PDLASET(l)

💖 NAME 💖

PDLASET — bestie, this is a LAPACK auxiliary routine (we're in the l manual, so you know it's the auxiliary girlies ✨) and it does exactly one thing: it initializes an M-by-N distributed matrix sub( A ) — that's A(IA:IA+M-1,JA:JA+N-1) to be precise — setting BETA on the diagonal and ALPHA on the offdiagonals. That's the whole gig. No cap. 👑

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🌈 SYNOPSIS 🌈

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

    CHARACTER       UPLO

    INTEGER         IA, JA, M, N

    DOUBLE          PRECISION ALPHA, BETA

    INTEGER         DESCA( * )

    DOUBLE          PRECISION A( * )

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🦋 PURPOSE 🦋

PDLASET 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. Two constants, one matrix slice, so much slay. 💅

📓 Notes

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.

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".

So here's the little legend for all that notation, and yes, you need every single one of these 🫶:

• NOTATION DTYPE_A (global) — STORED IN DESCA( DTYPE_ ) — EXPLANATION: the descriptor type. In this case, DTYPE_A = 1.
• NOTATION CTXT_A (global) — STORED IN DESCA( CTXT_ ) — EXPLANATION: 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.
• NOTATION M_A (global) — STORED IN DESCA( M_ ) — EXPLANATION: the number of rows in the global array A.
• NOTATION N_A (global) — STORED IN DESCA( N_ ) — EXPLANATION: the number of columns in the global array A.
• NOTATION MB_A (global) — STORED IN DESCA( MB_ ) — EXPLANATION: the blocking factor used to distribute the rows of the array.
• NOTATION NB_A (global) — STORED IN DESCA( NB_ ) — EXPLANATION: the blocking factor used to distribute the columns of the array.
• NOTATION RSRC_A (global) — STORED IN DESCA( RSRC_ ) — EXPLANATION: the process row over which the first row of the array A is distributed.
• NOTATION CSRC_A (global) — STORED IN DESCA( CSRC_ ) — EXPLANATION: the process column over which the first column of the array A is distributed.
• NOTATION LLD_A (local) — STORED IN DESCA( LLD_ ) — EXPLANATION: 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. All of it. Every last crumb. 😌
• 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) DOUBLE PRECISION. The constant to which the offdiagonal elements are to be set.
• BETA — (global input) DOUBLE PRECISION. The constant to which the diagonal elements are to be set.
• A — (local output) DOUBLE PRECISION 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.

fr fr, do not sleep on DESCA — she's the whole map. Without her nobody knows which process holds which piece, and your sub( A ) is just vibes. 🧚

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okay that's the whole page bestie, you ate that 🎀 this was PDLASET(l) from the LAPACK auxiliary routine manual, version 1.5 — signed, sealed and dated 12 May 1997, LAPACK version 1.5, and yes she's still iconic. periodt. 💜✨