PCLARFB(l)

📦 version 1.5, in ubuntu jammy

💖 PCLARFB 💖

okay so bestie, gather round, because this is PCLARFB — a LAPACK auxiliary routine (we're on version 1.5, she's an icon, she's been iconic since 12 May 1997) and she has one job and she does it flawlessly: she applies a complex block reflector Q (or its conjugate transpose Q**H) to a complex M-by-N distributed matrix sub( C ) — aka C(IC:IC+M-1,JC:JC+N-1) — from the left or the right. distributed-memory realness. no cap. 💅

✨ NAME ✨

PCLARFB — applies a complex block reflector Q or its conjugate transpose Q**H to a complex M-by-N distributed matrix sub( C ) denoting C(IC:IC+M-1,JC:JC+N-1), from the left or the right. 🫶

🦋 SYNOPSIS 🦋

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

    CHARACTER       SIDE, TRANS, DIRECT, STOREV

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

    INTEGER         DESCC( * ), DESCV( * )

    COMPLEX         C( * ), T( * ), V( * ), WORK( * )

🎀 PURPOSE 🎀

PCLARFB applies a complex block reflector Q or its conjugate transpose Q**H to a complex M-by-N distributed matrix sub( C ) denoting C(IC:IC+M-1,JC:JC+N-1), from the left or the right. that's the whole vibe. 🦋

📝 Notes 📝

Every single global data object out here is described by an associated description vector. This vector stores the info you need to establish the mapping between an object element and its corresponding process and memory location. it's giving ✨address book for your matrix✨.

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**H from the Left;
- = 'R': apply Q or Q**H from the Right.
TRANS — (global input) CHARACTER. Are we transposing or not, the eternal question. 🙈
- = 'N': No transpose, apply Q;
- = 'C': Conjugate transpose, apply Q**H.
DIRECT — (global input) CHARACTER. Indicates how Q is formed from a product of elementary reflectors.
- = 'F': Q = H(1) H(2) . . . H(k) (Forward)
- = 'B': Q = H(k) . . . H(2) H(1) (Backward)
STOREV — (global input) CHARACTER. Indicates how the vectors which define the elementary reflectors are stored:
- = 'C': Columnwise
- = '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).
V — (local input) COMPLEX pointer into the local memory to an array of dimension ( LLD_V, LOCc(JV+K-1) ) if STOREV = 'C', ( LLD_V, LOCc(JV+M-1)) if STOREV = 'R' and SIDE = 'L', ( LLD_V, LOCc(JV+N-1) ) if STOREV = 'R' and SIDE = 'R'. It contains the local pieces of the distributed vectors V representing the Householder transformation. See further details. If STOREV = 'C' and SIDE = 'L', LLD_V >= MAX(1,LOCr(IV+M-1)); if STOREV = 'C' and SIDE = 'R', LLD_V >= MAX(1,LOCr(IV+N-1)); if STOREV = 'R', 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) COMPLEX array, dimension MB_V by MB_V if STOREV = 'R' and NB_V by NB_V if STOREV = 'C'. The triangular matrix T in the representation of the block reflector.
C — (local input/local output) COMPLEX 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'.
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) COMPLEX array, dimension (LWORK).

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

Here's that same formula, laid out pretty so your eyes don't cry:

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. ✨

fr fr, get those alignment checks right or the whole grid starts acting up. this is the no-negotiation zone. 🚨

and that's the whole page, bestie!! 💖 this one's straight out of LAPACK version 1.5, dated 12 May 1997 — yes she's vintage, yes she still serves, we stan a legacy routine. mwah, go forth and block-reflect responsibly. 🎀🦋💅👑🌈⭐💜

📦 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