NAME

       PDTRTI2  -  compute  the  inverse  of  a  real  upper  or  lower  triangular  block  matrix  sub(  A  ) =
       A(IA:IA+N-1,JA:JA+N-1)

SYNOPSIS

       SUBROUTINE PDTRTI2( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )

           CHARACTER       DIAG, UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           DOUBLE          PRECISION A( * )

PURPOSE

       PDTRTI2  computes  the  inverse  of  a  real  upper  or  lower  triangular  block  matrix  sub(  A  )   =
       A(IA:IA+N-1,JA:JA+N-1).  This  matrix should be contained in one and only one process memory space (local
       operation).

       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':  sub( A ) is upper triangular;
               = 'L':  sub( A ) is lower triangular.

       DIAG    (global input) CHARACTER*1
               = 'N':  sub( A ) is non-unit triangular
               = 'U':  sub( A ) is 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) DOUBLE PRECISION pointer into the
               local  memory to an array of dimension (LLD_A,LOCc(JA+N-1)), 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, 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. If DIAG = 'U', the diagonal  elements  of  sub(  A  )  are  also  not
               referenced and are assumed to be 1.  On exit, the (triangular) inverse of the original matrix, in
               the same storage format.

       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    (local 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.