PDLACP3(l)

📦 version 1.5, in ubuntu jammy

✨ PDLACP3 — the lil helper that shuttles data between your global parallel array and a local replicated one ✨

okay bestie, buckle up, because this one is a LAPACK routine and it's lowkey a supporting character but it carries 🫶. It lives in the l manual, and yes, that's PDLACP3(l) for the girlies keeping score. Version energy: LAPACK routine version 1.5. Let's get into it 💅

🌸 NAME 🌸

PDLACP3 — she's an auxiliary routine that copies from a global parallel array into a local replicated array, or vise versa 🔁✨

🎀 SYNOPSIS 🎀

SUBROUTINE PDLACP3( M, I, A, DESCA, B, LDB, II, JJ, REV )

    INTEGER         I, II, JJ, LDB, M, REV

    INTEGER         DESCA( * )

    DOUBLE PRECISION A( * ), B( LDB, * )

💖 PURPOSE 💖

PDLACP3 is an auxiliary routine that copies from a global parallel array into a local replicated array, or vise versa. 🔄 Notice that the entire submatrix that is copied gets placed on one node or more. The receiving node can be specified precisely, or all nodes can receive, or just one row or column of nodes. no cap, it's giving flexible 😌

📓 Notes 📓

Every 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. (iykyk 🧠)

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".

Here's the whole lore, laid out for u:

  • 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. she's global but her handle is local, iconic 💅
  • 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 👑

  • M — (global input) INTEGER — M is the order of the square submatrix that is copied. M >= 0. Unchanged on exit. she comes in, she leaves, no notes 💅
  • I — (global input) INTEGER — A(I,I) is the global location that the copying starts from. Unchanged on exit.
  • A — (global input/output) DOUBLE PRECISION array, dimension (DESCA(LLD_),*) — On entry, the parallel matrix to be copied into or from. On exit, if REV=1, the copied data. Unchanged on exit if REV=0.
  • DESCA — (global and local input) INTEGER array of dimension DLEN_ — the array descriptor for the distributed matrix A. it's the vibe check for where everything lives 🗺️
  • B — (local input/output) DOUBLE PRECISION array of size (LDB,M) — If REV=0, this is the global portion of the array A(I:I+M-1,I:I+M-1). If REV=1, this is the unchanged on exit.
  • LDB — (local input) INTEGER — the leading dimension of B.
  • II — (global input) INTEGER — By using REV 0 & 1, data can be sent out and returned again. If REV=0, then II is destination row index for the node(s) receiving the replicated B. If II>=0,JJ>=0, then node (II,JJ) receives the data. If II=-1,JJ>=0, then all rows in column JJ receive the data. If II>=0,JJ=-1, then all cols in row II receive the data. If II=-1,JJ=-1, then all nodes receive the data. If REV<>0, then II is the source row index for the node(s) sending the replicated B. ok the negative-one thing is doing a LOT of work here and honestly? respect 😭
  • JJ — (global input) INTEGER — similar description as II above 👆
  • REV — (global input) INTEGER — use REV = 0 to send global A into locally replicated B (on node (II,JJ)). Use REV <> 0 to send locally replicated B from node (II,JJ) to its owner (which changes depending on its location in A) into the global A.
🚨 heads up bestie: REV = 0 and REV <> 0 are the two whole modes. don't freestyle it, pick one on purpose.

Implemented by: G. Henry, May 1, 1997 📝 (shoutout to G. Henry, the original main character of this file, May 1, 1997, no cap 🫡)

and that's the whole page!! 🌈💖 This was LAPACK version 1.5, dated 12 May 1997 — PDLACP3(l), signed, sealed, delivered, periodt ✨🦋🎀 Go copy something, you got this 💜

📦 where this page comes from