PSLASET(l)

✨ NAME ✨

okay bestie, say hi to PSLASET 💖 — she's a LAPACK auxiliary routine, living her best life on version 1.5, and she has exactly one job.

She initializes an M-by-N distributed matrix sub( A ) — meaning A(IA:IA+M-1,JA:JA+N-1) — to BETA on the diagonal and ALPHA on the offdiagonals. That's it. That's the assignment. And she DEVOURED. 🔥

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🦋 SYNOPSIS 🦋

SUBROUTINE PSLASET( UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )

    CHARACTER       UPLO

    INTEGER         IA, JA, M, N

    REAL            ALPHA, BETA

    INTEGER         DESCA( * )

    REAL            A( * )

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💅 PURPOSE 💅

So like, PSLASET initializes an M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1) to BETA on the diagonal and ALPHA on the offdiagonals. Simple. Elegant. No notes. 🌸

📖 Notes 📖

ngl this part is the lore drop you actually need, so don't skip it 🫶

Every global data object comes with an associated description vector. That vector stores all the info you need to establish the mapping between an element of the object and its corresponding process and memory location.

Let A be a generic term for any 2D block cyclicly distributed array. A global array like that has an associated description vector DESCA. And in the comments below, bestie, the character _ should be read as "of the global array". iykyk 💫

Here's the full rundown of what lives inside that descriptor:

• 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)).

Okay so now let K be the number of rows or columns of a distributed matrix, and assume 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 which part of the distributed matrix sub( A ) is getting set, and this one matters so listen up:
  • = 'U': the upper triangular part is set; the strictly lower triangular part of sub( A ) is not changed.
  • = 'L': the lower triangular part is set; the strictly upper triangular part of sub( A ) is not changed.
  • Otherwise: all of the matrix sub( A ) is set.
• 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. 💜
• ALPHA (global input) REAL — the constant to which the offdiagonal elements are to be set.
• BETA (global input) REAL — the constant to which the diagonal elements are to be set.
• A (local output) 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 set. On exit, the leading M-by-N submatrix sub( A ) is set as follows:

if UPLO = 'U', A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=j-1, 1<=j<=N,
if UPLO = 'L', A(IA+i-1,JA+j-1) = ALPHA, j+1<=i<=M, 1<=j<=N,
otherwise,     A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=M, 1<=j<=N,
IA+i.NE.JA+j,
and, for all UPLO, A(IA+i-1,JA+i-1) = BETA,
1<=i<=min(M,N).

• 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.

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fr fr, don't forget: UPLO decides what gets touched and what gets left completely alone, and the diagonal always gets BETA no matter which UPLO you picked. 💀🙈

and that's the whole page, bestie, you're officially fluent in PSLASET 🎀

This was brought to you by LAPACK version 1.5, dated 12 May 1997 — yes she's an elder but she's still THAT girl 💖✨🦋🌸💅🫶👑🌈⭐