PSLARED1D(l)

📦 version 1.5, in ubuntu jammy

💖 PSLARED1D 💖

okay bestie, gather round, because today we're talking about PSLARED1D — a LAPACK routine, version 1.5, straight out of the l manual section. she's a ScaLAPACK girlie. she takes a 1D array that's all spread out across your process rows and redistributes it so everybody's got the whole thing. no cap. ✨

🎀 NAME 🎀

PSLARED1D — redistribute a 1D array. It assumes that the input array, BYCOL, is distributed across rows and that all process columns contain the same copy of BYCOL. 💅

🦋 SYNOPSIS 🦋

SUBROUTINE PSLARED1D( N, IA, JA, DESC, BYCOL, BYALL, WORK, LWORK )

    INTEGER           IA, JA, LWORK, N

    INTEGER           DESC( * )

    REAL              BYALL( * ), BYCOL( * ), WORK( LWORK )

✨ PURPOSE ✨

PSLARED1D redistributes a 1D array and will contain the entire array. periodt. 👑

💜 Notes 💜

Every single global data object out there is described by an associated description vector, okay? That vector is literally storing all the info you need to establish the mapping between an object element and its corresponding process and memory location. iykyk. 🧚

So 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".

  • 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 🌈

NP = Number of local rows in BYCOL()

  • N (global input) INTEGER — the number of elements to be redistributed. N >= 0. 🍓
  • IA (global input) INTEGER — IA must be equal to 1.
  • JA (global input) INTEGER — JA must be equal to 1.
  • DESC (global/local input) INTEGER Array of dimension 8 — a 2D array descirptor, which describes BYCOL.
  • BYCOL (local input) distributed block cyclic REAL array — global dimension (N), local dimension NP. BYCOL is distributed across the process rows. All process columns are assumed to contain the same value.
  • BYALL (global output) REAL global dimension( N ) — local dimension (N). BYALL is exactly duplicated on all processes. It contains the same values as BYCOL, but it is replicated across all processes rather than being distributed.
BYALL(i) = BYCOL( NUMROC(i,NB,MYROW,0,NPROW ) on the procs whose
MYROW == mod((i-1)/NB,NPROW)
  • WORK (local workspace) REAL dimension (LWORK) — used to hold the buffers sent from one process to another.
  • LWORK (local input) INTEGER size of WORK array — LWORK >= NUMROC(N, DESC( NB_ ), 0, 0, NPCOL).
💀 bestie reminder: IA and JA must be 1. not 0, not 2, not "eh close enough". the routine will not be vibing with you otherwise.

and that's the whole page, no notes, she ate 💅✨

LAPACK version 1.5 — 12 May 1997 🫶 that's the version and the date this icon was borned, mwah, bye bestie! 🎀🦋💖

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