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🌸 NAME 🌸

okay bestie, this page is from the Library Functions Manual, and it's all about clasyf_rook.f — the actual path in the NAME line is:

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

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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") diagonal pivoting method. periodt 💅

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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. no cap, that's the whole vibe 🔥

🌈 Purpose:

CLASYF_ROOK computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") 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'). iconic behavior honestly 👑

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🎀 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 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.

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.

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💜 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 clasyf_rook.f.

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👑 Author 👑

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