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NAME

       PCTRTRS - solve a triangular system of the form   sub( A ) * X = sub( B ) or sub( A )**T *
       X = sub( B ) or   sub( A )**H * X = sub( B ),

SYNOPSIS

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

           CHARACTER       DIAG, TRANS, UPLO

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

           INTEGER         DESCA( * ), DESCB( * )

           COMPLEX         A( * ), B( * )

PURPOSE

       PCTRTRS solves a triangular system of the form

       where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a triangular  distributed  matrix  of
       order  N, and B(IB:IB+N-1,JB:JB+NRHS-1) is an N-by-NRHS distributed matrix denoted by sub(
       B ). A check is made to verify that sub( A ) is nonsingular.

       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

       UPLO    (global input) CHARACTER
               = 'U':  sub( A ) is upper triangular;
               = 'L':  sub( A ) is lower triangular.

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

       DIAG    (global input) CHARACTER
               = 'N':  sub( A ) is non-unit triangular;
               = 'U':  sub( A ) is unit triangular.

       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
               matrix sub( B ). NRHS >= 0.

       A       (local input) COMPLEX pointer into the local memory
               to  an  array  of  dimension  (LLD_A,LOCc(JA+N-1) ). This array contains the local
               pieces of the distributed triangular matrix sub( A ).  If UPLO = 'U', the  leading
               N-by-N upper triangular part of sub( A ) contains the upper triangular matrix, and
               the strictly lower triangular part of sub( A ) is not referenced.  If UPLO =  'L',
               the leading N-by-N lower triangular part of sub( A ) contains the lower triangular
               matrix, and the strictly upper triangular part of sub( A ) is not referenced.   If
               DIAG  =  'U',  the  diagonal  elements of sub( A ) are also not referenced and are
               assumed to be 1.

       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) COMPLEX pointer into the
               local memory to an array of dimension  (LLD_B,LOCc(JB+NRHS-1)).   On  entry,  this
               array  contains  the local pieces of the right hand side distributed matrix sub( B
               ). On exit, if INFO = 0, sub( B ) is overwritten by the solution 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    (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 = i, the i-th diagonal element of  sub(  A  )  is  zero,
               indicating  that  the  submatrix  is  singular  and  the solutions X have not been
               computed.