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



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

SYNOPSIS
       SUBROUTINE PSTRTRS( 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( * )

           REAL            A( * ), B( * )

PURPOSE
       PSTRTRS  solves a triangular system of the form sub( A ) * X = sub( B )
       or  sub(  A  )**T  *  X  =  sub(  B  ),  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 nonsin-
       gular.


       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
       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 )**T * X = sub( B ) (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) REAL pointer into the local memory
               to an array of dimension (LLD_A,LOCc(JA+N-1) ). This array con-
               tains  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) REAL 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, indi-
               cating that the submatrix is singular and the solutions X  have
               not been computed.



ScaLAPACK routine               31 October 2017                     PSTRTRS(3)