1HPL_pdtrsv(3)                HPL Library Functions               HPL_pdtrsv(3)
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NAME

6       HPL_pdtrsv - Solve triu( A ) x = b.
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SYNOPSIS

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

14       HPL_pdtrsv solves an upper triangular system of linear equations.
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16       The  rhs  is the last column of the N by N+1 matrix A. The solve starts
17       in the process  column owning the  Nth  column of A, so the rhs  b  may
18       need  to  be moved one process column to the left at the beginning. The
19       routine therefore needs  a column  vector in every process  column  but
20       the  one  owning  b. The result is  replicated in all process rows, and
21       returned in XR, i.e. XR is of size nq = LOCq( N ) in all processes.
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23       The algorithm uses decreasing one-ring broadcast in process  rows   and
24       columns   implemented   in terms of  synchronous communication point to
25       point primitives.  The  lookahead of depth 1 is used to  minimize   the
26       critical  path.  This entire operation is essentially ``latency'' bound
27       and an estimate of its running time is given by:
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29          (move rhs) lat + N / ( P bdwth ) +
30          (solve)    ((N / NB)-1) 2 (lat + NB / bdwth) +
31                     gam2 N^2 / ( P Q ),
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33       where  gam2   is an estimate of the   Level 2 BLAS rate  of  execution.
34       There  are   N / NB  diagonal blocks. One must exchange  2  messages of
35       length NB to compute the next  NB  entries of the vector  solution,  as
36       well as performing a total of N^2 floating point operations.
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ARGUMENTS

39       GRID    (local input)           HPL_T_grid *
40               On  entry,   GRID  points  to the data structure containing the
41               process grid information.
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43       AMAT    (local input/output)    HPL_T_pmat *
44               On entry,  AMAT  points  to the data structure  containing  the
45               local array information.
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SEE ALSO

48       HPL_pdgesv (3).
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52HPL 2.2                        February 24, 2016                 HPL_pdtrsv(3)
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