PDLAWIL(l)

🌸 PDLAWIL 🌸 — the PDLAWIL(l) glow-up, LAPACK routine version 1.5 bestie 💅

okay so. picture this: you're deep in ScaLAPACK land, version 1.5, and you need to move a transform into V. that's the whole vibe. let's get into it. ✨

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🎀 NAME 🎀

PDLAWIL — it gets the transform given by H44, H33, & H43H34 into V starting at row M. that's it, that's the girl. 👑

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🦋 SYNOPSIS 🦋

SUBROUTINE PDLAWIL( II, JJ, M, A, DESCA, H44, H33, H43H34, V )

    INTEGER         II, JJ, M

    DOUBLE          PRECISION H33, H43H34, H44

    INTEGER         DESCA( * )

    DOUBLE          PRECISION A( * ), V( * )

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💖 PURPOSE 💖

PDLAWIL gets the transform given by H44, H33, & H43H34 into V starting at row M. fr fr. 💫

📝 Notes 📝

so like, every single global data object out here is described by an associated description vector. that vector is storing all the info you need to establish the mapping between an object element and its corresponding process and memory location. no cap. 🫶

let A be a generic term for any 2D block cyclicly distributed array. such a global array has an associated description vector DESCA. in the following comments, the character _ should be read as "of the global array". iykyk. 💅

here's the whole notation roster, bestie — every single one of them:

• DTYPE_A (global) — stored in DESCA( DTYPE_ ) — the descriptor type. In this case, DTYPE_A = 1.
• CTXT_A (global) — stored in DESCA( CTXT_ ) — the BLACS context handle, indicating the BLACS process grid A is distributed over. The context itself is global, but the handle (the integer value) may vary.
• M_A (global) — stored in DESCA( M_ ) — the number of rows in the global array A.
• N_A (global) — stored in DESCA( N_ ) — the number of columns in the global array A.
• MB_A (global) — stored in DESCA( MB_ ) — the blocking factor used to distribute the rows of the array.
• NB_A (global) — stored in DESCA( NB_ ) — the blocking factor used to distribute the columns of the array.
• RSRC_A (global) — stored in DESCA( RSRC_ ) — the process row over which the first row of the array A is distributed.
• CSRC_A (global) — stored in DESCA( CSRC_ ) — the process column over which the first column of the array A is distributed.
• LLD_A (local) — stored in DESCA( LLD_ ) — the leading dimension of the local array. LLD_A >= MAX(1,LOCr(M_A)).

let K be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q.

LOCr( K ) denotes the number of elements of K that a process would receive if K were distributed over the p processes of its process column.

similarly, LOCc( K ) denotes the number of elements of K that a process would receive if K were distributed over the q processes of its process row.

the values of LOCr() and LOCc() may be determined via a call to the ScaLAPACK tool function, NUMROC:

LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).

an upper bound for these quantities may be computed by:

LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

slay. 💅

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✨ ARGUMENTS ✨

• II — (global input) INTEGER. Row owner of H(M+2,M+2). 👑
• JJ — (global input) INTEGER. Column owner of H(M+2,M+2). 🎀
• M — (global input) INTEGER. On entry, this is where the transform starts (row M). Unchanged on exit. the way she just stays the same? iconic. 💖
• A — (global input) DOUBLE PRECISION array, dimension (DESCA(LLD_),*). On entry, the Hessenberg matrix. Unchanged on exit. she's just there for the vibes, not changing a thing. 🌸
• DESCA — (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix A. Unchanged on exit. 🦋
• H44 H33 H43H34 — (global input) DOUBLE PRECISION. These three values are for the double shift QR iteration. Unchanged on exit. the trio. the main characters. 🔥
• V — (global output) DOUBLE PRECISION array of size 3. Contains the transform on output. ✨👑

reminder bestie: II, JJ, M, A, DESCA, and the H44/H33/H43H34 trio are all input — only V is the output. don't get it twisted. 💀

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Implemented by: G. Henry, November 17, 1996. 🫶

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and that's the whole page, no notes left behind, periodt. 💅 this was PDLAWIL(l) from <b>LAPACK version 1.5</b>, dated <b>12 May 1997</b> — mwah, take care of her, she's been carrying double shift QR since the 90s. 🎀✨