PDLACPY(l)

📦 version 1.5, in ubuntu jammy

💖 NAME 💖

PDLACPY — it copies all or part of a distributed matrix A to another distributed matrix B. that's it, that's the whole job. she's an auxiliary routine, she lives in the l manual section, and she is lowkey iconic for it. 💅

✨ SYNOPSIS ✨

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

    CHARACTER       UPLO

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

    INTEGER         DESCA( * ), DESCB( * )

    DOUBLE          PRECISION A( * ), B( * )

like… look at her. ten arguments. no thoughts. only copying. 🫶

🦋 PURPOSE 🦋

okay so PDLACPY copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PDLACPY 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).

not me just typing that exactly as the original wrote it 😭 bestie I am quoting, okay, I'm not the one who decided the direction of that assignment. periodt.

🌸 Notes

every 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 giving ✨paperwork✨ but it's necessary paperwork.

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) — 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) — DESCA( M_ ) — the number of rows in the global array A.
  • N_A (global) — DESCA( N_ ) — the number of columns in the global array A.
  • MB_A (global) — DESCA( MB_ ) — the blocking factor used to distribute the rows of the array.
  • NB_A (global) — DESCA( NB_ ) — the blocking factor used to distribute the columns of the array.
  • RSRC_A (global) — DESCA( RSRC_ ) — the process row over which the first row of the array A is distributed.
  • CSRC_A (global) — DESCA( CSRC_ ) — the process column over which the first column of the array A is distributed.
  • LLD_A (local) — 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 🎀

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

🦋 she's an output bestie, so don't come crying to me if you were using B as your input, the array literally does not care.

  • 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.
fr fr, that's all of it. no SEE ALSO, no exit statuses, no env vars, no bugs section — the original page is just vibes and index arithmetic, and we respect that. 👑

mwah 💋 this has been PDLACPY from LAPACK version 1.5, dated 12 May 1997. old enough to be a vintage queen and still out here doing local copies with zero communication. slay, honestly. 💜✨

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