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NAME

       PZPOSV  -  compute the solution to a complex system of linear equations
       sub( A ) * X = sub( B ),

SYNOPSIS

       SUBROUTINE PZPOSV( UPLO, N, NRHS, A, IA, JA, DESCA, B, IB,  JB,  DESCB,
                          INFO )

           CHARACTER      UPLO

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

           INTEGER        DESCA( * ), DESCB( * )

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

PURPOSE

       PZPOSV computes the solution to a complex system of linear equations

       where  sub(  A  )  denotes  A(IA:IA+N-1,JA:JA+N-1)  and  is  an  N-by-N
       hermitian distributed positive definite matrix  and  X  and  sub(  B  )
       denoting  B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed matrices.

       The Cholesky decomposition is used to factor sub( A ) as

                          sub( A ) = U**H * U,  if UPLO = ’U’, or

                          sub( A ) = L * L**H,  if UPLO = ’L’,

       where U is an upper triangular matrix  and  L  is  a  lower  triangular
       matrix.  The factored form of sub( A ) is then used to solve the system
       of equations.

       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

       This routine requires square block decomposition ( MB_A = NB_A ).

ARGUMENTS

       UPLO    (global input) CHARACTER
               = ’U’:  Upper triangle of sub( A ) is stored;
               = ’L’:  Lower triangle of sub( A ) is stored.

       N       (global input) INTEGER
               The  number  of  rows  and  columns to be operated on, i.e. the
               order of the distributed submatrix sub( A ). N >= 0.

       NRHS    (global input) INTEGER
               The number of right hand sides, i.e., the number of columns  of
               the distributed submatrix sub( B ). NRHS >= 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
               symmetric  distributed matrix sub( A ) to be factored.  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 distribu- ted matrix,
               and  its  strictly  upper triangular part is not referenced. On
               exit, if INFO = 0, this array contains the local pieces of  the
               factor  U  or  L  from  the Cholesky factori- zation sub( A ) =
               U**H*U or L*L**H.

       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.

       B       (local input/local output) COMPLEX*16 pointer into the
               local memory to an array of  dimension  (LLD_B,LOC(JB+NRHS-1)).
               On  entry,  the  local pieces of the right hand sides distribu-
               ted matrix sub( B ). On exit, if INFO = 0, sub( B  )  is  over-
               written with the solution distributed matrix X.

       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.

       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
               INFO = K, the leading minor of order K,
               A(IA:IA+K-1,JA:JA+K-1)  is  not  positive  definite,  and   the
               factorization  could not be completed, and the solution has not
               been computed.