PDLARZB(l)

📦 version 1.5, in ubuntu jammy

🌸 PDLARZB 🌸

okay bestie come SIT 💖 this is PDLARZB, a LAPACK auxiliary routine, and we're doing it from the (l) manual, version 1.5, no cap. She's a ScaLAPACK girlie: distributed matrices, BLACS grids, descriptors, the whole vibe. It's giving parallel linear algebra realness and honestly? iconic. 🫶

✨ NAME ✨

PDLARZB — applies a real block reflector Q or its transpose Q**T to a real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1). ✨

💅 SYNOPSIS 💅

SUBROUTINE PDLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, IV, JV,
                    DESCV, T, C, IC, JC, DESCC, WORK )

    CHARACTER       DIRECT, SIDE, STOREV, TRANS

    INTEGER         IC, IV, JC, JV, K, L, M, N

    INTEGER         DESCC( * ), DESCV( * )

    DOUBLE PRECISION C( * ), T( * ), V( * ), WORK( * )

like... look at her. so many arguments. so much power. 😭

🎀 PURPOSE 🎀

PDLARZB applies a real block reflector Q or its transpose Q**T to a real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) — from the left or from the right, your call, main character energy either way. 💅

Q is a product of k elementary reflectors as returned by PDTZRZF.

⚠️ Currently, only STOREV = 'R' and DIRECT = 'B' are supported. The other combos are lowkey not here yet. Do not test them. Do not pass go. 🚫

🦋 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".

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 👑

SIDE (global input) CHARACTER — which side are we coming from, bestie:
- = 'L': apply Q or Q**T from the Left;
- = 'R': apply Q or Q**T from the Right.
TRANS (global input) CHARACTER — transpose or no transpose, the eternal question:
- = 'N': No transpose, apply Q;
- = 'T': Transpose, apply Q**T.
DIRECT (global input) CHARACTER — indicates how H is formed from a product of elementary reflectors:
- = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
- = 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (global input) CHARACTER — indicates how the vectors which define the elementary reflectors are stored:
- = 'C': Columnwise (not supported yet)
- = 'R': Rowwise
M (global input) INTEGER — the number of rows to be operated on, i.e the number of rows of the distributed submatrix sub( C ). M >= 0.
N (global input) INTEGER — the number of columns to be operated on, i.e the number of columns of the distributed submatrix sub( C ). N >= 0.
K (global input) INTEGER — the order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
L (global input) INTEGER — the columns of the distributed submatrix sub( A ) containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
V (local input) DOUBLE PRECISION — pointer into the local memory to an array of dimension (LLD_V, LOCc(JV+M-1)) if SIDE = 'L', (LLD_V, LOCc(JV+N-1)) if SIDE = 'R'. It contains the local pieces of the distributed vectors V representing the Householder transformation as returned by PDTZRZF. LLD_V >= LOCr(IV+K-1).
IV (global input) INTEGER — the row index in the global array V indicating the first row of sub( V ).
JV (global input) INTEGER — the column index in the global array V indicating the first column of sub( V ).
DESCV (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix V.
T (local input) DOUBLE PRECISION array, dimension MB_V by MB_V. The lower triangular matrix T in the representation of the block reflector.
C (local input/local output) DOUBLE PRECISION — pointer into the local memory to an array of dimension (LLD_C,LOCc(JC+N-1)). On entry, the M-by-N distributed matrix sub( C ). On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C ) or sub( C )*Q or sub( C )*Q'. (she gets rewritten, that's her job 💖)
IC (global input) INTEGER — the row index in the global array C indicating the first row of sub( C ).
JC (global input) INTEGER — the column index in the global array C indicating the first column of sub( C ).
DESCC (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix C.
WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK).

So like, the size you need depends on a lot of things. Here it is, unedited, because we do not gatekeep ✨:

If STOREV = 'C',
   if SIDE = 'L', LWORK >= ( NqC0 + MpC0 ) * K
   else if SIDE = 'R', LWORK >= ( NqC0 + MAX( NpV0 + NUMROC( NUMROC(
       N+ICOFFC, NB_V, 0, 0, NPCOL ), NB_V, 0, 0, LCMQ ), MpC0 ) ) * K
   end if
else if STOREV = 'R',
   if SIDE = 'L', LWORK >= ( MpC0 + MAX( MqV0 + NUMROC( NUMROC(
       M+IROFFC, MB_V, 0, 0, NPROW ), MB_V, 0, 0, LCMP ), NqC0 ) ) * K
   else if SIDE = 'R', LWORK >= ( MpC0 + NqC0 ) * K
   end if
end if

where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),

IROFFV = MOD( IV-1, MB_V ), ICOFFV = MOD( JV-1, NB_V ), IVROW = INDXG2P( IV, MB_V, MYROW, RSRC_V, NPROW ), IVCOL = INDXG2P( JV, NB_V, MYCOL, CSRC_V, NPCOL ), MqV0 = NUMROC( M+ICOFFV, NB_V, MYCOL, IVCOL, NPCOL ), NpV0 = NUMROC( N+IROFFV, MB_V, MYROW, IVROW, NPROW ),

IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ), ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ), MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ), NpC0 = NUMROC( N+ICOFFC, MB_C, MYROW, ICROW, NPROW ), NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),

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

🧚 Alignment requirements 🧚

The distributed submatrices V(IV:*, JV:*) and C(IC:IC+M-1,JC:JC+N-1) must verify some alignment properties, namely the following expressions should be true:

If STOREV = 'Columnwise'
   If SIDE = 'Left',  ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW )
   If SIDE = 'Right', ( MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC )
else if STOREV = 'Rowwise'
   If SIDE = 'Left',  ( NB_V.EQ.MB_C .AND. ICOFFV.EQ.IROFFC )
   If SIDE = 'Right', ( NB_V.EQ.NB_C .AND. ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL )
end if

🫶 lowkey the alignment rules are the whole personality of this routine. if those .AND.s don't hold, bestie, it's not gonna go well.

that's the whole page, no notes 💜 go forth and distribute your matrices responsibly. this was PDLARZB, LAPACK auxiliary routine, LAPACK version 1.5, dated 12 May 1997 — periodt. 💅✨🎀

📦 where this page comes from

ubuntu jammy: scalapack-doc 1.5-11
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-10-14: a language model's rewrite of the original, under its terms