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



NAME
       PCGETRI - compute the inverse of a distributed matrix using the LU fac-
       torization computed by PCGETRF

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

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

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

           COMPLEX         A( * ), WORK( * )

PURPOSE
       PCGETRI  computes the inverse of a distributed matrix using the LU fac-
       torization computed by PCGETRF. This method inverts U and then computes
       the  inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA by solv-
       ing the system InvA*L = inv(U) for InvA.


       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
       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, the local pieces of the L and U obtained by the  factor-
               ization  sub( A ) = P*L*U computed by PCGETRF. 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) COMPLEX 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 physi-
               cally 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  sin-
               gular and its inverse could not be computed.



ScaLAPACK routine               31 October 2017                     PCGETRI(3)