ZLASYF(3)

🌈 ZLASYF(3) — Library Functions Manual 🌈

okay bestie, welcome to ZLASYF(3) from the Library Functions Manual — the header is literally pointing at /home/abui...RC/zlasyf.f(3), and we are about to make a complex symmetric partial factorization make sense. No cap. 💅

🌸 NAME 🌸

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

That's the file this page is named after, bestie. Slay. ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine ZLASYF (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

💖 Function/Subroutine Documentation 💖

📜 subroutine ZLASYF (...)

subroutine ZLASYF (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)

ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

🦋 Purpose 🦋

ZLASYF computes a partial factorization of a complex symmetric matrix A using the 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. Note that U**T denotes the transpose of U.

ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). That's the whole vibe: blocked code, Level 3 BLAS, main character energy. 🔥

🎀 Parameters 🎀

💌 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*16 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) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) 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) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

💌 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.

🚨 bestie, read the caveat: INFO > 0 means D is exactly singular after the factorization completed. That's not a slay; that's a "the math is cooked" moment. 💀

👑 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

Definition at line 176 of file zlasyf.f.

🖨️ Author 🖨️

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off: LAPACK Version 3.12.0, footer path /home/abui...RC/zlasyf.f(3). The footer has no date to report, bestie — the date actually mentioned in the page is November 2013 in Contributors. Periodt. 💖