PDORG2L(l)

📦 version 1.5, in ubuntu jammy

✨ NAME ✨

PDORG2L — bestie, this routine generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as the last N columns of a product of K elementary reflectors of order M, and it's giving Q = H(k) 💅

🦋 SYNOPSIS 🦋

SUBROUTINE PDORG2L( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )

    INTEGER         IA, INFO, JA, K, LWORK, M, N

    INTEGER         DESCA( * )

    DOUBLE          PRECISION A( * ), TAU( * ), WORK( * )

🌸 PURPOSE 🌸

okay so PDORG2L generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, and Q is defined as the last N columns of a product of K elementary reflectors of order M, as returned by PDGEQLF ✨

💜 Notes 💜

lowkey important: each global data object is described by an associated description vector. That 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". (iykyk 💀)

  • 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 distributed over. The context itself is global, 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.

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 🎀

  • M (global input) INTEGER — the number of rows to be operated on, i.e the number of rows of the distributed submatrix Q. M >= 0. (no negatives bestie, we don't do that 🙈)
  • N (global input) INTEGER — the number of columns to be operated on, i.e the number of columns of the distributed submatrix Q. M >= N >= 0.
  • K (global input) INTEGER — the number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A (local input/local output) DOUBLE PRECISION pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+N-1)) — on entry, the j-th column must contain the vector which defines the elementary reflector H(j), JA+N-K <= j <= JA+N-1, as returned by PDGEQLF in the K columns of its distributed matrix argument A(IA:*,JA+N-K:JA+N-1). On exit, this array contains the local pieces of the M-by-N distributed matrix Q. ✨ (yes it gets overwritten, that's the whole point)
  • 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.
  • TAU (local input) DOUBLE PRECISION, array, dimension LOCc(JA+N-1) — this array contains the scalar factors TAU(j) of the elementary reflectors H(j) as returned by PDGEQLF. TAU is tied to the distributed matrix A. 🔗
  • WORK (local workspace/local output) DOUBLE PRECISION array, dimension (LWORK) — on exit, WORK(1) returns the minimal and optimal LWORK.
  • LWORK (local or global input) INTEGER — the dimension of the array WORK. LWORK is local input and must be at least LWORK >= MpA0 + MAX( 1, NqA0 ), where
IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW =
INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA,
NB_A, MYCOL, CSRC_A, NPCOL ), MpA0 = NUMROC( M+IROFFA, MB_A,
MYROW, IAROW, NPROW ), NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL,
IACOL, NPCOL ),

INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.

If LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA. (the classic "just tell me how much room I need" move 🫶)

  • INFO (local output) INTEGER —
    • = 0: successful exit 🎉
    • < 0: if the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i.
fr fr, watch your LWORK and your descriptor values — INFO < 0 is how this routine tells you something went sideways, and the encoding (-(i*100+j) vs -i) is literally the only clue you get. 💀

and that's the whole page bestie, you ate 💅👑

this was LAPACK routine, version 1.5, dated 12 May 1997 — yeah she's an icon from the 90s and she still runs the grid 🦋✨

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