NAME

       PSPOTRS   -   solve   a   system  of  linear  equations    sub(  A  )  *  X  =  sub(  B  )
       A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1)

SYNOPSIS

       SUBROUTINE PSPOTRS( UPLO, N, NRHS, A, IA, JA, DESCA, B, IB, JB, DESCB, INFO )

           CHARACTER       UPLO

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

           INTEGER         DESCA( * ), DESCB( * )

           REAL            A( * ), B( * )

PURPOSE

       PSPOTRS solves a system of linear equations

       where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a N-by-N symmetric positive  definite
       distributed  matrix  using the Cholesky factorization sub( A ) = U**T*U or L*L**T computed
       by PSPOTRF.  sub( B ) denotes the distributed matrix 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 decomposition ( MB_A = NB_A ).

ARGUMENTS

       UPLO    (global input) CHARACTER
               = 'U':  Upper triangle of sub( A ) is stored;
               = 'L':  Lower triangle of sub( A ) is stored.

       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) REAL pointer into local memory to
               an  array  of  dimension  (LLD_A, LOCc(JA+N-1)). On entry, this array contains the
               factors L or U from the Cholesky facto- rization sub( A ) = L*L**T or  U**T*U,  as
               computed by PSPOTRF.

       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.

       B       (local input/local output) REAL pointer into the
               local  memory  to  an array of local dimension (LLD_B,LOCc(JB+NRHS-1)).  On entry,
               this array contains the the local pieces of the right hand sides  sub(  B  ).   On
               exit, this array contains the local pieces of 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.