SLASYF(3)

💖 NAME 💖

okay bestie, welcome to the SLASYF(3) page from the Library Functions Manual — the header path is doing its little /home/abui...RC/slasyf.f(3) thing, and under NAME the page is literally just this path:

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

not me being dramatic, that's just what it says 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

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

and the vibe is: SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. 🔥

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🦋 Function/Subroutine Documentation 🦋

here's the full signature, exactly as the source serves it:

subroutine SLASYF (character uplo, integer n, integer nb, integer kb, real,
       dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real,
       dimension( ldw, * ) w, integer ldw, integer info)

and yes, the main-character energy is real: SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

🌸 Purpose 🌸

the whole Purpose block is out here doing math in its finest !> comments, so here it is exactly:

!>
!> SLASYF 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.
!>
!> SLASYF is an auxiliary routine called by SSYTRF. 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 tells you 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, and the constraint is 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.

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 REAL array, dimension (LDA,N).

On entry, it's 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. It's the leading dimension of the array A, and LDA >= max(1,N).

IPIV

IPIV is INTEGER array, dimension (N). It holds the 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 REAL array, dimension (LDW,NB).

LDW

LDW is INTEGER. It's the leading dimension of the array W, and 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 🌈

the contributors block says exactly:

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

and the source says: Definition at line 175 of file slasyf.f. 🫶

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🎀 Author (generated) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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