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NAME

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

SYNOPSIS

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

           CHARACTER       UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           REAL            A( * )

PURPOSE

       PSPOTRF computes the Cholesky factorization of an N-by-N real symmetric
       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) REAL 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  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.