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NAME

       PZHEGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form

SYNOPSIS

       SUBROUTINE PZHEGST( IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, DESCB, SCALE, INFO )

           CHARACTER       UPLO

           INTEGER         IA, IB, IBTYPE, INFO, JA, JB, N

           DOUBLE          PRECISION SCALE

           INTEGER         DESCA( * ), DESCB( * )

           COMPLEX*16      A( * ), B( * )

PURPOSE

       PZHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form.

       In  the  following  sub(  A  )  denotes  A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B(
       IB:IB+N-1, JB:JB+N-1 ).

       If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, and sub( A ) is  overwritten
       by inv(U**H)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L**H)

       If IBTYPE = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or sub( B )*sub( A )*x =
       lambda*x, and sub( A ) is overwritten by U*sub( A )*U**H or L**H*sub( A )*L.

       sub( B ) must have been previously factorized as U**H*U or L*L**H by PZPOTRF.

       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
                =  1:  compute  inv(U**H)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L**H); = 2 or 3:
                compute U*sub( A )*U**H or L**H*sub( A )*L.

       UPLO    (global input) CHARACTER
               = 'U':  Upper triangle of sub( A ) is stored and sub( B ) is factored as U**H*U; =
               'L':  Lower triangle of sub( A ) is stored and sub( B ) is factored as L*L**H.

       N       (global input) INTEGER
               The order of the matrices sub( A ) and sub( B ).  N >= 0.

       A       (local input/local output) COMPLEX*16 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, and its strictly lower triangular part is not
               referenced.   If  UPLO = 'L', the leading N-by-N lower triangular part of sub( A )
               contains the  lower  triangular  part  of  the  matrix,  and  its  strictly  upper
               triangular part is not referenced.

               On  exit, if INFO = 0, the transformed matrix, stored in the same format as sub( A
               ).

       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.

       B       (local input) COMPLEX*16 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 triangular factor from the Cholesky factorization of sub( B ),
               as returned by PZPOTRF.

       IB      (global input) INTEGER
               B's global row index, which points to the beginning of the submatrix which  is  to
               be operated on.

       JB      (global input) INTEGER
               B's  global  column index, which points to the beginning of the submatrix which is
               to be operated on.

       DESCB   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix B.

       SCALE   (global output) DOUBLE PRECISION
               Amount by which the eigenvalues should be scaled to  compensate  for  the  scaling
               performed  in  this  routine.   At present, SCALE is always returned as 1.0, it is
               returned here to allow for future enhancement.

       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.