lahef_rook(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

💖 NAME 💖

okay bestie, welcome to the lahef_rook(3) page in the Library Functions Manual 🫶. This is all about lahef_rook — which is short for la{he,sy}f_rook — and it's literally the triangular factor step ✨.

🌸 SYNOPSIS 🌸

Here's the whole cast, no cap:

subroutine clahef_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — the complex Hermitian one 💅
subroutine clasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
subroutine dlasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
subroutine slasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
subroutine zlahef_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — the other complex Hermitian signature, sitting pretty ✨
subroutine zlasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.

🦋 Detailed Description 🦋

bestie, this section is literally just a handoff — the real tea is in the function docs right below 🫶.

🎀 Function Documentation 🎀

💅 subroutine `clahef_rook`

subroutine clahef_rook (character uplo, integer n, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

🌟 Purpose 🌟

okay so CLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. The partial factorization has this whole shape:

!> A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
!>       ( 0  U22 ) (  0   D  ) ( U12**H U22**H )
!>
!> A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
!>       ( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U.

CLAHEF_ROOK is an auxiliary routine called by CHETRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). iconic behavior, honestly 💅.

🍓 Parameters 🍓

UPLO — UPLO is CHARACTER*1. It says whether the upper or lower triangular part of the Hermitian matrix A is stored:
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. The order of the matrix A. N >= 0.
NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks.
KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
A — A is COMPLEX array, dimension (LDA,N). On entry, the Hermitian matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, A contains details of the partial factorization.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D.
- If UPLO = 'U':
  - Only the last KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged (yes bestie, that's the source spelling 💀), and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
- If UPLO = 'L':
  - Only the first KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W — W is COMPLEX array, dimension (LDW,NB).
LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
INFO — INFO is INTEGER.
- = 0: successful exit
- > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

👑 Author 👑

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

🌈 Contributors 🌈

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

📌 Definition at line 182 of file clahef_rook.f.

💅 subroutine `clasyf_rook`

subroutine clasyf_rook (character uplo, integer n, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

🌟 Purpose 🌟

okay so CLASYF_ROOK computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. The partial factorization has this whole shape:

!> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
!>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
!>
!> A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
!>       ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB.

CLASYF_ROOK is an auxiliary routine called by CSYTRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). periodt 💖.

🍓 Parameters 🍓

UPLO — UPLO is CHARACTER*1. It says whether the upper or lower triangular part of the symmetric matrix A is stored:
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. The order of the matrix A. N >= 0.
NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks.
KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
A — A is COMPLEX array, dimension (LDA,N). On entry, the symmetric matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, A contains details of the partial factorization.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D.
- If UPLO = 'U':
  - Only the last KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
- If UPLO = 'L':
  - Only the first KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W — W is COMPLEX array, dimension (LDW,NB).
LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
INFO
INFO — bestie, it's an INTEGER, and it's the vibe check at the end 💅
- = 0: slay, successful exit ✨
- > 0: if INFO = k, then D(k,k) is exactly zero. Like, the factorization finished its whole thing, but the block diagonal matrix D is exactly singular. Not a full-on error, but she's giving "I did the work and the answer is degenerate" 😭

👑 Author

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

🫶 Contributors:

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 182 of file clasyf_rook.f.

🌸 `dlasyf_rook` — the double precision edition, she's back and she's real

subroutine dlasyf_rook (character uplo, integer n, integer nb, integer kb,
    double precision, dimension( lda, * ) a, integer lda, integer,
    dimension( * ) ipiv, double precision, dimension( ldw, * ) w, integer
    ldw, integer info)

DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. Iconic behaviour, no notes 💖

✨ Purpose:

DLASYF_ROOK computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method — yes, the parentheses are literally empty in the source, she ate and left no crumbs 💀. The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. So KB is basically D's main character energy, lowkey 🌈

DLASYF_ROOK is an auxiliary routine called by DSYTRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). Fr fr, it's the backstage crew making the whole show work 🎀

🌟 Parameters

UPLO — UPLO is CHARACTER*1. She specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. The order of the matrix A. N >= 0.
NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks — like, give her at least two, she needs room 🦋
KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. She's an output girlie, don't expect her to have opinions on entry 💜
A — A is DOUBLE PRECISION array, dimension (LDA,N).
- On entry, the symmetric matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
- On exit, A contains details of the partial factorization. So she comes in as a matrix and leaves as ✨lore✨
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D. Listen closely, this one's a whole saga 📖
- If UPLO = 'U':
  - Only the last KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
- If UPLO = 'L':
  - Only the first KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W — W is DOUBLE PRECISION array, dimension (LDW,NB). That's it, that's her whole description. She's mysterious like that 🙈
LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
INFO — INFO is INTEGER.
- = 0: successful exit ✨
- > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular. Completed but singular is such a mood ngl 💀

👑 Author

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

🫶 Contributors:

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 182 of file dlasyf_rook.f.

🦋 `slasyf_rook` — same energy, single precision, still iconic

subroutine slasyf_rook (character uplo, integer n, integer nb, integer kb,
    real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
    real, dimension( ldw, * ) w, integer ldw, integer info)

SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. Same routine, different precision, still serving 🔥

✨ Purpose:

SLASYF_ROOK computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method (empty parens again — we respect the source's choices 💅). The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. She's literally the same girl as DLASYF_ROOK, just living in REAL land 🌸

SLASYF_ROOK is an auxiliary routine called by SSYTRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). Bestie, she's the support act that makes the headliner possible 👑

🌟 Parameters

UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. The order of the matrix A. N >= 0.
NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks.
KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
A — A is REAL array, dimension (LDA,N).
- On entry, the symmetric matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
- On exit, A contains details of the partial factorization.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D.
- If UPLO = 'U':
  - Only the last KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
- If UPLO = 'L':
  - Only the first KB elements of IPIV are set.
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W — W is REAL array, dimension (LDW,NB). Still mysterious, still not elaborating 🎀
LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
INFO — INFO is INTEGER.
- = 0: successful exit ✨
- > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

👑 Author

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

🫶 Contributors:

🎀 Contributors 🎀

November 2013, Igor Kozachenko, — Computer Science Division, University of California, Berkeley 💖
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, — School of Mathematics, University of Manchester ✨

Definition at line 182 of file slasyf_rook.f.

💜 `zlahef_rook` 💜

okay bestie, this is where the complex Hermitian edition shows up and it is lowkey the same blueprint, just wearing a conjugate-transpose fit 🦋

subroutine zlahef_rook (character uplo, integer n, integer nb, integer kb,
    complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
    ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

✨ Purpose ✨

ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. 🫶 The partial factorization has this shape:

A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. The actual order comes back to you in the argument KB, and it's either NB or NB-1, or N if N <= NB. 📏 And remember, U**H means the conjugate transpose of U — that little H is doing so much work, periodt.

ZLAHEF_ROOK is an auxiliary routine called by ZHETRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). ⚡

🌸 Parameters 🌸

UPLO — UPLO is CHARACTER*1. Tells us whether the upper or lower triangular part of the Hermitian matrix A is stored:
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. The order of the matrix A. N >= 0. 🧮
NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks. (like, don't starve it, it needs room for pairs 🍓)
KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. 💅
A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the Hermitian matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, A contains details of the partial factorization. 👑
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 📐
IPIV — IPIV is INTEGER array, dimension (N). All the tea on the interchanges and the block structure of D:
- If UPLO = 'U':
  - Only the last KB elements of IPIV are set. 🎯
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block. 😭 (yes, two at once, main character energy)
- If UPLO = 'L':
  - Only the first KB elements of IPIV are set. 🎯
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W — W is COMPLEX*16 array, dimension (LDW,NB). 🧺
LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N). 📏
INFO — INFO is INTEGER:
- = 0: successful exit 🎉
- > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular. ⚠️ (translation: it finished, but D is genuinely singular, so don't act surprised)

👑 Author 👑

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

🎀 Contributors 🎀

November 2013, Igor Kozachenko, — Computer Science Division, University of California, Berkeley 💖
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, — School of Mathematics, University of Manchester ✨

Definition at line 182 of file zlahef_rook.f.

🌈 `zlasyf_rook` 🌈

okay so ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method — note the quotes around "rook" this time, we're being fancy 💅

subroutine zlasyf_rook (character uplo, integer n, integer nb, integer kb,
    complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
    ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

✨ Purpose ✨

ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. 🦋 Here's the form, and yes it's the transpose version, not the H version — keep up bestie:

A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order is handed back in the argument KB, and it's either NB or NB-1, or N if N <= NB. 📏

ZLASYF_ROOK is an auxiliary routine called by ZSYTRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). 🔥

🌸 Parameters 🌸

UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
- = 'U': Upper triangular
- = 'L': Lower triangular
N — N is INTEGER. The order of the matrix A. N >= 0. 🧮
NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks. 🫶
KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. ⭐
A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the symmetric matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, A contains details of the partial factorization. 🐚
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 📐
IPIV — IPIV is INTEGER array, dimension (N). The interchanges and the block structure of D, spelled out:
- If UPLO = 'U':
  - Only the last KB elements of IPIV are set. 🎯
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block. 💀
- If UPLO = 'L':
  - Only the first KB elements of IPIV are set. 🎯
  - If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
  - If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W — W is COMPLEX*16 array, dimension (LDW,NB). 🧺
LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N). 📏
INFO — INFO is INTEGER:
- = 0: successful exit 🎉
- > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular. ⚠️ (fr fr, it's singular — no cap, no rescuing it)

👑 Author 👑

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

🎀 Contributors 🎀

November 2013, Igor Kozachenko, — Computer Science Division, University of California, Berkeley 💖
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, — School of Mathematics, University of Manchester ✨

Definition at line 182 of file zlasyf_rook.f.

✨ AUTHOR ✨

ok so nobody actually wrote this page by hand, bestie — it's generated automatically by Doxygen for LAPACK from the source code. so the "author" is basically a robot that read the source and typed all this up 💅 ngl that's kind of iconic of it.

so yeah, if you spot a typo in here, don't come for a human, because there isn't one to come for 🫶 the source code is the main character, Doxygen is just the hype account, and LAPACK is the whole entire franchise 👑

and that's the whole page, fr fr — you made it to the end 🎀 this was lahef_rook(3) from LAPACK, Version 3.12.0, and the footer is just that version stamp plus the page name (no date on this one, it's giving minimal 😌). now go forth and factor things, bestie 💖✨

📦 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

lahef_rook(3)

💖 NAME 💖

🌸 SYNOPSIS 🌸

🦋 Detailed Description 🦋

🎀 Function Documentation 🎀

💅 subroutine clahef_rook

🌟 Purpose 🌟

🍓 Parameters 🍓

👑 Author 👑

🌈 Contributors 🌈

💅 subroutine clasyf_rook

🌟 Purpose 🌟

🍓 Parameters 🍓

👑 Author

🫶 Contributors:

🌸 dlasyf_rook — the double precision edition, she's back and she's real

✨ Purpose:

🌟 Parameters

👑 Author

🫶 Contributors:

🦋 slasyf_rook — same energy, single precision, still iconic

✨ Purpose:

🌟 Parameters

👑 Author

🫶 Contributors:

🎀 Contributors 🎀

💜 zlahef_rook 💜

✨ Purpose ✨

🌸 Parameters 🌸

👑 Author 👑

🎀 Contributors 🎀

🌈 zlasyf_rook 🌈

✨ Purpose ✨

🌸 Parameters 🌸

👑 Author 👑

🎀 Contributors 🎀

✨ AUTHOR ✨

💅 subroutine `clahef_rook`

💅 subroutine `clasyf_rook`

🌸 `dlasyf_rook` — the double precision edition, she's back and she's real

🦋 `slasyf_rook` — same energy, single precision, still iconic

💜 `zlahef_rook` 💜

🌈 `zlasyf_rook` 🌈