SRC/zlahef_rook.f(3)

💖 NAME 💖

SRC/zlahef_rook.f — that's the page title, bestie, and it's from the Library Functions Manual. This is the Doxygen-generated manpage for the zlahef_rook Fortran subroutine, and we're gonna get into every single detail. ✨

✨ SYNOPSIS ✨

Functions/Subroutines:

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

🦋 FUNCTION/SUBROUTINE DOCUMENTATION 🦋

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 🎀

Okay so ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. Yes, the empty () is literally in the source — I'm not editing the vibes. 💅

The partial factorization has the form:

!>
!> 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     )
!>

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.

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 — specifies 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*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) — 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.

Yes, inerchaged is the source spelling — I'm keeping it exactly, no autocorrect energy here. 🫶

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.

💜 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.

💅 AUTHOR 💅

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole page, bestie! Footer vibes: LAPACK Version 3.12.0, source SRC/zlahef_rook.f(3). The footer doesn't list a separate date, so no invented date from me — just the version and source, periodt. 💖✨🎀