/home/abui...syf_rook.f(3)

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasyf_rook.f

okay so bestie, that's the file. yes it's a whole mouthful. yes we're gonna get through it together. this is a Library Functions Manual page and it's serving major "LAPACK internals" energy 🧚✨

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

• 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. (the manpage literally has a stray quote in there, (rook")diagonalpivotingmethod — we do not fix, we do not judge, we simply report 💀)

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🔥 Function/Subroutine Documentation 🔥

⭐ subroutine SLASYF_ROOK

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. periodt. 👑

🌸 Purpose:

!>
!> SLASYF_ROOK computes a partial factorization of a real symmetric
!> matrix A using the bounded Bunch-Kaufman () diagonal
!> pivoting method. 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.
!>
!> 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').
!>

lowkey the whole vibe is: it's the helper routine. it's not the main character, it's the bestie behind the main character, but it's doing blocked code with Level 3 BLAS so honestly? main character energy anyway 🦋

💖 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
!>

the "which triangle are we even talking about" flag. 'U' = upper triangular, 'L' = lower triangular. pick one, bestie, it matters 💅

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

the order of the matrix A. and N >= 0, no negative nonsense allowed 🙈

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.
!>

the max number of columns of A that should be factored. NB should be at least 2 so that 2-by-2 pivot blocks can actually happen — so like, don't set it to 1 and then act surprised 😭

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.
!>

the number of columns of A that were actually factored. it's either NB-1, NB, or N if N <= NB. it's giving "we tried our best and this is the receipt" 🧾✨

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.
!>

the matrix itself, a REAL array of dimension (LDA,N). on entry it's your symmetric matrix A — and heads up bestie, whichever triangle you didn't pick? not referenced. it's just sitting there, unbothered, unread. on exit, A holds the details of the partial factorization 👑

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

leading dimension of A. gotta be LDA >= max(1,N). no cap 🫶

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,
!>             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.
!>

IPIV is an INTEGER array of dimension (N) — the details of the interchanges and the block structure of D. this is the spicy one so let's break it down 🍓

if UPLO = 'U':

• only the last KB elements of IPIV are set.
• IPIV(k) > 0 → rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.
• IPIV(k) < 0 and IPIV(k-1) < 0 → rows and columns k and -IPIV(k) were interchanged, and rows and columns k-1 and -IPIV(k-1) were inerchaged (yes, "inerchaged" — that's the source, we're keeping it, love that for us 💀), 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.
• IPIV(k) > 0 → rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.
• IPIV(k) < 0 and IPIV(k+1) < 0 → 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.

negative IPIV = 2-by-2 block, positive IPIV = 1-by-1 block. that's the whole iykyk of it 😌

W

!>          W is REAL array, dimension (LDW,NB)
!>

W is a REAL array, dimension (LDW,NB). werk area. that's it, that's the whole description, the source gives us nothing more and we respect that 🙈

LDW

!>          LDW is INTEGER
!>          The leading dimension of the array W.  LDW >= max(1,N).
!>

leading dimension of W, and it's gotta be LDW >= max(1,N). same rules as LDA, keeping the symmetry, we love consistency 💜

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.
!>

the vibe check of the whole operation ✨

• = 0 → successful exit, we slayed, everything's fine.
• > 0 → if INFO = k, then D(k,k) is exactly zero. the factorization has been completed BUT the block diagonal matrix D is exactly singular. so like... we finished, but it's singular, so be careful. no cap, that's a real caveat 🔥

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(the whole squad, respectfully 🫶)

🌈 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
!>
!>

look at that contributor timeline — November 2013 and September 2007, iconic longevity, they've been at this 🎀

Definition at line 182 of file slasyf_rook.f.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. (the robots wrote the docs, we just made them cute 🧚)

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ok bestie that's genuinely everything — every parameter, every flag value, every dimension, every stray typo, all of it. nothing dropped, nothing invented. you're so welcome 💖

LAPACK · Version 3.12.0 · /home/abui...syf_rook.f(3) — mwah, go factor something symmetric, ily 💅✨🌸