pzheevx.f

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      SUBROUTINE pzheevx( JOBZ, RANGE, UPLO, N, A, IA, JA, DESCA, VL,
     $                    VU, IL, IU, ABSTOL, M, NZ, W, ORFAC, Z, IZ,
     $                    JZ, DESCZ, WORK, LWORK, RWORK, LRWORK, IWORK,
     $                    LIWORK, IFAIL, ICLUSTR, GAP, INFO )
*
*  -- ScaLAPACK routine (version 1.7) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     May 25, 2001
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE, UPLO
      INTEGER            IA, IL, INFO, IU, IZ, JA, JZ, LIWORK, LRWORK,
     $                   LWORK, M, N, NZ
      DOUBLE PRECISION   ABSTOL, ORFAC, VL, VU
*     ..
*     .. Array Arguments ..
      INTEGER            DESCA( * ), DESCZ( * ), ICLUSTR( * ),
     $                   IFAIL( * ), IWORK( * )
      DOUBLE PRECISION   GAP( * ), RWORK( * ), W( * )
      COMPLEX*16         A( * ), WORK( * ), Z( * )
*     ..
*
*  Purpose
*  =======
*
*  PZHEEVX computes selected eigenvalues and, optionally, eigenvectors
*  of a complex hermitian matrix A by calling the recommended sequence
*  of ScaLAPACK routines.  Eigenvalues/vectors can be selected by
*  specifying a range of values or a range of indices for the desired
*  eigenvalues.
*
*  Notes
*  =====
*
*  Each global data object is described by an associated description
*  vector.  This vector stores the information required to establish
*  the mapping between an object element and its corresponding process
*  and memory location.
*
*  Let A be a generic term for any 2D block cyclicly distributed array.
*  Such a global array has an associated description vector DESCA.
*  In the following comments, the character _ should be read as
*  "of the global array".
*
*  NOTATION        STORED IN      EXPLANATION
*  --------------- -------------- --------------------------------------
*  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
*                                 DTYPE_A = 1.
*  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
*                                 the BLACS process grid A is distribu-
*                                 ted over. The context itself is glo-
*                                 bal, but the handle (the integer
*                                 value) may vary.
*  M_A    (global) DESCA( M_ )    The number of rows in the global
*                                 array A.
*  N_A    (global) DESCA( N_ )    The number of columns in the global
*                                 array A.
*  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
*                                 the rows of the array.
*  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
*                                 the columns of the array.
*  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
*                                 row of the array A is distributed.
*  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
*                                 first column of the array A is
*                                 distributed.
*  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
*                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
*
*  Let K be the number of rows or columns of a distributed matrix,
*  and assume that its process grid has dimension p x q.
*  LOCr( K ) denotes the number of elements of K that a process
*  would receive if K were distributed over the p processes of its
*  process column.
*  Similarly, LOCc( K ) denotes the number of elements of K that a
*  process would receive if K were distributed over the q processes of
*  its process row.
*  The values of LOCr() and LOCc() may be determined via a call to the
*  ScaLAPACK tool function, NUMROC:
*          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
*          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
*  An upper bound for these quantities may be computed by:
*          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
*          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
*  PZHEEVX assumes IEEE 754 standard compliant arithmetic.  To port
*  to a system which does not have IEEE 754 arithmetic, modify
*  the appropriate SLmake.inc file to include the compiler switch
*  -DNO_IEEE.  This switch only affects the compilation of pdlaiect.c.
*
*  Arguments
*  =========
*
*     NP = the number of rows local to a given process.
*     NQ = the number of columns local to a given process.
*
*  JOBZ    (global input) CHARACTER*1
*          Specifies whether or not to compute the eigenvectors:
*          = 'N':  Compute eigenvalues only.
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  RANGE   (global input) CHARACTER*1
*          = 'A': all eigenvalues will be found.
*          = 'V': all eigenvalues in the interval [VL,VU] will be found.
*          = 'I': the IL-th through IU-th eigenvalues will be found.
*
*  UPLO    (global input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          Hermitian matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (global input) INTEGER
*          The number of rows and columns of the matrix A.  N >= 0.
*
*  A       (local input/workspace) block cyclic COMPLEX*16 array,
*          global dimension (N, N),
*          local dimension ( LLD_A, LOCc(JA+N-1) )
*
*          On entry, the Hermitian matrix A.  If UPLO = 'U', only the
*          upper triangular part of A is used to define the elements of
*          the Hermitian matrix.  If UPLO = 'L', only the lower
*          triangular part of A is used to define the elements of the
*          Hermitian matrix.
*
*          On exit, the lower triangle (if UPLO='L') or the upper
*          triangle (if UPLO='U') of A, including the diagonal, is
*          destroyed.
*
*  IA      (global input) INTEGER
*          A's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*
*  JA      (global input) INTEGER
*          A's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*
*  DESCA   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix A.
*          If DESCA( CTXT_ ) is incorrect, PZHEEVX cannot guarantee
*          correct error reporting.
*
*  VL      (global input) DOUBLE PRECISION
*          If RANGE='V', the lower bound of the interval to be searched
*          for eigenvalues.  Not referenced if RANGE = 'A' or 'I'.
*
*  VU      (global input) DOUBLE PRECISION
*          If RANGE='V', the upper bound of the interval to be searched
*          for eigenvalues.  Not referenced if RANGE = 'A' or 'I'.
*
*  IL      (global input) INTEGER
*          If RANGE='I', the index (from smallest to largest) of the
*          smallest eigenvalue to be returned.  IL >= 1.
*          Not referenced if RANGE = 'A' or 'V'.
*
*  IU      (global input) INTEGER
*          If RANGE='I', the index (from smallest to largest) of the
*          largest eigenvalue to be returned.  min(IL,N) <= IU <= N.
*          Not referenced if RANGE = 'A' or 'V'.
*
*  ABSTOL  (global input) DOUBLE PRECISION
*          If JOBZ='V', setting ABSTOL to PDLAMCH( CONTEXT, 'U') yields
*          the most orthogonal eigenvectors.
*
*          The absolute error tolerance for the eigenvalues.
*          An approximate eigenvalue is accepted as converged
*          when it is determined to lie in an interval [a,b]
*          of width less than or equal to
*
*                  ABSTOL + EPS *   max( |a|,|b| ) ,
*
*          where EPS is the machine precision.  If ABSTOL is less than
*          or equal to zero, then EPS*norm(T) will be used in its place,
*          where norm(T) is the 1-norm of the tridiagonal matrix
*          obtained by reducing A to tridiagonal form.
*
*          Eigenvalues will be computed most accurately when ABSTOL is
*          set to twice the underflow threshold 2*PDLAMCH('S') not zero.
*          If this routine returns with ((MOD(INFO,2).NE.0) .OR.
*          (MOD(INFO/8,2).NE.0)), indicating that some eigenvalues or
*          eigenvectors did not converge, try setting ABSTOL to
*          2*PDLAMCH('S').
*
*          See "Computing Small Singular Values of Bidiagonal Matrices
*          with Guaranteed High Relative Accuracy," by Demmel and
*          Kahan, LAPACK Working Note #3.
*
*          See "On the correctness of Parallel Bisection in Floating
*          Point" by Demmel, Dhillon and Ren, LAPACK Working Note #70
*
*  M       (global output) INTEGER
*          Total number of eigenvalues found.  0 <= M <= N.
*
*  NZ      (global output) INTEGER
*          Total number of eigenvectors computed.  0 <= NZ <= M.
*          The number of columns of Z that are filled.
*          If JOBZ .NE. 'V', NZ is not referenced.
*          If JOBZ .EQ. 'V', NZ = M unless the user supplies
*          insufficient space and PZHEEVX is not able to detect this
*          before beginning computation.  To get all the eigenvectors
*          requested, the user must supply both sufficient
*          space to hold the eigenvectors in Z (M .LE. DESCZ(N_))
*          and sufficient workspace to compute them.  (See LWORK below.)
*          PZHEEVX is always able to detect insufficient space without
*          computation unless RANGE .EQ. 'V'.
*
*  W       (global output) DOUBLE PRECISION array, dimension (N)
*          On normal exit, the first M entries contain the selected
*          eigenvalues in ascending order.
*
*  ORFAC   (global input) DOUBLE PRECISION
*          Specifies which eigenvectors should be reorthogonalized.
*          Eigenvectors that correspond to eigenvalues which are within
*          tol=ORFAC*norm(A) of each other are to be reorthogonalized.
*          However, if the workspace is insufficient (see LWORK),
*          tol may be decreased until all eigenvectors to be
*          reorthogonalized can be stored in one process.
*          No reorthogonalization will be done if ORFAC equals zero.
*          A default value of 10^-3 is used if ORFAC is negative.
*          ORFAC should be identical on all processes.
*
*  Z       (local output) COMPLEX*16 array,
*          global dimension (N, N),
*          local dimension ( LLD_Z, LOCc(JZ+N-1) )
*          If JOBZ = 'V', then on normal exit the first M columns of Z
*          contain the orthonormal eigenvectors of the matrix
*          corresponding to the selected eigenvalues.  If an eigenvector
*          fails to converge, then that column of Z contains the latest
*          approximation to the eigenvector, and the index of the
*          eigenvector is returned in IFAIL.
*          If JOBZ = 'N', then Z is not referenced.
*
*  IZ      (global input) INTEGER
*          Z's global row index, which points to the beginning of the
*          submatrix which is to be operated on.
*
*  JZ      (global input) INTEGER
*          Z's global column index, which points to the beginning of
*          the submatrix which is to be operated on.
*
*  DESCZ   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix Z.
*          DESCZ( CTXT_ ) must equal DESCA( CTXT_ )
*
*  WORK    (local workspace/output) COMPLEX*16 array,
*          dimension (LWORK)
*          WORK(1) returns workspace adequate workspace to allow
*          optimal performance.
*
*  LWORK   (local input) INTEGER
*          Size of WORK array.  If only eigenvalues are requested:
*            LWORK >= N + MAX( NB * ( NP0 + 1 ), 3 )
*          If eigenvectors are requested:
*            LWORK >= N + ( NP0 + MQ0 + NB ) * NB
*          with NQ0 = NUMROC( NN, NB, 0, 0, NPCOL ).
*
*          For optimal performance, greater workspace is needed, i.e.
*            LWORK >= MAX( LWORK, NHETRD_LWORK )
*          Where LWORK is as defined above, and
*          NHETRD_LWORK = N + 2*( ANB+1 )*( 4*NPS+2 ) +
*            ( NPS + 1 ) * NPS
*
*          ICTXT = DESCA( CTXT_ )
*          ANB = PJLAENV( ICTXT, 3, 'PZHETTRD', 'L', 0, 0, 0, 0 )
*          SQNPC = SQRT( DBLE( NPROW * NPCOL ) )
*          NPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB )
*
*          NUMROC is a ScaLAPACK tool functions;
*          PJLAENV is a ScaLAPACK envionmental inquiry function
*          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
*          the subroutine BLACS_GRIDINFO.
*
*          If LWORK = -1, then LWORK is global input and a workspace
*          query is assumed; the routine only calculates the
*          optimal size for all work arrays. Each of these
*          values is returned in the first entry of the corresponding
*          work array, and no error message is issued by PXERBLA.
*
*  RWORK   (local workspace/output) DOUBLE PRECISION array,
*             dimension max(3,LRWORK)
*          On return, WORK(1) contains the optimal amount of
*          workspace required for efficient execution.
*          if JOBZ='N' RWORK(1) = optimal amount of workspace
*             required to compute eigenvalues efficiently
*          if JOBZ='V' RWORK(1) = optimal amount of workspace
*             required to compute eigenvalues and eigenvectors
*             efficiently with no guarantee on orthogonality.
*             If RANGE='V', it is assumed that all eigenvectors
*             may be required.
*
*  LRWORK   (local input) INTEGER
*          Size of RWORK
*          See below for definitions of variables used to define LRWORK.
*          If no eigenvectors are requested (JOBZ = 'N') then
*             LRWORK >= 5 * NN + 4 * N
*          If eigenvectors are requested (JOBZ = 'V' ) then
*             the amount of workspace required to guarantee that all
*             eigenvectors are computed is:
*             LRWORK >= 4*N + MAX( 5*NN, NP0 * MQ0 ) +
*               ICEIL( NEIG, NPROW*NPCOL)*NN
*
*             The computed eigenvectors may not be orthogonal if the
*             minimal workspace is supplied and ORFAC is too small.
*             If you want to guarantee orthogonality (at the cost
*             of potentially poor performance) you should add
*             the following to LRWORK:
*                (CLUSTERSIZE-1)*N
*             where CLUSTERSIZE is the number of eigenvalues in the
*             largest cluster, where a cluster is defined as a set of
*             close eigenvalues: { W(K),...,W(K+CLUSTERSIZE-1) |
*                                  W(J+1) <= W(J) + ORFAC*2*norm(A) }
*          Variable definitions:
*             NEIG = number of eigenvectors requested
*             NB = DESCA( MB_ ) = DESCA( NB_ ) =
*                  DESCZ( MB_ ) = DESCZ( NB_ )
*             NN = MAX( N, NB, 2 )
*             DESCA( RSRC_ ) = DESCA( NB_ ) = DESCZ( RSRC_ ) =
*                              DESCZ( CSRC_ ) = 0
*             NP0 = NUMROC( NN, NB, 0, 0, NPROW )
*             MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL )
*             ICEIL( X, Y ) is a ScaLAPACK function returning
*             ceiling(X/Y)
*
*          When LRWORK is too small:
*             If LRWORK is too small to guarantee orthogonality,
*             PZHEEVX attempts to maintain orthogonality in
*             the clusters with the smallest
*             spacing between the eigenvalues.
*             If LRWORK is too small to compute all the eigenvectors
*             requested, no computation is performed and INFO=-25
*             is returned.  Note that when RANGE='V', PZHEEVX does
*             not know how many eigenvectors are requested until
*             the eigenvalues are computed.  Therefore, when RANGE='V'
*             and as long as LRWORK is large enough to allow PZHEEVX to
*             compute the eigenvalues, PZHEEVX will compute the
*             eigenvalues and as many eigenvectors as it can.
*
*          Relationship between workspace, orthogonality & performance:
*             If CLUSTERSIZE >= N/SQRT(NPROW*NPCOL), then providing
*             enough space to compute all the eigenvectors
*             orthogonally will cause serious degradation in
*             performance. In the limit (i.e. CLUSTERSIZE = N-1)
*             PZSTEIN will perform no better than ZSTEIN on 1
*             processor.
*             For CLUSTERSIZE = N/SQRT(NPROW*NPCOL) reorthogonalizing
*             all eigenvectors will increase the total execution time
*             by a factor of 2 or more.
*             For CLUSTERSIZE > N/SQRT(NPROW*NPCOL) execution time will
*             grow as the square of the cluster size, all other factors
*             remaining equal and assuming enough workspace.  Less
*             workspace means less reorthogonalization but faster
*             execution.
*
*          If LRWORK = -1, then LRWORK is global input and a workspace
*          query is assumed; the routine only calculates the size
*          required for optimal performance for all work arrays. Each of
*          these values is returned in the first entry of the
*          corresponding work arrays, and no error message is issued by
*          PXERBLA.
*
*  IWORK   (local workspace) INTEGER array
*          On return, IWORK(1) contains the amount of integer workspace
*          required.
*
*  LIWORK  (local input) INTEGER
*          size of IWORK
*          LIWORK >= 6 * NNP
*          Where:
*            NNP = MAX( N, NPROW*NPCOL + 1, 4 )
*          If LIWORK = -1, then LIWORK is global input and a workspace
*          query is assumed; the routine only calculates the minimum
*          and optimal size for all work arrays. Each of these
*          values is returned in the first entry of the corresponding
*          work array, and no error message is issued by PXERBLA.
*
*  IFAIL   (global output) INTEGER array, dimension (N)
*          If JOBZ = 'V', then on normal exit, the first M elements of
*          IFAIL are zero.  If (MOD(INFO,2).NE.0) on exit, then
*          IFAIL contains the
*          indices of the eigenvectors that failed to converge.
*          If JOBZ = 'N', then IFAIL is not referenced.
*
*  ICLUSTR (global output) integer array, dimension (2*NPROW*NPCOL)
*          This array contains indices of eigenvectors corresponding to
*          a cluster of eigenvalues that could not be reorthogonalized
*          due to insufficient workspace (see LWORK, ORFAC and INFO).
*          Eigenvectors corresponding to clusters of eigenvalues indexed
*          ICLUSTR(2*I-1) to ICLUSTR(2*I), could not be
*          reorthogonalized due to lack of workspace. Hence the
*          eigenvectors corresponding to these clusters may not be
*          orthogonal.  ICLUSTR() is a zero terminated array.
*          (ICLUSTR(2*K).NE.0 .AND. ICLUSTR(2*K+1).EQ.0) if and only if
*          K is the number of clusters
*          ICLUSTR is not referenced if JOBZ = 'N'
*
*  GAP     (global output) DOUBLE PRECISION array,
*             dimension (NPROW*NPCOL)
*          This array contains the gap between eigenvalues whose
*          eigenvectors could not be reorthogonalized. The output
*          values in this array correspond to the clusters indicated
*          by the array ICLUSTR. As a result, the dot product between
*          eigenvectors correspoding to the I^th cluster may be as high
*          as ( C * n ) / GAP(I) where C is a small constant.
*
*  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:  if (MOD(INFO,2).NE.0), then one or more eigenvectors
*                  failed to converge.  Their indices are stored
*                  in IFAIL.  Ensure ABSTOL=2.0*PDLAMCH( 'U' )
*                  Send e-mail to scalapack@cs.utk.edu
*                if (MOD(INFO/2,2).NE.0),then eigenvectors corresponding
*                  to one or more clusters of eigenvalues could not be
*                  reorthogonalized because of insufficient workspace.
*                  The indices of the clusters are stored in the array
*                  ICLUSTR.
*                if (MOD(INFO/4,2).NE.0), then space limit prevented
*                  PZHEEVX from computing all of the eigenvectors
*                  between VL and VU.  The number of eigenvectors
*                  computed is returned in NZ.
*                if (MOD(INFO/8,2).NE.0), then PZSTEBZ failed to compute
*                  eigenvalues.  Ensure ABSTOL=2.0*PDLAMCH( 'U' )
*                  Send e-mail to scalapack@cs.utk.edu
*
*  Alignment requirements
*  ======================
*
*  The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
*  must verify some alignment properties, namely the following
*  expressions should be true:
*
*  ( MB_A.EQ.NB_A.EQ.MB_Z .AND. IROFFA.EQ.IROFFZ .AND. IROFFA.EQ.0 .AND.
*    IAROW.EQ.IZROW )
*  where
*  IROFFA = MOD( IA-1, MB_A ) and ICOFFA = MOD( JA-1, NB_A ).
*
*  =====================================================================
*
*  Differences between PZHEEVX and ZHEEVX
*  ======================================
*
*  A, LDA -> A, IA, JA, DESCA
*  Z, LDZ -> Z, IZ, JZ, DESCZ
*  WORKSPACE needs are larger for PZHEEVX.
*  LIWORK parameter added
*
*  ORFAC, ICLUSTER() and GAP() parameters added
*  meaning of INFO is changed
*
*  Functional differences:
*  PZHEEVX does not promise orthogonality for eigenvectors associated
*  with tighly clustered eigenvalues.
*  PZHEEVX does not reorthogonalize eigenvectors
*  that are on different processes. The extent of reorthogonalization
*  is controlled by the input parameter LWORK.
*
*  Version 1.4 limitations:
*     DESCA(MB_) = DESCA(NB_)
*     DESCA(M_) = DESCZ(M_)
*     DESCA(N_) = DESCZ(N_)
*     DESCA(MB_) = DESCZ(MB_)
*     DESCA(NB_) = DESCZ(NB_)
*     DESCA(RSRC_) = DESCZ(RSRC_)
*
*     .. 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 )
      DOUBLE PRECISION   ZERO, ONE, TEN, FIVE
      PARAMETER          ( ZERO = 0.0d+0, one = 1.0d+0, ten = 10.0d+0,
     $                   five = 5.0d+0 )
      INTEGER            IERREIN, IERRCLS, IERRSPC, IERREBZ
      parameter( ierrein = 1, ierrcls = 2, ierrspc = 4,
     $                   ierrebz = 8 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, QUICKRETURN,
     $                   VALEIG, WANTZ
      CHARACTER          ORDER
      INTEGER            ANB, CSRC_A, I, IAROW, ICOFFA, ICTXT, IINFO,
     $                   INDD, INDD2, INDE, INDE2, INDIBL, INDISP,
     $                   indrwork, indtau, indwork, iroffa, iroffz,
     $                   iscale, isizestebz, isizestein, izrow,
     $                   lallwork, liwmin, llrwork, llwork, lrwmin,
     $                   lrwopt, lwmin, lwopt, maxeigs, mb_a, mq0,
     $                   mycol, myrow, nb, nb_a, neig, nhetrd_lwopt, nn,
     $                   nnp, np0, npcol, nprocs, nprow, nps, nq0,
     $                   nsplit, nzz, offset, rsrc_a, rsrc_z, sizeheevx,
     $                   sizestein, sqnpc
      DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
     $                   SIGMA, SMLNUM, VLL, VUU
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM1( 4 ), IDUM2( 4 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ICEIL, INDXG2P, NUMROC, PJLAENV
      DOUBLE PRECISION   PDLAMCH, PZLANHE
      EXTERNAL           lsame, iceil, indxg2p, numroc, pjlaenv,
     $                   pdlamch, pzlanhe
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, chk1mat, dgebr2d, dgebs2d,
     $                   dlasrt, dscal, igamn2d, pchk1mat, pchk2mat,
     $                   pdlared1d, pdstebz, pxerbla, pzelget, pzhentrd,
     $                   pzlascl, pzstein, pzunmtr
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dcmplx, ichar, int, max, min, mod,
     $                   sqrt
*     ..
*     .. 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
*
      quickreturn = ( n.EQ.0 )
*
*     Test the input arguments.
*
      ictxt = desca( ctxt_ )
      CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
      info = 0
*
      wantz = lsame( jobz, 'V' )
      IF( nprow.EQ.-1 ) THEN
         info = -( 800+ctxt_ )
      ELSE IF( wantz ) THEN
         IF( ictxt.NE.descz( ctxt_ ) ) THEN
            info = -( 2100+ctxt_ )
         END IF
      END IF
      IF( info.EQ.0 ) THEN
         CALL chk1mat( n, 4, n, 4, ia, ja, desca, 8, info )
         IF( wantz )
     $      CALL chk1mat( n, 4, n, 4, iz, jz, descz, 21, info )
*
         IF( info.EQ.0 ) THEN
*
*     Get machine constants.
*
            safmin = pdlamch( ictxt, 'Safe minimum' )
            eps = pdlamch( ictxt, 'Precision' )
            smlnum = safmin / eps
            bignum = one / smlnum
            rmin = sqrt( smlnum )
            rmax = min( sqrt( bignum ), one / sqrt( sqrt( safmin ) ) )
*
            nprocs = nprow*npcol
            lower = lsame( uplo, 'L' )
            alleig = lsame( range, 'A' )
            valeig = lsame( range, 'V' )
            indeig = lsame( range, 'I' )
*
*     Set up pointers into the WORK array
*
            indtau = 1
            indwork = indtau + n
            llwork = lwork - indwork + 1
*
*     Set up pointers into the RWORK array
*
            inde = 1
            indd = inde + n
            indd2 = indd + n
            inde2 = indd2 + n
            indrwork = inde2 + n
            llrwork = lrwork - indrwork + 1
*
*     Set up pointers into the IWORK array
*
            isizestein = 3*n + nprocs + 1
            isizestebz = max( 4*n, 14, nprocs )
            indibl = ( max( isizestein, isizestebz ) ) + 1
            indisp = indibl + n
*
*     Compute the total amount of space needed
*
            lquery = .false.
            IF( lwork.EQ.-1 .OR. liwork.EQ.-1 .OR. lrwork.EQ.-1 )
     $         lquery = .true.
*
            nnp = max( n, nprocs+1, 4 )
            liwmin = 6*nnp
*
            nprocs = nprow*npcol
            nb_a = desca( nb_ )
            mb_a = desca( mb_ )
            nb = nb_a
            nn = max( n, nb, 2 )
*
            rsrc_a = desca( rsrc_ )
            csrc_a = desca( csrc_ )
            iroffa = mod( ia-1, mb_a )
            icoffa = mod( ja-1, nb_a )
            iarow = indxg2p( 1, nb_a, myrow, rsrc_a, nprow )
            np0 = numroc( n+iroffa, nb, 0, 0, nprow )
            mq0 = numroc( n+icoffa, nb, 0, 0, npcol )
            IF( wantz ) THEN
               rsrc_z = descz( rsrc_ )
               iroffz = mod( iz-1, mb_a )
               izrow = indxg2p( 1, nb_a, myrow, rsrc_z, nprow )
            ELSE
               iroffz = 0
               izrow = 0
            END IF
*
            IF( ( .NOT.wantz ) .OR. ( valeig .AND. ( .NOT.lquery ) ) )
     $           THEN
               lwmin = n + max( nb*( np0+1 ), 3 )
               lwopt = lwmin
               lrwmin = 5*nn + 4*n
               IF( wantz ) THEN
                  mq0 = numroc( max( n, nb, 2 ), nb, 0, 0, npcol )
                  lrwopt = 4*n + max( 5*nn, np0*mq0 ) +
     $                     iceil( n, nprow*npcol )*nn
               ELSE
                  lrwopt = lrwmin
               END IF
               neig = 0
            ELSE
               IF( alleig .OR. valeig ) THEN
                  neig = n
               ELSE IF( indeig ) THEN
                  neig = iu - il + 1
               END IF
               mq0 = numroc( max( neig, nb, 2 ), nb, 0, 0, npcol )
               nq0 = numroc( nn, nb, 0, 0, npcol )
               lwmin = n + ( np0+nq0+nb )*nb
               lrwmin = 4*n + max( 5*nn, np0*mq0 ) +
     $                  iceil( neig, nprow*npcol )*nn
               lrwopt = lrwmin
               lwopt = lwmin
*
            END IF
*
*           Compute how much workspace is needed to use the
*           new TRD code
*
            anb = pjlaenv( ictxt, 3, 'PZHETTRD', 'L', 0, 0, 0, 0 )
            sqnpc = int( sqrt( dble( nprow*npcol ) ) )
            nps = max( numroc( n, 1, 0, 0, sqnpc ), 2*anb )
            nhetrd_lwopt = 2*( anb+1 )*( 4*nps+2 ) + ( nps+2 )*nps
            lwopt = max( lwopt, n+nhetrd_lwopt )
*
         END IF
         IF( info.EQ.0 ) THEN
            IF( myrow.EQ.0 .AND. mycol.EQ.0 ) THEN
               rwork( 1 ) = abstol
               IF( valeig ) THEN
                  rwork( 2 ) = vl
                  rwork( 3 ) = vu
               ELSE
                  rwork( 2 ) = zero
                  rwork( 3 ) = zero
               END IF
               CALL dgebs2d( ictxt, 'ALL', ' ', 3, 1, rwork, 3 )
            ELSE
               CALL dgebr2d( ictxt, 'ALL', ' ', 3, 1, rwork, 3, 0, 0 )
            END IF
            IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
               info = -1
            ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
               info = -2
            ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
               info = -3
            ELSE IF( valeig .AND. n.GT.0 .AND. vu.LE.vl ) THEN
               info = -10
            ELSE IF( indeig .AND. ( il.LT.1 .OR. il.GT.max( 1, n ) ) )
     $                THEN
               info = -11
            ELSE IF( indeig .AND. ( iu.LT.min( n, il ) .OR. iu.GT.n ) )
     $                THEN
               info = -12
            ELSE IF( lwork.LT.lwmin .AND. lwork.NE.-1 ) THEN
               info = -23
            ELSE IF( lrwork.LT.lrwmin .AND. lrwork.NE.-1 ) THEN
               info = -25
            ELSE IF( liwork.LT.liwmin .AND. liwork.NE.-1 ) THEN
               info = -27
            ELSE IF( valeig .AND. ( abs( rwork( 2 )-vl ).GT.five*eps*
     $               abs( vl ) ) ) THEN
               info = -9
            ELSE IF( valeig .AND. ( abs( rwork( 3 )-vu ).GT.five*eps*
     $               abs( vu ) ) ) THEN
               info = -10
            ELSE IF( abs( rwork( 1 )-abstol ).GT.five*eps*
     $               abs( abstol ) ) THEN
               info = -13
            ELSE IF( iroffa.NE.0 ) THEN
               info = -6
            ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
               info = -( 800+nb_ )
            END IF
            IF( wantz ) THEN
               IF( iroffa.NE.iroffz ) THEN
                  info = -19
               ELSE IF( iarow.NE.izrow ) THEN
                  info = -19
               ELSE IF( desca( m_ ).NE.descz( m_ ) ) THEN
                  info = -( 2100+m_ )
               ELSE IF( desca( n_ ).NE.descz( n_ ) ) THEN
                  info = -( 2100+n_ )
               ELSE IF( desca( mb_ ).NE.descz( mb_ ) ) THEN
                  info = -( 2100+mb_ )
               ELSE IF( desca( nb_ ).NE.descz( nb_ ) ) THEN
                  info = -( 2100+nb_ )
               ELSE IF( desca( rsrc_ ).NE.descz( rsrc_ ) ) THEN
                  info = -( 2100+rsrc_ )
               ELSE IF( desca( csrc_ ).NE.descz( csrc_ ) ) THEN
                  info = -( 2100+csrc_ )
               ELSE IF( ictxt.NE.descz( ctxt_ ) ) THEN
                  info = -( 2100+ctxt_ )
               END IF
            END IF
         END IF
         IF( wantz ) THEN
            idum1( 1 ) = ichar( 'V' )
         ELSE
            idum1( 1 ) = ichar( 'N' )
         END IF
         idum2( 1 ) = 1
         IF( lower ) THEN
            idum1( 2 ) = ichar( 'L' )
         ELSE
            idum1( 2 ) = ichar( 'U' )
         END IF
         idum2( 2 ) = 2
         IF( alleig ) THEN
            idum1( 3 ) = ichar( 'A' )
         ELSE IF( indeig ) THEN
            idum1( 3 ) = ichar( 'I' )
         ELSE
            idum1( 3 ) = ichar( 'V' )
         END IF
         idum2( 3 ) = 3
         IF( lquery ) THEN
            idum1( 4 ) = -1
         ELSE
            idum1( 4 ) = 1
         END IF
         idum2( 4 ) = 4
         IF( wantz ) THEN
            CALL pchk2mat( n, 4, n, 4, ia, ja, desca, 8, n, 4, n, 4, iz,
     $                     jz, descz, 21, 4, idum1, idum2, info )
         ELSE
            CALL pchk1mat( n, 4, n, 4, ia, ja, desca, 8, 4, idum1,
     $                     idum2, info )
         END IF
         work( 1 ) = dcmplx( lwopt )
         rwork( 1 ) = dble( lrwopt )
         iwork( 1 ) = liwmin
      END IF
*
      IF( info.NE.0 ) THEN
         CALL pxerbla( ictxt, 'PZHEEVX', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( quickreturn ) THEN
         IF( wantz ) THEN
            nz = 0
            iclustr( 1 ) = 0
         END IF
         m = 0
         work( 1 ) = dcmplx( lwopt )
         rwork( 1 ) = dble( lrwmin )
         iwork( 1 ) = liwmin
         RETURN
      END IF
*
*     Scale matrix to allowable range, if necessary.
*
      abstll = abstol
      iscale = 0
      IF( valeig ) THEN
         vll = vl
         vuu = vu
      ELSE
         vll = zero
         vuu = zero
      END IF
*
      anrm = pzlanhe( 'M', uplo, n, a, ia, ja, desca,
     $       rwork( indrwork ) )
*
      IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
         iscale = 1
         sigma = rmin / anrm
         anrm = anrm*sigma
      ELSE IF( anrm.GT.rmax ) THEN
         iscale = 1
         sigma = rmax / anrm
         anrm = anrm*sigma
      END IF
*
      IF( iscale.EQ.1 ) THEN
         CALL pzlascl( uplo, one, sigma, n, n, a, ia, ja, desca, iinfo )
         IF( abstol.GT.0 )
     $      abstll = abstol*sigma
         IF( valeig ) THEN
            vll = vl*sigma
            vuu = vu*sigma
            IF( vuu.EQ.vll ) THEN
               vuu = vuu + 2*max( abs( vuu )*eps, safmin )
            END IF
         END IF
      END IF
*
*     Call PZHENTRD to reduce Hermitian matrix to tridiagonal form.
*
      lallwork = llrwork
*
      CALL pzhentrd( uplo, n, a, ia, ja, desca, rwork( indd ),
     $               rwork( inde ), work( indtau ), work( indwork ),
     $               llwork, rwork( indrwork ), llrwork, iinfo )
*
*
*     Copy the values of D, E to all processes
*
*     Here PxLARED1D is used to redistribute the tridiagonal matrix.
*     PxLARED1D, however, doesn't yet work with arbritary matrix
*     distributions so we have PxELGET as a backup.
*
      offset = 0
      IF( ia.EQ.1 .AND. ja.EQ.1 .AND. rsrc_a.EQ.0 .AND. csrc_a.EQ.0 )
     $     THEN
         CALL pdlared1d( n, ia, ja, desca, rwork( indd ),
     $                   rwork( indd2 ), rwork( indrwork ), llrwork )
*
         CALL pdlared1d( n, ia, ja, desca, rwork( inde ),
     $                   rwork( inde2 ), rwork( indrwork ), llrwork )
         IF( .NOT.lower )
     $      offset = 1
      ELSE
         DO 10 i = 1, n
            CALL pzelget( 'A', ' ', work( indd2+i-1 ), a, i+ia-1,
     $                    i+ja-1, desca )
            rwork( indd2+i-1 ) = dble( work( indd2+i-1 ) )
   10    CONTINUE
         IF( lsame( uplo, 'U' ) ) THEN
            DO 20 i = 1, n - 1
               CALL pzelget( 'A', ' ', work( inde2+i-1 ), a, i+ia-1,
     $                       i+ja, desca )
               rwork( inde2+i-1 ) = dble( work( inde2+i-1 ) )
   20       CONTINUE
         ELSE
            DO 30 i = 1, n - 1
               CALL pzelget( 'A', ' ', work( inde2+i-1 ), a, i+ia,
     $                       i+ja-1, desca )
               rwork( inde2+i-1 ) = dble( work( inde2+i-1 ) )
   30       CONTINUE
         END IF
      END IF
*
*     Call PDSTEBZ and, if eigenvectors are desired, PZSTEIN.
*
      IF( wantz ) THEN
         order = 'B'
      ELSE
         order = 'E'
      END IF
*
      CALL pdstebz( ictxt, range, order, n, vll, vuu, il, iu, abstll,
     $              rwork( indd2 ), rwork( inde2+offset ), m, nsplit, w,
     $              iwork( indibl ), iwork( indisp ), rwork( indrwork ),
     $              llrwork, iwork( 1 ), isizestebz, iinfo )
*
*
*     IF PDSTEBZ fails, the error propogates to INFO, but
*     we do not propogate the eigenvalue(s) which failed because:
*     1)  This should never happen if the user specifies
*         ABSTOL = 2 * PDLAMCH( 'U' )
*     2)  PDSTEIN will confirm/deny whether the eigenvalues are
*         close enough.
*
      IF( iinfo.NE.0 ) THEN
         info = info + ierrebz
         DO 40 i = 1, m
            iwork( indibl+i-1 ) = abs( iwork( indibl+i-1 ) )
   40    CONTINUE
      END IF
      IF( wantz ) THEN
*
         IF( valeig ) THEN
*
*           Compute the maximum number of eigenvalues that we can
*           compute in the
*           workspace that we have, and that we can store in Z.
*
*           Loop through the possibilities looking for the largest
*           NZ that we can feed to PZSTEIN and PZUNMTR
*
*           Since all processes must end up with the same value
*           of NZ, we first compute the minimum of LALLWORK
*
            CALL igamn2d( ictxt, 'A', ' ', 1, 1, lallwork, 1, 1, 1, -1,
     $                    -1, -1 )
*
            maxeigs = descz( n_ )
*
            DO 50 nz = min( maxeigs, m ), 0, -1
               mq0 = numroc( nz, nb, 0, 0, npcol )
               sizestein = iceil( nz, nprocs )*n + max( 5*n, np0*mq0 )
               sizeheevx = sizestein
               IF( sizeheevx.LE.lallwork )
     $            GO TO 60
   50       CONTINUE
   60       CONTINUE
         ELSE
            nz = m
         END IF
         nz = max( nz, 0 )
         IF( nz.NE.m ) THEN
            info = info + ierrspc
*
            DO 70 i = 1, m
               ifail( i ) = 0
   70       CONTINUE
*
*     The following code handles a rare special case
*       - NZ .NE. M means that we don't have enough room to store
*         all the vectors.
*       - NSPLIT .GT. 1 means that the matrix split
*     In this case, we cannot simply take the first NZ eigenvalues
*     because PDSTEBZ sorts the eigenvalues by block when
*     a split occurs.  So, we have to make another call to
*     PDSTEBZ with a new upper limit - VUU.
*
            IF( nsplit.GT.1 ) THEN
               CALL dlasrt( 'I', m, w, iinfo )
               nzz = 0
               IF( nz.GT.0 ) THEN
*
                  vuu = w( nz ) - ten*( eps*anrm+safmin )
                  IF( vll.GE.vuu ) THEN
                     nzz = 0
                  ELSE
                     CALL pdstebz( ictxt, range, order, n, vll, vuu, il,
     $                             iu, abstll, rwork( indd2 ),
     $                             rwork( inde2+offset ), nzz, nsplit,
     $                             w, iwork( indibl ), iwork( indisp ),
     $                             rwork( indrwork ), llrwork,
     $                             iwork( 1 ), isizestebz, iinfo )
                  END IF
*
                  IF( mod( info / ierrebz, 1 ).EQ.0 ) THEN
                     IF( nzz.GT.nz .OR. iinfo.NE.0 ) THEN
                        info = info + ierrebz
                     END IF
                  END IF
               END IF
               nz = min( nz, nzz )
*
            END IF
         END IF
         CALL pzstein( n, rwork( indd2 ), rwork( inde2+offset ), nz, w,
     $                 iwork( indibl ), iwork( indisp ), orfac, z, iz,
     $                 jz, descz, rwork( indrwork ), lallwork,
     $                 iwork( 1 ), isizestein, ifail, iclustr, gap,
     $                 iinfo )
*
         IF( iinfo.GE.nz+1 )
     $      info = info + ierrcls
         IF( mod( iinfo, nz+1 ).NE.0 )
     $      info = info + ierrein
*
*     Z = Q * Z
*
*
         IF( nz.GT.0 ) THEN
            CALL pzunmtr( 'L', uplo, 'N', n, nz, a, ia, ja, desca,
     $                    work( indtau ), z, iz, jz, descz,
     $                    work( indwork ), llwork, iinfo )
         END IF
*
      END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
      IF( iscale.EQ.1 ) THEN
         CALL dscal( m, one / sigma, w, 1 )
      END IF
*
      work( 1 ) = dcmplx( lwopt )
      rwork( 1 ) = dble( lrwopt )
      iwork( 1 ) = liwmin
*
      RETURN
*
*     End of PZHEEVX
*
      END