      SUBROUTINE PDLAED0( N, D, E, Q, IQ, JQ, DESCQ, WORK, IWORK, INFO )
*
*  -- ScaLAPACK auxiliary routine (version 1.7) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     December 31, 1998
*
*     .. Scalar Arguments ..
      INTEGER            INFO, IQ, JQ, N
*     ..
*     .. Array Arguments ..
      INTEGER            DESCQ( * ), IWORK( * )
      DOUBLE PRECISION   D( * ), E( * ), Q( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  PDLAED0 computes all eigenvalues and corresponding eigenvectors of a
*  symmetric tridiagonal matrix using the divide and conquer method.
*
*
*  Arguments
*  =========
*
*  N       (global input) INTEGER
*          The order of the tridiagonal matrix T.  N >= 0.
*
*  D       (global input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the diagonal elements of the tridiagonal matrix.
*          On exit, if INFO = 0, the eigenvalues in descending order.
*
*  E       (global input/output) DOUBLE PRECISION array, dimension (N-1)
*          On entry, the subdiagonal elements of the tridiagonal matrix.
*          On exit, E has been destroyed.
*
*  Q       (local output) DOUBLE PRECISION array,
*          global dimension (N, N),
*          local dimension ( LLD_Q, LOCc(JQ+N-1))
*          Q  contains the orthonormal eigenvectors of the symmetric
*          tridiagonal matrix.
*          On output, Q is distributed across the P processes in block
*          cyclic format.
*
*  IQ      (global input) INTEGER
*          Q's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*
*  JQ      (global input) INTEGER
*          Q's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*
*  DESCQ   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix Z.
*
*
*  WORK    (local workspace ) DOUBLE PRECISION array, dimension (LWORK)
*          LWORK = 6*N + 2*NP*NQ, with
*          NP = NUMROC( N, MB_Q, MYROW, IQROW, NPROW )
*          NQ = NUMROC( N, NB_Q, MYCOL, IQCOL, NPCOL )
*          IQROW = INDXG2P( IQ, NB_Q, MYROW, RSRC_Q, NPROW )
*          IQCOL = INDXG2P( JQ, MB_Q, MYCOL, CSRC_Q, NPCOL )
*
*  IWORK   (local workspace/output) INTEGER array, dimension (LIWORK)
*          LIWORK = 2 + 7*N + 8*NPCOL
*
*  INFO    (global output) INTEGER
*          = 0:  successful exit
*          < 0:  If the i-th argument is an array and the j-entry had
*                an illegal value, then INFO = -(i*100+j), if the i-th
*                argument is a scalar and had an illegal value, then
*                INFO = -i.
*          > 0:  The algorithm failed to compute the INFO/(N+1) th
*                eigenvalue while working on the submatrix lying in
*                global rows and columns mod(INFO,N+1).
*
*  =====================================================================
*
*     .. Parameters ..
*
      INTEGER            BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
     $                   MB_, NB_, RSRC_, CSRC_, LLD_
      PARAMETER          ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
     $                   CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
     $                   RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, ID, IDCOL, IDROW, IID, IINFO, IIQ, IM1, IM2,
     $                   IPQ, IQCOL, IQROW, J, JJD, JJQ, LDQ, MATSIZ,
     $                   MYCOL, MYROW, N1, NB, NBL, NBL1, NPCOL, NPROW,
     $                   SUBPBS, TSUBPBS
*     ..
*     .. External Subroutines ..
      EXTERNAL           BLACS_GRIDINFO, DGEBR2D, DGEBS2D, DGERV2D,
     $                   DGESD2D, DSTEQR, INFOG2L, PDLAED1, PXERBLA
*     ..
*     .. External Functions ..
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MIN
*     ..
*     .. Executable Statements ..
*
*       This is just to keep ftnchek and toolpack/1 happy
      IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
     $    RSRC_.LT.0 )RETURN
*
*     Test the input parameters.
*
      CALL BLACS_GRIDINFO( DESCQ( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
      INFO = 0
      IF( DESCQ( NB_ ).GT.N .OR. N.LT.2 )
     $   INFO = -1
      IF( INFO.NE.0 ) THEN
         CALL PXERBLA( DESCQ( CTXT_ ), 'PDLAED0', -INFO )
         RETURN
      END IF
*
      NB = DESCQ( NB_ )
      LDQ = DESCQ( LLD_ )
      CALL INFOG2L( IQ, JQ, DESCQ, NPROW, NPCOL, MYROW, MYCOL, IIQ, JJQ,
     $              IQROW, IQCOL )
*
*     Determine the size and placement of the submatrices, and save in
*     the leading elements of IWORK.
*
      TSUBPBS = ( N-1 ) / NB + 1
      IWORK( 1 ) = TSUBPBS
      SUBPBS = 1
   10 CONTINUE
      IF( IWORK( SUBPBS ).GT.1 ) THEN
         DO 20 J = SUBPBS, 1, -1
            IWORK( 2*J ) = ( IWORK( J )+1 ) / 2
            IWORK( 2*J-1 ) = IWORK( J ) / 2
   20    CONTINUE
         SUBPBS = 2*SUBPBS
         GO TO 10
      END IF
      DO 30 J = 2, SUBPBS
         IWORK( J ) = IWORK( J ) + IWORK( J-1 )
   30 CONTINUE
*
*     Divide the matrix into TSUBPBS submatrices of size at most NB
*     using rank-1 modifications (cuts).
*
      DO 40 I = NB + 1, N, NB
         IM1 = I - 1
         D( IM1 ) = D( IM1 ) - ABS( E( IM1 ) )
         D( I ) = D( I ) - ABS( E( IM1 ) )
   40 CONTINUE
*
*     Solve each submatrix eigenproblem at the bottom of the divide and
*     conquer tree. D is the same on each process.
*
      DO 50 ID = 1, N, NB
         CALL INFOG2L( IQ-1+ID, JQ-1+ID, DESCQ, NPROW, NPCOL, MYROW,
     $                 MYCOL, IID, JJD, IDROW, IDCOL )
         MATSIZ = MIN( NB, N-ID+1 )
         IF( MYROW.EQ.IDROW .AND. MYCOL.EQ.IDCOL ) THEN
            IPQ = IID + ( JJD-1 )*LDQ
            CALL DSTEQR( 'I', MATSIZ, D( ID ), E( ID ), Q( IPQ ), LDQ,
     $                   WORK, INFO )
            IF( INFO.NE.0 ) THEN
               CALL PXERBLA( DESCQ( CTXT_ ), 'DSTEQR', -INFO )
               RETURN
            END IF
            IF( MYROW.NE.IQROW .OR. MYCOL.NE.IQCOL ) THEN
               CALL DGESD2D( DESCQ( CTXT_ ), MATSIZ, 1, D( ID ), MATSIZ,
     $                       IQROW, IQCOL )
            END IF
         ELSE IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) THEN
            CALL DGERV2D( DESCQ( CTXT_ ), MATSIZ, 1, D( ID ), MATSIZ,
     $                    IDROW, IDCOL )
         END IF
   50 CONTINUE
*
      IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) THEN
         CALL DGEBS2D( DESCQ( CTXT_ ), 'A', ' ', N, 1, D, N )
      ELSE
         CALL DGEBR2D( DESCQ( CTXT_ ), 'A', ' ', N, 1, D, N, IQROW,
     $                 IQCOL )
      END IF
*
*     Successively merge eigensystems of adjacent submatrices
*     into eigensystem for the corresponding larger matrix.
*
*     while ( SUBPBS > 1 )
*
   60 CONTINUE
      IF( SUBPBS.GT.1 ) THEN
         IM2 = SUBPBS - 2
         DO 80 I = 0, IM2, 2
            IF( I.EQ.0 ) THEN
               NBL = IWORK( 2 )
               NBL1 = IWORK( 1 )
               IF( NBL1.EQ.0 )
     $            GO TO 70
               ID = 1
               MATSIZ = MIN( N, NBL*NB )
               N1 = NBL1*NB
            ELSE
               NBL = IWORK( I+2 ) - IWORK( I )
               NBL1 = NBL / 2
               IF( NBL1.EQ.0 )
     $            GO TO 70
               ID = IWORK( I )*NB + 1
               MATSIZ = MIN( NB*NBL, N-ID+1 )
               N1 = NBL1*NB
            END IF
*
*     Merge lower order eigensystems (of size N1 and MATSIZ - N1)
*     into an eigensystem of size MATSIZ.
*
            CALL PDLAED1( MATSIZ, N1, D( ID ), ID, Q, IQ, JQ, DESCQ,
     $                    E( ID+N1-1 ), WORK, IWORK( SUBPBS+1 ), IINFO )
            IF( IINFO.NE.0 ) THEN
               INFO = IINFO*( N+1 ) + ID
            END IF
*
   70       CONTINUE
            IWORK( I / 2+1 ) = IWORK( I+2 )
   80    CONTINUE
         SUBPBS = SUBPBS / 2
*
         GO TO 60
      END IF
*
*     end while
*
   90 CONTINUE
      RETURN
*
*     End of PDLAED0
*
      END
