIN, LCOLS, LNWIN, ONE, WORK(IPU),
     $                             LNWIN, H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             ZERO, WORK(IPW), LNWIN )
                              CALL SLAMOV( 'All', LNWIN, LCOLS,
     $                             WORK(IPW), LNWIN,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
                        END IF
 93                     CONTINUE
                        INDXS = ICEIL(LKBOT,NB)*NB + 1
                        DO 95 INDX = INDXS, N, NB
                           CALL INFOG2L( LKTOP, INDX,
     $                          DESCH, NPROW, NPCOL, MYROW, MYCOL,
     $                          ILOC, JLOC, RSRC1, CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
                              LCOLS = MIN( NB, N-INDX+1 )
                              CALL SGEMM( 'Transpose', 'No Transpose',
     $                             LNWIN, LCOLS, LNWIN, ONE, WORK(IPU),
     $                             LNWIN, H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             ZERO, WORK(IPW),
     $                             LNWIN )
                              CALL SLAMOV( 'All', LNWIN, LCOLS,
     $                             WORK(IPW), LNWIN,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
 95                     CONTINUE
                     END IF
                  END IF
               ELSE
                  KS = LNWIN-LNS/2*3
*
*                 The LNWIN-by-LNWIN matrix U containing the accumulated
*                 orthogonal transformations has the following structure:
*
*                     [ U11  U12 ]
*                 U = [          ],
*                     [ U21  U22 ]
*
*                 where U21 is KS-by-KS upper triangular and U12 is
*                 (LNWIN-KS)-by-(LNWIN-KS) lower triangular.
*                 Here, KS = LNS.
*
*                 Update the columns of H and Z affected by the bulge
*                 chasing.
*
*                 Compute H2*U21 + H1*U11 in workspace.
*
                  IF( DIR.EQ.2 .AND. LENCBUF.GT.0 .AND.
     $                 MYCOL.EQ.LCSRC ) THEN
                     IF( WANTT ) THEN
                        DO 100 INDX = 1, LKTOP-LIROFFH-1, NB
                           CALL INFOG2L( INDX, LKTOP, DESCH, NPROW,
     $                          NPCOL, MYROW, MYCOL, ILOC, JLOC, RSRC1,
     $                          CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
                              JLOC1 = INDXG2L( LKTOP+LNWIN-KS, NB,
     $                             MYCOL, DESCH( CSRC_ ), NPCOL )
                              LROWS = MIN( NB, LKTOP-INDX )
                              CALL SLAMOV( 'All', LROWS, KS,
     $                             H((JLOC1-1)*LLDH+ILOC ), LLDH,
     $                             WORK(IPW), LROWS )
                              CALL STRMM( 'Right', 'Upper',
     $                             'No transpose','Non-unit', LROWS,
     $                             KS, ONE, WORK( IPU+LNWIN-KS ), LNWIN,
     $                             WORK(IPW), LROWS )
                              CALL SGEMM('No transpose', 'No transpose',
     $                             LROWS, KS, LNWIN-KS, ONE,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             WORK( IPU ), LNWIN, ONE, WORK(IPW),
     $                             LROWS )
*
*                             Compute H1*U12 + H2*U22 in workspace.
*
                              CALL SLAMOV( 'All', LROWS, LNWIN-KS,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             WORK( IPW+KS*LROWS ), LROWS )
                              CALL STRMM( 'Right', 'Lower',
     $                             'No transpose', 'Non-Unit',
     $                             LROWS, LNWIN-KS, ONE,
     $                             WORK( IPU+LNWIN*KS ), LNWIN,
     $                             WORK( IPW+KS*LROWS ), LROWS )
                              CALL SGEMM('No transpose', 'No transpose',
     $                             LROWS, LNWIN-KS, KS, ONE,
     $                             H((JLOC1-1)*LLDH+ILOC), LLDH,
     $                             WORK( IPU+LNWIN*KS+LNWIN-KS ), LNWIN,
     $                             ONE, WORK( IPW+KS*LROWS ), LROWS )
*
*                             Copy workspace to H.
*
                              CALL SLAMOV( 'All', LROWS, LNWIN,
     $                             WORK(IPW), LROWS,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
 100                    CONTINUE
                     END IF
*
                     IF( WANTZ ) THEN
*
*                       Compute Z2*U21 + Z1*U11 in workspace.
*
                        DO 110 INDX = 1, N, NB
                           CALL INFOG2L( INDX, LKTOP, DESCZ, NPROW,
     $                          NPCOL, MYROW, MYCOL, ILOC, JLOC, RSRC1,
     $                          CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
                              JLOC1 = INDXG2L( LKTOP+LNWIN-KS, NB,
     $                             MYCOL, DESCZ( CSRC_ ), NPCOL )
                              LROWS = MIN(NB,N-INDX+1)
                              CALL SLAMOV( 'All', LROWS, KS,
     $                             Z((JLOC1-1)*LLDZ+ILOC ), LLDZ,
     $                             WORK(IPW), LROWS )
                              CALL STRMM( 'Right', 'Upper',
     $                             'No transpose', 'Non-unit',
     $                             LROWS, KS, ONE, WORK( IPU+LNWIN-KS ),
     $                             LNWIN, WORK(IPW), LROWS )
                              CALL SGEMM( 'No transpose',
     $                             'No transpose', LROWS, KS, LNWIN-KS,
     $                             ONE, Z((JLOC-1)*LLDZ+ILOC), LLDZ,
     $                             WORK( IPU ), LNWIN, ONE, WORK(IPW),
     $                             LROWS )
*
*                             Compute Z1*U12 + Z2*U22 in workspace.
*
                              CALL SLAMOV( 'All', LROWS, LNWIN-KS,
     $                             Z((JLOC-1)*LLDZ+ILOC), LLDZ,
     $                             WORK( IPW+KS*LROWS ), LROWS)
                              CALL STRMM( 'Right', 'Lower',
     $                             'No transpose', 'Non-unit',
     $                             LROWS, LNWIN-KS, ONE,
     $                             WORK( IPU+LNWIN*KS ), LNWIN,
     $                             WORK( IPW+KS*LROWS ), LROWS )
                              CALL SGEMM( 'No transpose',
     $                             'No transpose', LROWS, LNWIN-KS, KS,
     $                             ONE, Z((JLOC1-1)*LLDZ+ILOC), LLDZ,
     $                             WORK( IPU+LNWIN*KS+LNWIN-KS ), LNWIN,
     $                             ONE, WORK( IPW+KS*LROWS ),
     $                             LROWS )
*
*                             Copy workspace to Z.
*
                              CALL SLAMOV( 'All', LROWS, LNWIN,
     $                             WORK(IPW), LROWS,
     $                             Z((JLOC-1)*LLDZ+ILOC), LLDZ )
                           END IF
 110                    CONTINUE
                     END IF
                  END IF
*
                  IF( DIR.EQ.1 .AND. LENRBUF.GT.0 .AND.
     $                 MYROW.EQ.LRSRC ) THEN
                     IF( WANTT ) THEN
                        INDXS = ICEIL(LKBOT,NB)*NB + 1
                        DO 120 INDX = INDXS, N, NB
                           CALL INFOG2L( LKTOP, INDX,
     $                          DESCH, NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                          JLOC, RSRC1, CSRC1 )
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC1 ) THEN
*
*                             Compute U21**T*H2 + U11**T*H1 in workspace.
*
                              ILOC1 = INDXG2L( LKTOP+LNWIN-KS, NB,
     $                             MYROW, DESCH( RSRC_ ), NPROW )
                              LCOLS = MIN( NB, N-INDX+1 )
                              CALL SLAMOV( 'All', KS, LCOLS,
     $                             H((JLOC-1)*LLDH+ILOC1), LLDH,
     $                             WORK(IPW), LNWIN )
                              CALL STRMM( 'Left', 'Upper', 'Transpose',
     $                             'Non-unit', KS, LCOLS, ONE,
     $                             WORK( IPU+LNWIN-KS ), LNWIN,
     $                             WORK(IPW), LNWIN )
                              CALL SGEMM( 'Transpose', 'No transpose',
     $                             KS, LCOLS, LNWIN-KS, ONE, WORK(IPU),
     $                             LNWIN, H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             ONE, WORK(IPW), LNWIN )
*
*                             Compute U12**T*H1 + U22**T*H2 in workspace.
*
                              CALL SLAMOV( 'All', LNWIN-KS, LCOLS,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH,
     $                             WORK( IPW+KS ), LNWIN )
                              CALL STRMM( 'Left', 'Lower', 'Transpose',
     $                             'Non-unit', LNWIN-KS, LCOLS, ONE,
     $                             WORK( IPU+LNWIN*KS ), LNWIN,
     $                             WORK( IPW+KS ), LNWIN )
                              CALL SGEMM( 'Transpose', 'No Transpose',
     $                             LNWIN-KS, LCOLS, KS, ONE,
     $                             WORK( IPU+LNWIN*KS+LNWIN-KS ), LNWIN,
     $                             H((JLOC-1)*LLDH+ILOC1), LLDH,
     $                             ONE, WORK( IPW+KS ), LNWIN )
*
*                             Copy workspace to H.
*
                              CALL SLAMOV( 'All', LNWIN, LCOLS,
     $                             WORK(IPW), LNWIN,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
 120                    CONTINUE
                     END IF
                  END IF
               END IF
*
*              Update position information about current window.
*
               IF( DIR.EQ.2 ) THEN
                  IF( LKBOT.EQ.KBOT ) THEN
                     LKTOP = KBOT+1
                     LKBOT = KBOT+1
                     IWORK( 1+(WIN-1)*5 ) = LKTOP
                     IWORK( 2+(WIN-1)*5 ) = LKBOT
                     IWORK( 5+(WIN-1)*5 ) = 2
                  ELSE
                     LKTOP = MIN( LKTOP + LNWIN - LCHAIN,
     $                    ICEIL( LKTOP, NB )*NB - LCHAIN + 1,
     $                    KBOT )
                     IWORK( 1+(WIN-1)*5 ) = LKTOP
                     LKBOT = MIN( LKBOT + LNWIN - LCHAIN,
     $                    ICEIL( LKBOT, NB )*NB, KBOT )
                     IWORK( 2+(WIN-1)*5 ) = LKBOT
                     LNWIN = LKBOT-LKTOP+1
                     IF( LNWIN.EQ.LCHAIN ) IWORK(5+(WIN-1)*5) = 2
                  END IF
               END IF
 75            CONTINUE
 70         CONTINUE
 65      CONTINUE
*
*        If bulges were chasen off from first window, the window is
*        removed.
*
         IF( ICHOFF.GT.0 ) THEN
            DO 128 WIN = 2, ANMWIN
               IWORK( 1+(WIN-2)*5 ) = IWORK( 1+(WIN-1)*5 )
               IWORK( 2+(WIN-2)*5 ) = IWORK( 2+(WIN-1)*5 )
               IWORK( 3+(WIN-2)*5 ) = IWORK( 3+(WIN-1)*5 )
               IWORK( 4+(WIN-2)*5 ) = IWORK( 4+(WIN-1)*5 )
               IWORK( 5+(WIN-2)*5 ) = IWORK( 5+(WIN-1)*5 )
 128        CONTINUE
            ANMWIN = ANMWIN - 1
            IPIW = 6+(ANMWIN-1)*5
         END IF
*
*        If we have no more windows, return.
*
         IF( ANMWIN.LT.1 ) RETURN
*
      ELSE
*
*        Set up windows such that as many bulges as possible can be
*        moved over the border to the next block. Make sure that the
*        cross border window is at least (NTINY+1)-by-(NTINY+1), unless
*        we are chasing off the bulges from the last window. This is
*        accomplished by setting the bottom index LKBOT such that the
*        local window has the correct size.
*
*        If LKBOT then becomes larger than KBOT, the endpoint of the whole
*        global submatrix, or LKTOP from a window located already residing
*        at the other side of the border, this is taken care of by some
*        dirty tricks.
*
         DO 130 WIN = 1, ANMWIN
            LKTOP1 = IWORK( 1+(WIN-1)*5 )
            LKBOT = IWORK( 2+(WIN-1)*5 )
            LNWIN = MAX( 6, MIN( LKBOT - LKTOP1 + 1, LCHAIN ) )
            LKBOT1 = MAX( MIN( KBOT, ICEIL(LKTOP1,NB)*NB+LCHAIN),
     $           MIN( KBOT, MIN( LKTOP1+2*LNWIN-1,
     $           (ICEIL(LKTOP1,NB)+1)*NB ) ) )
            IWORK( 2+(WIN-1)*5 ) = LKBOT1
 130     CONTINUE
         ICHOFF = 0
*
*        Keep a record over what windows that were moved over the borders
*        such that we can delay some windows due to lack of space on the
*        other side of the border; we do not want to leave any of the
*        bulges behind...
*
*        IWORK( 5+(WIN-1)*5 ) = 0: window WIN has not been processed
*        IWORK( 5+(WIN-1)*5 ) = 1: window WIN is being processed (need to
*                                  know for updates)
*        IWORK( 5+(WIN-1)*5 ) = 2: window WIN has been fully processed
*
*        So, start by marking all windows as not processed.
*
         DO 135 WIN = 1, ANMWIN
            IWORK( 5+(WIN-1)*5 ) = 0
 135     CONTINUE
*
*        Do the cross border bulge-chase as follows: Start from the
*        first window (the one that is closest to be chased off the
*        diagonal of H) and take the odd windows first followed by the
*        even ones. To not get into hang-problems on processor meshes
*        with at least one odd dimension, the windows will in such a case
*        be processed in chunks of {the minimum odd process dimension}-1
*        windows to avoid overlapping processor scopes in forming the
*        cross border computational windows and the cross border update
*        regions.
*
         WCHUNK = MAX( 1, MIN( ANMWIN, NPROW-1, NPCOL-1 ) )
         NUMCHUNK = ICEIL( ANMWIN, WCHUNK )
*
*        Based on the computed chunk of windows, start working with
*        crossborder bulge-chasing. Repeat this as long as there is
*        still work left to do (137 is a kind of do-while statement).
*
 137     CONTINUE
*
*        Zero out LENRBUF and LENCBUF each time we restart this loop.
*
         LENRBUF = 0
         LENCBUF = 0
*
         DO 140 ODDEVEN = 1, MIN( 2, ANMWIN )
         DO 150 CHUNKNUM = 1, NUMCHUNK
            IPNEXT = 1
            DO 160 WIN = ODDEVEN+(CHUNKNUM-1)*WCHUNK,
     $           MIN(ANMWIN,MAX(1,ODDEVEN+(CHUNKNUM)*WCHUNK-1)), 2
*
*              Get position and size of the WIN:th active window and
*              make sure that we skip the cross border bulge for this
*              window if the window is not shared between several data
*              layout blocks (and processors).
*
*              Also, delay windows that do not have sufficient size of
*              the other side of the border. Moreover, make sure to skip
*              windows that was already processed in the last round of
*              the do-while loop (137).
*
               IF( IWORK( 5+(WIN-1)*5 ).EQ.2 ) GO TO 165
               LKTOP = IWORK( 1+(WIN-1)*5 )
               LKBOT = IWORK( 2+(WIN-1)*5 )
               IF( WIN.GT.1 ) THEN
                  LKTOP2 = IWORK( 1+(WIN-2)*5 )
               ELSE
                  LKTOP2 = KBOT+1
               END IF
               IF( ICEIL(LKTOP,NB).EQ.ICEIL(LKBOT,NB) .OR.
     $              LKBOT.GE.LKTOP2 ) GO TO 165
               LNWIN = LKBOT - LKTOP + 1
               IF( LNWIN.LE.NTINY .AND. LKBOT.NE.KBOT .AND.
     $              .NOT. MOD(LKBOT,NB).EQ.0  ) GO TO 165
*
*              If window is going to be processed, mark it as processed.
*
               IWORK( 5+(WIN-1)*5 ) = 1
*
*              Extract processors for current cross border window,
*              as below:
*
*                        1 | 2
*                        --+--
*                        3 | 4
*
               RSRC1 = IWORK( 3+(WIN-1)*5 )
               CSRC1 = IWORK( 4+(WIN-1)*5 )
               RSRC2 = RSRC1
               CSRC2 = MOD( CSRC1+1, NPCOL )
               RSRC3 = MOD( RSRC1+1, NPROW )
               CSRC3 = CSRC1
               RSRC4 = MOD( RSRC1+1, NPROW )
               CSRC4 = MOD( CSRC1+1, NPCOL )
*
*              Form group of four processors for cross border window.
*
               IF( ( MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1 ) .OR.
     $              ( MYROW.EQ.RSRC2 .AND. MYCOL.EQ.CSRC2 ) .OR.
     $              ( MYROW.EQ.RSRC3 .AND. MYCOL.EQ.CSRC3 ) .OR.
     $              ( MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4 ) ) THEN
*
*                 Compute the upper and lower parts of the active
*                 window.
*
                  DIM1 = NB - MOD(LKTOP-1,NB)
                  DIM4 = LNWIN - DIM1
*
*                 Temporarily compute a new value of the size of the
*                 computational window that is larger than or equal to
*                 NTINY+1; call the *real* value DIM.
*
                  DIM = LNWIN
                  LNWIN = MAX(NTINY+1,LNWIN)
*
*                 Divide workspace.
*
                  IPU = IPNEXT
                  IPH = IPU + DIM**2
                  IPUU = IPH + LNWIN**2
                  IPV = IPUU + LNWIN**2
                  IPNEXT = IPH
                  IF( DIM.LT.LNWIN ) THEN
                     CALL SLASET( 'All', LNWIN, LNWIN, ZERO,
     $                    ONE, WORK( IPH ), LNWIN )
                  ELSE
                     CALL SLASET( 'All', DIM, DIM, ZERO,
     $                    ZERO, WORK( IPH ), LNWIN )
                  END IF
*
*                 Form the active window.
*
                  IF( MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1 ) THEN
                     ILOC = INDXG2L( LKTOP, NB, MYROW,
     $                    DESCH( RSRC_ ), NPROW )
                     JLOC = INDXG2L( LKTOP, NB, MYCOL,
     $                    DESCH( CSRC_ ), NPCOL )
                     CALL SLAMOV( 'All', DIM1, DIM1,
     $                    H((JLOC-1)*LLDH+ILOC), LLDH, WORK(IPH),
     $                    LNWIN )
                     IF( RSRC1.NE.RSRC4 .OR. CSRC1.NE.CSRC4 ) THEN
*                       Proc#1 <==> Proc#4
                        CALL SGESD2D( ICTXT, DIM1, DIM1,
     $                       WORK(IPH), LNWIN, RSRC4, CSRC4 )
                        CALL SGERV2D( ICTXT, DIM4, DIM4,
     $                       WORK(IPH+DIM1*LNWIN+DIM1),
     $                       LNWIN, RSRC4, CSRC4 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4 ) THEN
                     ILOC = INDXG2L( LKTOP+DIM1, NB, MYROW,
     $                    DESCH( RSRC_ ), NPROW )
                     JLOC = INDXG2L( LKTOP+DIM1, NB, MYCOL,
     $                    DESCH( CSRC_ ), NPCOL )
                     CALL SLAMOV( 'All', DIM4, DIM4,
     $                    H((JLOC-1)*LLDH+ILOC), LLDH,
     $                    WORK(IPH+DIM1*LNWIN+DIM1),
     $                    LNWIN )
                     IF( RSRC4.NE.RSRC1 .OR. CSRC4.NE.CSRC1 ) THEN
*                       Proc#4 <==> Proc#1
                        CALL SGESD2D( ICTXT, DIM4, DIM4,
     $                       WORK(IPH+DIM1*LNWIN+DIM1),
     $                       LNWIN, RSRC1, CSRC1 )
                        CALL SGERV2D( ICTXT, DIM1, DIM1,
     $                       WORK(IPH), LNWIN, RSRC1, CSRC1 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC2 .AND. MYCOL.EQ.CSRC2 ) THEN
                     ILOC = INDXG2L( LKTOP, NB, MYROW,
     $                    DESCH( RSRC_ ), NPROW )
                     JLOC = INDXG2L( LKTOP+DIM1, NB, MYCOL,
     $                    DESCH( CSRC_ ), NPCOL )
                     CALL SLAMOV( 'All', DIM1, DIM4,
     $                    H((JLOC-1)*LLDH+ILOC), LLDH,
     $                    WORK(IPH+DIM1*LNWIN), LNWIN )
                     IF( RSRC2.NE.RSRC1 .OR. CSRC2.NE.CSRC1 ) THEN
*                       Proc#2 ==> Proc#1
                        CALL SGESD2D( ICTXT, DIM1, DIM4,
     $                       WORK(IPH+DIM1*LNWIN),
     $                       LNWIN, RSRC1, CSRC1 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC2 .AND. MYCOL.EQ.CSRC2 ) THEN
                     IF( RSRC2.NE.RSRC4 .OR. CSRC2.NE.CSRC4 ) THEN
*                       Proc#2 ==> Proc#4
                        CALL SGESD2D( ICTXT, DIM1, DIM4,
     $                       WORK(IPH+DIM1*LNWIN),
     $                       LNWIN, RSRC4, CSRC4 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC3 .AND. MYCOL.EQ.CSRC3 ) THEN
                     ILOC = INDXG2L( LKTOP+DIM1, NB, MYROW,
     $                    DESCH( RSRC_ ), NPROW )
                     JLOC = INDXG2L( LKTOP+DIM1-1, NB, MYCOL,
     $                    DESCH( CSRC_ ), NPCOL )
                     CALL SLAMOV( 'All', 1, 1,
     $                    H((JLOC-1)*LLDH+ILOC), LLDH,
     $                    WORK(IPH+(DIM1-1)*LNWIN+DIM1),
     $                    LNWIN )
                     IF( RSRC3.NE.RSRC1 .OR. CSRC3.NE.CSRC1 ) THEN
*                       Proc#3 ==> Proc#1
                        CALL SGESD2D( ICTXT, 1, 1,
     $                       WORK(IPH+(DIM1-1)*LNWIN+DIM1),
     $                       LNWIN, RSRC1, CSRC1 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC3 .AND. MYCOL.EQ.CSRC3 ) THEN
                     IF( RSRC3.NE.RSRC4 .OR. CSRC3.NE.CSRC4 ) THEN
*                       Proc#3 ==> Proc#4
                        CALL SGESD2D( ICTXT, 1, 1,
     $                       WORK(IPH+(DIM1-1)*LNWIN+DIM1),
     $                       LNWIN, RSRC4, CSRC4 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1 ) THEN
                     IF( RSRC1.NE.RSRC2 .OR. CSRC1.NE.CSRC2 ) THEN
*                       Proc#1 <== Proc#2
                        CALL SGERV2D( ICTXT, DIM1, DIM4,
     $                       WORK(IPH+DIM1*LNWIN),
     $                       LNWIN, RSRC2, CSRC2 )
                     END IF
                     IF( RSRC1.NE.RSRC3 .OR. CSRC1.NE.CSRC3 ) THEN
*                       Proc#1 <== Proc#3
                        CALL SGERV2D( ICTXT, 1, 1,
     $                       WORK(IPH+(DIM1-1)*LNWIN+DIM1),
     $                       LNWIN, RSRC3, CSRC3 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4 ) THEN
                     IF( RSRC4.NE.RSRC2 .OR. CSRC4.NE.CSRC2 ) THEN
*                       Proc#4 <== Proc#2
                        CALL SGERV2D( ICTXT, DIM1, DIM4,
     $                       WORK(IPH+DIM1*LNWIN),
     $                       LNWIN, RSRC2, CSRC2 )
                     END IF
                     IF( RSRC4.NE.RSRC3 .OR. CSRC4.NE.CSRC3 ) THEN
*                       Proc#4 <== Proc#3
                        CALL SGERV2D( ICTXT, 1, 1,
     $                       WORK(IPH+(DIM1-1)*LNWIN+DIM1),
     $                       LNWIN, RSRC3, CSRC3 )
                     END IF
                  END IF
*
*                 Prepare for call to SLAQR6 - it could happen that no
*                 bulges where introduced in the pre-cross border step
*                 since the chain was too long to fit in the top-left
*                 part of the cross border window. In such a case, the
*                 bulges are introduced here instead.  It could also
*                 happen that the bottom-right part is too small to hold
*                 the whole chain -- in such a case, the bulges are
*                 chasen off immediately, as well.
*
                  IF( (MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1) .OR.
     $                 (MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4) ) THEN
                     IF( LKTOP.EQ.KTOP .AND. LKBOT.EQ.KBOT .AND.
     $                    (DIM1.LE.LCHAIN .OR. DIM1.LE.NTINY ) ) THEN
                        JOB = 'All steps'
                        ICHOFF = 1
                     ELSEIF( LKTOP.EQ.KTOP .AND.
     $                    ( DIM1.LE.LCHAIN .OR. DIM1.LE.NTINY ) ) THEN
                        JOB = 'Introduce and chase'
                     ELSEIF( LKBOT.EQ.KBOT ) THEN
                        JOB = 'Off-chase bulges'
                        ICHOFF = 1
                     ELSE
                        JOB = 'Chase bulges'
                     END IF
                     KU = LNWIN - KDU + 1
                     KWH = KDU + 1
                     NHO = ( LNWIN-KDU+1-4 ) - ( KDU+1 ) + 1
                     KWV = KDU + 4
                     NVE = LNWIN - KDU - KWV + 1
                     CALL SLASET( 'All', LNWIN, LNWIN,
     $                    ZERO, ONE, WORK(IPUU), LNWIN )
*
*                    Small-bulge multi-shift QR sweep.
*
                     LKS = MAX(1, NS - WIN*LNS + 1)
                     CALL SLAQR6( JOB, WANTT, .TRUE., LKACC22, LNWIN,
     $                    1, DIM, LNS, SR( LKS ), SI( LKS ),
     $                    WORK(IPH), LNWIN, 1, DIM,
     $                    WORK(IPUU), LNWIN, WORK(IPU), 3,
     $                    WORK( IPH+KU-1 ), LNWIN, NVE,
     $                    WORK( IPH+KWV-1 ), LNWIN, NHO,
     $                    WORK( IPH-1+KU+(KWH-1)*LNWIN ), LNWIN )
*
*                    Copy local submatrices of H back to global matrix.
*
                     IF( MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1 ) THEN
                        ILOC = INDXG2L( LKTOP, NB, MYROW,
     $                       DESCH( RSRC_ ), NPROW )
                        JLOC = INDXG2L( LKTOP, NB, MYCOL,
     $                       DESCH( CSRC_ ), NPCOL )
                        CALL SLAMOV( 'All', DIM1, DIM1, WORK(IPH),
     $                       LNWIN, H((JLOC-1)*LLDH+ILOC),
     $                       LLDH )
                     END IF
                     IF( MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4 ) THEN
                        ILOC = INDXG2L( LKTOP+DIM1, NB, MYROW,
     $                       DESCH( RSRC_ ), NPROW )
                        JLOC = INDXG2L( LKTOP+DIM1, NB, MYCOL,
     $                       DESCH( CSRC_ ), NPCOL )
                        CALL SLAMOV( 'All', DIM4, DIM4,
     $                       WORK(IPH+DIM1*LNWIN+DIM1),
     $                       LNWIN, H((JLOC-1)*LLDH+ILOC), LLDH )
                     END IF
*
*                    Copy actual submatrix of U to the correct place of
*                    the buffer.
*
                     CALL SLAMOV( 'All', DIM, DIM,
     $                    WORK(IPUU), LNWIN, WORK(IPU), DIM )
                  END IF
*
*                 Return data to process 2 and 3.
*
                  RWS3 = MIN(3,DIM4)
                  CLS3 = MIN(3,DIM1)
                  IF( MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1 ) THEN
                     IF( RSRC1.NE.RSRC3 .OR. CSRC1.NE.CSRC3 ) THEN
*                       Proc#1 ==> Proc#3
                        CALL SGESD2D( ICTXT, RWS3, CLS3,
     $                       WORK( IPH+(DIM1-CLS3)*LNWIN+DIM1 ),
     $                       LNWIN, RSRC3, CSRC3 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4 ) THEN
                     IF( RSRC4.NE.RSRC2 .OR. CSRC4.NE.CSRC2 ) THEN
*                       Proc#4 ==> Proc#2
                        CALL SGESD2D( ICTXT, DIM1, DIM4,
     $                       WORK( IPH+DIM1*LNWIN),
     $                       LNWIN, RSRC2, CSRC2 )
                     END IF
                  END IF
                  IF( MYROW.EQ.RSRC2 .AND. MYCOL.EQ.CSRC2 ) THEN
                     ILOC = INDXG2L( LKTOP, NB, MYROW,
     $                    DESCH( RSRC_ ), NPROW )
                     JLOC = INDXG2L( LKTOP+DIM1, NB, MYCOL,
     $                    DESCH( CSRC_ ), NPCOL )
                     IF( RSRC2.NE.RSRC4 .OR. CSRC2.NE.CSRC4 ) THEN
*                       Proc#2 <== Proc#4
                        CALL SGERV2D( ICTXT, DIM1, DIM4,
     $                       WORK(IPH+DIM1*LNWIN),
     $                       LNWIN, RSRC4, CSRC4 )
                     END IF
                     CALL SLAMOV( 'All', DIM1, DIM4,
     $                    WORK( IPH+DIM1*LNWIN ), LNWIN,
     $                    H((JLOC-1)*LLDH+ILOC), LLDH )
                  END IF
                  IF( MYROW.EQ.RSRC3 .AND. MYCOL.EQ.CSRC3 ) THEN
                     ILOC = INDXG2L( LKTOP+DIM1, NB, MYROW,
     $                    DESCH( RSRC_ ), NPROW )
                     JLOC = INDXG2L( LKTOP+DIM1-CLS3, NB, MYCOL,
     $                    DESCH( CSRC_ ), NPCOL )
                     IF( RSRC3.NE.RSRC1 .OR. CSRC3.NE.CSRC1 ) THEN
*                       Proc#3 <== Proc#1
                        CALL SGERV2D( ICTXT, RWS3, CLS3,
     $                       WORK( IPH+(DIM1-CLS3)*LNWIN+DIM1 ),
     $                       LNWIN, RSRC1, CSRC1 )
                     END IF
                     CALL SLAMOV( 'Upper', RWS3, CLS3,
     $                    WORK( IPH+(DIM1-CLS3)*LNWIN+DIM1 ),
     $                    LNWIN, H((JLOC-1)*LLDH+ILOC),
     $                    LLDH )
                     IF( RWS3.GT.1 .AND. CLS3.GT.1 ) THEN
                        ELEM = WORK( IPH+(DIM1-CLS3)*LNWIN+DIM1+1 )
                        IF( ELEM.NE.ZERO ) THEN
                           CALL SLAMOV( 'Lower', RWS3-1, CLS3-1,
     $                          WORK( IPH+(DIM1-CLS3)*LNWIN+DIM1+1 ),
     $                          LNWIN, H((JLOC-1)*LLDH+ILOC+1), LLDH )
                        END IF
                     END IF
                  END IF
*
*                 Restore correct value of LNWIN.
*
                  LNWIN = DIM
*
               END IF
*
*              Increment counter for buffers of orthogonal
*              transformations.
*
               IF( MYROW.EQ.RSRC1 .OR. MYCOL.EQ.CSRC1 .OR.
     $              MYROW.EQ.RSRC4 .OR. MYCOL.EQ.CSRC4 ) THEN
                  IF( MYROW.EQ.RSRC1 .OR. MYROW.EQ.RSRC4 )
     $               LENRBUF = LENRBUF + LNWIN*LNWIN
                  IF( MYCOL.EQ.CSRC1 .OR. MYCOL.EQ.CSRC4 )
     $               LENCBUF = LENCBUF + LNWIN*LNWIN
               END IF
*
*              If no cross border bulge chasing was performed for the
*              current WIN:th window, the processor jump to this point
*              and consider the next one.
*
 165           CONTINUE
*
 160        CONTINUE
*
*           Broadcast orthogonal transformations -- this will only happen
*           if the buffer associated with the orthogonal transformations
*           is not empty (controlled by LENRBUF, for row-wise
*           broadcasts, and LENCBUF, for column-wise broadcasts).
*
            DO 170 DIR = 1, 2
               BCDONE = .FALSE.
               DO 180 WIN = ODDEVEN+(CHUNKNUM-1)*WCHUNK,
     $              MIN(ANMWIN,MAX(1,ODDEVEN+(CHUNKNUM)*WCHUNK-1)), 2
                  IF( ( LENRBUF.EQ.0 .AND. LENCBUF.EQ.0 ) .OR.
     $                 BCDONE ) GO TO 185
                  RSRC1 = IWORK( 3+(WIN-1)*5 )
                  CSRC1 = IWORK( 4+(WIN-1)*5 )
                  RSRC4 = MOD( RSRC1+1, NPROW )
                  CSRC4 = MOD( CSRC1+1, NPCOL )
                  IF( ( MYROW.EQ.RSRC1 .AND. MYCOL.EQ.CSRC1 ) .OR.
     $                 ( MYROW.EQ.RSRC4 .AND. MYCOL.EQ.CSRC4 ) ) THEN
                     IF( DIR.EQ.1 .AND. LENRBUF.GT.0 .AND.
     $                    NPCOL.GT.1 .AND. NPROCS.GT.2 ) THEN
                        IF( MYROW.EQ.RSRC1 .OR. ( MYROW.EQ.RSRC4
     $                       .AND. RSRC4.NE.RSRC1 ) ) THEN
                           CALL SGEBS2D( ICTXT, 'Row', '1-Tree',
     $                          LENRBUF, 1, WORK, LENRBUF )
                        ELSE
                           CALL SGEBR2D( ICTXT, 'Row', '1-Tree',
     $                          LENRBUF, 1, WORK, LENRBUF, RSRC1,
     $                          CSRC1 )
                        END IF
                     ELSEIF( DIR.EQ.2 .AND. LENCBUF.GT.0 .AND.
     $                       NPROW.GT.1 .AND. NPROCS.GT.2 ) THEN
                        IF( MYCOL.EQ.CSRC1 .OR. ( MYCOL.EQ.CSRC4
     $                       .AND. CSRC4.NE.CSRC1 ) ) THEN
                           CALL SGEBS2D( ICTXT, 'Col', '1-Tree',
     $                          LENCBUF, 1, WORK, LENCBUF )
                        ELSE
                           CALL SGEBR2D( ICTXT, 'Col', '1-Tree',
     $                          LENCBUF, 1, WORK(1+LENRBUF), LENCBUF,
     $                          RSRC1, CSRC1 )
                        END IF
                     END IF
                     IF( LENRBUF.GT.0 .AND. ( MYCOL.EQ.CSRC1 .OR.
     $                    ( MYCOL.EQ.CSRC4 .AND. CSRC4.NE.CSRC1 ) ) )
     $                  CALL SLAMOV( 'All', LENRBUF, 1, WORK, LENRBUF,
     $                       WORK(1+LENRBUF), LENCBUF )
                     BCDONE = .TRUE.
                  ELSEIF( MYROW.EQ.RSRC1 .AND. DIR.EQ.1 ) THEN
                     IF( LENRBUF.GT.0 .AND. NPCOL.GT.1 )
     $                  CALL SGEBR2D( ICTXT, 'Row', '1-Tree', LENRBUF,
     $                       1, WORK, LENRBUF, RSRC1, CSRC1 )
                     BCDONE = .TRUE.
                  ELSEIF( MYCOL.EQ.CSRC1 .AND. DIR.EQ.2 ) THEN
                     IF( LENCBUF.GT.0 .AND. NPROW.GT.1 )
     $                  CALL SGEBR2D( ICTXT, 'Col', '1-Tree', LENCBUF,
     $                       1, WORK(1+LENRBUF), LENCBUF, RSRC1, CSRC1 )
                     BCDONE = .TRUE.
                  ELSEIF( MYROW.EQ.RSRC4 .AND. DIR.EQ.1 ) THEN
                     IF( LENRBUF.GT.0 .AND. NPCOL.GT.1 )
     $                  CALL SGEBR2D( ICTXT, 'Row', '1-Tree', LENRBUF,
     $                       1, WORK, LENRBUF, RSRC4, CSRC4 )
                     BCDONE = .TRUE.
                  ELSEIF( MYCOL.EQ.CSRC4 .AND. DIR.EQ.2 ) THEN
                     IF( LENCBUF.GT.0 .AND. NPROW.GT.1 )
     $                  CALL SGEBR2D( ICTXT, 'Col', '1-Tree', LENCBUF,
     $                       1, WORK(1+LENRBUF), LENCBUF, RSRC4, CSRC4 )
                     BCDONE = .TRUE.
                  END IF
 185              CONTINUE
 180           CONTINUE
 170        CONTINUE
*
*           Prepare for computing cross border updates by exchanging
*           data in cross border update regions in H and Z.
*
            DO 190 DIR = 1, 2
               WINID = 0
               IPW3 = 1
               DO 200 WIN = ODDEVEN+(CHUNKNUM-1)*WCHUNK,
     $              MIN(ANMWIN,MAX(1,ODDEVEN+(CHUNKNUM)*WCHUNK-1)), 2
                  IF( IWORK( 5+(WIN-1)*5 ).NE.1 ) GO TO 205
*
*                 Make sure this part of the code is only executed when
*                 there has been some work performed on the WIN:th
*                 window.
*
                  LKTOP = IWORK( 1+(WIN-1)*5 )
                  LKBOT = IWORK( 2+(WIN-1)*5 )
*
*                 Extract processor indices associated with
*                 the current window.
*
                  RSRC1 = IWORK( 3+(WIN-1)*5 )
                  CSRC1 = IWORK( 4+(WIN-1)*5 )
                  RSRC4 = MOD( RSRC1+1, NPROW )
                  CSRC4 = MOD( CSRC1+1, NPCOL )
*
*                 Compute local number of rows and columns
*                 of H and Z to exchange.
*
                  IF(((MYCOL.EQ.CSRC1.OR.MYCOL.EQ.CSRC4).AND.DIR.EQ.2)
     $                 .OR.((MYROW.EQ.RSRC1.OR.MYROW.EQ.RSRC4).AND.
     $                 DIR.EQ.1)) THEN
                     WINID = WINID + 1
                     LNWIN = LKBOT - LKTOP + 1
                     IPU = IPNEXT
                     DIM1 = NB - MOD(LKTOP-1,NB)
                     DIM4 = LNWIN - DIM1
                     IPNEXT = IPU + LNWIN*LNWIN
                     IF( DIR.EQ.2 ) THEN
                        IF( WANTZ ) THEN
                           ZROWS = NUMROC( N, NB, MYROW, DESCZ( RSRC_ ),
     $                          NPROW )
                        ELSE
                           ZROWS = 0
                        END IF
                        IF( WANTT ) THEN
                           HROWS = NUMROC( LKTOP-1, NB, MYROW,
     $                          DESCH( RSRC_ ), NPROW )
                        ELSE
                           HROWS = 0
                        END IF
                     ELSE
                        ZROWS = 0
                        HROWS = 0
                     END IF
                     IF( DIR.EQ.1 ) THEN
                        IF( WANTT ) THEN
                           HCOLS = NUMROC( N - (LKTOP+DIM1-1), NB,
     $                          MYCOL, CSRC4, NPCOL )
                           IF( MYCOL.EQ.CSRC4 ) HCOLS = HCOLS - DIM4
                        ELSE
                           HCOLS = 0
                        END IF
                     ELSE
                        HCOLS = 0
                     END IF
                     IPW = MAX( 1 + LENRBUF + LENCBUF, IPW3 )
                     IPW1 = IPW + HROWS * LNWIN
                     IF( WANTZ ) THEN
                        IPW2 = IPW1 + LNWIN * HCOLS
                        IPW3 = IPW2 + ZROWS * LNWIN
                     ELSE
                        IPW3 = IPW1 + LNWIN * HCOLS
                     END IF
                  END IF
*
*                 Let each process row and column involved in the updates
*                 exchange data in H and Z with their neighbours.
*
                  IF( DIR.EQ.2 .AND. WANTT .AND. LENCBUF.GT.0 ) THEN
                     IF( MYCOL.EQ.CSRC1 .OR. MYCOL.EQ.CSRC4 ) THEN
                        DO 210 INDX = 1, NPROW
                           IF( MYCOL.EQ.CSRC1 ) THEN
                              CALL INFOG2L( 1+(INDX-1)*NB, LKTOP, DESCH,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC1, RSRC, CSRC1 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', HROWS, DIM1,
     $                                H((JLOC1-1)*LLDH+ILOC), LLDH,
     $                                WORK(IPW), HROWS )
                                 IF( NPCOL.GT.1 ) THEN
                                    EAST = MOD( MYCOL + 1, NPCOL )
                                    CALL SGESD2D( ICTXT, HROWS, DIM1,
     $                                   WORK(IPW), HROWS, RSRC, EAST )
                                    CALL SGERV2D( ICTXT, HROWS, DIM4,
     $                                   WORK(IPW+HROWS*DIM1), HROWS,
     $                                   RSRC, EAST )
                                 END IF
                              END IF
                           END IF
                           IF( MYCOL.EQ.CSRC4 ) THEN
                              CALL INFOG2L( 1+(INDX-1)*NB, LKTOP+DIM1,
     $                             DESCH, NPROW, NPCOL, MYROW, MYCOL,
     $                             ILOC, JLOC4, RSRC, CSRC4 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', HROWS, DIM4,
     $                                H((JLOC4-1)*LLDH+ILOC), LLDH,
     $                                WORK(IPW+HROWS*DIM1), HROWS )
                                 IF( NPCOL.GT.1 ) THEN
                                    WEST = MOD( MYCOL - 1 + NPCOL,
     $                                   NPCOL )
                                    CALL SGESD2D( ICTXT, HROWS, DIM4,
     $                                   WORK(IPW+HROWS*DIM1), HROWS,
     $                                   RSRC, WEST )
                                    CALL SGERV2D( ICTXT, HROWS, DIM1,
     $                                   WORK(IPW), HROWS, RSRC, WEST )
                                 END IF
                              END IF
                           END IF
 210                    CONTINUE
                     END IF
                  END IF
*
                  IF( DIR.EQ.1 .AND. WANTT .AND. LENRBUF.GT.0 ) THEN
                     IF( MYROW.EQ.RSRC1 .OR. MYROW.EQ.RSRC4 ) THEN
                        DO 220 INDX = 1, NPCOL
                           IF( MYROW.EQ.RSRC1 ) THEN
                              IF( INDX.EQ.1 ) THEN
                                 IF( LKBOT.LT.N ) THEN
                                    CALL INFOG2L( LKTOP, LKBOT+1, DESCH,
     $                                   NPROW, NPCOL, MYROW, MYCOL,
     $                                   ILOC1, JLOC, RSRC1, CSRC )
                                 ELSE
                                    CSRC = -1
                                 END IF
                              ELSEIF( MOD(LKBOT,NB).NE.0 ) THEN
                                 CALL INFOG2L( LKTOP,
     $                                (ICEIL(LKBOT,NB)+(INDX-2))*NB+1,
     $                                DESCH, NPROW, NPCOL, MYROW, MYCOL,
     $                                ILOC1, JLOC, RSRC1, CSRC )
                              ELSE
                                 CALL INFOG2L( LKTOP,
     $                                (ICEIL(LKBOT,NB)+(INDX-1))*NB+1,
     $                                DESCH, NPROW, NPCOL, MYROW, MYCOL,
     $                                ILOC1, JLOC, RSRC1, CSRC )
                              END IF
                              IF( MYCOL.EQ.CSRC ) THEN
                                 CALL SLAMOV( 'All', DIM1, HCOLS,
     $                                H((JLOC-1)*LLDH+ILOC1), LLDH,
     $                                WORK(IPW1), LNWIN )
                                 IF( NPROW.GT.1 ) THEN
                                    SOUTH = MOD( MYROW + 1, NPROW )
                                    CALL SGESD2D( ICTXT, DIM1, HCOLS,
     $                                   WORK(IPW1), LNWIN, SOUTH,
     $                                   CSRC )
                                    CALL SGERV2D( ICTXT, DIM4, HCOLS,
     $                                   WORK(IPW1+DIM1), LNWIN, SOUTH,
     $                                   CSRC )
                                 END IF
                              END IF
                           END IF
                           IF( MYROW.EQ.RSRC4 ) THEN
                              IF( INDX.EQ.1 ) THEN
                                 IF( LKBOT.LT.N ) THEN
                                    CALL INFOG2L( LKTOP+DIM1, LKBOT+1,
     $                                   DESCH, NPROW, NPCOL, MYROW,
     $                                   MYCOL, ILOC4, JLOC, RSRC4,
     $                                   CSRC )
                                 ELSE
                                    CSRC = -1
                                 END IF
                              ELSEIF( MOD(LKBOT,NB).NE.0 ) THEN
                                 CALL INFOG2L( LKTOP+DIM1,
     $                                (ICEIL(LKBOT,NB)+(INDX-2))*NB+1,
     $                                DESCH, NPROW, NPCOL, MYROW, MYCOL,
     $                                ILOC4, JLOC, RSRC4, CSRC )
                              ELSE
                                 CALL INFOG2L( LKTOP+DIM1,
     $                                (ICEIL(LKBOT,NB)+(INDX-1))*NB+1,
     $                                DESCH, NPROW, NPCOL, MYROW, MYCOL,
     $                                ILOC4, JLOC, RSRC4, CSRC )
                              END IF
                              IF( MYCOL.EQ.CSRC ) THEN
                                 CALL SLAMOV( 'All', DIM4, HCOLS,
     $                                H((JLOC-1)*LLDH+ILOC4), LLDH,
     $                                WORK(IPW1+DIM1), LNWIN )
                                 IF( NPROW.GT.1 ) THEN
                                    NORTH = MOD( MYROW - 1 + NPROW,
     $                                   NPROW )
                                    CALL SGESD2D( ICTXT, DIM4, HCOLS,
     $                                   WORK(IPW1+DIM1), LNWIN, NORTH,
     $                                   CSRC )
                                    CALL SGERV2D( ICTXT, DIM1, HCOLS,
     $                                   WORK(IPW1), LNWIN, NORTH,
     $                                   CSRC )
                                 END IF
                              END IF
                           END IF
 220                    CONTINUE
                     END IF
                  END IF
*
                  IF( DIR.EQ.2 .AND. WANTZ .AND. LENCBUF.GT.0) THEN
                     IF( MYCOL.EQ.CSRC1 .OR. MYCOL.EQ.CSRC4 ) THEN
                        DO 230 INDX = 1, NPROW
                           IF( MYCOL.EQ.CSRC1 ) THEN
                              CALL INFOG2L( 1+(INDX-1)*NB, LKTOP,
     $                             DESCZ, NPROW, NPCOL, MYROW, MYCOL,
     $                             ILOC, JLOC1, RSRC, CSRC1 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', ZROWS, DIM1,
     $                                Z((JLOC1-1)*LLDZ+ILOC), LLDZ,
     $                                WORK(IPW2), ZROWS )
                                 IF( NPCOL.GT.1 ) THEN
                                    EAST = MOD( MYCOL + 1, NPCOL )
                                    CALL SGESD2D( ICTXT, ZROWS, DIM1,
     $                                   WORK(IPW2), ZROWS, RSRC,
     $                                   EAST )
                                    CALL SGERV2D( ICTXT, ZROWS, DIM4,
     $                                   WORK(IPW2+ZROWS*DIM1),
     $                                   ZROWS, RSRC, EAST )
                                 END IF
                              END IF
                           END IF
                           IF( MYCOL.EQ.CSRC4 ) THEN
                              CALL INFOG2L( 1+(INDX-1)*NB,
     $                             LKTOP+DIM1, DESCZ, NPROW, NPCOL,
     $                             MYROW, MYCOL, ILOC, JLOC4, RSRC,
     $                             CSRC4 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', ZROWS, DIM4,
     $                                Z((JLOC4-1)*LLDZ+ILOC), LLDZ,
     $                                WORK(IPW2+ZROWS*DIM1), ZROWS )
                                 IF( NPCOL.GT.1 ) THEN
                                    WEST = MOD( MYCOL - 1 + NPCOL,
     $                                   NPCOL )
                                    CALL SGESD2D( ICTXT, ZROWS, DIM4,
     $                                   WORK(IPW2+ZROWS*DIM1),
     $                                   ZROWS, RSRC, WEST )
                                    CALL SGERV2D( ICTXT, ZROWS, DIM1,
     $                                   WORK(IPW2), ZROWS, RSRC,
     $                                   WEST )
                                 END IF
                              END IF
                           END IF
 230                    CONTINUE
                     END IF
                  END IF
*
*                 If no exchanges was performed for the current window,
*                 all processors jump to this point and try the next
*                 one.
*
 205              CONTINUE
*
 200           CONTINUE
*
*              Compute crossborder bulge-chase updates.
*
               WINID = 0
               IF( DIR.EQ.1 ) THEN
                  IPNEXT = 1
               ELSE
                  IPNEXT = 1 + LENRBUF
               END IF
               IPW3 = 1
               DO 240 WIN = ODDEVEN+(CHUNKNUM-1)*WCHUNK,
     $              MIN(ANMWIN,MAX(1,ODDEVEN+(CHUNKNUM)*WCHUNK-1)), 2
                  IF( IWORK( 5+(WIN-1)*5 ).NE.1 ) GO TO 245
*
*                 Only perform this part of the code if there was really
*                 some work performed on the WIN:th window.
*
                  LKTOP = IWORK( 1+(WIN-1)*5 )
                  LKBOT = IWORK( 2+(WIN-1)*5 )
                  LNWIN = LKBOT - LKTOP + 1
*
*                 Extract the processor indices associated with
*                 the current window.
*
                  RSRC1 = IWORK( 3+(WIN-1)*5 )
                  CSRC1 = IWORK( 4+(WIN-1)*5 )
                  RSRC4 = MOD( RSRC1+1, NPROW )
                  CSRC4 = MOD( CSRC1+1, NPCOL )
*
                  IF(((MYCOL.EQ.CSRC1.OR.MYCOL.EQ.CSRC4).AND.DIR.EQ.2)
     $                 .OR.((MYROW.EQ.RSRC1.OR.MYROW.EQ.RSRC4).AND.
     $                 DIR.EQ.1)) THEN
*
*                    Set up workspaces.
*
                     WINID = WINID + 1
                     LKTOP = IWORK( 1+(WIN-1)*5 )
                     LKBOT = IWORK( 2+(WIN-1)*5 )
                     LNWIN = LKBOT - LKTOP + 1
                     DIM1 = NB - MOD(LKTOP-1,NB)
                     DIM4 = LNWIN - DIM1
                     IPU = IPNEXT + (WINID-1)*LNWIN*LNWIN
                     IF( DIR.EQ.2 ) THEN
                        IF( WANTZ ) THEN
                           ZROWS = NUMROC( N, NB, MYROW, DESCZ( RSRC_ ),
     $                          NPROW )
                        ELSE
                           ZROWS = 0
                        END IF
                        IF( WANTT ) THEN
                           HROWS = NUMROC( LKTOP-1, NB, MYROW,
     $                          DESCH( RSRC_ ), NPROW )
                        ELSE
                           HROWS = 0
                        END IF
                     ELSE
                        ZROWS = 0
                        HROWS = 0
                     END IF
                     IF( DIR.EQ.1 ) THEN
                        IF( WANTT ) THEN
                           HCOLS = NUMROC( N - (LKTOP+DIM1-1), NB,
     $                          MYCOL, CSRC4, NPCOL )
                           IF( MYCOL.EQ.CSRC4 ) HCOLS = HCOLS - DIM4
                        ELSE
                           HCOLS = 0
                        END IF
                     ELSE
                        HCOLS = 0
                     END IF
*
*                    IPW  = local copy of overlapping column block of H
*                    IPW1 = local copy of overlapping row block of H
*                    IPW2 = local copy of overlapping column block of Z
*                    IPW3 = workspace for right hand side of matrix
*                           multiplication
*
                     IPW = MAX( 1 + LENRBUF + LENCBUF, IPW3 )
                     IPW1 = IPW + HROWS * LNWIN
                     IF( WANTZ ) THEN
                        IPW2 = IPW1 + LNWIN * HCOLS
                        IPW3 = IPW2 + ZROWS * LNWIN
                     ELSE
                        IPW3 = IPW1 + LNWIN * HCOLS
                     END IF
*
*                    Recompute job to see if special structure of U
*                    could possibly be exploited.
*
                     IF( LKTOP.EQ.KTOP .AND. LKBOT.EQ.KBOT ) THEN
                        JOB = 'All steps'
                     ELSEIF( LKTOP.EQ.KTOP .AND.
     $                    ( DIM1.LT.LCHAIN+1 .OR. DIM1.LE.NTINY ) )
     $                    THEN
                        JOB = 'Introduce and chase'
                     ELSEIF( LKBOT.EQ.KBOT ) THEN
                        JOB = 'Off-chase bulges'
                     ELSE
                        JOB = 'Chase bulges'
                     END IF
                  END IF
*
*                 Test if to exploit sparsity structure of
*                 orthogonal matrix U.
*
                  KS = DIM1+DIM4-LNS/2*3
                  IF( .NOT. BLK22 .OR. DIM1.NE.KS .OR.
     $                 DIM4.NE.KS .OR. LSAME(JOB,'I') .OR.
     $                 LSAME(JOB,'O') .OR. LNS.LE.2 ) THEN
*
*                    Update the columns of H and Z.
*
                     IF( DIR.EQ.2 .AND. WANTT .AND. LENCBUF.GT.0 ) THEN
                        DO 250 INDX = 1, MIN(LKTOP-1,1+(NPROW-1)*NB), NB
                           IF( MYCOL.EQ.CSRC1 ) THEN
                              CALL INFOG2L( INDX, LKTOP, DESCH, NPROW,
     $                             NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                             RSRC, CSRC1 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', HROWS, DIM1,
     $                                LNWIN, ONE, WORK( IPW ), HROWS,
     $                                WORK( IPU ), LNWIN, ZERO,
     $                                WORK(IPW3), HROWS )
                                 CALL SLAMOV( 'All', HROWS, DIM1,
     $                                WORK(IPW3), HROWS,
     $                                H((JLOC-1)*LLDH+ILOC), LLDH )
                              END IF
                           END IF
                           IF( MYCOL.EQ.CSRC4 ) THEN
                              CALL INFOG2L( INDX, LKTOP+DIM1, DESCH,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC, RSRC, CSRC4 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', HROWS, DIM4,
     $                                LNWIN, ONE, WORK( IPW ), HROWS,
     $                                WORK( IPU+LNWIN*DIM1 ), LNWIN,
     $                                ZERO, WORK(IPW3), HROWS )
                                 CALL SLAMOV( 'All', HROWS, DIM4,
     $                                WORK(IPW3), HROWS,
     $                                H((JLOC-1)*LLDH+ILOC), LLDH )
                              END IF
                           END IF
 250                    CONTINUE
                     END IF
*
                     IF( DIR.EQ.2 .AND. WANTZ .AND. LENCBUF.GT.0 ) THEN
                        DO 260 INDX = 1, MIN(N,1+(NPROW-1)*NB), NB
                           IF( MYCOL.EQ.CSRC1 ) THEN
                              CALL INFOG2L( INDX, LKTOP, DESCZ, NPROW,
     $                             NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                             RSRC, CSRC1 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', ZROWS, DIM1,
     $                                LNWIN, ONE, WORK( IPW2 ),
     $                                ZROWS, WORK( IPU ), LNWIN,
     $                                ZERO, WORK(IPW3), ZROWS )
                                 CALL SLAMOV( 'All', ZROWS, DIM1,
     $                                WORK(IPW3), ZROWS,
     $                                Z((JLOC-1)*LLDZ+ILOC), LLDZ )
                              END IF
                           END IF
                           IF( MYCOL.EQ.CSRC4 ) THEN
                              CALL INFOG2L( INDX, LKTOP+DIM1, DESCZ,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC, RSRC, CSRC4 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', ZROWS, DIM4,
     $                                LNWIN, ONE, WORK( IPW2 ),
     $                                ZROWS,
     $                                WORK( IPU+LNWIN*DIM1 ), LNWIN,
     $                                ZERO, WORK(IPW3), ZROWS )
                                 CALL SLAMOV( 'All', ZROWS, DIM4,
     $                                WORK(IPW3), ZROWS,
     $                                Z((JLOC-1)*LLDZ+ILOC), LLDZ )
                              END IF
                           END IF
 260                    CONTINUE
                     END IF
*
*                    Update the rows of H.
*
                     IF( DIR.EQ.1 .AND. WANTT .AND. LENRBUF.GT.0 ) THEN
                        IF( LKBOT.LT.N ) THEN
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC4 .AND.
     $                          MOD(LKBOT,NB).NE.0 ) THEN
                              INDX = LKBOT + 1
                              CALL INFOG2L( LKTOP, INDX, DESCH, NPROW,
     $                             NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                             RSRC1, CSRC4 )
                              CALL SGEMM( 'Transpose', 'No Transpose',
     $                             DIM1, HCOLS, LNWIN, ONE, WORK(IPU),
     $                             LNWIN, WORK( IPW1 ), LNWIN, ZERO,
     $                             WORK(IPW3), DIM1 )
                              CALL SLAMOV( 'All', DIM1, HCOLS,
     $                             WORK(IPW3), DIM1,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
                           IF( MYROW.EQ.RSRC4.AND.MYCOL.EQ.CSRC4 .AND.
     $                          MOD(LKBOT,NB).NE.0 ) THEN
                              INDX = LKBOT + 1
                              CALL INFOG2L( LKTOP+DIM1, INDX, DESCH,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC, RSRC4, CSRC4 )
                              CALL SGEMM( 'Transpose', 'No Transpose',
     $                             DIM4, HCOLS, LNWIN, ONE,
     $                             WORK( IPU+DIM1*LNWIN ), LNWIN,
     $                             WORK( IPW1), LNWIN, ZERO,
     $                             WORK(IPW3), DIM4 )
                              CALL SLAMOV( 'All', DIM4, HCOLS,
     $                             WORK(IPW3), DIM4,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
                           INDXS = ICEIL(LKBOT,NB)*NB + 1
                           IF( MOD(LKBOT,NB).NE.0 ) THEN
                              INDXE = MIN(N,INDXS+(NPCOL-2)*NB)
                           ELSE
                              INDXE = MIN(N,INDXS+(NPCOL-1)*NB)
                           END IF
                           DO 270 INDX = INDXS, INDXE, NB
                              IF( MYROW.EQ.RSRC1 ) THEN
                                 CALL INFOG2L( LKTOP, INDX, DESCH,
     $                                NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                                JLOC, RSRC1, CSRC )
                                 IF( MYCOL.EQ.CSRC ) THEN
                                    CALL SGEMM( 'Transpose',
     $                                   'No Transpose', DIM1, HCOLS,
     $                                   LNWIN, ONE, WORK( IPU ), LNWIN,
     $                                   WORK( IPW1 ), LNWIN, ZERO,
     $                                   WORK(IPW3), DIM1 )
                                    CALL SLAMOV( 'All', DIM1, HCOLS,
     $                                   WORK(IPW3), DIM1,
     $                                   H((JLOC-1)*LLDH+ILOC), LLDH )
                                 END IF
                              END IF
                              IF( MYROW.EQ.RSRC4 ) THEN
                                 CALL INFOG2L( LKTOP+DIM1, INDX, DESCH,
     $                                NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                                JLOC, RSRC4, CSRC )
                                 IF( MYCOL.EQ.CSRC ) THEN
                                    CALL SGEMM( 'Transpose',
     $                                   'No Transpose', DIM4, HCOLS,
     $                                   LNWIN, ONE,
     $                                   WORK( IPU+LNWIN*DIM1 ), LNWIN,
     $                                   WORK( IPW1 ), LNWIN,
     $                                   ZERO, WORK(IPW3), DIM4 )
                                    CALL SLAMOV( 'All', DIM4, HCOLS,
     $                                   WORK(IPW3), DIM4,
     $                                   H((JLOC-1)*LLDH+ILOC), LLDH )
                                 END IF
                              END IF
 270                       CONTINUE
                        END IF
                     END IF
                  ELSE
*
*                    Update the columns of H and Z.
*
*                    Compute H2*U21 + H1*U11 on the left side of the border.
*
                     IF( DIR.EQ.2 .AND. WANTT .AND. LENCBUF.GT.0 ) THEN
                        INDXE = MIN(LKTOP-1,1+(NPROW-1)*NB)
                        DO 280 INDX = 1, INDXE, NB
                           IF( MYCOL.EQ.CSRC1 ) THEN
                              CALL INFOG2L( INDX, LKTOP, DESCH, NPROW,
     $                             NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                             RSRC, CSRC1 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', HROWS, KS,
     $                                WORK( IPW+HROWS*DIM4), HROWS,
     $                                WORK(IPW3), HROWS )
                                 CALL STRMM( 'Right', 'Upper',
     $                                'No transpose',
     $                                'Non-unit', HROWS, KS, ONE,
     $                                WORK( IPU+DIM4 ), LNWIN,
     $                                WORK(IPW3), HROWS )
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', HROWS, KS, DIM4,
     $                                ONE, WORK( IPW ), HROWS,
     $                                WORK( IPU ), LNWIN, ONE,
     $                                WORK(IPW3), HROWS )
                                 CALL SLAMOV( 'All', HROWS, KS,
     $                                WORK(IPW3), HROWS,
     $                                H((JLOC-1)*LLDH+ILOC), LLDH )
                              END IF
                           END IF
*
*                          Compute H1*U12 + H2*U22 on the right side of
*                          the border.
*
                           IF( MYCOL.EQ.CSRC4 ) THEN
                              CALL INFOG2L( INDX, LKTOP+DIM1, DESCH,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC, RSRC, CSRC4 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', HROWS, DIM4,
     $                                WORK(IPW), HROWS, WORK( IPW3 ),
     $                                HROWS )
                                 CALL STRMM( 'Right', 'Lower',
     $                                'No transpose',
     $                                'Non-unit', HROWS, DIM4, ONE,
     $                                WORK( IPU+LNWIN*KS ), LNWIN,
     $                                WORK( IPW3 ), HROWS )
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', HROWS, DIM4, KS,
     $                                ONE, WORK( IPW+HROWS*DIM4),
     $                                HROWS,
     $                                WORK( IPU+LNWIN*KS+DIM4 ), LNWIN,
     $                                ONE, WORK( IPW3 ), HROWS )
                                 CALL SLAMOV( 'All', HROWS, DIM4,
     $                                WORK(IPW3), HROWS,
     $                                H((JLOC-1)*LLDH+ILOC), LLDH )
                              END IF
                           END IF
 280                    CONTINUE
                     END IF
*
                     IF( DIR.EQ.2 .AND. WANTZ .AND. LENCBUF.GT.0 ) THEN
*
*                       Compute Z2*U21 + Z1*U11 on the left side
*                       of border.
*
                        INDXE = MIN(N,1+(NPROW-1)*NB)
                        DO 290 INDX = 1, INDXE, NB
                           IF( MYCOL.EQ.CSRC1 ) THEN
                              CALL INFOG2L( INDX, I, DESCZ, NPROW,
     $                             NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                             RSRC, CSRC1 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', ZROWS, KS,
     $                                WORK( IPW2+ZROWS*DIM4),
     $                                ZROWS, WORK(IPW3), ZROWS )
                                 CALL STRMM( 'Right', 'Upper',
     $                                'No transpose',
     $                                'Non-unit', ZROWS, KS, ONE,
     $                                WORK( IPU+DIM4 ), LNWIN,
     $                                WORK(IPW3), ZROWS )
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', ZROWS, KS,
     $                                DIM4, ONE, WORK( IPW2 ),
     $                                ZROWS, WORK( IPU ), LNWIN,
     $                                ONE, WORK(IPW3), ZROWS )
                                 CALL SLAMOV( 'All', ZROWS, KS,
     $                                WORK(IPW3), ZROWS,
     $                                Z((JLOC-1)*LLDZ+ILOC), LLDZ )
                              END IF
                           END IF
*
*                          Compute Z1*U12 + Z2*U22 on the right side
*                          of border.
*
                           IF( MYCOL.EQ.CSRC4 ) THEN
                              CALL INFOG2L( INDX, I+DIM1, DESCZ,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC, RSRC, CSRC4 )
                              IF( MYROW.EQ.RSRC ) THEN
                                 CALL SLAMOV( 'All', ZROWS, DIM4,
     $                                WORK(IPW2), ZROWS,
     $                                WORK( IPW3 ), ZROWS )
                                 CALL STRMM( 'Right', 'Lower',
     $                                'No transpose',
     $                                'Non-unit', ZROWS, DIM4,
     $                                ONE, WORK( IPU+LNWIN*KS ),
     $                                LNWIN, WORK( IPW3 ), ZROWS )
                                 CALL SGEMM( 'No transpose',
     $                                'No transpose', ZROWS, DIM4,
     $                                KS, ONE,
     $                                WORK( IPW2+ZROWS*(DIM4)),
     $                                ZROWS,
     $                                WORK( IPU+LNWIN*KS+DIM4 ),
     $                                LNWIN, ONE, WORK( IPW3 ),
     $                                ZROWS )
                                 CALL SLAMOV( 'All', ZROWS, DIM4,
     $                                WORK(IPW3), ZROWS,
     $                                Z((JLOC-1)*LLDZ+ILOC), LLDZ )
                              END IF
                           END IF
 290                    CONTINUE
                     END IF
*
                     IF( DIR.EQ.1 .AND. WANTT .AND. LENRBUF.GT.0) THEN
                        IF ( LKBOT.LT.N ) THEN
*
*                          Compute U21**T*H2 + U11**T*H1 on the upper
*                          side of the border.
*
                           IF( MYROW.EQ.RSRC1.AND.MYCOL.EQ.CSRC4.AND.
     $                          MOD(LKBOT,NB).NE.0 ) THEN
                              INDX = LKBOT + 1
                              CALL INFOG2L( LKTOP, INDX, DESCH, NPROW,
     $                             NPCOL, MYROW, MYCOL, ILOC, JLOC,
     $                             RSRC1, CSRC4 )
                              CALL SLAMOV( 'All', KS, HCOLS,
     $                             WORK( IPW1+DIM4 ), LNWIN,
     $                             WORK(IPW3), KS )
                              CALL STRMM( 'Left', 'Upper', 'Transpose',
     $                             'Non-unit', KS, HCOLS, ONE,
     $                             WORK( IPU+DIM4 ), LNWIN,
     $                             WORK(IPW3), KS )
                              CALL SGEMM( 'Transpose', 'No transpose',
     $                             KS, HCOLS, DIM4, ONE, WORK(IPU),
     $                             LNWIN, WORK(IPW1), LNWIN,
     $                             ONE, WORK(IPW3), KS )
                              CALL SLAMOV( 'All', KS, HCOLS,
     $                             WORK(IPW3), KS,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
*
*                          Compute U12**T*H1 + U22**T*H2 one the lower
*                          side of the border.
*
                           IF( MYROW.EQ.RSRC4.AND.MYCOL.EQ.CSRC4.AND.
     $                          MOD(LKBOT,NB).NE.0 ) THEN
                              INDX = LKBOT + 1
                              CALL INFOG2L( LKTOP+DIM1, INDX, DESCH,
     $                             NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                             JLOC, RSRC4, CSRC4 )
                              CALL SLAMOV( 'All', DIM4, HCOLS,
     $                             WORK( IPW1 ), LNWIN,
     $                             WORK( IPW3 ), DIM4 )
                              CALL STRMM( 'Left', 'Lower', 'Transpose',
     $                             'Non-unit', DIM4, HCOLS, ONE,
     $                             WORK( IPU+LNWIN*KS ), LNWIN,
     $                             WORK( IPW3 ), DIM4 )
                              CALL SGEMM( 'Transpose', 'No Transpose',
     $                             DIM4, HCOLS, KS, ONE,
     $                             WORK( IPU+LNWIN*KS+DIM4 ), LNWIN,
     $                             WORK( IPW1+DIM1 ), LNWIN,
     $                             ONE, WORK( IPW3), DIM4 )
                              CALL SLAMOV( 'All', DIM4, HCOLS,
     $                             WORK(IPW3), DIM4,
     $                             H((JLOC-1)*LLDH+ILOC), LLDH )
                           END IF
*
*                          Compute U21**T*H2 + U11**T*H1 on upper side
*                          on border.
*
                           INDXS = ICEIL(LKBOT,NB)*NB+1
                           IF( MOD(LKBOT,NB).NE.0 ) THEN
                              INDXE = MIN(N,INDXS+(NPCOL-2)*NB)
                           ELSE
                              INDXE = MIN(N,INDXS+(NPCOL-1)*NB)
                           END IF
                           DO 300 INDX = INDXS, INDXE, NB
                              IF( MYROW.EQ.RSRC1 ) THEN
                                 CALL INFOG2L( LKTOP, INDX, DESCH,
     $                                NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                                JLOC, RSRC1, CSRC )
                                 IF( MYCOL.EQ.CSRC ) THEN
                                    CALL SLAMOV( 'All', KS, HCOLS,
     $                                   WORK( IPW1+DIM4 ), LNWIN,
     $                                   WORK(IPW3), KS )
                                    CALL STRMM( 'Left', 'Upper',
     $                                   'Transpose', 'Non-unit',
     $                                   KS, HCOLS, ONE,
     $                                   WORK( IPU+DIM4 ), LNWIN,
     $                                   WORK(IPW3), KS )
                                    CALL SGEMM( 'Transpose',
     $                                   'No transpose', KS, HCOLS,
     $                                   DIM4, ONE, WORK(IPU), LNWIN,
     $                                   WORK(IPW1), LNWIN, ONE,
     $                                   WORK(IPW3), KS )
                                    CALL SLAMOV( 'All', KS, HCOLS,
     $                                   WORK(IPW3), KS,
     $                                   H((JLOC-1)*LLDH+ILOC), LLDH )
                                 END IF
                              END IF
*
*                             Compute U12**T*H1 + U22**T*H2 on lower
*                             side of border.
*
                              IF( MYROW.EQ.RSRC4 ) THEN
                                 CALL INFOG2L( LKTOP+DIM1, INDX, DESCH,
     $                                NPROW, NPCOL, MYROW, MYCOL, ILOC,
     $                                JLOC, RSRC4, CSRC )
                                 IF( MYCOL.EQ.CSRC ) THEN
                                    CALL SLAMOV( 'All', DIM4, HCOLS,
     $                                   WORK( IPW1 ), LNWIN,
     $                                   WORK( IPW3 ), DIM4 )
                                    CALL STRMM( 'Left', 'Lower',
     $                                   'Transpose','Non-unit',
     $                                   DIM4, HCOLS, ONE,
     $                                   WORK( IPU+LNWIN*KS ), LNWIN,
     $                                   WORK( IPW3 ), DIM4 )
                                    CALL SGEMM( 'Transpose',
     $                                   'No Transpose', DIM4, HCOLS,
     $                                   KS, ONE,
     $                                   WORK( IPU+LNWIN*KS+DIM4 ),
     $                                   LNWIN, WORK( IPW1+DIM1 ),
     $                                   LNWIN, ONE, WORK( IPW3),
     $                                   DIM4 )
                                    CALL SLAMOV( 'All', DIM4, HCOLS,
     $                                   WORK(IPW3), DIM4,
     $                                   H((JLOC-1)*LLDH+ILOC), LLDH )
                                 END IF
                              END IF
 300                       CONTINUE
                        END IF
                     END IF
                  END IF
*
*                 Update window information - mark processed windows are
*                 completed.
*
                  IF( DIR.EQ.2 ) THEN
                     IF( LKBOT.EQ.KBOT ) THEN
                        LKTOP = KBOT+1
                        LKBOT = KBOT+1
                        IWORK( 1+(WIN-1)*5 ) = LKTOP
                        IWORK( 2+(WIN-1)*5 ) = LKBOT
                     ELSE
                        LKTOP = MIN( LKTOP + LNWIN - LCHAIN,
     $                       MIN( KBOT, ICEIL( LKBOT, NB )*NB ) -
     $                       LCHAIN + 1 )
                        IWORK( 1+(WIN-1)*5 ) = LKTOP
                        LKBOT = MIN( MAX( LKBOT + LNWIN - LCHAIN,
     $                       LKTOP + NWIN - 1), MIN( KBOT,
     $                       ICEIL( LKBOT, NB )*NB ) )
                        IWORK( 2+(WIN-1)*5 ) = LKBOT
                     END IF
                     IF( IWORK( 5+(WIN-1)*5 ).EQ.1 )
     $                    IWORK( 5+(WIN-1)*5 ) = 2
                     IWORK( 3+(WIN-1)*5 ) = RSRC4
                     IWORK( 4+(WIN-1)*5 ) = CSRC4
                  END IF
*
*                 If nothing was done for the WIN:th window, all
*                 processors come here and consider the next one
*                 instead.
*
 245              CONTINUE
 240           CONTINUE
 190        CONTINUE
 150     CONTINUE
 140     CONTINUE
*
*        Chased off bulges from first window?
*
         IF( NPROCS.GT.1 )
     $      CALL IGAMX2D( ICTXT, 'All', '1-Tree', 1, 1, ICHOFF, 1,
     $           -1, -1, -1, -1, -1 )
*
*        If the bulge was chasen off from first window it is removed.
*
         IF( ICHOFF.GT.0 ) THEN
            DO 198 WIN = 2, ANMWIN
               IWORK( 1+(WIN-2)*5 ) = IWORK( 1+(WIN-1)*5 )
               IWORK( 2+(WIN-2)*5 ) = IWORK( 2+(WIN-1)*5 )
               IWORK( 3+(WIN-2)*5 ) = IWORK( 3+(WIN-1)*5 )
               IWORK( 4+(WIN-2)*5 ) = IWORK( 4+(WIN-1)*5 )
 198        CONTINUE
            ANMWIN = ANMWIN - 1
            IPIW = 6+(ANMWIN-1)*5
         END IF
*
*        If we have no more windows, return.
*
         IF( ANMWIN.LT.1 ) RETURN
*
*        Check for any more windows to bring over the border.
*
         WINFIN = 0
         DO 199 WIN = 1, ANMWIN
            WINFIN = WINFIN+IWORK( 5+(WIN-1)*5 )
 199     CONTINUE
         IF( WINFIN.LT.2*ANMWIN ) GO TO 137
*
*        Zero out process mark for each window - this is legal now when
*        the process starts over with local bulge-chasing etc.
*
         DO 201 WIN = 1, ANMWIN
            IWORK( 5+(WIN-1)*5 ) = 0
 201     CONTINUE
*
      END IF
*
*     Go back to local bulge-chase and see if there is more work to do.
*
      GO TO 20
*
*     End of PSLAQR5
*
      END