HPL_pdlange(3)

💖 HPL_pdlange — it's giving norms, bestie 💖

okay so this is a page from the HPL Library Functions manual (the whole HPL 2.2 situation), and today's main character is HPL_pdlange. Sit down, hydrate, and let's compute a matrix norm together. 🫶

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✨ NAME ✨

HPL_pdlange — Compute ||A||. that's it, that's the whole job, she computes a norm and she does it flawlessly 💅

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🌸 SYNOPSIS 🌸

#include "hpl.h"

double HPL_pdlange( const HPL_T_grid * GRID, const HPL_T_NORM NORM,
const int M, const int N, const int NB, const double * A, const int LDA
);

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🦋 DESCRIPTION 🦋

so HPL_pdlange hands you back the value of the one norm, or the infinity norm, or the element of largest absolute value of a distributed matrix A, depending on the vibe you requested:

• max(abs(A(i,j))) when NORM = HPL_NORM_A,
• norm1(A), when NORM = HPL_NORM_1,
• normI(A), when NORM = HPL_NORM_I,

where norm1 is the one norm of a matrix (maximum column sum) and normI is the infinity norm of a matrix (maximum row sum).

okay important lore drop 🔥 — max(abs(A(i,j))) is not a matrix norm. like, technically speaking, not a norm. she's just the biggest absolute value hanging out in there. don't let anyone tell you otherwise, no cap.

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👑 ARGUMENTS 👑

every single one of these, in order, because we respect the interface in this house 🎀

• GRID — (local input) const HPL_T_grid * — on entry, GRID points to the data structure containing the process grid information. it's the map, bestie 🗺️
• NORM — (global input) const HPL_T_NORM — on entry, NORM specifies the value to be returned by this function, as described up above. you pick the flavor, she picks the math ✨
• M — (global input) const int — on entry, M specifies the number of rows of the matrix A. M must be at least zero.
• N — (global input) const int — on entry, N specifies the number of columns of the matrix A. N must be at least zero.
• NB — (global input) const int — on entry, NB specifies the blocking factor used to partition and distribute the matrix. NB must be larger than one.
• A — (local input) const double * — on entry, A points to an array of dimension (LDA,LocQ(N)), that contains the local pieces of the distributed matrix A. local pieces only, she's distributed, that's the whole point 💀
• LDA — (local input) const int — on entry, LDA specifies the leading dimension of the array A. LDA must be at least max(1,LocP(M)).

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🌈 SEE ALSO 🌈

the girlies she runs with:

• HPL_pdlaprnt (3)
• HPL_fprintf (3)

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💜 and that's the page 💜

written up as part of HPL 2.2, dated February 24, 2016 — and yeah, she still eats. go forth, compute your norms, and remember: max(abs(A(i,j))) is not a matrix norm, iykyk. periodt. 💅🌸✨