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NAME

       PDGETRS - solve a system of distributed linear equations   op( sub( A )
       ) * X = sub( B )  with a general N-by-N distributed  matrix  sub(  A  )
       using the LU factorization computed by PDGETRF

SYNOPSIS

       SUBROUTINE PDGETRS( TRANS,  N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB,
                           DESCB, INFO )

           CHARACTER       TRANS

           INTEGER         IA, IB, INFO, JA, JB, N, NRHS

           INTEGER         DESCA( * ), DESCB( * ), IPIV( * )

           DOUBLE          PRECISION A( * ), B( * )

PURPOSE

       PDGETRS solves a system  of  distributed  linear  equations  sub(  A  )
       denotes  A(IA:IA+N-1,JA:JA+N-1),  op(  A  )  =  A  or A**T and sub( B )
       denotes B(IB:IB+N-1,JB:JB+NRHS-1).

       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

       This routine requires square block data decomposition ( MB_A=NB_A ).

ARGUMENTS

       TRANS   (global input) CHARACTER
               Specifies the form of the system of equations:
               = ’N’:  sub( A )    * X = sub( B )  (No transpose)
               = ’T’:  sub( A )**T * X = sub( B )  (Transpose)
               = ’C’:  sub( A )**T * X = sub( B )  (Transpose)

       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.

       NRHS    (global input) INTEGER
               The number of right hand sides, i.e., the number of columns  of
               the distributed submatrix sub( B ). NRHS >= 0.

       A       (local input) DOUBLE PRECISION 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  factors  L
               and  U  from  the  factorization  sub(  A  )  = P*L*U; the unit
               diagonal elements of L are not stored.

       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 )
               This array contains the pivoting information.  IPIV(i)  ->  The
               global row local row i was swapped with.  This array is tied to
               the distributed matrix A.

       B       (local input/local output) DOUBLE PRECISION pointer into the
               local memory to an array of dimension  (LLD_B,LOCc(JB+NRHS-1)).
               On  entry,  the right hand sides sub( B ). On exit, sub( B ) is
               overwritten by the solution distributed matrix X.

       IB      (global input) INTEGER
               The row index in the global array B indicating the first row of
               sub( B ).

       JB      (global input) INTEGER
               The  column  index  in  the global array B indicating the first
               column of sub( B ).

       DESCB   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix B.

       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.