PSLATRA(l)

📦 version 1.5, in ubuntu jammy

💅 PSLATRA — the tea (from the l manual, aka LAPACK auxiliary routine territory)

okay so bestie, welcome to PSLATRA, a LAPACK auxiliary routine, and she's giving "quiet little math gremlin who does exactly one thing and does it flawlessly." No cap. Let's get into it. 🎀

✨ NAME ✨

PSLATRA — compute the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ).

That's it. That's her whole job. Iconic behavior, honestly. 👑

✨ SYNOPSIS ✨

REAL FUNCTION PSLATRA( N, A, IA, JA, DESCA )

    INTEGER   IA, JA, N

    INTEGER   DESCA( * )

    REAL      A( * )

✨ PURPOSE ✨

PSLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). And here's the slay part: the result is left on every process of the grid. Not one process. Not the main character process. Every process. Sharing is caring fr fr. 🫶

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, the descriptor lore, laid out one item at a time because we don't do ugly tables here:

  • 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. She's a vibe, not a constant. 💀
  • 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 girlies stay winning ✨

✨ ARGUMENTS ✨

  • N — (global input) INTEGER. The number of rows and columns to be operated on i.e the order of the distributed submatrix sub( A ). N >= 0. No negativity allowed in this household. 🚫
  • A — (local input) 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 the trace is to be computed. It's just her lil slice of the big picture. 🌸
  • 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. Yes she's both global and local, she contains multitudes, main character energy fr. 👑
heads up bestie: nothing here is deprecated or cursed — PSLATRA is a well-behaved queen. Just keep N >= 0 and your descriptor correct, and you're golden. 💖

and that's the whole page, no crumbs left. LAPACK version 1.5, dated 12 May 1997 — so yeah she's vintage, she's archival, she's serving retro tech realness and we're obsessed. mwah, study safe, bye bestie!! 🦋💜✨

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