gebrd(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

🎀 gebrd(3) — reduction to bidiagonal 🎀

ok so you've landed on gebrd from the Library Functions Manual, section 3, and honestly bestie you're in the right place. grab a boba, we're reducing matrices to bidiagonal form and it's gonna be a whole thing 💅

🌸 NAME 🌸

gebrd — reduction to bidiagonal. that's it, that's the name. she's concise, she's iconic, no notes ✨

✨ SYNOPSIS ✨

🦋 Functions

subroutine cgebrd (m, n, a, lda, d, e, tauq, taup, work, lwork, info) — CGEBRD, the complex one 💜
subroutine dgebrd (m, n, a, lda, d, e, tauq, taup, work, lwork, info) — DGEBRD, the double precision one 🫶
subroutine sgebrd (m, n, a, lda, d, e, tauq, taup, work, lwork, info) — SGEBRD, the single precision one 🌸
subroutine zgebrd (m, n, a, lda, d, e, tauq, taup, work, lwork, info) — ZGEBRD, the double complex one 👑

like, yes, they all have the same argument list. that's the vibe. the letter at the front tells you which flavor of numbers you're working with, iykyk 🌈

🧚 Detailed Description 🧚

so this section is literally empty in the original. no extra lore, no bonus commentary, nothing. we respect a minimalist queen ig 💀

👑 Function Documentation 👑

💜 subroutine cgebrd (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( * ) tauq, complex, dimension( * ) taup, complex, dimension( * ) work, integer lwork, integer info)

CGEBRD

⭐ Purpose:

!>
!> CGEBRD reduces a general complex M-by-N matrix A to upper or lower
!> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!>

so real talk: you hand her a general complex M-by-N matrix, and she hands you back a bidiagonal one. the transformation is unitary, and the relation is Q**H * A * P = B. if m >= n you get an upper bidiagonal B; if m < n you get a lower bidiagonal B. that's the whole deal, no cap 🫶

🌸 Parameters

M — M is INTEGER. the number of rows in the matrix A. must satisfy M >= 0 ✨
N — N is INTEGER. the number of columns in the matrix A. must satisfy N >= 0 ✨
A — A is COMPLEX array, dimension (LDA,N).

On entry, this is the M-by-N general matrix that's about to get reduced. On exit, it's giving two completely different personalities depending on the shape:

if m >= n: the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors; and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors 💖
if m < n: the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors; and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors 💖

See Further Details (scroll down bestie, it's the good part) 🦋

LDA — LDA is INTEGER. the leading dimension of the array A. must satisfy LDA >= max(1,M) 👑
D — D is REAL array, dimension (min(M,N)). the diagonal elements of the bidiagonal matrix B, where D(i) = A(i,i) ✨
E — E is REAL array, dimension (min(M,N)-1). the off-diagonal elements of the bidiagonal matrix B:
- if m >= n: E(i) = A(i,i+1) for i = 1,2,...,n-1
- if m < n: E(i) = A(i+1,i) for i = 1,2,...,m-1 🌸
TAUQ — TAUQ is COMPLEX array, dimension (min(M,N)). the scalar factors of the elementary reflectors which represent the unitary matrix Q. See Further Details 💜
TAUP — TAUP is COMPLEX array, dimension (min(M,N)). the scalar factors of the elementary reflectors which represent the unitary matrix P. See Further Details 💜
WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, then WORK(1) returns the optimal LWORK 🫶
LWORK — LWORK is INTEGER. the length of the array WORK.
- LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise.
- for optimum performance LWORK >= (M+N)*NB, where NB is the optimal blocksize 🔥
- 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.

🧚 Further Details:

!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
!>  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
!>  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
!>  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!>

so Q and P are built out of elementary reflectors, and each one is a rank-one-ish update of the identity: H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H, where tauq and taup are complex scalars and v and u are complex vectors. the vector tails get stashed inside A on exit and the scalars go into TAUQ(i) and TAUP(i) — see the diagram above for exactly which entries go where. it's giving organized chaos and honestly? we stan 🎀

Definition at line 205 of file cgebrd.f.

🌈 subroutine dgebrd (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) tauq, double precision, dimension( * ) taup, double precision, dimension( * ) work, integer lwork, integer info)

DGEBRD

⭐ Purpose:

!>
!> DGEBRD reduces a general real M-by-N matrix A to upper or lower
!> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!>

same energy, real numbers this time. you give her a general real M-by-N matrix A, she gives you upper or lower bidiagonal B via an orthogonal transformation: Q**T * A * P = B. note it's Q**T here, not Q**H — because everything's real, bestie 😌. m >= n means upper bidiagonal, m < n means lower bidiagonal 🦋

🌸 Parameters

M — M is INTEGER. the number of rows in the matrix A. must satisfy M >= 0 ✨
N — N is INTEGER. the number of columns in the matrix A. must satisfy N >= 0 ✨
A — A is DOUBLE PRECISION array, dimension (LDA,N).

On entry, the M-by-N general matrix to be reduced. On exit:

if m >= n: the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors 💖
if m < n: the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors 💖

See Further Details 🦋

LDA — LDA is INTEGER. the leading dimension of the array A. must satisfy LDA >= max(1,M) 👑
D — D is DOUBLE PRECISION array, dimension (min(M,N)). the diagonal elements of the bidiagonal matrix B, where D(i) = A(i,i) ✨
E — E is DOUBLE PRECISION array, dimension (min(M,N)-1). the off-diagonal elements of the bidiagonal matrix B:
- if m >= n: E(i) = A(i,i+1) for i = 1,2,...,n-1
- if m < n: E(i) = A(i+1,i) for i = 1,2,...,m-1 🌸
TAUQ — TAUQ is DOUBLE PRECISION array, dimension (min(M,N)). the scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details 💜
TAUP — TAUP is DOUBLE PRECISION array, dimension (min(M,N)). the scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details 💜
WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, then WORK(1) returns the optimal LWORK 🫶
LWORK — LWORK is INTEGER. the length of the array WORK.
- LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise.
- for optimum performance LWORK >= (M+N)*NB, where NB is the optimal blocksize 🔥
- 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. 🚨

part 1 of 3, bestie — don't go anywhere, the rest is right behind this 🫶

💖 Author

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

🔍 Further Details

okay bestie, so the matrices Q and P are literally represented as products of elementary reflectors — no cap:

If m >= n,

Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T

where tauq and taup are real scalars, and v and u are real vectors;

v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).

If m < n,

Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T

where tauq and taup are real scalars, and v and u are real vectors;

v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).

The contents of A on exit are illustrated by the following examples — yes, they’re iconic:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
  (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
  (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
  (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
  (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
  (  v1  v2  v3  v4  v5 )

where d and e denote diagonal and off-diagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).

📍 Definition at line 204 of file dgebrd.f.

🌸 SGEBRD — real bidiagonal reduction, slay

subroutine sgebrd (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) d, real, dimension( * ) e, real,
    dimension( * ) tauq, real, dimension( * ) taup, real, dimension( * )
    work, integer lwork, integer info)
SGEBRD

✨ Purpose

SGEBRD reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. periodt.

🎀 Parameters

M — M is INTEGER; the number of rows in the matrix A. M >= 0.
N — N is INTEGER; the number of columns in the matrix A. N >= 0.
A — A is REAL array, dimension (LDA,N). On entry, the M-by-N general matrix to be reduced. On exit:
- if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors;
- if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. See Further Details.
LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
D — D is REAL array, dimension (min(M,N)); the diagonal elements of the bidiagonal matrix B: D(i) = A(i,i).
E — E is REAL array, dimension (min(M,N)-1); the off-diagonal elements of the bidiagonal matrix B: if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
TAUQ — TAUQ is REAL array, dimension (min(M,N)); the scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details.
TAUP — TAUP is REAL array, dimension (min(M,N)); the scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details.
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 length of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise. For optimum performance LWORK >= (M+N)*NB, where NB is the optimal blocksize. 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.

🔍 Further Details

okay so the matrices Q and P are represented as products of elementary reflectors — same energy as above, bestie:

If m >= n,

Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T

where tauq and taup are real scalars, and v and u are real vectors;

v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).

If m < n,

Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T

where tauq and taup are real scalars, and v and u are real vectors;

v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).

The contents of A on exit are illustrated by the following examples:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
  (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
  (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
  (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
  (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
  (  v1  v2  v3  v4  v5 )

where d and e denote diagonal and off-diagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).

📍 Definition at line 204 of file sgebrd.f.

🦋 ZGEBRD — complex bidiagonal reduction, main character energy

subroutine zgebrd (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, double precision, dimension( * ) d, double precision,
    dimension( * ) e, complex*16, dimension( * ) tauq, complex*16,
    dimension( * ) taup, complex*16, dimension( * ) work, integer lwork,
    integer info)
ZGEBRD

✨ Purpose

ZGEBRD reduces a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation: Q**H * A * P = B.

If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

🎀 Parameters

M — M is INTEGER; the number of rows in the matrix A. M >= 0.
N — N is INTEGER; the number of columns in the matrix A. N >= 0.
A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the M-by-N general matrix to be reduced. On exit:
- if m >= n, the diagonal and the first superdiagonal are overwritten with the upper bidiagonal matrix B; the elements below the diagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors;
- if m < n, the diagonal and the first subdiagonal are overwritten with the lower bidiagonal matrix B; the elements below the first subdiagonal, with the array TAUQ, represent the unitary matrix Q as a product of elementary reflectors, and the elements above the diagonal, with the array TAUP, represent the unitary matrix P as a product of elementary reflectors. See Further Details.
LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
D — D is DOUBLE PRECISION array, dimension (min(M,N)); the diagonal elements of the bidiagonal matrix B: D(i) = A(i,i).
E —
E — DOUBLE PRECISION array, dimension (min(M,N)-1). These are the off-diagonal elements of the bidiagonal matrix B, bestie: if m >= n, then E(i) = A(i,i+1) for i = 1,2,...,n-1; if m < n, then E(i) = A(i+1,i) for i = 1,2,...,m-1. 💖
TAUQ — COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors that represent the unitary matrix Q. See Further Details. ✨
TAUP — COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors that represent the unitary matrix P. See Further Details. 🎀
WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🦋
LWORK — INTEGER. The length of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise. For optimum performance LWORK >= (M+N)*NB, where NB is the optimal blocksize. 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. = 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.

🔍 Further Details:

The matrices Q and P are represented as products of elementary reflectors:

If m >= n,

Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H

where tauq and taup are complex scalars, and v and u are complex vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). 🧚

If m < n,

Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H

where tauq and taup are complex scalars, and v and u are complex vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). 💀

The contents of A on exit are illustrated by the following examples:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
  (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
  (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
  (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
  (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
  (  v1  v2  v3  v4  v5 )

where d and e denote diagonal and off-diagonal elements of B, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i). 🌈

Definition at line 204 of file zgebrd.f. 📌

👑 Author

Generated automatically by Doxygen for LAPACK from the source code. 🫶

That's the footer, bestie: source is LAPACK, version 3.12.0, and the page is gebrd(3) — date isn't listed in this footer. 💖

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms