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

okay bestie, this page comes from the Library Functions Manual — it's the docs for dlasyf_rook.f, and the main character is the DLASYF_ROOK subroutine. Let's get into it. 💅✨

NAME

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

That's the source file this whole page is about, periodt. 🫶

SYNOPSIS

Functions/Subroutines

subroutine DLASYF_ROOK (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)

The synopsis blurb is exactly: DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman (rook")diagonalpivotingmethod.

Function/Subroutine Documentation

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 *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.

Purpose:

okay so the whole point: DLASYF_ROOK computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. The partial factorization has this exact form:

!>
!> DLASYF_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.
!>
!> 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').
!>

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

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'). No cap.

Parameters

UPLO

UPLO is CHARACTER*1. It 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 DOUBLE PRECISION array, dimension (LDA,N). On entry, it's 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.

W

W is DOUBLE PRECISION 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 dlasyf_rook.f.

Author

Generated automatically by Doxygen for LAPACK from the source code. (Yep, the docs wrote themselves. 💅)

---

that's the whole page, bestie 🫶💖 — LAPACK Version 3.12.0, page /home/abui...syf_rook.f(3). The footer doesn't give a date, so no date to spill. byeee ✨💅