PDLARED1D(l)

📦 version 1.5, in ubuntu jammy

✨ NAME ✨

PDLARED1D — okay so bestie, this one redistributes a 1D array. 💅 It assumes that the input array, BYCOL, is distributed across rows and that all process column contain the same copy of BYCOL. That's the whole assignment. No cap.

🌈 SYNOPSIS 🌈

SUBROUTINE PDLARED1D( N, IA, JA, DESC, BYCOL, BYALL, WORK, LWORK )

    INTEGER           IA, JA, LWORK, N

    INTEGER           DESC( * )

    DOUBLE            PRECISION BYALL( * ), BYCOL( * ), WORK( LWORK )

🎀 PURPOSE 🎀

PDLARED1D redistributes a 1D array and will contain the entire array. 🦋 She's giving "gather the girlies back together" energy and honestly? Iconic.

📓 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. It's the group chat of data structures fr fr.

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. she moves around, it's a whole thing.
  • 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. Zero is fine, she's flexible.
  • IA (global input) INTEGER — IA must be equal to 1. Not 2. Not 0. One. Periodt.
  • JA (global input) INTEGER — JA must be equal to 1. Same deal, bestie.
  • DESC (global/local input) INTEGER Array of dimension 8 — A 2D array descirptor, which describes BYCOL. Yes she's an 8-element glow-up passport for the array.
  • BYCOL (local input) distributed block cyclic DOUBLE PRECISION array — global dimension (N), local dimension NP. BYCOL is distributed across the process rows. All process columns are assumed to contain the same value. Everyone's got the same copy, no drama.
  • BYALL (global output) DOUBLE PRECISION — 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) DOUBLE PRECISION dimension (LWORK) — Used to hold the buffers sent from one process to another. It's the messenger bag. She carries the goods.
  • LWORK (local input) INTEGER size of WORK array — LWORK >= NUMROC(N, DESC( NB_ ), 0, 0, NPCOL)
⚠️ Real talk: those IA = 1 and JA = 1 requirements are not suggestions, and the LWORK bound is a whole boundary. Respect the numbers or the routine will simply not be your friend. 💀

And that's the page, bestie!! 🫶 This whole thing is LAPACK version 1.5, dated 12 May 1997 — vintage, honestly, but she still eats. 💖✨ Go redistribute something. 🌸

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