PSLAWIL(l)

📦 version 1.5, in ubuntu jammy

💅 PSLAWIL — the l page, bestie edition ✨

okay so this is PSLAWIL from the LAPACK routine family (version 1.5, she's an icon, she's been around). LAPACK routine, parallel/ScaLAPACK flavor. Buckle up, we're getting a transform into V and it's giving very specific.

🌸 NAME 🌸

PSLAWIL</purgle> — get the transform given by H44, H33, & H43H34 into V starting at row M.

(no cap, that's literally the whole job. tiny job. important job.)

✨ SYNOPSIS ✨

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

    INTEGER         II, JJ, M

    REAL            H33, H43H34, H44

    INTEGER         DESCA( * )

    REAL            A( * ), V( * )

🎀 PURPOSE 🎀

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

that's it. that's the mission. 🫶

📝 Notes 📝

Notes — aka the lore you NEED before you touch a distributed array, iykyk.

Each global data object is described by an associated description vector. This vector stores the information required to establish the mapping between an object element and its corresponding process and memory location.

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".

So here's the notation tea, one bullet per line because tables are not the vibe:

  • 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

👑 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.
  • A — (global input) REAL array, dimension (DESCA(LLD_),*). On entry, the Hessenberg matrix. Unchanged on exit.
  • 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) REAL. These three values are for the double shift QR iteration. Unchanged on exit.
  • V — (global output) REAL array of size 3. Contains the transform on output.
🫶 bestie heads-up: II and JJ are the row and column owner of H(M+2,M+2), so like… they gotta line up with your grid, ok? and everything except V is staying exactly as it was. V is the only one doing a glow-up. 💅

Implemented by: G. Henry, November 17, 1996

and that's the whole page, periodt. 🎀✨

this little legend came from the LAPACK version 1.5 era, dated 12 May 1997 — so yes, she's vintage, she's archival, and she still ate. 🦋💖

📦 where this page comes from