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.