SRC/clahef_rook.f(3)

💖 NAME 💖

okay so bestie, this page is SRC/clahef_rook.f, from the Library Functions Manual, and it’s the whole glow-up for the clahef_rook subroutine. no cap. 💅

✨ SYNOPSIS ✨

Functions/Subroutines 🎀

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

🦋 Function/Subroutine Documentation 🦋

subroutine clahef_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)

Purpose 🌸

so CLAHEF_ROOK computes a partial factorization of a complex Hermitian 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**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  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. note that U**H denotes the conjugate transpose of U.

CLAHEF_ROOK is an auxiliary routine called by CHETRF_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 and it says 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 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 interchanged, 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.
  • 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, and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

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.

bestie, that INFO > 0 case is not a vibe: the factorization finished, but 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 💅

Definition at line 182 of file clahef_rook.f.

Author (the page-generator one) 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

✨ okay that’s the whole thing, bestie! this footer vibe is LAPACK Version 3.12.0, file SRC/clahef_rook.f(3). byeee! 💖🎀