larra(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

✨ NAME ✨

larra — bestie, this is literally the step in stemr 🎀 like it's the splitting-points girlie of the LAPACK universe, and no cap, she eats.

🌸 SYNOPSIS 🌸

💜 Functions

  • subroutine dlarra (n, d, e, e2, spltol, tnrm, nsplit, isplit, info) — DLARRA computes the splitting points with the specified threshold. (double precision version, she's giving precision 💅)
  • subroutine slarra (n, d, e, e2, spltol, tnrm, nsplit, isplit, info) — SLARRA computes the splitting points with the specified threshold. (single precision twin, same energy fr fr)

🦋 Detailed Description 🦋

okay so real talk: this page is the full documentation dump, and below you'll find every single function doc in all its glory. no skips, no cuts, we're reading the whole thing together bestie 🫶

👑 Function Documentation 👑

⭐ subroutine dlarra (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) e2, double precision spltol, double precision tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)

subroutine dlarra (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) e2, double precision spltol, double precision tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)

DLARRA computes the splitting points with the specified threshold. she's the main character of this page ngl 💅

🔥 Purpose:

Compute the splitting points with threshold SPLTOL. DLARRA sets any off-diagonal elements to zero. like, literally zero. gone. periodt ✨

🌈 Parameters

  • N

N is INTEGER. The order of the matrix. N > 0. (no zero-sized matrix shenanigans, she said positive only 🙈)

  • D

D is DOUBLE PRECISION array, dimension (N). On entry, the N diagonal elements of the tridiagonal matrix T. the main-character diagonal, yup 🎀

  • E

E is DOUBLE PRECISION array, dimension (N). On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched. so she only zeroes her chosen spots, the rest stay exactly as they were — respectful queen 🫶

  • E2

E2 is DOUBLE PRECISION array, dimension (N). On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero. yes bestie, SQUARES — like the subdiagonal but pre-squared, iykyk 🔥

  • SPLTOL

SPLTOL is DOUBLE PRECISION. The threshold for splitting. Two criteria can be used: SPLTOL<0 : criterion based on absolute off-diagonal value; SPLTOL>0 : criterion that preserves relative accuracy. so like, negative means absolute-value vibes, positive means relative-accuracy vibes — pick your fighter 💀

  • TNRM

TNRM is DOUBLE PRECISION. The norm of the matrix. that's it, that's the whole parameter, she's just the norm 🌸

  • NSPLIT

NSPLIT is INTEGER. The number of blocks T splits into. 1 <= NSPLIT <= N. the block count, bounded and beautiful ⭐

  • ISPLIT

ISPLIT is INTEGER array, dimension (N). The splitting points, at which T breaks up into blocks. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. it's giving "cut here, cut here, cut here" and honestly? obsessed with the indexing 💅

  • INFO

INFO is INTEGER. = 0: successful exit. that's the only value listed, and it's the one we like 😭✨

💖 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Contributors:

Beresford Parlett, University of California, Berkeley, USA

Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA

Definition at line 134 of file dlarra.f.

🌟 subroutine slarra (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) e2, real spltol, real tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)

subroutine slarra (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) e2, real spltol, real tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)

SLARRA computes the splitting points with the specified threshold. same job, single precision, still iconic 🦋

🔥 Purpose:

Compute the splitting points with threshold SPLTOL. SLARRA sets any off-diagonal elements to zero. zeroed. deleted. bye 💀

🌈 Parameters

  • N

N is INTEGER. The order of the matrix. N > 0. (again: positive only, she does not do zero 🙈)

  • D

D is REAL array, dimension (N). On entry, the N diagonal elements of the tridiagonal matrix T. the diagonal, but make it REAL 🎀

  • E

E is REAL array, dimension (N). On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched. selective zeroing only, we love a considerate algorithm 🫶

  • E2

E2 is REAL array, dimension (N). On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero. SQUARES again, don't forget the squares bestie 🔥

  • SPLTOL

SPLTOL is REAL. The threshold for splitting. Two criteria can be used: SPLTOL<0 : criterion based on absolute off-diagonal value; SPLTOL>0 : criterion that preserves relative accuracy. same two modes, same drama, pick wisely 💅

  • TNRM

TNRM is REAL. The norm of the matrix. still just vibing as the norm 🌸

  • NSPLIT

NSPLIT is INTEGER. The number of blocks T splits into. 1 <= NSPLIT <= N. bounded block baddie ⭐

  • ISPLIT

ISPLIT is INTEGER array, dimension (N). The splitting points, at which T breaks up into blocks. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. literally the same slicing scheme, and it still slays 💖

  • INFO

INFO is INTEGER. = 0: successful exit. success only, we don't know her otherwise 😭✨

💖 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Contributors:

Beresford Parlett, University of California, Berkeley, USA

Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA

Definition at line 134 of file slarra.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. (yes, the robots wrote the docs, we just gave them a glow-up ✨)

ok that's the whole page bestie, every flag, every parameter, every contributor — nothing dropped, nothing guessed 💅

LAPACK, Version 3.12.0, and this little larra(3) page — written by Doxygen, narrated by me, delivered with love 🎀 mwah, go split some matrices responsibly 🫶💖

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