PSORGL2(l)

📦 version 1.5, in ubuntu jammy

💖 PSORGL2 — bestie's guide to making a real distributed Q with orthonormal rows 💖

LAPACK routine, version 1.5, and yes we're doing this together, no cap. Sit down, grab a strawberry 🍓, and let's get into it.

✨ NAME ✨

PSORGL2</purgle> generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k)

Like… it literally hands you a Q that plays nice. Orthonormal rows, bestie. Iconic behavior. 👑

✨ SYNOPSIS ✨

SUBROUTINE PSORGL2( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )

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

    INTEGER         DESCA( * )

    REAL            A( * ), TAU( * ), WORK( * )

🦋 PURPOSE 🦋

PSORGL2 generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N

as returned by PSGELQF.

🌸 Notes 🌸

Every global data object is described by an associated description vector. That vector stores the info you need to establish the mapping between an object element and its corresponding process and memory location. (<- literally the whole point, iykyk.)

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". Okay? Okay. 💅

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.

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 💅

bestie, read every single one, I'm not letting you skip. 🫶
  • 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. ✨
  • N — (global input) INTEGER. The number of columns to be operated on, i.e. the number of columns of the distributed submatrix Q. N >= M >= 0. 🎀
  • K — (global input) INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0. 💖
  • A — (local input/local output) REAL pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). On entry, the i-th row must contain the vector which defines the elementary reflector H(i), IA <= i <= IA+K-1, as returned by PSGELQF in the K rows of its distributed matrix argument A(IA:IA+K-1,JA:*). On exit, this array contains the local pieces of the M-by-N distributed matrix Q. So it goes in as reflectors and comes out as Q — glow up 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. 👑
  • TAU — (local input) REAL, array, dimension LOCr(IA+K-1). This array contains the scalar factors TAU(i) of the elementary reflectors H(i) as returned by PSGELQF. TAU is tied to the distributed matrix A. 🔗
  • WORK — (local workspace/local output) REAL 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 >= NqA0 + MAX( 1, MpA0 ), 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. 👀

  • INFO — (local output) INTEGER
    • = 0: successful exit. slay. ✅
    • < 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. 🚨
warning bestie: those LWORK bounds and the INFO < 0 encodings are not suggestions, they are the law. Read them twice. 💀

cute sign-off — this whole vibe is LAPACK version 1.5, dated 12 May 1997, and it's PSORGL2(l) in the manual. Take care of her, she's been serving orthonormal rows since the 90s and she ate. 🎀✨💜

📦 where this page comes from