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



NAME
       PCTRTRI  -  compute  the  inverse  of  a upper or lower triangular dis-
       tributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1)

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

           CHARACTER       DIAG, UPLO

           INTEGER         IA, INFO, JA, N

           INTEGER         DESCA( * )

           COMPLEX         A( * )

PURPOSE
       PCTRTRI 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 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
               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) COMPLEX 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  tri-
               angular part of the matrix sub( A ) contains the upper triangu-
               lar 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 com-
               puted.



ScaLAPACK routine               31 October 2017                     PCTRTRI(3)