HPL_pdtrsv(3)

💖 HPL_pdtrsv 💖

okay bestie, sit down, grab a boba, because we're talking about HPL_pdtrsv from the HPL library functions, and it's literally the moment. this one solves triu( A ) x = b ✨ like, that's the whole vibe.

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🦋 SYNOPSIS 🦋

#include "hpl.h"

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

look at her. two pointers, one dream. 💅

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🌸 DESCRIPTION 🌸

so HPL_pdtrsv solves an upper triangular system of linear equations. that's the assignment. no notes. 👑

the rhs? it's the last column of the N by N+1 matrix A. and here's the tea: the solve starts in the process column that owns the Nth column of A, which means the rhs b may need to get moved one process column to the left at the beginning. so rude of it, but okay. 🙈

because of that little shuffle, the routine needs a column vector in every process column but the one owning b. the result then gets replicated in all process rows and returned in XR — meaning XR is of size nq = LOCq( N ) in all processes. same size everywhere, we love consistency. 💖

the algorithm itself? it 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 there to minimize the critical path, because we're efficient like that. 🧚

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. and get this — you gotta exchange 2 messages of length NB to compute the next NB entries of the vector solution, plus do a total of N^2 floating point operations. it's giving math girlboss. 🔥

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✨ ARGUMENTS ✨

• GRID — (local input) HPL_T_grid * — on entry, GRID points to the data structure containing the process grid information. she's the map, bestie. 🗺️
• AMAT — (local input/output) HPL_T_pmat * — on entry, AMAT points to the data structure containing the local array information. she's the data, she goes in and comes out. main character energy fr fr. 👑

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🎀 SEE ALSO 🎀

• HPL_pdgesv (3) — her sister. go say hi. 🫶

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HPL 2.2 · February 24, 2016 — that's the version and the date, babes, and that's the whole page. slay, you understood it, i'm so proud of you, no cap 💅💖✨