NAME

       PSPOTRI  -  compute  the  inverse of a real symmetric positive definite distributed matrix
       sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the Cholesky factorization sub( A )  =  U**T*U  or
       L*L**T computed by PSPOTRF

SYNOPSIS

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

           CHARACTER       UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           REAL            A( * )

PURPOSE

       PSPOTRI computes the inverse of a real symmetric positive definite distributed matrix sub(
       A ) = A(IA:IA+N-1,JA:JA+N-1) using the Cholesky factorization sub( A ) = U**T*U or  L*L**T
       computed by PSPOTRF.

       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

       UPLO    (global input) CHARACTER*1
               = '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, the local
               pieces of the triangular factor U or L from  the  Cholesky  factorization  of  the
               distributed matrix sub( A ) = U**T*U or  L*L**T, as computed by PSPOTRF.  On exit,
               the local pieces of the upper or lower triangle of the (symmetric) inverse of sub(
               A ), overwriting the input factor U or 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 = i, the (i,i) element of the factor U or L is zero, and
               the inverse could not be computed.