SRC/slasyf_rook.f(3)

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version 3.12.1 · 7 versions
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💅 SRC/slasyf_rook.f(3) — Library Functions Manual 🎀

okay so bestie, this page is literally from the Library Functions Manual and it's all about SRC/slasyf_rook.f — one tiny Fortran file that does some very main-character linear algebra. let's get into it ✨

✨ NAME ✨

SRC/slasyf_rook.f — that's it, that's the name, she's lowkey mysterious 🦋

🌸 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")diagonalpivotingmethod. yes bestie, the docs really typed it like that, no notes 💀

👑 Function/Subroutine Documentation 👑

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.

🧚 Purpose 🧚

so the vibe is: SLASYF_ROOK computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. the partial factorization has this form, and yes we're gonna write it out in full because she's iconic:

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. periodt 💅

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'). she's a helper girly, a supporting character who's secretly carrying the whole plot 🫶

💖 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. pick your fave side, both are valid 🌈
  • N — N is INTEGER. the order of the matrix A. N >= 0. no negative girlies 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. like, at least two, bestie, the 2-by-2 blocks need room to breathe 💀
  • 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 the "what actually happened" number, not the "what we hoped for" number 🎀
  • 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. glow-up alert ✨
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N). respect the leading dimension or perish 🔥
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges and the block structure of D. here's the tea, split by UPLO:
    • 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.
bestie note: the negative-IPIV case means a 2-by-2 block, and the index you compare against flips depending on UPLO — k-1 for upper, k+1 for lower. do NOT mix those up, iykyk 😭
  • W — W is REAL array, dimension (LDW,NB). that's the whole description, she's a woman of few words 💅
  • LDW — LDW is INTEGER. the leading dimension of the array W. LDW >= max(1,N). same energy as LDA, keep her big enough ⭐
  • INFO — INFO is INTEGER. the receipts:
    • = 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.
so INFO > 0 is not an "oops we stopped" — the work is done, the matrix is just singular. very "the math is mathing but the determinant isn't" 💀

🦋 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 🍓

definition at line 182 of file slasyf_rook.f. 🧚

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a very diligent robot 🫶

and that's the whole page, bestie — LAPACK Version 3.12.0, SRC/slasyf_rook.f(3), slay, no cap, go factor something symmetric 💖✨🎀

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