PSLARED2D(l)

📦 version 1.5, in ubuntu jammy

💖 PSLARED2D(l) 💖

okay bestie, gather round, because this is a LAPACK routine — from the legendary LAPACK version 1.5 era — and she's here to do one (1) job and do it slayfully. it's giving parallel redistribution, it's giving collective communication, it's giving "everyone gets a copy, no cap." 🫶

✨ NAME ✨

PSLARED2D — redistribute a 1D array. It assumes that the input array, BYROW, is distributed across columns and that all process rows contain the same copy of BYROW.

🌸 SYNOPSIS 🌸

SUBROUTINE PSLARED2D( N, IA, JA, DESC, BYROW, BYALL, WORK, LWORK )

    INTEGER           IA, JA, LWORK, N

    INTEGER           DESC( * )

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

👑 PURPOSE 👑

PSLARED2D redistributes a 1D array and will contain the entire array. periodt. 💅

🧚 Notes 🧚

okay so first, some lore you literally cannot skip. 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

💅 ARGUMENTS 💅

NP = Number of local rows in BYROW()

  • 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 DLEN_ — a 2D array descriptor, which describes BYROW.
  • BYROW — (local input) distributed block cyclic REAL array — global dimension (N), local dimension NP. BYCOL is distributed across the process columns. All process rows 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 >=
LWORK >= NUMROC(N, DESC( NB_ ), 0, 0, NPCOL)
no cap, watch those IA and JA values — they must be 1, bestie. the routine is not asking. 🙈

and that's the whole vibe. LAPACK version 1.5, dated 12 May 1997 — iconic, historic, and still out here redistributing arrays like the main character she is. mwah 💋

📦 where this page comes from