SRC/clasyf_rook.f(3)

🦋 NAME 🦋

SRC/clasyf_rook.f — ok so welcome to the whole file, bestie 💅 (the header up top is SRC/clasyf_rook.f(3) from the Library Functions Manual, and yes we're reading a Fortran file's manpage, we're that kinda girlie rn)

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✨ SYNOPSIS ✨

Functions/Subroutines 🌸

• 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")diagonalpivotingmethod.

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💖 Function/Subroutine Documentation 💖

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)

CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.

🎀 Purpose:

!>
!> CLASYF_ROOK computes a partial factorization of a complex 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.
!>
!> 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').
!>

Like, it's giving "helper function that does the actual blocked work" energy, and honestly? Iconic. ✨

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💜 Parameters 💜

okay bestie here come all the args, stay with me, they all matter 🫶

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 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,
!>             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.
!>

(and yes, "inerchaged" is a typo in the original source — we stan a messy queen, keeping it exactly as written 💀)

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.
!>

⚠️ real talk: INFO > 0 means D(k,k) is exactly zero — the factorization finished but the block diagonal matrix D is exactly singular. Not a crash, but absolutely not the vibe. 😭

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🌈 Author 🌈

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

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🧚 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
!>
!>

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⭐ Definition at line 182 of file clasyf_rook.f. ⭐

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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k that's the whole page, no skips, no crumbs 💅 she's LAPACK Version 3.12.0, file SRC/clasyf_rook.f(3), and that's the group chat sign-off — bye bestie, go pivot something 🦋✨