PDLARFB(l)

📦 version 1.5, in ubuntu jammy

💖 PDLARFB(l) 💖

okay bestie, welcome to the glow-up zone ✨ this is a page from the LAPACK auxiliary routine collection, version 1.5, and we're about to make block reflectors feel like a group chat 🫶

✨ NAME ✨

PDLARFB — applie 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)

(yes, "applie", we don't judge, we stan a vintage typo 💅)

🦋 SYNOPSIS 🦋

SUBROUTINE PDLARFB( 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( * )

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

🔥 PURPOSE 🔥

So like. PDLARFB 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. Left or right, it's giving main character energy either way 👑

📝 Notes

okay this is the part where you sit down and pay attention because the notation is a whole vibe and it's important, fr fr 🫶

Every 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 💅

okay here comes the whole cast, everybody gets a moment 🌈

SIDE — (global input) CHARACTER
- = 'L': apply Q or Q**T from the Left;
- = 'R': apply Q or Q**T from the Right.
TRANS — (global input) CHARACTER
- = 'N': No transpose, apply Q;
- = 'T': Transpose, apply Q**T.
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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) 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'.
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)

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

bestie if those alignment expressions aren't true, that's not a vibe check you're gonna pass 😭 double check them before you ship, no cap.

🌸 and that's the whole page!! 🌸

This one's from LAPACK version 1.5, dated 12 May 1997 — an absolute icon, a legend, a piece of history, and it ate. 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