NAME

       PSTRTRI  -  compute  the  inverse  of  a  upper  or  lower  triangular  distributed  matrix  sub(  A  ) =
       A(IA:IA+N-1,JA:JA+N-1)

SYNOPSIS

       SUBROUTINE PSTRTRI( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )

           CHARACTER       DIAG, UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           REAL            A( * )

PURPOSE

       PSTRTRI  computes  the  inverse  of  a  upper  or  lower  triangular  distributed  matrix  sub(  A  )   =
       A(IA:IA+N-1,JA:JA+N-1).

       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
               Specifies whether the distributed matrix sub( A ) is upper or lower triangular:
               = 'U':  Upper triangular,
               = 'L':  Lower triangular.

       DIAG    (global input) CHARACTER
               Specifies whether or not the distributed matrix sub( A ) is unit triangular:
               = 'N':  Non-unit triangular,
               = 'U':  Unit triangular.

       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  triangular  matrix  sub(  A  ).   If UPLO = 'U', the leading N-by-N upper
               triangular part of the matrix sub( A ) contains the upper triangular matrix to be  inverted,  and
               the  strictly lower triangular part of sub( A ) is not referenced.  If UPLO = 'L', the leading N-
               by-N lower triangular part of the matrix sub( A ) contains the lower triangular matrix,  and  the
               strictly  upper triangular part of sub( A ) is not referenced.  On exit, the (triangular) inverse
               of the original matrix.

       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, A(IA+K-1,JA+K-1) is exactly zero.  The triangular matrix sub( A ) is singular  and  its
               inverse can not be computed.