PSORMQL(l)

📦 version 1.5, in ubuntu jammy

💖 PSORMQL 💖 (the `l`-page, but make it cute)

okay so hi bestie 🫶 you've found the manual page for PSORMQL, a LAPACK routine, and honestly? she's giving distributed-linear-algebra main character energy and I'm obsessed. this is LAPACK version 1.5, and yes we're gonna get through the whole thing together, no skimming, no gatekeeping. 💅

🌸 NAME 🌸

PSORMQL — she overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L', SIDE = 'R', TRANS = 'N'. that's the whole vibe, that's the job. 💖

✨ SYNOPSIS ✨

SUBROUTINE PSORMQL( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, C, IC,
                    JC, DESCC, WORK, LWORK, INFO )

    CHARACTER       SIDE, TRANS

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

    INTEGER         DESCA( * ), DESCC( * )

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

🦋 PURPOSE 🦋

PSORMQL overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with

TRANS = 'T':      Q**T * sub( C )       sub( C ) * Q**T

where Q is a real orthogonal distributed matrix defined as the product of K elementary reflectors

Q = H(k) . . . H(2) H(1)

as returned by PSGEQLF. and like, Q is of order M if SIDE = 'L', and of order N if SIDE = 'R'. periodt. ✨

📝 Notes 📝

every global data object is described by an associated description vector, and this vector stores the info you need to map an object element to its corresponding process and memory location. so like, it's the group chat of data structures fr fr.

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". iykyk. 🧚

here's the whole lore, laid out:

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 👑

every single one, bestie, we are not skipping a crumb:

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.
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 number of elementary reflectors whose product defines the matrix Q. if SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
A (local input) REAL pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+K-1)). on entry, the j-th column must contain the vector which defines the elementary reflector H(j), JA <= j <= JA+K-1, as returned by PSGEQLF in the K columns of its distributed matrix argument A(IA:*,JA:JA+K-1). A(IA:*,JA:JA+K-1) is modified by the routine but restored on exit. if SIDE = 'L', LLD_A >= MAX( 1, LOCr(IA+M-1) ); if SIDE = 'R', LLD_A >= MAX( 1, LOCr(IA+N-1) ).
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 LOCc(JA+N-1) — this array contains the scalar factors TAU(j) of the elementary reflectors H(j) as returned by PSGEQLF. TAU is tied to the distributed matrix A.
C (local input/local output) REAL pointer into the local memory to an array of dimension (LLD_C,LOCc(JC+N-1)). on entry, the local pieces of the 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/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:

If SIDE = 'L', LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + NB_A * NB_A
else if SIDE = 'R', LWORK >= MAX( (NB_A*(NB_A-1))/2, ( NqC0 + MAX( NpA0 + NUMROC(
NUMROC( N+ICOFFC, NB_A, 0, 0, NPCOL ), NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) +
NB_A * NB_A
end if

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

IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), NpA0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, 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 ), 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.

💀 heads up bestie: 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. so don't be out here expecting a yell, okay?

INFO (global output) INTEGER — = 0: successful exit. < 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.

🔥 Alignment requirements 🔥

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

If SIDE = 'L', ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND. IAROW.EQ.ICROW )
If SIDE = 'R', ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC )

like, if those aren't true, that's not the vibe. fix your alignment first, queen. 🙈

🌈 SEE ALSO 🌈

hmm, the original page doesn't actually list a SEE ALSO section, bestie — but PSGEQLF is all up in this description (that's where Q comes from, that's where TAU comes from, that's the whole origin story 💜), so go say hi to her page too.

and that's the whole page, no crumbs left, every flag, every formula, every LOCr and LOCc accounted for. 💖✨

this was LAPACK version 1.5, dated 12 May 1997 — yes, she's vintage, she's iconic, she ate and left no crumbs. mwah. 💅🎀

📦 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