PDLACP2(l)

📦 version 1.5, in ubuntu jammy

💖 PDLACP2 💖

okay bestie, welcome to PDLACP2(l) — a LAPACK auxiliary routine, version 1.5, and she's serving pure local-copy realness. no drama, no network, just vibes and memcpy energy. let's get into it 🫶

✨ NAME ✨

PDLACP2 — copies all or part of a distributed matrix A to another distributed matrix B. that's it. that's the whole job. and she does it flawlessly. 💅

🌸 SYNOPSIS 🌸

SUBROUTINE PDLACP2( 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( * )

🦋 PURPOSE 🦋

okay so here's the tea, bestie: PDLACP2 copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed. none. zero. not a single message gets sent. it is purely a local copy — the page says 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). (yep, that's literally how the page writes it, and the argument descriptions below walk through the copy going from A into B — iykyk. 😭)

and PDLACP2 requires that only the dimension of the matrix operands is distributed. that's the whole rule. respect it. 🎀

📓 Notes 📓

every global data object gets described by an associated description vector. this vector stores all the info you need to establish the mapping between an object element and its corresponding process and memory location. it's giving ✨paperwork✨ but make it essential.

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 notation breakdown, no skips, no cuts, we keep every crumb:

  • 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

like, that's the math, and she's gorgeous. 📐✨

👑 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.
  • 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.
  • 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 every single argument, every single bound, every single formula. nothing got left on read. 🫶

and that's the page, bestie!! she's LAPACK version 1.5, dated 12 May 1997, and she's still out here copying submatrices with zero communication and maximum main character energy. periodt. 👑💖✨

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