pchegvx.f

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      SUBROUTINE pchegvx( IBTYPE, JOBZ, RANGE, UPLO, N, A, IA, JA,
     $                    DESCA, B, IB, JB, DESCB, 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.
*     October 15, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE, UPLO
      INTEGER            IA, IB, IBTYPE, IL, INFO, IU, IZ, JA, JB, JZ,
     $                   LIWORK, LRWORK, LWORK, M, N, NZ
      REAL               ABSTOL, ORFAC, VL, VU
*     ..
*     .. Array Arguments ..
*
      INTEGER            DESCA( * ), DESCB( * ), DESCZ( * ),
     $                   ICLUSTR( * ), IFAIL( * ), IWORK( * )
      REAL               GAP( * ), RWORK( * ), W( * )
      COMPLEX            A( * ), B( * ), WORK( * ), Z( * )
*     ..
*
*  Purpose
*
*  =======
*
*  PCHEGVX computes all the eigenvalues, and optionally,
*  the eigenvectors
*  of a complex generalized Hermitian-definite eigenproblem, of the form
*  sub( A )*x=(lambda)*sub( B )*x,  sub( A )*sub( B )x=(lambda)*x,  or
*  sub( B )*sub( A )*x=(lambda)*x.
*  Here sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ) is assumed to be
*  Hermitian, and sub( B ) denoting B( IB:IB+N-1, JB:JB+N-1 ) is assumed
*  to be Hermitian positive definite.
*
*  Notes
*  =====
*
*
*  Each global data object is described by an associated description
*  vector.  This vector stores the information required to establish
*  the mapping between an object element and its corresponding process
*  and memory location.
*
*  Let A be a generic term for any 2D block cyclicly distributed array.
*  Such a global array has an associated description vector DESCA.
*  In the following comments, the character _ should be read as
*  "of the global array".
*
*  NOTATION        STORED IN      EXPLANATION
*  --------------- -------------- --------------------------------------
*  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
*                                 DTYPE_A = 1.
*  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
*                                 the BLACS process grid A is distribu-
*                                 ted over. The context itself is glo-
*                                 bal, but the handle (the integer
*                                 value) may vary.
*  M_A    (global) DESCA( M_ )    The number of rows in the global
*                                 array A.
*  N_A    (global) DESCA( N_ )    The number of columns in the global
*                                 array A.
*  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
*                                 the rows of the array.
*  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
*                                 the columns of the array.
*  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
*                                 row of the array A is distributed.
*  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
*                                 first column of the array A is
*                                 distributed.
*  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
*                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
*
*  Let K be the number of rows or columns of a distributed matrix,
*  and assume that its process grid has dimension p x q.
*  LOCr( K ) denotes the number of elements of K that a process
*  would receive if K were distributed over the p processes of its
*  process column.
*  Similarly, LOCc( K ) denotes the number of elements of K that a
*  process would receive if K were distributed over the q processes of
*  its process row.
*  The values of LOCr() and LOCc() may be determined via a call to the
*  ScaLAPACK tool function, NUMROC:
*          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
*          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
*  An upper bound for these quantities may be computed by:
*          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
*          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
*
*  Arguments
*  =========
*
*  IBTYPE   (global input) INTEGER
*          Specifies the problem type to be solved:
*          = 1:  sub( A )*x = (lambda)*sub( B )*x
*          = 2:  sub( A )*sub( B )*x = (lambda)*x
*          = 3:  sub( B )*sub( A )*x = (lambda)*x
*
*  JOBZ    (global input) CHARACTER*1
*          = '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
*          = 'U':  Upper triangles of sub( A ) and sub( B ) are stored;
*          = 'L':  Lower triangles of sub( A ) and sub( B ) are stored.
*
*  N       (global input) INTEGER
*          The order of the matrices sub( A ) and sub( B ).  N >= 0.
*
*  A       (local input/local output) COMPLEX pointer into the
*          local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
*          On entry, this array contains the local pieces of the
*          N-by-N Hermitian distributed matrix sub( A ). If UPLO = 'U',
*          the leading N-by-N upper triangular part of sub( A ) contains
*          the upper triangular part of the matrix.  If UPLO = 'L', the
*          leading N-by-N lower triangular part of sub( A ) contains
*          the lower triangular part of the matrix.
*
*          On exit, if JOBZ = 'V', then if INFO = 0, sub( A ) contains
*          the distributed matrix Z of eigenvectors.  The eigenvectors
*          are normalized as follows:
*          if IBTYPE = 1 or 2, Z**H*sub( B )*Z = I;
*          if IBTYPE = 3, Z**H*inv( sub( B ) )*Z = I.
*          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
*          or the lower triangle (if UPLO='L') of sub( A ), including
*          the diagonal, is destroyed.
*
*  IA      (global input) INTEGER
*          The row index in the global array A indicating the first
*          row of sub( A ).
*
*  JA      (global input) INTEGER
*          The column index in the global array A indicating the
*          first column of sub( A ).
*
*  DESCA   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix A.
*          If DESCA( CTXT_ ) is incorrect, PCHEGVX cannot guarantee
*          correct error reporting.
*
*  B       (local input/local output) COMPLEX pointer into the
*          local memory to an array of dimension (LLD_B, LOCc(JB+N-1)).
*          On entry, this array contains the local pieces of the
*          N-by-N Hermitian distributed matrix sub( B ). If UPLO = 'U',
*          the leading N-by-N upper triangular part of sub( B ) contains
*          the upper triangular part of the matrix.  If UPLO = 'L', the
*          leading N-by-N lower triangular part of sub( B ) contains
*          the lower triangular part of the matrix.
*
*          On exit, if INFO <= N, the part of sub( B ) containing the
*          matrix is overwritten by the triangular factor U or L from
*          the Cholesky factorization sub( B ) = U**H*U or
*          sub( B ) = L*L**H.
*
*  IB      (global input) INTEGER
*          The row index in the global array B indicating the first
*          row of sub( B ).
*
*  JB      (global input) INTEGER
*          The column index in the global array B indicating the
*          first column of sub( B ).
*
*  DESCB   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix B.
*          DESCB( CTXT_ ) must equal DESCA( CTXT_ )
*
*  VL      (global input) REAL
*          If RANGE='V', the lower bound of the interval to be searched
*          for eigenvalues.  Not referenced if RANGE = 'A' or 'I'.
*
*  VU      (global input) REAL
*          If RANGE='V', the upper bound of the interval to be searched
*          for eigenvalues.  Not referenced if RANGE = 'A' or 'I'.
*
*  IL      (global input) INTEGER
*          If RANGE='I', the index (from smallest to largest) of the
*          smallest eigenvalue to be returned.  IL >= 1.
*          Not referenced if RANGE = 'A' 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) REAL
*          If JOBZ='V', setting ABSTOL to PSLAMCH( 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*PSLAMCH('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*PSLAMCH('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 PCHEGVX 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.)
*          PCHEGVX is always able to detect insufficient space without
*          computation unless RANGE .EQ. 'V'.
*
*  W       (global output) REAL array, dimension (N)
*          On normal exit, the first M entries contain the selected
*          eigenvalues in ascending order.
*
*  ORFAC   (global input) REAL
*          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 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
*          The row index in the global array Z indicating the first
*          row of sub( Z ).
*
*  JZ      (global input) INTEGER
*          The column index in the global array Z indicating the
*          first column of sub( Z ).
*
*  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 array,
*             dimension (LWORK)
*          WORK(1) returns the optimal workspace.
*
*  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, N + NHETRD_LWOPT,
*              NHEGST_LWOPT )
*          Where LWORK is as defined above, and
*            NHETRD_LWORK = 2*( ANB+1 )*( 4*NPS+2 ) +
*              ( NPS + 1 ) * NPS
*            NHEGST_LWOPT =  2*NP0*NB + NQ0*NB + NB*NB
*
*            NB = DESCA( MB_ )
*            NP0 = NUMROC( N, NB, 0, 0, NPROW )
*            NQ0 = NUMROC( N, NB, 0, 0, NPCOL )
*            ICTXT = DESCA( CTXT_ )
*            ANB = PJLAENV( ICTXT, 3, 'PCHETTRD', '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 correspondingwork array, and no
*          error message is issued by PXERBLA.
*
*  RWORK   (local workspace/output) REAL array,
*             dimension max(3,LRWORK)
*          On return, RWORK(1) contains the amount of workspace
*             required for optimal efficiency
*          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 when computing optimal workspace.
*
*  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,
*             PCHEGVX 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', PCHEGVX 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 PCHEGVX to
*             compute the eigenvalues, PCHEGVX 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)
*             PCSTEIN will perform no better than CSTEIN 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 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.
*
*  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   (output) INTEGER array, dimension (N)
*          IFAIL provides additional information when INFO .NE. 0
*          If (MOD(INFO/16,2).NE.0) then IFAIL(1) indicates the order of
*          the smallest minor which is not positive definite.
*          If (MOD(INFO,2).NE.0) on exit, then IFAIL contains the
*          indices of the eigenvectors that failed to converge.
*
*          If neither of the above error conditions hold and JOBZ = 'V',
*          then the first M elements of IFAIL are set to zero.
*
*  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) REAL 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.  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
*                  PCHEGVX 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 PCSTEBZ failed to
*                  compute eigenvalues.
*                  Send e-mail to scalapack@cs.utk.edu
*                if (MOD(INFO/16,2).NE.0), then B was not positive
*                  definite.  IFAIL(1) indicates the order of
*                  the smallest minor which is not positive definite.
*
*  Alignment requirements
*  ======================
*
*  The distributed submatrices A(IA:*, JA:*), C(IC:IC+M-1,JC:JC+N-1),
*  and B( IB:IB+N-1, JB:JB+N-1 ) must verify some alignment properties,
*  namely the following expressions should be true:
*
*     DESCA(MB_) = DESCA(NB_)
*     IA = IB = IZ
*     JA = IB = JZ
*     DESCA(M_) = DESCB(M_) =DESCZ(M_)
*     DESCA(N_) = DESCB(N_)= DESCZ(N_)
*     DESCA(MB_) = DESCB(MB_) = DESCZ(MB_)
*     DESCA(NB_) = DESCB(NB_) = DESCZ(NB_)
*     DESCA(RSRC_) = DESCB(RSRC_) = DESCZ(RSRC_)
*     DESCA(CSRC_) = DESCB(CSRC_) = DESCZ(CSRC_)
*     MOD( IA-1, DESCA( MB_ ) ) = 0
*     MOD( JA-1, DESCA( NB_ ) ) = 0
*     MOD( IB-1, DESCB( MB_ ) ) = 0
*     MOD( JB-1, DESCB( NB_ ) ) = 0
*
*  =====================================================================
*
*     .. 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 )
      COMPLEX            ONE
      parameter( one = 1.0e+0 )
      REAL               FIVE, ZERO
      PARAMETER          ( FIVE = 5.0e+0, zero = 0.0e+0 )
      INTEGER            IERRNPD
      parameter( ierrnpd = 16 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
      CHARACTER          TRANS
      INTEGER            ANB, IACOL, IAROW, IBCOL, IBROW, ICOFFA,
     $                   ICOFFB, ICTXT, IROFFA, IROFFB, LIWMIN, LRWMIN,
     $                   lrwopt, lwmin, lwopt, mq0, mycol, myrow, nb,
     $                   neig, nhegst_lwopt, nhetrd_lwopt, nn, np0,
     $                   npcol, nprow, nps, nq0, sqnpc
      REAL               EPS, SCALE
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM1( 5 ), IDUM2( 5 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ICEIL, INDXG2P, NUMROC, PJLAENV
      REAL               PSLAMCH
      EXTERNAL           LSAME, ICEIL, INDXG2P, NUMROC, PJLAENV, PSLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, chk1mat, pcheevx, pchengst,
     $                   pchk1mat, pchk2mat, pcpotrf, pctrmm, pctrsm,
     $                   pxerbla, sgebr2d, sgebs2d, sscal
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, cmplx, dble, ichar, int, max, min, mod,
     $                   real, 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
*
*     Get grid parameters
*
      ictxt = desca( ctxt_ )
      CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
*
*     Test the input parameters
*
      info = 0
      IF( nprow.EQ.-1 ) THEN
         info = -( 900+ctxt_ )
      ELSE IF( desca( ctxt_ ).NE.descb( ctxt_ ) ) THEN
         info = -( 1300+ctxt_ )
      ELSE IF( desca( ctxt_ ).NE.descz( ctxt_ ) ) THEN
         info = -( 2600+ctxt_ )
      ELSE
*
*     Get machine constants.
*
         eps = pslamch( desca( ctxt_ ), 'Precision' )
*
         wantz = lsame( jobz, 'V' )
         upper = lsame( uplo, 'U' )
         alleig = lsame( range, 'A' )
         valeig = lsame( range, 'V' )
         indeig = lsame( range, 'I' )
         CALL chk1mat( n, 4, n, 4, ia, ja, desca, 9, info )
         CALL chk1mat( n, 4, n, 4, ib, jb, descb, 13, info )
         CALL chk1mat( n, 4, n, 4, iz, jz, descz, 26, info )
         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 sgebs2d( desca( ctxt_ ), 'ALL', ' ', 3, 1, rwork,
     $                       3 )
            ELSE
               CALL sgebr2d( desca( ctxt_ ), 'ALL', ' ', 3, 1, rwork, 3,
     $                       0, 0 )
            END IF
            iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
     $              nprow )
            ibrow = indxg2p( ib, descb( mb_ ), myrow, descb( rsrc_ ),
     $              nprow )
            iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
     $              npcol )
            ibcol = indxg2p( jb, descb( nb_ ), mycol, descb( csrc_ ),
     $              npcol )
            iroffa = mod( ia-1, desca( mb_ ) )
            icoffa = mod( ja-1, desca( nb_ ) )
            iroffb = mod( ib-1, descb( mb_ ) )
            icoffb = mod( jb-1, descb( nb_ ) )
*
*     Compute the total amount of space needed
*
            lquery = .false.
            IF( lwork.EQ.-1 .OR. liwork.EQ.-1 .OR. lrwork.EQ.-1 )
     $         lquery = .true.
*
            liwmin = 6*max( n, ( nprow*npcol )+1, 4 )
*
            nb = desca( mb_ )
            nn = max( n, nb, 2 )
            np0 = numroc( nn, nb, 0, 0, nprow )
*
            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 )
               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 )
               lwmin = n + ( np0+mq0+nb )*nb
               lwopt = lwmin
               lrwmin = 4*n + max( 5*nn, np0*mq0 ) +
     $                  iceil( neig, nprow*npcol )*nn
               lrwopt = lrwmin
*
            END IF
*
*           Compute how much workspace is needed to use the
*           new TRD and GST algorithms
*
            anb = pjlaenv( ictxt, 3, 'PCHETTRD', '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+4 )*nps
            nb = desca( mb_ )
            np0 = numroc( n, nb, 0, 0, nprow )
            nq0 = numroc( n, nb, 0, 0, npcol )
            nhegst_lwopt = 2*np0*nb + nq0*nb + nb*nb
            lwopt = max( lwopt, n+nhetrd_lwopt, nhegst_lwopt )
*
*       Version 1.0 Limitations
*
            IF( ibtype.LT.1 .OR. ibtype.GT.3 ) THEN
               info = -1
            ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
               info = -2
            ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
               info = -3
            ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
               info = -4
            ELSE IF( n.LT.0 ) THEN
               info = -5
            ELSE IF( iroffa.NE.0 ) THEN
               info = -7
            ELSE IF( icoffa.NE.0 ) THEN
               info = -8
            ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
               info = -( 900+nb_ )
            ELSE IF( desca( m_ ).NE.descb( m_ ) ) THEN
               info = -( 1300+m_ )
            ELSE IF( desca( n_ ).NE.descb( n_ ) ) THEN
               info = -( 1300+n_ )
            ELSE IF( desca( mb_ ).NE.descb( mb_ ) ) THEN
               info = -( 1300+mb_ )
            ELSE IF( desca( nb_ ).NE.descb( nb_ ) ) THEN
               info = -( 1300+nb_ )
            ELSE IF( desca( rsrc_ ).NE.descb( rsrc_ ) ) THEN
               info = -( 1300+rsrc_ )
            ELSE IF( desca( csrc_ ).NE.descb( csrc_ ) ) THEN
               info = -( 1300+csrc_ )
            ELSE IF( desca( ctxt_ ).NE.descb( ctxt_ ) ) THEN
               info = -( 1300+ctxt_ )
            ELSE IF( desca( m_ ).NE.descz( m_ ) ) THEN
               info = -( 2200+m_ )
            ELSE IF( desca( n_ ).NE.descz( n_ ) ) THEN
               info = -( 2200+n_ )
            ELSE IF( desca( mb_ ).NE.descz( mb_ ) ) THEN
               info = -( 2200+mb_ )
            ELSE IF( desca( nb_ ).NE.descz( nb_ ) ) THEN
               info = -( 2200+nb_ )
            ELSE IF( desca( rsrc_ ).NE.descz( rsrc_ ) ) THEN
               info = -( 2200+rsrc_ )
            ELSE IF( desca( csrc_ ).NE.descz( csrc_ ) ) THEN
               info = -( 2200+csrc_ )
            ELSE IF( desca( ctxt_ ).NE.descz( ctxt_ ) ) THEN
               info = -( 2200+ctxt_ )
            ELSE IF( iroffb.NE.0 .OR. ibrow.NE.iarow ) THEN
               info = -11
            ELSE IF( icoffb.NE.0 .OR. ibcol.NE.iacol ) THEN
               info = -12
            ELSE IF( valeig .AND. n.GT.0 .AND. vu.LE.vl ) THEN
               info = -15
            ELSE IF( indeig .AND. ( il.LT.1 .OR. il.GT.max( 1, n ) ) )
     $                THEN
               info = -16
            ELSE IF( indeig .AND. ( iu.LT.min( n, il ) .OR. iu.GT.n ) )
     $                THEN
               info = -17
            ELSE IF( valeig .AND. ( abs( rwork( 2 )-vl ).GT.five*eps*
     $               abs( vl ) ) ) THEN
               info = -14
            ELSE IF( valeig .AND. ( abs( rwork( 3 )-vu ).GT.five*eps*
     $               abs( vu ) ) ) THEN
               info = -15
            ELSE IF( abs( rwork( 1 )-abstol ).GT.five*eps*
     $               abs( abstol ) ) THEN
               info = -18
            ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
               info = -28
            ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
               info = -30
            ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
               info = -32
            END IF
         END IF
         idum1( 1 ) = ibtype
         idum2( 1 ) = 1
         IF( wantz ) THEN
            idum1( 2 ) = ichar( 'V' )
         ELSE
            idum1( 2 ) = ichar( 'N' )
         END IF
         idum2( 2 ) = 2
         IF( upper ) THEN
            idum1( 3 ) = ichar( 'U' )
         ELSE
            idum1( 3 ) = ichar( 'L' )
         END IF
         idum2( 3 ) = 3
         IF( alleig ) THEN
            idum1( 4 ) = ichar( 'A' )
         ELSE IF( indeig ) THEN
            idum1( 4 ) = ichar( 'I' )
         ELSE
            idum1( 4 ) = ichar( 'V' )
         END IF
         idum2( 4 ) = 4
         IF( lquery ) THEN
            idum1( 5 ) = -1
         ELSE
            idum1( 5 ) = 1
         END IF
         idum2( 5 ) = 5
         CALL pchk2mat( n, 4, n, 4, ia, ja, desca, 9, n, 4, n, 4, ib,
     $                  jb, descb, 13, 5, idum1, idum2, info )
         CALL pchk1mat( n, 4, n, 4, iz, jz, descz, 26, 0, idum1, idum2,
     $                  info )
      END IF
*
      iwork( 1 ) = liwmin
      work( 1 ) = cmplx( real( lwopt ) )
      rwork( 1 ) = real( lrwopt )
*
      IF( info.NE.0 ) THEN
         CALL pxerbla( ictxt, 'PCHEGVX ', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Form a Cholesky factorization of sub( B ).
*
      CALL pcpotrf( uplo, n, b, ib, jb, descb, info )
      IF( info.NE.0 ) THEN
         iwork( 1 ) = liwmin
         work( 1 ) = cmplx( real( lwopt ) )
         rwork( 1 ) = real( lrwopt )
         ifail( 1 ) = info
         info = ierrnpd
         RETURN
      END IF
*
*     Transform problem to standard eigenvalue problem and solve.
*
      CALL pchengst( ibtype, uplo, n, a, ia, ja, desca, b, ib, jb,
     $               descb, scale, work, lwork, info )
      CALL pcheevx( 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 )
*
      IF( wantz ) THEN
*
*        Backtransform eigenvectors to the original problem.
*
         neig = m
         IF( ibtype.EQ.1 .OR. ibtype.EQ.2 ) THEN
*
*           For sub( A )*x=(lambda)*sub( B )*x and
*           sub( A )*sub( B )*x=(lambda)*x; backtransform eigenvectors:
*           x = inv(L)'*y or inv(U)*y
*
            IF( upper ) THEN
               trans = 'N'
            ELSE
               trans = 'C'
            END IF
*
            CALL pctrsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
     $                   b, ib, jb, descb, z, iz, jz, descz )
*
         ELSE IF( ibtype.EQ.3 ) THEN
*
*           For sub( B )*sub( A )*x=(lambda)*x;
*           backtransform eigenvectors: x = L*y or U'*y
*
            IF( upper ) THEN
               trans = 'C'
            ELSE
               trans = 'N'
            END IF
*
            CALL pctrmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
     $                   b, ib, jb, descb, z, iz, jz, descz )
         END IF
      END IF
*
      IF( scale.NE.one ) THEN
         CALL sscal( n, scale, w, 1 )
      END IF
*
      iwork( 1 ) = liwmin
      work( 1 ) = cmplx( real( lwopt ) )
      rwork( 1 ) = real( lrwopt )
      RETURN
*
*     End of PCHEGVX
*
      END