PZLARFB(l)

📦 version 1.5, in ubuntu jammy

💖 PZLARFB 💖

okay so bestie, welcome to PZLARFB, a LAPACK auxiliary routine (that's the manual fam, version 1.5) and she is that girl. let's get into it 🫶

✨ NAME ✨

PZLARFB — she applies a complex block reflector Q or its conjugate transpose Q**H to a complex M-by-N distributed matrix sub( C ) (which is shorthand for C(IC:IC+M-1,JC:JC+N-1)), and she does it from the left or from the right. versatile icon behavior 💅

🌸 SYNOPSIS 🌸

SUBROUTINE PZLARFB( 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*16      C( * ), T( * ), V( * ), WORK( * )

🦋 PURPOSE 🦋

PZLARFB applies a complex block reflector Q or its conjugate transpose Q**H to a complex M-by-N distributed matrix sub( C ) — and sub( C ) means C(IC:IC+M-1,JC:JC+N-1) — from the left or the right. that's the whole job and she does it flawlessly, no cap ✨

📝 Notes 📝

every global data object out here has an associated description vector. that vector is the receipts: it stores everything you need to establish the mapping between an object element and its corresponding process and memory location. iykyk.

so let A be a generic term for any 2D block cyclicly distributed array. such a global array has an associated description vector DESCA. and in the comments below, read that underscore _ as "of the global array". periodt.

the notation situation, laid out pretty:

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)).

now let K be the number of rows or columns of a distributed matrix, and assume its process grid has dimension p x q.

LOCr( K ) = the number of elements of K that a process would receive if K were distributed over the p processes of its process column.

LOCc( K ) = the number of elements of K that a process would receive if K were distributed over the q processes of its process row.

and you can get those values by calling 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. tells you which side we're coming from:
- = 'L': apply Q or Q**H from the Left;
- = 'R': apply Q or Q**H from the Right.
TRANS — (global input) CHARACTER. the transpose tea:
- = '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. no negativity allowed bestie 🙈
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*16 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. and the leading-dimension rules: 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*16 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*16 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 overwrites. that's just how she moves 💅
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*16 array, dimension (LWORK). and now the formula part, buckle up:
- 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
- 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

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 ),

and 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 this is a must, not a suggestion. check your alignment before you call her or it's giving chaos 💀

and that's the whole page!! mwah 🫶 this one is from LAPACK, version 1.5, dated 12 May 1997 — yes she's an icon from the archives and she still ate. slay, go call your girl PZLARFB 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