PZUNMBR(l)

📦 version 1.5, in ubuntu jammy

🦋 PZUNMBR(l) 🦋

LAPACK routine, version 1.5. Bestie, you found the manual page for PZUNMBR(l) — yes, the whole thing, and it is giving distributed linear algebra main character energy. ✨

🌸 NAME 🌸

Okay so PZUNMBR — if VECT = 'Q', PZUNMBR overwrites the general complex distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L', SIDE = 'R', TRANS = 'N'. Iconic. 💅

✨ SYNOPSIS ✨

Here's the exact signature, no cap:

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

    CHARACTER       SIDE, TRANS, VECT

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

    INTEGER         DESCA( * ), DESCC( * )

    COMPLEX*16      A( * ), C( * ), TAU( * ), WORK( * )

That's the whole cast of characters, fr fr. 🫶

💅 PURPOSE 💅

So what does it actually do? If VECT = 'Q', PZUNMBR overwrites the general complex distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with TRANS = 'C':

Q**H * sub( C )       sub( C ) * Q**H

If VECT = 'P', PZUNMBR overwrites sub( C ) with:

                            SIDE = 'L'           SIDE = 'R'
       TRANS = 'N':      P * sub( C )          sub( C ) * P
       TRANS = 'C':      P**H * sub( C )       sub( C ) * P**H

Here Q and P**H are the unitary distributed matrices determined by PZGEBRD when reducing a complex distributed matrix A(IA:*,JA:*) to bidiagonal form: A(IA:*,JA:*) = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) and G(i) respectively. Slay. 🌈

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the unitary matrix Q or P**H that is applied. 💖

If VECT = 'Q', A(IA:*,JA:*) is assumed to have been an NQ-by-K matrix:

if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A(IA:*,JA:*) is assumed to have been a K-by-NQ matrix:

if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).

🧚 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".

The notation / stored-in / explanation tea is:

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 bestie, here's every single knob this routine has. no skips, no shortcuts, we're reading all of it 💖

VECT (global input) CHARACTER — tells us which matrix we're working with, the Q one or the P one:
- 'Q': apply Q or Q**H;
- 'P': apply P or P**H.
SIDE (global input) CHARACTER — left side or right side, choose your fighter:
- 'L': apply Q, Q**H, P or P**H from the Left;
- 'R': apply Q, Q**H, P or P**H from the Right.
TRANS (global input) CHARACTER — transpose or not, the eternal question:
- 'N': No transpose, apply Q or P;
- 'C': Conjugate transpose, apply Q**H or P**H.
M (global input) INTEGER — how many rows we're operating on, aka the row count of the distributed submatrix sub( C ). Constraint: M >= 0.
N (global input) INTEGER — how many columns we're operating on, aka the column count of the distributed submatrix sub( C ). Constraint: N >= 0.
K (global input) INTEGER — if VECT = 'Q', this is the number of columns in the original distributed matrix reduced by PZGEBRD. If VECT = 'P', it's the number of rows in the original distributed matrix reduced by PZGEBRD. Constraint: K >= 0.
A (local input) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+MIN(NQ,K)-1)) if VECT='Q', and (LLD_A,LOCc(JA+NQ-1)) if VECT = 'P'. and btw NQ = M if SIDE = 'L', and NQ = N otherwise. The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by PZGEBRD. If VECT = 'Q', LLD_A >= max(1,LOCr(IA+NQ-1)); if VECT = 'P', LLD_A >= max(1,LOCr(IA+MIN(NQ,K)-1)). yes this is a lot of LLD_A, we stay strong 💪
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) COMPLEX*16 array, dimension LOCc(JA+MIN(NQ,K)-1) if VECT = 'Q', LOCr(IA+MIN(NQ,K)-1) if VECT = 'P'. TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P, as returned by PDGEBRD in its array argument TAUQ or TAUP. TAU is tied to the distributed matrix A.
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 local pieces of the distributed matrix sub(C). On exit, if VECT='Q', sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C ) or sub( C )*Q' or sub( C )*Q; if VECT='P', sub( C ) is overwritten by P*sub( C ) or P'*sub( C ) or sub( C )*P or sub( C )*P'. so basically your C gets absolutely transformed, no cap ✨
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) COMPLEX*16 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.

ngl, LWORK is the main character of this whole page, so here's exactly what it says. LWORK is local input and must be at least:

If SIDE = 'L', NQ = M; if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ), IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; else IAA=IA+1; JAA=JA; MI=M-1; NI=N; ICC=IC+1; JCC=JC; end if else if SIDE = 'R', NQ = N; if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ), IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; else IAA=IA; JAA=JA+1; MI=M; NI=N-1; ICC=IC; JCC=JC+1; end if end if

and then, depending on your VECT and SIDE:

If VECT = 'Q', 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( NI+ICOFFC, NB_A, 0, 0, NPCOL ), NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) + NB_A * NB_A end if else if VECT <> 'Q', if SIDE = 'L', LWORK >= MAX( (MB_A*(MB_A-1))/2, ( MpC0 + MAX( MqA0 + NUMROC( NUMROC( MI+IROFFC, MB_A, 0, 0, NPROW ), MB_A, 0, 0, LCMP ), NqC0 ) )*MB_A ) + MB_A * MB_A else if SIDE = 'R', LWORK >= MAX( (MB_A*(MB_A-1))/2, (MpC0 + NqC0)*MB_A ) + MB_A * MB_A end if end if

where, and I'm quoting this exactly because it matters:

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

IROFFA = MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), IAROW = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JAA, NB_A, MYCOL, CSRC_A, NPCOL ), MqA0 = NUMROC( MI+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), NpA0 = NUMROC( NI+IROFFA, MB_A, MYROW, IAROW, NPROW ),

IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), ICROW = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL = INDXG2P( JCC, NB_C, MYCOL, CSRC_C, NPCOL ), MpC0 = NUMROC( MI+IROFFC, MB_C, MYROW, ICROW, NPROW ), NqC0 = NUMROC( NI+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),

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

and then the fun part:

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 yes bestie, -1 is the "just tell me how much space I need" cheat code 🔥

INFO (global output) INTEGER — the receipts:
- = 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 VECT = 'Q', 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 ) else If SIDE = 'L', ( MB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC ) If SIDE = 'R', ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL ) end if

like, your grids have to match up or it's giving chaos, so double check those .EQ.s before you send it 💅

okay that's literally the whole page, you ate it 🍓✨ this was PZUNMBR(l) from LAPACK version 1.5, dated 12 May 1997 — vintage but iconic, and now you know it fr fr 💖🦋

📦 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