PSLACPY(l)

📦 version 1.5, in ubuntu jammy

🌸 PSLACPY — LAPACK auxiliary routine 💖

okay bestie, welcome to PSLACPY(l), a LAPACK auxiliary routine and honestly? a little legend. she's the one who copies stuff. that's the whole job. and she does it locally.

✨ NAME ✨

PSLACPY — copies all or part of a distributed matrix A to another distributed matrix B. no cap, that's it. that's her whole thing. 🦋

🌈 SYNOPSIS 🌈

SUBROUTINE PSLACPY( UPLO, M, N, A, IA, JA, DESCA, B, IB, JB, DESCB )

    CHARACTER       UPLO

    INTEGER         IA, IB, JA, JB, M, N

    INTEGER         DESCA( * ), DESCB( * )

    REAL            A( * ), B( * )

look at that signature. eleven arguments. she's lowkey high maintenance but she delivers. 💅

🎀 PURPOSE 🎀

PSLACPY copies all or part of a distributed matrix A to another distributed matrix B.

and here's the part that makes her iconic: no communication is performed. zero. none. not a single message passed between processes. PSLACPY performs a local copy sub( A ) := sub( B ), where sub( A ) denotes A(IA:IA+M-1,JA:JA+N-1) and sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1).

so like, everybody does their own little corner and nobody has to talk about it. the dream, honestly. 😌

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".

here's the whole lore, itemized for ur convenience:

  • 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 rise up 📐✨

👑 ARGUMENTS 👑

  • UPLO — (global input) CHARACTER. specifies the part of the distributed matrix sub( A ) to be copied:
    • = 'U': upper triangular part is copied; the strictly lower triangular part of sub( A ) is not referenced;
    • = 'L': lower triangular part is copied; the strictly upper triangular part of sub( A ) is not referenced;
    • otherwise: all of the matrix sub( A ) is copied.

(yes bestie, the "otherwise" branch is the chaos option and it's valid. live ur truth.)

  • M — (global input) INTEGER. the number of rows to be operated on, i.e the number of rows of the distributed submatrix sub( A ). M >= 0.
  • N — (global input) INTEGER. the number of columns to be operated on, i.e the number of columns of the distributed submatrix sub( A ). N >= 0.
  • A — (local input) REAL pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N-1) ). this array contains the local pieces of the distributed matrix sub( A ) to be copied from.
  • IA — (global input) INTEGER. the row index in the global array A indicating the first row of sub( A ).
  • JA — (global input) INTEGER. the column index in the global array A indicating the first column of sub( A ).
  • DESCA — (global and local input) INTEGER array of dimension DLEN_. the array descriptor for the distributed matrix A.
  • B — (local output) REAL pointer into the local memory to an array of dimension (LLD_B, LOCc(JB+N-1) ). this array contains on exit the local pieces of the distributed matrix sub( B ) set as follows:
    • if UPLO = 'U', B(IB+i-1,JB+j-1) = A(IA+i-1,JA+j-1), 1<=i<=j, 1<=j<=N;
    • if UPLO = 'L', B(IB+i-1,JB+j-1) = A(IA+i-1,JA+j-1), j<=i<=M, 1<=j<=N;
    • otherwise, B(IB+i-1,JB+j-1) = A(IA+i-1,JA+j-1), 1<=i<=M, 1<=j<=N.

the indexing goblins have been fed, we're good. 🙈

  • IB — (global input) INTEGER. the row index in the global array B indicating the first row of sub( B ).
  • JB — (global input) INTEGER. the column index in the global array B indicating the first column of sub( B ).
  • DESCB — (global and local input) INTEGER array of dimension DLEN_. the array descriptor for the distributed matrix B.
heads up: PSLACPY does not do any communication. if you were hoping she'd gossip across the process grid for you — she will not. that's a different routine's job, bestie. 🫶

that's the whole page!! now go forth and copy ur local pieces. 💖

LAPACK version 1.5 · 12 May 1997 — yeah she's vintage, she's been serving since '97 and she still eats. mwah. 💅🌸🦋✨

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