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NAME

       PSGESV  -  compute  the  solution  to a real system of linear equations
       sub( A ) * X = sub( B ),

SYNOPSIS

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

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

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

           REAL           A( * ), B( * )

PURPOSE

       PSGESV computes the solution to a real system of linear equations

       where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed matrix
       and  X  and  sub(  B  )  =  B(IB:IB+N-1,JB:JB+NRHS-1)   are   N-by-NRHS
       distributed matrices.

       The LU decomposition with partial pivoting and row interchanges is used
       to factor sub( A ) as sub( A ) = P * L * U, where P is a permu-  tation
       matrix, L is unit lower triangular, and U is upper triangular.  L and U
       are stored in sub( A ). The factored form of sub( A ) is then  used  to
       solve the system of equations sub( A ) * X = sub( B ).

       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 decomposition ( MB_A = 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.

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

       A       (local input/local output) REAL pointer into the
               local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).  On
               entry, the local pieces of the N-by-N distributed matrix sub( A
               ) to be factored. On exit, 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 output) 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) REAL pointer into the
               local memory to an array of dimension  (LLD_B,LOCc(JB+NRHS-1)).
               On  entry,  the right hand side distributed matrix sub( B ). On
               exit, if INFO = 0, 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.  > 0:  If
               INFO = K, U(IA+K-1,JA+K-1) is exactly zero.  The  factorization
               has  been  completed,  but the factor U is exactly singular, so
               the solution could not be computed.