PZLACPY(l)

📦 version 1.5, in ubuntu jammy

🦋 PZLACPY 🦋

okay bestie, sit down, hydrate, because today we're talking about PZLACPY(l) — a LAPACK auxiliary routine, version 1.5, and honestly? it's giving "simple but essential." no cap. it's a lil copy-paste gremlin for distributed matrices and i'm obsessed with how unbothered it is. 💅

✨ NAME ✨

PZLACPY — copies all or part of a distributed matrix A to another distributed matrix B. that's it. that's the whole job. 🎀

🌸 SYNOPSIS 🌸

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

    CHARACTER       UPLO

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

    INTEGER         DESCA( * ), DESCB( * )

    COMPLEX*16      A( * ), B( * )

look at that signature. ten arguments, zero drama. 🫶

💖 PURPOSE 💖

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

No communication is performed — like, literally none, it's a purely local glow-up. PZLACPY 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).

(and yes bestie, the manpage really does write it as sub( A ) := sub( B ), even though the description reads like it's copying A into B. i am simply reporting the lore, not rewriting it. 🙈)

📓 Notes 📓

Every global data object is described by an associated description vector. This vector stores the info 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".

  • 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 👑

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) COMPLEX*16 pointer into the local memory 🦋

Pointer 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*16 pointer into the local memory ✨

Pointer 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.

reminder bestie: the indices IA, JA, IB, JB are global and the A/B pointers are local — do not mix those up or the vibe check will fail. 💀

and that's the whole page, periodt. this was PZLACPY(l) from LAPACK version 1.5, dated 12 May 1997 — old enough to be a vintage icon, still slaying in every ScaLAPACK build. mwah. 💅💖🦋

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