PSTRTI2(3)    ScaLAPACK routine of NEC Numeric Library Collection   PSTRTI2(3)



NAME
       PSTRTI2 - 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 PSTRTI2( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )

           CHARACTER       DIAG, UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           REAL            A( * )

PURPOSE
       PSTRTI2 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 con-
       tained in one and only one process memory space (local operation).


       Notes
       =====

       Each global data object is described by an associated description  vec-
       tor.  This vector stores the information required to establish the map-
       ping 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 col-
       umn.
       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) REAL 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 trian-
               gular 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.



ScaLAPACK routine               31 October 2017                     PSTRTI2(3)