PCLACPY(l)

✨ NAME ✨

PCLACPY — the iconic little routine that copie all or part of a distributed matrix A to another distributed matrix B 💅

This one lives in the LAPACK auxiliary routine lineup, version 1.5, and bestie it is a whole mood: it's a copy routine, but make it distributed. 🦋

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🌸 SYNOPSIS 🌸

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

    CHARACTER       UPLO

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

    INTEGER         DESCA( * ), DESCB( * )

    COMPLEX         A( * ), B( * )

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💖 PURPOSE 💖

okay so here's the tea 🍓: PCLACPY copies all or part of a distributed matrix A to another distributed matrix B. And the way that it does this? No communication is performed. None. Zero. It just does a local copy, like:

sub( A ) := sub( B )

where sub( A ) means A(IA:IA+M-1,JA:JA+N-1) and sub( B ) means B(IB:IB+M-1,JB:JB+N-1). Local queen behaviour only, no gossip between processes 💅

📝 Notes 📝

Every global data object has an associated description vector, and that vector is holding all the info you need to map an object element to its process and memory location. iykyk.

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". (Not me explaining the underscore, but here we are 🙈)

• 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

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🎀 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. slay, no notes 💅
• 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. fr fr, don't be out here passing negatives.
• 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) COMPLEX 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) COMPLEX 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. 🫶

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heads up bestie: PCLACPY does no communication, so it only touches whatever local pieces you already own. It's a local copy, periodt. ✨

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signing off from the group chat 🎀 this was LAPACK version 1.5, dated 12 May 1997, and yes the vibe is immaculate, the routine is iconic, and you understood all of it. no cap. 💜🦋💅