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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.