CLASYF(3)

Hii bestie 💖 this is clasyf.f(3), from the Library Functions Manual — and yes, it’s giving main-character LAPACK energy.

💖 NAME 💖

Okay so this whole page is about this exact file, no cap:

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

✨ SYNOPSIS ✨

Under Functions/Subroutines, we’ve got this icon:

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

And the vibe check: CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method. Slay.

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, exactly as it lives:

subroutine CLASYF (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)

Again for the people in the back: CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

🌸 Purpose 🌸

Bestie, the source-comment block is literally right here — equations and all, kept exact so nothing gets lost:

!> CLASYF 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.
!>
!> CLASYF is an auxiliary routine called by CSYTRF. It uses blocked code
!> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
!> A22 (if UPLO = 'L').
!>

So yeah: order of D is at most NB, actual order comes back in KB, and KB is either NB or NB-1, or N if N <= NB. Also U**T means the transpose of U — periodt.

🎀 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. Constraint: 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, 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 — the leading dimension of the array A. Constraint: 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 array, dimension (LDW,NB).

🧚 LDW 🧚

LDW is INTEGER — 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.

💜 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 clasyf.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you at the very end, bestie: the footer says LAPACK Version 3.12.0 and points back to /home/abui...RC/clasyf.f(3) 💖 That footer line doesn’t give a separate date, so I’m not inventing one — mwah 💋✨