DLASYF(3)

💅 DLASYF(3) — okay bestie, let’s factor 💅

This is the manual page for DLASYF(3), straight out of the Library Functions Manual. She’s a LAPACK girlie with main character energy: a subroutine that computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. The source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasyf.f, and yes, that path is long enough to need its own emotional support water bottle. 🫶

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🌸 NAME 🌸

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasyf.f — the file behind all this DLASYF excellence. No cap.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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💖 Function/Subroutine Documentation 💖

👑 The DLASYF signature, periodt 👑

   subroutine DLASYF (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 computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. That’s the whole assignment, and she ate. 💅

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🎀 Purpose 🎀

Okay so here’s the vibe, bestie: DLASYF computes a partial factorization of a real 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.

DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 if UPLO = 'U' or A22 if UPLO = 'L'. Literally iconic blocked-code behavior, fr fr. 🔥

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🌈 Parameters 🌈

🌸 UPLO 🌸

UPLO is CHARACTER*1. She 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. It’s the order of the matrix A. Constraint: N >= 0.

🎀 NB 🎀

NB is INTEGER. It’s 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. Like, don’t skimp on NB, bestie.

⭐ KB ⭐

KB is INTEGER. It’s 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, 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. She’s not just a matrix, she’s a matrix with lore. 😭

🔥 LDA 🔥

LDA is INTEGER. It’s the leading dimension of the array A. Constraint: LDA >= max(1,N).

🍓 IPIV 🍓

IPIV is INTEGER array, dimension (N). It holds 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 DOUBLE PRECISION array, dimension (LDW,NB).

💖 LDW 💖

LDW is INTEGER. It’s the leading dimension of the array W. Constraint: 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.

⚠️ Okay so this is the dramatic part: INFO > 0 means D(k,k) is exactly zero, and D is exactly singular. The factorization still completed, but bestie, she is singular. Periodt.

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🌺 Author 🌺

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

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🫶 Contributors 🫶

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley.

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Definition at line 175 of file dlasyf.f.

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🌈 Author (the Doxygen one) 🌈

Generated automatically by Doxygen for LAPACK from the source code. The automation ate, lowkey. ✨

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That’s the whole tea, bestie: this footer energy is LAPACK Version 3.12.0 and /home/abui...RC/dlasyf.f(3). Stay factored, stay iconic. 💖🎀🦋