HPL_pdrpanrlT(3)

💖 HPL_pdrpanrlT 💖

okay bestie, welcome to the HPL_pdrpanrlT page from the HPL Library Functions — this is the one about right-looking recursive panel factorization and honestly? it's giving main character energy in the linear algebra world. ✨

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🌸 NAME 🌸

HPL_pdrpanrlT — Right-looking recursive panel factorization. no cap, that's literally the whole job description. 🎀

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🦋 SYNOPSIS 🦋

#include "hpl.h"

void HPL_pdrpanrlT( HPL_T_panel * PANEL, const int M, const int N, const
int ICOFF, double * WORK );

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✨ DESCRIPTION ✨

So HPL_pdrpanrlT recursively factorizes a panel of columns using the recursive Right-looking variant of the one-dimensional algorithm. 💅 The lower triangular N0-by-N0 upper block of the panel is stored in transpose form. yes, transpose form, that's the whole T in the name, iykyk.

Bi-directional exchange is used to perform the swap::broadcast operations at once for one column in the panel. 🫶 This results in a lower number of slightly larger messages than usual — fewer texts, longer texts, group-chat behavior fr fr.

On P processes and assuming bi-directional links, the running time of this function can be approximated by (when N is equal to N0):

N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) +
N0^2 * ( M - N0/3 ) * gam2-3

where M is the local number of rows of the panel, lat and bdwth are the latency and bandwidth of the network for double precision real words, and gam2-3 is an estimate of the Level 2 and Level 3 BLAS rate of execution. 👑

The recursive algorithm allows indeed to almost achieve Level 3 BLAS performance in the panel factorization. iconic behavior honestly. But on a large number of modern machines, this operation is however latency bound 😭 — meaning that its cost can be estimated by only the latency portion N0 * log_2(P) * lat.

and bestie, listen: mono-directional links will double this communication cost. double. not a vibe. 💀

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💅 ARGUMENTS 💅

• PANEL (local input/output) — HPL_T_panel * On entry, PANEL points to the data structure containing the panel information. it's the whole mood board for the panel, okay?
• M (local input) — const int On entry, M specifies the local number of rows of sub(A).
• N (local input) — const int On entry, N specifies the local number of columns of sub(A).
• ICOFF (global input) — const int On entry, ICOFF specifies the row and column offset of sub(A) in A.
• WORK (local workspace) — double * On entry, WORK is a workarray of size at least 2*(4+2*N0). yes, that exact expression, don't get cute with it. 🙈

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🌈 SEE ALSO 🌈

the whole friend group, go say hi:

• HPL_dlocmax (3)
• HPL_dlocswpN (3)
• HPL_dlocswpT (3)
• HPL_pdmxswp (3)
• HPL_pdpancrN (3)
• HPL_pdpancrT (3)
• HPL_pdpanllN (3)
• HPL_pdpanllT (3)
• HPL_pdpanrlN (3)
• HPL_pdpanrlT (3)
• HPL_pdrpancrN (3)
• HPL_pdrpancrT (3)
• HPL_pdrpanllN (3)
• HPL_pdrpanllT (3)
• HPL_pdrpanrlN (3)
• HPL_pdfact (3)

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and that's the whole page bestie!! 🎀✨ this masterpiece is from HPL 2.2, dated February 24, 2016 — an absolute classic, we stan a vintage release. 💜 mwah, go factorize something. 🦋🌸