NAME

       PCPOTRF - compute the Cholesky factorization of an N-by-N complex hermitian positive definite distributed
       matrix sub( A ) denoting A(IA:IA+N-1, JA:JA+N-1)

SYNOPSIS

       SUBROUTINE PCPOTRF( UPLO, N, A, IA, JA, DESCA, INFO )

           CHARACTER       UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           COMPLEX         A( * )

PURPOSE

       PCPOTRF computes the Cholesky factorization of an N-by-N complex hermitian positive definite  distributed
       matrix sub( A ) denoting A(IA:IA+N-1, JA:JA+N-1).

       The factorization has the form

                 sub( A ) = U' * U ,  if UPLO = 'U', or

                 sub( A ) = L  * L',  if UPLO = 'L',

       where U is an upper triangular matrix and L is lower triangular.

       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.

       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 ) 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 UPLO = 'U', the
               upper triangular part of the distributed matrix contains the Cholesky factor U, if  UPLO  =  'L',
               the lower triangular part of the distribu- ted matrix contains the Cholesky factor L.

       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.

       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.