HPL_pdtrsv man page

HPL_pdtrsv — Solve triu( A ) x = b.


#include "hpl.h"
 void HPL_pdtrsv( HPL_T_grid * GRID, HPL_T_pmat * AMAT );


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.


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).


October 26, 2012 HPL 2.1 HPL Library Functions