PSLACP3(l)

📦 version 1.5, in ubuntu jammy

🦋 NAME 🦋

okay so bestie, meet PSLACP3 — she's a LAPACK routine (manual section l), and she's an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. yes, "vise versa," the manpage said it like that, we're keeping it, it's iconic 💅

✨ SYNOPSIS ✨

SUBROUTINE PSLACP3( M, I, A, DESCA, B, LDB, II, JJ, REV )

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

    INTEGER         DESCA( * )

    REAL            A( * ), B( LDB, * )

like, that's the whole vibe check right there 🫶

🌸 PURPOSE 🌸

PSLACP3 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. so basically: you pick who gets the data, and she makes it happen, no cap ✨

💖 Notes 💖

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". iykyk 🧚

  • 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

math girlies stay winning 🔥

💅 ARGUMENTS 💅

  • M — (global input) INTEGER. M is the order of the square submatrix that is copied. M >= 0. Unchanged on exit.
  • I — (global input) INTEGER. A(I,I) is the global location that the copying starts from. Unchanged on exit.
  • A — (global input/output) REAL 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.
  • B — (local input/output) REAL 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.
  • 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.
Implemented by: G. Henry, May 1, 1997 — shoutout to G. Henry, the original main character 👑

and that's the whole page bestie!! this is LAPACK version 1.5, dated 12 May 1997, and it lives in manual section l — so if you ever need her, that's where she's at 💜✨🎀

📦 where this page comes from