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NAME

       PDGETRI  -  compute  the  inverse  of a distributed matrix using the LU
       factorization computed by PDGETRF

SYNOPSIS

       SUBROUTINE PDGETRI( N, A, IA, JA,  DESCA,  IPIV,  WORK,  LWORK,  IWORK,
                           LIWORK, INFO )

           INTEGER         IA, INFO, JA, LIWORK, LWORK, N

           INTEGER         DESCA( * ), IPIV( * ), IWORK( * )

           DOUBLE          PRECISION A( * ), WORK( * )

PURPOSE

       PDGETRI  computes  the  inverse  of  a  distributed matrix using the LU
       factorization computed by PDGETRF.  This  method  inverts  U  and  then
       computes  the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA
       by solving the system InvA*L = inv(U) for InvA.

       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

       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)).  On
               entry,  the  local  pieces  of  the  L  and  U  obtained by the
               factorization sub( A ) = P*L*U computed by PDGETRF. On exit, if
               INFO  =  0,  sub(  A  )  contains  the  inverse of the original
               distributed matrix sub( A ).

       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.

       IPIV    (local input) INTEGER array, dimension LOCr(M_A)+MB_A
               keeps track of the pivoting information. IPIV(i) is the  global
               row index the local row i was swapped with.  This array is tied
               to the distributed matrix A.

       WORK    (local workspace/local output) DOUBLE PRECISION array,
               dimension (LWORK) On exit,  WORK(1)  returns  the  minimal  and
               optimal LWORK.

       LWORK   (local or global input) INTEGER
               The dimension of the array WORK.  LWORK is local input and must
               be at least LWORK = LOCr(N+MOD(IA-1,MB_A))*NB_A. WORK  is  used
               to keep a copy of at most an entire column block of sub( A ).

               If LWORK = -1, then LWORK is global input and a workspace query
               is assumed; the routine only calculates the minimum and optimal
               size  for  all work arrays. Each of these values is returned in
               the first entry of the corresponding work array, and  no  error
               message is issued by PXERBLA.

       IWORK   (local workspace/local output) INTEGER array,
               dimension  (LIWORK)  On  exit, IWORK(1) returns the minimal and
               optimal LIWORK.

       LIWORK  (local or global input) INTEGER
               The  dimension  of  the  array  IWORK  used  as  workspace  for
               physically  transposing  the pivots.  LIWORK is local input and
               must be at least if NPROW == NPCOL then LIWORK =  LOCc(  N_A  +
               MOD(JA-1,  NB_A) ) + NB_A, else LIWORK =  LOCc( N_A + MOD(JA-1,
               NB_A) ) + MAX( CEIL(CEIL(LOCr(M_A)/MB_A)/(LCM/NPROW)),  NB_A  )
               where  LCM  is  the  least  common multiple of process rows and
               columns (NPROW and NPCOL).  end if

               If LIWORK = -1, then LIWORK is global  input  and  a  workspace
               query  is  assumed; the routine only calculates the minimum and
               optimal size for all work  arrays.  Each  of  these  values  is
               returned  in  the  first entry of the corresponding work array,
               and no error message is issued by PXERBLA.

       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,  U(IA+K-1,IA+K-1)  is  exactly  zero; the matrix is
               singular and its inverse could not be computed.