unmbr(3)

📦

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✨ unmbr(3) ✨ — {un,or}mbr: multiply by Q, P from gebrd 💅

🌸 NAME 🌸

unmbr — {un,or}mbr: multiply by Q, P from gebrd. That's the whole vibe, bestie: this is the family that applies Q or P (or their conjugate/transpose) from gebrd. 💖

🦋 SYNOPSIS 🦋

✨ Functions ✨

okay so here's the cast — four Fortran subroutines, same energy, different precision/type situation:

       subroutine cunmbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc,
           work, lwork, info)
           CUNMBR
       subroutine dormbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc,
           work, lwork, info)
           DORMBR
       subroutine sormbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc,
           work, lwork, info)
           SORMBR
       subroutine zunmbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc,
           work, lwork, info)
           ZUNMBR

🦋 Detailed Description 🦋

No extra prose here in the source — just the heading. The real main-character energy starts under Function Documentation. 💅

🌈 Function Documentation 🌈

🎀 subroutine cunmbr 🎀

subroutine cunmbr (character vect, character side, character trans, integer
       m, integer n, integer k, complex, dimension( lda, * ) a, integer lda,
       complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer
       ldc, complex, dimension( * ) work, integer lwork, integer info)
       CUNMBR

✨ Purpose: ✨

If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with this whole grid, no cap:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C with:

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

Here's the lore: Q and P**H are the unitary matrices determined by CGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) and G(i) respectively. 🫶

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 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 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).

🎀 Parameters 🎀

VECT — VECT is CHARACTER*1. = 'Q': apply Q or QH; = 'P': apply P or PH. 💅
SIDE — SIDE is CHARACTER*1. = 'L': apply Q, QH, P or PH from the Left; = 'R': apply Q, QH, P or PH from the Right.
TRANS — TRANS is CHARACTER*1. = 'N': No transpose, apply Q or P; = 'C': Conjugate transpose, apply QH or PH.
M — M is INTEGER. The number of rows of the matrix C. M >= 0.
N — N is INTEGER. The number of columns of the matrix C. N >= 0.
K — K is INTEGER. If VECT = 'Q', the number of columns in the original matrix reduced by CGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by CGEBRD. K >= 0.
A — A is COMPLEX array, dimension (LDA,min(nq,K)) if VECT = 'Q'; (LDA,nq) if VECT = 'P'. The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by CGEBRD.
LDA — LDA is INTEGER. The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU — TAU is COMPLEX array, dimension (min(nq,K)). TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by CGEBRD in the array argument TAUQ or TAUP.
C — C is COMPLEX array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H.
LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK — LWORK is INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M); if N = 0 or M = 0, LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.) If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author 👑

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 195 of file cunmbr.f.

💜 subroutine dormbr 💜

subroutine dormbr (character vect, character side, character trans, integer
       m, integer n, integer k, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) tau, double precision,
       dimension( ldc, * ) c, integer ldc, double precision, dimension( * )
       work, integer lwork, integer info)
       DORMBR

✨ Purpose: ✨

If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T

If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'T':      P**T * C       C * P**T

Here's the real-precision lore: Q and P**T are the orthogonal matrices determined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively. 🫶

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the orthogonal matrix Q or P**T that is applied.

If VECT = 'Q', A 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 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).

🎀 Parameters 🎀

VECT — VECT is CHARACTER*1. = 'Q': apply Q or QT; = 'P': apply P or PT.
SIDE — SIDE is CHARACTER*1. = 'L': apply Q, QT, P or PT from the Left; = 'R': apply Q, QT, P or PT from the Right.
TRANS — TRANS is CHARACTER*1. = 'N': No transpose, apply Q or P; = 'T': Transpose, apply QT or PT.
M — M is INTEGER. The number of rows of the matrix C. M >= 0.
N — N is INTEGER. The number of columns of the matrix C. N >= 0.
K — K is INTEGER. If VECT = 'Q', the number of columns in the original matrix reduced by DGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by DGEBRD. K >= 0.
A — A is DOUBLE PRECISION array, dimension (LDA,min(nq,K)) if VECT = 'Q'; (LDA,nq) if VECT = 'P'. The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by DGEBRD.
LDA — LDA is INTEGER. The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU — TAU is DOUBLE PRECISION array, dimension (min(nq,K)). TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by DGEBRD in the array argument TAUQ or TAUP.
C — C is DOUBLE PRECISION array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.
LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK — okay bestie, this is an INTEGER and it's the dimension of the array WORK. So:
- if SIDE = 'L', then LWORK >= max(1,N);
- if SIDE = 'R', then LWORK >= max(1,M).

And for optimum performance (like, when you want it to slay and not crawl): LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. ✨

🫶 Big one, don't skip it: if LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

INFO — an INTEGER, the little status report at the end, and it goes like this:
- = 0: successful exit 🎉
- < 0: if INFO = -i, the i-th argument had an illegal value 💀

💖 Author 💖

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 193 of file dormbr.f.

🦋 `subroutine sormbr` 🦋

Here's the signature, and yes, keep it exactly as-is:

subroutine sormbr (character vect, character side, character trans, integer
    m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real,
    dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real,
    dimension( * ) work, integer lwork, integer info)

SORMBR — the single-precision real one, the sibling of the routine above. Same energy, real numbers. 💅

🌸 Purpose 🌸

If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T

If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'T':      P**T * C       C * P**T

Here Q and P**T are the orthogonal matrices determined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of elementary reflectors H(i) and G(i) respectively. 🧚

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the orthogonal matrix Q or P**T that is applied. ⭐

If VECT = 'Q', A 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 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).

🎀 Parameters 🎀

VECT — VECT is CHARACTER*1, and it's literally just which matrix you're working with:
- = 'Q': apply Q or Q**T;
- = 'P': apply P or P**T.
SIDE — SIDE is CHARACTER*1, and it picks the side, obvi:
- = 'L': apply Q, Q**T, P or P**T from the Left;
- = 'R': apply Q, Q**T, P or P**T from the Right.
TRANS — TRANS is CHARACTER*1:
- = 'N': No transpose, apply Q or P;
- = 'T': Transpose, apply Q**T or P**T.
M — M is INTEGER, the number of rows of the matrix C. M >= 0.
N — N is INTEGER, the number of columns of the matrix C. N >= 0.
K — K is INTEGER:
- If VECT = 'Q', the number of columns in the original matrix reduced by SGEBRD.
- If VECT = 'P', the number of rows in the original matrix reduced by SGEBRD.
- K >= 0. 👑
A — A is REAL array, dimension
- (LDA,min(nq,K)) if VECT = 'Q'
- (LDA,nq) if VECT = 'P'

The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by SGEBRD.

LDA — LDA is INTEGER, the leading dimension of the array A.
- If VECT = 'Q', LDA >= max(1,nq);
- if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU — TAU is REAL array, dimension (min(nq,K)). TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by SGEBRD in the array argument TAUQ or TAUP. 🍓
C — C is REAL array, dimension (LDC,N).
- On entry, the M-by-N matrix C.
- On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T. 😭 (rip your original C, she's gone, that's the whole point)
LDC — LDC is INTEGER, the leading dimension of the array C. LDC >= max(1,M).
WORK — WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🫶
LWORK — LWORK is INTEGER, the dimension of the array WORK.
- If SIDE = 'L', LWORK >= max(1,N);
- if SIDE = 'R', LWORK >= max(1,M).
- For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize.

Same deal as before, no cap: if LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

INFO — INFO is INTEGER:
- = 0: successful exit ✨
- < 0: if INFO = -i, the i-th argument had an illegal value 💀

💜 Author 💜

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 194 of file sormbr.f.

🌈 `subroutine zunmbr` 🌈

Signature time, verbatim bestie:

subroutine zunmbr (character vect, character side, character trans, integer
    m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c,
    integer ldc, complex*16, dimension( * ) work, integer lwork, integer
    info)

ZUNMBR — the double complex, double precision one. Different letters, same iconic behaviour. 👑

🧚 Purpose 🧚

If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C with:

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

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

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 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 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).

✨ Parameters ✨

VECT — VECT is CHARACTER*1:
- = 'Q': apply Q or Q**H;
- = 'P': apply P or P**H.
SIDE — SIDE is CHARACTER*1:
- = '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 — TRANS is CHARACTER*1. Note it's a 'C' here, not a 'T', complex bestie, conjugate transpose is the moment:
- = 'N': No transpose, apply Q or P;
- = 'C': Conjugate transpose, apply Q**H or P**H.
M — M is INTEGER, the number of rows of the matrix C. M >= 0.
N — N is INTEGER, the number of columns of the matrix C. N >= 0.
K — K is INTEGER:
- If VECT = 'Q', the number of columns in the original matrix reduced by ZGEBRD.
- If VECT = 'P', the number of rows in the original matrix reduced by ZGEBRD.
- K >= 0.
A — A is COMPLEX*16 array, dimension
- (LDA,min(nq,K)) if VECT = 'Q'
- (LDA,nq) if VECT = 'P'

The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by ZGEBRD. 🎀

LDA — LDA is INTEGER, the leading dimension of the array A.
- If VECT = 'Q', LDA >= max(1,nq);
- if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU — TAU is COMPLEX*16 array, dimension (min(nq,K)). TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by ZGEBRD in the array argument TAUQ or TAUP. 🍓
C — C is COMPLEX*16 array, dimension (LDC,N).
- On entry, the M-by-N matrix C.
- On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H. 💀 she's been replaced, respectfully
LDC — LDC is INTEGER, the leading dimension of the array C. LDC >= max(1,M).
WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🫶
LWORK — and the workspace size is literally the very next thing, stay with me 💜

Okay so we're still in the parameter docs, and this part is giving workspace math + error-code clarity 💅✨

LWORK — INTEGER, bestie. It's the dimension of the array WORK. Here's the strict tea:
- If SIDE = 'L', LWORK >= max(1,N).
- If SIDE = 'R', LWORK >= max(1,M).
- If N = 0 or M = 0, LWORK >= 1.
- For optimum performance, LWORK >= max(1,N*NB) if SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.)
- If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO — INTEGER, obviously. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Illegal value means exactly that, no sugarcoating 🚨

Author 🫶

These legends are on the credits, no cap:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 194 of file zunmbr.f.

Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

Wrapped with love from LAPACK, Version 3.12.0, unmbr(3) — source and version secured, and this footer doesn't stamp a date, so we're not inventing one, bestie 💖✨🎀

📦 where this page comes from

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💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

unmbr(3)

✨ unmbr(3) ✨ — {un,or}mbr: multiply by Q, P from gebrd 💅

🌸 NAME 🌸

🦋 SYNOPSIS 🦋

✨ Functions ✨

🦋 Detailed Description 🦋

🌈 Function Documentation 🌈

🎀 subroutine cunmbr 🎀

✨ Purpose: ✨

🎀 Parameters 🎀

👑 Author 👑

💜 subroutine dormbr 💜

✨ Purpose: ✨

🎀 Parameters 🎀

💖 Author 💖

🦋 subroutine sormbr 🦋

🌸 Purpose 🌸

🎀 Parameters 🎀

💜 Author 💜

🌈 subroutine zunmbr 🌈

🧚 Purpose 🧚

✨ Parameters ✨

Author 🫶

Author 💅

🦋 `subroutine sormbr` 🦋

🌈 `subroutine zunmbr` 🌈