PCLATRA(l)

📦 version 1.5, in ubuntu jammy

💖 PCLATRA — LAPACK auxiliary routine, bestie edition 💖

okay so quick vibe check: this is PCLATRA from the LAPACK crew (auxiliary routine, version 1.5, she's an OG). she computes a trace. that's it. that's the whole job. and she does it beautifully. 🎀

✨ NAME ✨

PCLATRA — computes the trace of an N-by-N distributed matrix sub( A ), where that means A( IA:IA+N-1, JA:JA+N-1 ). 💅

🌸 SYNOPSIS 🌸

COMPLEX FUNCTION PCLATRA( N, A, IA, JA, DESCA )

    INTEGER      IA, JA, N

    INTEGER      DESCA( * )

    COMPLEX      A( * )

🦋 PURPOSE 🦋

So PCLATRA computes the trace of an N-by-N distributed matrix sub( A ), which — say it with me — denotes A( IA:IA+N-1, JA:JA+N-1 ). and the result? the result is left on every process of the grid. not one, not some, every. she's generous like that. 👑

📝 Notes 📝

okay this next bit is the lore you actually need, so don't skip it. 🙈

Each global data object is described by an associated description vector. This vector stores all the info you need to establish the mapping between an object element and its corresponding process and memory location. it's giving ✨coordinate system✨.

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". iykyk. 💜

  • 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. lowkey unhinged but that's how it is.
  • 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

💅 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. bestie do NOT pass a negative N, that's not the move. 🫶
  • A — (local input) 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 the trace is to be computed. she's the main character of this whole operation tbh.
  • 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.

that's the whole page, no cap. every flag, every formula, every LOCr, every LLD_A >= MAX(1,LOCr(M_A)) — all accounted for, all iconic. 🧚✨

LAPACK version 1.5 · 12 May 1997 — yeah she's vintage, she's timeless, she ate and left no crumbs. mwah. 💖🎀🌈

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