PDLASE2(l)

💖 PDLASE2 💖

okay so bestie, welcome to PDLASE2, a LAPACK auxiliary routine (we're on version 1.5 here, vintage but still slaying 💅). It's a little Fortran subroutine that paints a distributed matrix with exactly the values you tell it to. Let's get into it 🫶

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✨ NAME ✨

PDLASE2 — 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 🌸

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🌈 SYNOPSIS 🌈

SUBROUTINE PDLASE2( 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 🦋

So like, PDLASE2 initializes an M-by-N distributed matrix sub( A ) — that's A(IA:IA+M-1,JA:JA+N-1) — setting it to BETA on the diagonal and ALPHA on the offdiagonals. That's the whole glow-up ✨. One thing tho, and it's important: PDLASE2 requires that only dimension of the matrix operand is distributed. That's the vibe check it needs to pass 💀.

📝 Notes 📝

Every global data object has a little bestie called a description vector that follows it around. This vector stores the info you need to map an object element to its corresponding process and memory location. iykyk 🧚

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".

Here's the whole lore dump of what lives where 👑

• 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

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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.
• 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.

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okay that's the whole thing, no cap 🎀 go forth and set your diagonals, bestie. this page is from LAPACK version 1.5, dated 12 May 1997 (yes she's an elder icon and she still ate 👑). mwah, bye 💜🌈