HPL_pdrpanllN(3)

✨ HPL_pdrpanllN ✨

okay bestie, welcome to the HPL_pdrpanllN page from the HPL library functions manual 💖 this one is a whole vibe: it's the Left-looking recursive panel factorization. yes queen, we're doing linear algebra in the group chat now 🫶

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🌸 NAME 🌸

HPL_pdrpanllN — Left-looking recursive panel factorization. that's it, that's the girl 💅

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🦋 SYNOPSIS 🦋

#include "hpl.h"

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

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👑 DESCRIPTION 👑

so HPL_pdrpanllN recursively factorizes a panel of columns using the recursive Left-looking variant of the one-dimensional algorithm. lowkey iconic. ✨

the lower triangular N0-by-N0 upper block of the panel is stored in no-transpose form (i.e. just like the input matrix itself). no flipping, no transposing, we're keeping it exactly how it came in 🎀

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, bigger texts, we love efficiency fr fr 💬

on P processes, and assuming bi-directional links, the running time of this function can be approximated by this (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. okay werk 👑

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. not a drill, that's literally double 💀

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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 giving ✨the source of truth✨
• 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. like, where does the little sub-matrix live inside the big one? there. found her 📍
• WORK — (local workspace) double *. on entry, WORK is a workarray of size at least 2*(4+2*N0). give her room to breathe, she needs it 🫶

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🌈 SEE ALSO 🌈

the whole friend group, no cap:

• 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_pdrpanllT (3)
• HPL_pdrpanrlN (3)
• HPL_pdrpanrlT (3)
• HPL_pdfact (3)

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and that's the page, bestie!! this one's from HPL 2.2, dated February 24, 2016 🎀 go forth and factorize those panels, you absolute main character 💅✨