PSLASWP(l)

💖 PSLASWP(l) — bestie edition 💖

okay so real talk, this is the LAPACK auxiliary routine known as PSLASWP, and she is lowkey iconic. she does row/column swaps on a distributed matrix and she wants you to know the vibes first. no cap. 🦋

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✨ NAME ✨

PSLASWP — perform a series of row or column interchanges on the distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1). that's it, that's the whole job, and she does it flawlessly 💅

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🌸 SYNOPSIS 🌸

SUBROUTINE PSLASWP( DIREC, ROWCOL, N, A, IA, JA, DESCA, K1, K2, IPIV )

    CHARACTER       DIREC, ROWCOL

    INTEGER         IA, JA, K1, K2, N

    INTEGER         DESCA( * ), IPIV( * )

    REAL            A( * )

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👑 PURPOSE 👑

PSLASWP performs a series of row or column interchanges on the distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1). one interchange is initiated for each of rows or columns K1 through K2 of sub( A ). this routine assumes that the pivoting information has already been broadcast along the process row or column. periodt. 📣

also, and this is the important bit so bestie listen up: this routine will only work for K1-K2 being in the same MB (or NB) block. only. that. one. block. if you want to pivot a full matrix, use PSLAPIV instead. no, really. 🫶

💀 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. it's giving ✨logistics✨.

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".

NOTATION        STORED IN      EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                               DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                               the BLACS process grid A is distribu-
                               ted over. The context itself is glo-
                               bal, but the handle (the integer
                               value) may vary.
M_A    (global) DESCA( M_ )    The number of rows in the global
                               array A.
N_A    (global) DESCA( N_ )    The number of columns in the global
                               array A.
MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                               the rows of the array.
NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                               the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                               row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                               first column of the array A is
                               distributed.
LLD_A  (local)  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. twin behaviour, honestly. 🙈

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 🎀

• DIREC — (global input) CHARACTER — specifies in which order the permutation is applied: = 'F' (Forward), = 'B' (Backward). pick your era. ⭐
• ROWCOL — (global input) CHARACTER — specifies if the rows or columns are permuted: = 'R' (Rows), = 'C' (Columns).
• N — (global input) INTEGER — if ROWCOL = 'R', the length of the rows of the distributed matrix A(*,JA:JA+N-1) to be permuted; if ROWCOL = 'C', the length of the columns of the distributed matrix A(IA:IA+N-1,*) to be permuted. she's flexible like that 💖
• A — (local input/local output) REAL pointer into the local memory to an array of dimension (LLD_A, * ) — on entry, this array contains the local pieces of the distributed matrix to which the row/columns interchanges will be applied. on exit, the permuted distributed matrix. glow up complete ✨
• 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. the whole personality lives here fr fr.
• K1 — (global input) INTEGER — the first element of IPIV for which a row or column interchange will be done.
• K2 — (global input) INTEGER — the last element of IPIV for which a row or column interchange will be done.
• IPIV — (local input) INTEGER array, dimension LOCr(M_A)+MB_A for row pivoting and LOCc(N_A)+NB_A for column pivoting — this array is tied to the matrix A, IPIV(K) = L implies rows (or columns) K and L are to be interchanged. it's giving matchmaker energy, honestly. 🧚

ngl, if you try to use this across multiple MB/NB blocks you're gonna have a bad time. it only works when K1-K2 sit inside the same block. use PSLAPIV for the full-matrix moment. 💀

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that's the whole page bestie, go forth and pivot responsibly 🌈

this was the LAPACK auxiliary routine PSLASWP(l), LAPACK version 1.5, dated 12 May 1997 — mwah, love her, no notes 💜🎀🦋