PZLASET(l)

💖 PZLASET 💖

okay bestie, welcome to the LAPACK auxiliary routine glow-up, PZLASET, living its best life in LAPACK version 1.5 🌸 (yes, this is a PZ routine — the P is for parallel/distributed, and the Z is for COMPLEX*16 because we are fancy 💅).

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✨ NAME ✨

PZLASET — initialize 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.

That's it. That's the job. We're setting numbers, and we're setting them correctly. 👑

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🎀 SYNOPSIS 🎀

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

    CHARACTER       UPLO

    INTEGER         IA, JA, M, N

    COMPLEX*16      ALPHA, BETA

    INTEGER         DESCA( * )

    COMPLEX*16      A( * )

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🦋 PURPOSE 🦋

PZLASET 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. no cap, that's the whole personality 🌈

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📝 Notes (the lore, if you will)

Each 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. it's giving "your data's home address" 🏠

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". bestie, read it like it's a surname: M_A = "M, of the global array A" 🫶

• DTYPE_A(global) — DESCA( DTYPE_ ) — The descriptor type. In this case, DTYPE_A = 1.
• CTXT_A (global) — 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) — DESCA( M_ ) — The number of rows in the global array A.
• N_A (global) — DESCA( N_ ) — The number of columns in the global array A.
• MB_A (global) — DESCA( MB_ ) — The blocking factor used to distribute the rows of the array.
• NB_A (global) — DESCA( NB_ ) — The blocking factor used to distribute the columns of the array.
• RSRC_A (global) — DESCA( RSRC_ ) — The process row over which the first row of the array A is distributed.
• CSRC_A (global) — DESCA( CSRC_ ) — The process column over which the first column of the array A is distributed.
• LLD_A (local) — 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 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.

(yes bestie, anything that isn't 'U' or 'L' gets the full send 🚀)

• 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) COMPLEX*16. The constant to which the offdiagonal elements are to be set.
• BETA — (global input) COMPLEX*16. The constant to which the diagonal elements are to be set.
• A — (local output) COMPLEX*16 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).

(the IA+i.NE.JA+j bit is the "not the diagonal" check — the diagonal is BETA's moment and nobody else's 💅)

• 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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reminder bestie: every global data object is described by an associated description vector, and this vector stores the info you need to map an object element to its process and memory location. that's not a vibe, that's a requirement. 🧚

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okay that's the whole page, you ate it, you understood it, we're obsessed 💖 signed off with love from LAPACK version 1.5, dated 12 May 1997 — an absolute icon, no notes. 🎀🦋✨