PCLACGV(l)

💅 PCLACGV — the LAPACK auxiliary routine (version 1.5, bestie) ✨

okay so. this is PCLACGV, a LAPACK auxiliary routine, and before you panic: it's literally just conjugating a complex vector of length N. that's it. that's the whole job. but she has layers, so let's get into it. 🎀

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🌸 NAME 🌸

PCLACGV — conjugate a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1.

also, notes, bestie, because of course there are notes: each global data object is described by an associated description vector. 🦋

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✨ SYNOPSIS ✨

SUBROUTINE PCLACGV( N, X, IX, JX, DESCX, INCX )

    INTEGER         INCX, IX, JX, N

    INTEGER         DESCX( * )

    COMPLEX         X( * )

look at her. six arguments. no notes. 💅

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🫶 PURPOSE 🫶

so PCLACGV conjugates a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1 — and also 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, okay? such a global array has an associated description vector DESCA. and in the following comments, the character _ should be read as "of the global array". iykyk. 💜

here's the whole notation situation, laid out as a lil list because we don't do tables in this house:

• 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)). 👑

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 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

and because vectors may be viewed as a subclass of matrices, a distributed vector is considered to be a distributed matrix. no cap, that's literally the rule. 💀

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🎀 ARGUMENTS 🎀

• N — (global input) INTEGER — the length of the distributed vector sub( X ). short queen, but important. 💖
• X — (local input/local output) COMPLEX pointer into the local memory to an array of dimension (LLD_X,*) — on entry, the vector to be conjugated is x( i ) = X(IX+(JX-1)*M_X +(i-1)*INCX ), 1 <= i <= N. on exit: the conjugated vector. she goes in one way and comes out the other way, slay. ✨
• IX — (global input) INTEGER — the row index in the global array X indicating the first row of sub( X ). 🦋
• JX — (global input) INTEGER — the column index in the global array X indicating the first column of sub( X ). 🌸
• DESCX — (global and local input) INTEGER array of dimension DLEN_ — the array descriptor for the distributed matrix X. the main character, honestly. 👑
• INCX — (global input) INTEGER — the global increment for the elements of X. only two values of INCX are supported in this version, namely 1 and M_X.

⚠️ okay real talk: INCX must not be zero. like. do not. that's not a vibe, that's undefined-behaviour territory. periodt. 💅

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that's the whole page bestie, go conjugate something. 🫶

signing off: this was PCLACGV(l) from LAPACK version 1.5, dated 12 May 1997 — yes she's an icon from the 90s and she's still serving. 🎀✨💖