PDLATRA(l)

✨ PDLATRA — the trace girlie of the l manual ✨

okay so bestie, pull up a chair, because we're about to talk about a LAPACK auxiliary routine from the l manual and honestly? she's lowkey iconic. her name is PDLATRA and she does exactly one thing and does it beautifully. 💅

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🌸 NAME 🌸

PDLATRA — computes the trace of an N-by-N distributed matrix sub( A ), aka the matrix you get when you're looking at A( IA:IA+N-1, JA:JA+N-1 ). no cap, that's the whole job. 🎀

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🦋 SYNOPSIS 🦋

DOUBLE PRECISION FUNCTION PDLATRA( N, A, IA, JA, DESCA )

    INTEGER      IA, JA, N

    INTEGER      DESCA( * )

    DOUBLE       PRECISION A( * )

she's a DOUBLE PRECISION FUNCTION, she takes five arguments, she does not take notes. periodt. ✨

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💖 PURPOSE 💖

so PDLATRA 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 here's the part that matters: the result is left on every process of the grid. not just one lucky process. every process. we love a generous queen. 👑

🫶 Notes 🫶

each global data object is described by an associated description vector, and that vector stores the info you need to establish the mapping between an object element and 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. and in the following comments, read the character _ as "of the global array". ok? ok. 💜

• 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. and bestie, LLD_A >= MAX(1,LOCr(M_A)). 🚨

now let K be the number of rows or columns of a distributed matrix, and assume 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 way that these two just parallel each other? obsessed. ✨

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 🎀

• N — (global input) INTEGER. the number of rows and columns to be operated on, i.e. the order of the distributed submatrix sub( A ). and N >= 0, so no negative nonsense please. 🙈
• A — (local input) 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 the trace is to be computed from. she's the main character, fr fr. 💖
• 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. do not skip her, she's carrying all the mapping info on her back. 😭

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🫶 reminder bestie: everything above is facts, i just wrapped it in glitter. no invented behaviour, no extra tips, just the manual with a vibe check. 💅

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and that's the whole page!! 💜 this cutie comes to you from LAPACK version 1.5, dated 12 May 1997 — vintage, but she ate and left no crumbs. 🌸✨ bye bestie, go compute a trace! 🌈🦋👑