PCLASET(l)

🌸 NAME 🌸

okay so bestie, gather round — PCLASET(l) is a LAPACK auxiliary routine (we're on version 1.5, hey queen) and what it does is initialize an M-by-N distributed matrix sub( A ), aka A(IA:IA+M-1,JA:JA+N-1), setting BETA on the diagonal and ALPHA on the offdiagonals. That's it. That's the whole vibe. ✨

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✨ SYNOPSIS ✨

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

    CHARACTER       UPLO

    INTEGER         IA, JA, M, N

    COMPLEX         ALPHA, BETA

    INTEGER         DESCA( * )

    COMPLEX         A( * )

nine arguments, one character, two complex scalars, no notes. we love a low-maintenance icon 💅

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💖 PURPOSE 💖

PCLASET initializes an M-by-N distributed matrix sub( A ) — that's A(IA:IA+M-1,JA:JA+N-1) if you're keeping score — to BETA on the diagonal and ALPHA on the offdiagonals. filling in the blanks, but make it distributed.

📓 Notes 📓

okay this is the part where the descriptor lore drops, and honestly? it's giving essential.

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.

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

math class but make it cute. lowkey obsessed with NUMROC. 🧚

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🎀 ARGUMENTS 🎀

• UPLO — (global input) CHARACTER. Specifies the part of the distributed matrix sub( A ) to be set:
  • = 'U': Upper triangular part is set; the strictly lower triangular part of sub( A ) is not changed.
  • = 'L': 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. no negative row energy allowed bestie 🫶
• 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. same rules, same slay
• ALPHA — (global input) COMPLEX. The constant to which the offdiagonal elements are to be set. the off-diagonal main character ✨
• BETA — (global input) COMPLEX. The constant to which the diagonal elements are to be set. diagonal royalty 👑
• A — (local output) 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 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).

heads up: A is a local output — it's a pointer into your local memory, and the dimension is (LLD_A,LOCc(JA+N-1)). Don't get it twisted. 💀

• 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. the whole personality of the matrix, honestly 🌈

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and that's the whole page, bestie — no cap, every flag, every formula, every 1<=i<=j-1, all of it accounted for. periodt. 💅

this one came from LAPACK version 1.5, dated 12 May 1997, and it's still out here being iconic. mwah. 🎀✨