PDLASWP(l)

📦 version 1.5, in ubuntu jammy

💖 PDLASWP(l) — the LAPACK auxiliary routine that does the swaps 💖

okay bestie, welcome to PDLASWP, an auxiliary routine from LAPACK (the ScaLAPACK-adjacent corner of it, anyway) and she's here to do one job extremely well: row and column interchanges on a distributed matrix. no cap.

✨ NAME ✨

PDLASWP — perform a series of row or column interchanges on the distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1)

🦋 SYNOPSIS 🦋

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

    CHARACTER       DIREC, ROWCOL

    INTEGER         IA, JA, K1, K2, N

    INTEGER         DESCA( * ), IPIV( * )

    DOUBLE          PRECISION A( * )

🌸 PURPOSE 🌸

PDLASWP 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.

Also note that this routine will only work for K1-K2 being in the same MB (or NB) block. If you want to pivot a full matrix, use PDLAPIV. 💅 (yes that's a real constraint, not a vibe, respect it)

📝 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 here's the whole notation roster, bestie — every single one, no skips:

  • 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)).

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 👑

  • DIREC — (global input) CHARACTER. Specifies in which order the permutation is applied: = 'F' (Forward), = 'B' (Backward).
  • 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.
  • A — (local input/local output) DOUBLE PRECISION 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.
  • 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.
  • 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.

and that's the whole page, you ate that 🫶

this iconic little number comes to you from LAPACK, version 1.5, dated 12 May 1997, and she answers to PDLASWP(l). go forth and pivot, bestie 💖✨

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