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HPL_pdtrsv(3)                HPL Library Functions               HPL_pdtrsv(3)

NAME
       HPL_pdtrsv - Solve triu( A ) x = b.

SYNOPSIS
       #include "hpl.h"

       void HPL_pdtrsv( HPL_T_grid * GRID, HPL_T_pmat * AMAT );

DESCRIPTION
       HPL_pdtrsv solves an upper triangular system of linear equations.

       The rhs is the last column of the N by N+1 matrix A. The solve starts
       in the process  column owning the  Nth  column of A, so the rhs b may
       need to be moved one process column to the left at the beginning. The
       routine therefore needs  a column  vector in every process column but
       the one owning  b. The result is  replicated in all process rows, and
       returned in XR, i.e. XR is of size nq = LOCq( N ) in all processes.

       The algorithm uses decreasing one-ring broadcast in process rows  and
       columns  implemented  in terms of  synchronous communication point to
       point primitives.  The  lookahead of depth 1 is used to minimize  the
       critical path. This entire operation is essentially ``latency'' bound
       and an estimate of its running time is given by:

          (move rhs) lat + N / ( P bdwth ) +
          (solve)    ((N / NB)-1) 2 (lat + NB / bdwth) +
                     gam2 N^2 / ( P Q ),

       where  gam2   is an estimate of the   Level 2 BLAS rate of execution.
       There are  N / NB  diagonal blocks. One must exchange  2  messages of
       length NB to compute the next  NB  entries of the vector solution, as
       well as performing a total of N^2 floating point operations.

ARGUMENTS
       GRID    (local input)           HPL_T_grid *
               On entry,  GRID  points  to the data structure containing the
               process grid information.

       AMAT    (local input/output)    HPL_T_pmat *
               On entry,  AMAT  points  to the data structure containing the
               local array information.

SEE ALSO
       HPL_pdgesv (3).

HPL 2.1                        October 26, 2012                  HPL_pdtrsv(3)